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Business Statistics
For Contemporary Decision-Making
Third Canadian Edition
K EN BLACK
University of Houston—Clear Lake
TIFFANY BAYLEY
University of Western Ontario
IGNACIO CASTILLO
Wilfrid Laurier University
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Brief Contents
PREFACE
vii
UNIT I Introduction
1
Introduction to Statistics and Business Analytics 1-1
2
Visualizing Data with Charts and Graphs 2-1
3
Descriptive Statistics 3-1
4
Probability 4-1
UNIT II Distributions and Sampling
5
Discrete Distributions 5-1
6
Continuous Distributions 6-1
7
Sampling and Sampling Distributions 7-1
UNIT III Making Inferences About Population Parameters
8
Statistical Inference: Estimation for Single Populations 8-1
9
Statistical Inference: Hypothesis Testing for Single Populations 9-1
10
Statistical Inferences About Two Populations 10-1
11Analysis of Variance and Design of Experiments
11-1
UNIT IV Regression Analysis and Forecasting
12
Correlation and Simple Regression Analysis 12-1
13
Multiple Regression Analysis 13-1
14
Building Multiple Regression Models 14-1
15
Time-Series Forecasting and Index Numbers 15-1
UNIT V Special Topics
16Analysis of Categorical Data 16-1
17
Nonparametric Statistics
18
Statistical Quality Control 18-1
19
Decision Analysis 19-1
17-1
xv
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xvi
Br ie f Contents
A P P EN D IX A
Tables A-1
A P P EN D IX B
aking Inferences About Population Parameters:
M
A Brief Summary B-1
A P P EN D IX C Answers to Selected Odd-Numbered Quantitative
Problems
GLOSSARY
INDEX
I-1
G-1
C-1
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CHAPTER 1
Introduction to Statistics and
Business Analytics
LEARNING OBJECTIVES
The primary objective of Chapter 1 is to introduce you to the world of statistics and
analytics thereby enabling you to:
1.1
Define important statistical terms, including
population, sample, and parameter, as they relate to
descriptive and inferential statistics.
1.3
Explain the differences between the four dimensions
of big data.
1.4
Compare and contrast the three categories of
business analytics.
1.2
Explain the difference between variables,
measurement, and data, and compare the four
different levels of data: nominal, ordinal, interval,
and ratio.
1.5
Describe the data mining and data visualization
processes.
Decision Dilemma
iStock.com/Kailash soni
India is the second-most-populous country in the world, with
more than 1.25-billion people. Nearly 70% of the people live in
rural areas, scattered about the countryside in 600,000 villages.
In fact, it may be said that more than one in every ten people in the
world live in rural India. While it has a per capita income of less
than US$1 per day, rural India, which has been described in the
past as poor and semi-literate, now contributes about one-half of
the country’s gross national product (GNP). However, rural India
still has the most households in the world without electricity, with
the number of such households exceeding 300,000.
Despite its poverty and economic disadvantages, there
are compelling reasons for companies to market their goods
and ­services to rural India. This market has been growing at
five times the rate of the urban Indian market. There is increasing agricultural productivity, leading to growth in disposable
­income, and there is a reduction in the gap between the tastes of
urban and rural customers. The literacy level is increasing, and
people are becoming more conscious of their lifestyles and of
opportunities for a better life. Around 60% of all middle-income
©istockphoto.com/kailash soni
Statistics Describe the State of Business
in India’s Countryside
households in India are in rural areas, and more than one-third
of all rural households now have a main source of income other
than farming. Virtually every home has a radio, almost ­one-third
have a television, and more than one-half of rural households
benefit from banking services. Forty-two percent of the people
living in India’s villages and small towns use toothpaste, and
that proportion is increasing as rural incomes rise and as there
is greater awareness of oral hygiene.
1-1
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1-2
Ch a pte r 1
Introduction to Statistics and Business Analytics
Consumers are gaining more disposable income due to the
movement of manufacturing jobs to rural areas. It is estimated that
nearly 75% of the factories that opened in India in the past decade
were built in rural areas. Products that are selling well to people
in rural India include televisions, fans, bicycles, bath soap, two- or
three-wheelers, and cars. According to MART, a New Delhi–based
research organization, rural India buys 46% of all soft drinks and
49% of motorcycles sold in India. Because of such factors, many
global and Indian firms, such as Microsoft, General Electric,
Kellogg’s, Colgate-Palmolive, Hindustan-Unilever, Godrej, Nirma,
Novartis, Dabur, Tata Motors, and Vodafone India, have entered the
rural Indian market with enthusiasm. Marketing to rural customers
often involves persuading them to try products that they may not
have used before. Rural India is a huge, relatively untapped market for businesses. However, entering such a market is not without
risks and obstacles. The dilemma facing companies is whether to
enter this marketplace and, if so, to what extent and how.
Managerial, Statistical, and Analytical Questions
1. Are the statistics presented in this report exact figures or
­estimates?
2. How and where could the business analysts have gathered
such data?
3. In measuring the potential of the rural Indian marketplace,
what other statistics could have been gathered?
4. What levels of data measurement are represented by data on
rural India?
5. How can managers use these and other statistics to make better decisions about entering this marketplace?
6. What big data might be available on rural India?
Sources: Adapted from “Marketing to Rural India: Making the Ends
Meet,” India Knowledge@Wharton, March 8, 2007, knowledge.wharton.
upenn.edu/india/article.cfm?articleid=4172; “Rural Segment Quickly
Catching Up,” India Brand Equity Foundation (IBEF), September 2015,
www.ibef.org/industry/indian-rural-market.aspx; Mamta Kapur, Sanjay
Dawar, and Vineet R. Ahuja, “Unlocking the Wealth in Rural Markets,”
Harvard Business Review, June 2014, hbr.org/2014/06/unlocking-thewealth-in-rural-markets; Nancy Joseph, “Much of Rural India Still
Waits for Electricity,” Perspectives Newsletter, University of Washington,
October 2013, artsci.washington.edu/news/2013-10/much-rural-indiastill-waits-electricity.
Introduction
Every minute of the working day, decisions are made by businesses around the world that
determine whether companies will be profitable and grow or whether they will stagnate
and die. Most of these decisions are made with the assistance of information gathered about
the marketplace, the economic and financial environment, the workforce, the competition,
and other factors. Such information usually comes in the form of data or is accompanied
by data. Business statistics and business analytics provide the tools by which such data are
­collected, analyzed, summarized, and presented to facilitate the decision-making process, and
both business statistics and business analytics play an important role in the ongoing saga of
decision-making within the dynamic world of business.
There is a wide variety of uses and applications of statistics in business. Several examples
follow.
• A survey of 1,465 workers by Hotjobs found that 55% of workers believe that the quality
of their work is perceived the same when they work remotely as when they are physically
in the office.
• In a survey of 477 executives by the Association of Executive Search Consultants, 48% of
men and 67% of women said they were more likely to negotiate for less business travel
compared with five years earlier.
• A survey of 1,007 adults by RBC Capital Markets showed that 37% of adults would be
willing to drive 8 to 15 km to save 5 cents on a litre of gas.
• A Deloitte Retail “Green” survey of 1,080 adults revealed that 54% agreed that plastic,
non-compostable shopping bags should be banned.
• A survey by Statistics Canada determined that in 2017, the average annual household net
expenditure in Canada was $86,070 and that households spent an average of $3,986 annually on recreation.1 In addition, employment rates and wages increased more in Canada
than in the United States between 2000 and 2017.2
1
Statistics Canada, “Household Spending by Household Type,” Table 11-10-0222-01, December 12, 2018,
www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1110022401.
2
André Bernard and René Morissette, Statistics Canada, “Economic Insights: Employment Rates and Wages
of Core-Aged Workers in Canada and the United States, 2000 to 2017,” June 4, 2018, www150.statcan.gc.ca/
n1/pub/11-626-x/11-626-x2018082-eng.htm.
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1.1
Basic Statistical Concepts
1-3
• In a 2014 survey of 17 countries conducted by GlobeScan for the National Geographic
Society, Canada ranked 16th out of 17 when it came to environmental and climate footprint. This was due mostly to Canadian preferences for bigger houses and an established
culture of using privately owned cars as opposed to transit.3
Note that, in most of these examples, business analysts have conducted a study and provided rich and interesting information that can be used in business decision-making.
In this text, we will examine several types of graphs for visualizing data as we study ways
to arrange or structure data into forms that are both meaningful and useful to decision-makers.
We will learn about techniques for sampling from a population that allow studies of the business world to be conducted in a less expensive and more timely manner. We will explore various ways to forecast future values and we will examine techniques for predicting trends. This
text also includes many statistical and analytics tools for testing hypotheses and for estimating
population values. These and many other exciting statistics and statistical techniques await us
on this journey through business statistics and analytics. Let us begin.
1.1
Basic Statistical Concepts
LEARNING OBJECTIVE 1.1
Define important statistical terms, including population, sample, and parameter, as they
relate to descriptive and inferential statistics.
Business statistics, like many areas of study, has its own language. It is important to begin our
study with an introduction of some basic concepts in order to understand and communicate
about the subject. We begin with a discussion of the word statistics. This word has many different meanings in our culture. Webster’s Third New International Dictionary gives a comprehensive definition of statistics as a science dealing with the collection, analysis, interpretation, and
presentation of numerical data. Viewed from this perspective, statistics includes all the topics
presented in this text. Figure 1.1 captures the key elements of business statistics.
FIGURE 1.1 The Key Elements
of Statistics
Collect
data
Analyze
data
Interpret
data
Present
findings
The study of statistics can be organized in a variety of ways. One of the main ways is
to subdivide statistics into two branches: descriptive statistics and inferential statistics. To
understand the difference between descriptive and inferential statistics, definitions of population
3
GlobeScan, “Environmental Behaviour of Canadians: Mining National Geographic’s and GlobeScan’s
­ reendex Research,” November 3, 2016, globescan.com/wp-content/uploads/2017/07/GlobeScan_PCO_
G
Greendex_CAN_Report.pdf.
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1-4
Ch a pte r 1
Introduction to Statistics and Business Analytics
and sample are helpful. Webster’s Third New International Dictionary defines population as a
collection of persons, objects, or items of interest. The population can be a widely defined category, such as “all automobiles,” or it can be narrowly defined, such as “all Ford Escape crossover vehicles produced from Year 1 to Year 2.” A population can be a group of people, such as
“all workers employed by Microsoft,” or it can be a set of objects, such as “all Toyota RAV4s
produced in February of Year 1 by Toyota Canada at the Woodstock, Ontario, plant.” The
analyst defines the population to be whatever he or she is studying. When analysts
gather data from the whole population for a given measurement of interest, they call it a census.
Most people are familiar with the Canadian Census. Every five years, the government attempts
to measure all persons living in this country. As another example, if an analyst is interested in
ascertaining the grade point average for all students at the University of Toronto, one way to
do so is to conduct a census of all students currently enrolled there.
A sample is a portion of the whole and, if properly taken, is representative of the whole.
For various reasons (explained in Chapter 7), analysts often prefer to work with a sample of
the population instead of the entire population. For example, in conducting quality control
experiments to determine the average life of light bulbs, a light bulb manufacturer might randomly sample only 75 light bulbs during a production run. Because of time and money limitations, a human resources manager might take a random sample of 40 employees instead of
using a census to measure company morale.
If a business analyst is using data gathered on a group to describe or reach conclusions
about that same group, the statistics are called descriptive statistics. For example, if an
instructor produces statistics to summarize a class’s examination results and uses those statistics to reach conclusions about that class only, the statistics are descriptive. The instructor can
use these statistics to discuss class average, talk about the range of class scores, or present any
other data measurements for the class based on the test.
Most athletic statistics, such as batting averages, save percentages, and first downs, are
descriptive statistics because they are used to describe an individual or team effort. Many
of the statistical data generated by businesses are descriptive. They might include number of
employees on vacation during June, average salary at the Edmonton office, corporate sales
for the current fiscal year, average managerial satisfaction score on a company-wide census
of employee attitudes, and average return on investment for Lululemon for the first ten years
of operations.
Another type of statistics is called inferential statistics. If an analyst gathers data from a
sample and uses the statistics generated to reach conclusions about the population from which the
sample was taken, the statistics are inferential statistics. The data gathered from the sample are
used to infer something about a larger group. Inferential statistics are sometimes referred to as
inductive statistics. The use and importance of inferential statistics continue to grow.
One application of inferential statistics is in pharmaceutical research. Some new drugs are
expensive to produce, and therefore tests must be limited to small samples of patients. Utilizing
inferential statistics, analysts can design experiments with small, randomly selected samples of
patients and attempt to reach conclusions and make inferences about the population.
Market analysts use inferential statistics to study the impact of advertising on various
market segments. Suppose a soft drink company creates an advertisement depicting a dispensing machine that talks to the buyer, and market analysts want to measure the impact of
the new advertisement on various age groups. The analyst could stratify the population into
age categories ranging from young to old, randomly sample each stratum, and use inferential
statistics to determine the effectiveness of the advertisement for the various age groups in
the population. The advantage of using inferential statistics is that they enable the analyst to
effectively study a wide range of phenomena without having to conduct a census. Most of the
topics discussed in this text pertain to inferential statistics.
A descriptive measure of the population is called a parameter. Parameters are usually
denoted by Greek letters. Examples of parameters are population mean (μ), population
variance (σ2), and population standard deviation (σ). A descriptive measure of a sample is
called a statistic. Statistics are usually denoted by Roman letters. Examples of statistics are
¯), sample variance (s2), and sample standard deviation (s).
sample mean (​​ x ​​
Differentiation between the terms parameter and statistic is important only in the use of
inferential statistics. A business analyst often wants to estimate the value of a parameter or
conduct tests about the parameter. However, the calculation of parameters is usually either
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1.2
Variables, Data, and Data Measurement
1-5
impossible or infeasible because of the amount of time and money required to take a census.
In such cases, the business analyst can take a random sample of the population, calculate
a statistic on the sample, and infer by estimation the value of the parameter. The basis for
­inferential statistics, then, is the ability to make decisions about parameters without having to
complete a census of the population.
For example, a manufacturer of washing machines would probably want to determine the
average number of loads that a new machine can wash before it needs repairs. The parameter
is the population mean or average number of washes per machine before repair. A company
analyst takes a sample of machines, computes the number of washes before repair for each
­machine, averages the numbers, and estimates the population value or parameter by using
the statistic, which in this case is the sample average. Figure 1.2 demonstrates the inferential
process.
Calculate x
to estimate
Population
FIGURE 1.2 Process of Inferential Statistics to Estimate a
Population Mean ( μ)
Sample
x
(statistic)
(parameter)
Select a
random sample
Inferences about parameters are made under uncertainty. Unless parameters are computed directly from the population, the statistician never knows with certainty whether the
estimates or inferences made from samples are true. In an effort to estimate the level of confidence in the result of the process, statisticians use probability statements. For this and other
reasons, part of this text is devoted to probability (Chapter 4).
Concept Check
Fill in the blanks.
1. Descriptive statistics can be used to
or graphically.
2. Statistical inference is inference about a
1.2
the data to describe a data sample either numerically
from a random data
drawn from it.
Variables, Data, and Data Measurement
LEARNING OBJECTIVE 1.2
Explain the difference between variables, measurement, and data, and compare the four
different levels of data: nominal, ordinal, interval, and ratio.
Business statistics is about measuring phenomena in the business world and organizing,
analyzing, and presenting the resulting numerical information in such a way that better, more
informed business decisions can be made. Most business statistics studies contain variables,
measurements, and data.
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1-6
Ch a pte r 1
Introduction to Statistics and Business Analytics
In business statistics, a variable is a characteristic of any entity being studied that is
c­ apable of taking on different values. Some examples of variables in business might include
return on investment, advertising dollars, labour productivity, stock price, historic cost, total
sales, market share, age of worker, earnings per share, kilometres driven to work, time spent
in store shopping, and many, many others. In business statistics studies, most variables produce a measurement that can be used for analysis. A measurement occurs when a standard
process is used to assign numbers to particular attributes or characteristics of a variable. Many
measurements are obvious, such as the time a customer spends shopping in a store, the age of
the worker, or the number of kilometres driven to work. However, some measurements, such
as labour productivity, customer satisfaction, and return on investment, have to be defined
by the business analyst or by experts within the field. Once such measurements are recorded
and stored, they can be denoted as “data.” It can be said that data are recorded measurements.
The processes of measuring and data gathering are basic to all that we do in business statistics and analytics. It is data that are analyzed by business statisticians and analysts in order
to learn more about the variables being studied. Sometimes, sets of data are organized into
­databases as a way to store data or as a means for more conveniently analyzing data or comparing variables. Valid data are the lifeblood of business statistics and business analytics, and
it is ­important that the business analyst pay thoughtful attention to the creation of meaningful, valid data before embarking on analysis and reaching conclusions (see Thinking Critically
About Statistics in Business Today 1.1).
Thinking Critically About Statistics in Business Today 1.1
Cellular Phone Use in Japan
The Communications and Information Network Association of
Japan conducts an annual study of cellular phone use in Japan.
A recent survey was taken as part of this study using a sample
of 1,200 cellphone users split evenly between men and women
and almost equally distributed over six age brackets. The survey
was administered in the greater Tokyo and Osaka metropolitan
areas. The study produced several interesting findings.
Of the respondents, 90.7% said that their main-use terminal
was a smartphone, while 9.2% said it was a feature phone. Of the
smartphone users, 41.5% reported that their second ­device was
a tablet (with telecom subscription), compared to the ­response
the previous year, where 35.9% said that a tablet was their second device. Smartphone users in the survey reported that the two
decisive factors in purchasing a new smartphone were purchase
price (87.7%) and monthly payment cost (87.6%). Feature phone
users also indicated purchase price and monthly cost as decisive
factors in purchasing their next feature phone, with rates of
80.8% and 78.8%, respectively. In terms of usage of smartphone
features and services, the most popular use was voice communication (96.3%) followed by SNS message (92.1%) and email
(91.8%).
Things to Ponder
1. In what way was this study an example of inferential
statistics?
2. What is the population of this study?
3. What are some of the variables being studied?
4. How might a study such as this yield information that is useful to business decision-makers?
Source: Adapted from “CIAJ Releases Report on the Study of
Mobile Phone Use,” Communications and Information Network
Association of Japan (CIAJ), July 26, 2017, www.ciaj.or.jp/en/news/
news2017/451.html.
Immense volumes of numerical data are gathered by businesses every day, representing myriad items. For example, numbers represent dollar costs of items produced,
geographical locations of retail outlets, masses of shipments, and rankings of employees at yearly reviews. Not all such data should be analyzed in the same way statistically
­because the entities represented by the numbers are different. For this reason, the business
analyst needs to know the level of data measurement represented by the numbers being
analyzed.
The disparate use of numbers can be illustrated by the numbers 40 and 80, which could
represent the masses of two objects being shipped, the ratings received on a consumer test by
two different products, or the hockey jersey numbers of a centre and a winger. Although 80 kg
is twice as much as 40 kg, the winger is probably not twice as big as the centre! Averaging the
two masses seems reasonable but averaging the hockey jersey numbers makes no sense. The
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1.2
Variables, Data, and Data Measurement
appropriateness of the data analysis depends on the level of measurement of the data gathered. The phenomenon represented by the numbers determines the level of data measurement. Four common levels of data measurement are:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Nominal is the lowest level of data measurement, followed by ordinal, interval, and ratio.
Ratio is the highest level of data, as shown in Figure 1.3.
Nominal Level
The lowest level of data measurement is the nominal level. Numbers representing nominallevel data (the word level is often omitted) can be used only to classify or categorize. Employee
identification numbers are an example of nominal data. The numbers are used only to
differentiate employees and not to make a value statement about them. Many demographic
questions in surveys result in data that are nominal because the questions are used for classification only. The following is an example of a question that would result in nominal data:
Which of the following employment classifications best describes your area of work?
a. Educator
b. Construction worker
c. Manufacturing worker
d. Lawyer
e. Doctor
f. Other
Suppose that, for computing purposes, an educator is assigned a 1, a construction
worker is assigned a 2, a manufacturing worker is assigned a 3, and so on. These numbers
should be used only to classify respondents. The number 1 does not denote the top classification. It is used only to differentiate an educator (1) from a lawyer (4) or any other
occupation.
Other types of variables that often produce nominal-level data are sex, religion, ethni­city,
geographic location, and place of birth. Social insurance numbers, telephone numbers, and
employee ID numbers are further examples of nominal data. Statistical techniques that are
appropriate for analyzing nominal data are limited. However, some of the more widely used
statistics, such as the chi-square statistic, can be applied to nominal data, often producing
useful information.
Ordinal Level
Ordinal-level data measurement is higher than nominal level. In addition to having
the nominal-level capabilities, ordinal-level measurement can be used to rank or order
objects. For example, using ordinal data, a supervisor can evaluate three ­employees by
ranking their productivity with the numbers 1 through 3. The supervisor could identify
one employee as the most productive, one as the least productive, and one as somewhere
in between by using ordinal data. However, the supervisor could not use ordinal data
to establish that the intervals between the employees ranked 1 and 2 and between the
­employees ranked 2 and 3 are equal; that is, the ­supervisor could not say that the differences in the amount of productivity ­between the workers ranked 1, 2, and 3 are necessarily the same. With ordinal data, the distances between consecutive numbers are not
always equal.
1-7
Highest level of data measurement
Ratio
Interval
Ordinal
Nominal
Lowest level of data measurement
FIGURE 1.3 Hierarchy of
Levels of Data
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1-8
Ch a pte r 1
Introduction to Statistics and Business Analytics
Some Likert-type scales on questionnaires are considered by many analysts to be ordinal
in level. The following is an example of such a scale:
This computer tutorial is
____
not
helpful
1
____
____
somewhat moderately
helpful
helpful
2
3
____
very
helpful
4
____
extremely
helpful
5
When this survey question is coded for the computer, only the numbers 1 through 5 will
remain, not the descriptions. Virtually everyone would agree that a 5 is higher than a 4 on this
scale and that it is possible to rank responses. However, most respondents would not consider
the differences between not helpful, somewhat helpful, moderately helpful, very helpful, and
extremely helpful to be equal.
Mutual funds are sometimes rated in terms of investment risk by using measures of
default risk, currency risk, and interest rate risk. These three measures are applied to investments by rating them as high, medium, or low risk. Suppose high risk is assigned a 3, medium
risk a 2, and low risk a 1. If a fund is awarded a 3 rather than a 2, it carries more risk, and so
on. However, the differences in risk between categories 1, 2, and 3 are not necessarily equal.
Thus, these measurements of risk are only ordinal-level measurements. Another example of
the use of ordinal numbers in business is the ranking of the 50 best employers in Canada in
Report on Business magazine. The numbers ranking the companies are only ordinal in measurement. Certain statistical techniques are specifically suited to ordinal data, but many other
techniques are not appropriate for use on ordinal data.
Because nominal and ordinal data are often derived from imprecise measurements
such as demographic questions, the categorization of people or objects, or the ranking
of items, nominal and ordinal data are nonmetric data and are sometimes referred to as
qualitative data.
Interval Level
Interval-level data measurement is the next to the highest level of data, in which the distances
between consecutive numbers have meaning and the data are always numerical. The distances
represented by the differences between consecutive numbers are equal; that is, interval data
have equal intervals. An example of interval measurement is Celsius temperature. With
Celsius temperature numbers, the temperatures can be ranked, and the amounts of heat
between consecutive readings, such as 20°, 21°, and 22°, are the same.
In addition, with interval-level data, the zero point is a matter of convention or convenience and not a natural or fixed zero point. Zero is just another point on the scale
and does not mean the absence of the phenomenon. For example, zero degrees Celsius is
not the lowest possible temperature. Some other examples of interval-level data are the percentage change in employment, the percentage return on a stock, and the dollar change in
share price.
Ratio Level
Ratio-level data measurement is the highest level of data measurement. Ratio data have the
same properties as interval data, but ratio data have an absolute zero and the ratio of two numbers is meaningful. The notion of absolute zero means that zero is fixed, and the zero value in
the data represents the absence of the characteristic being studied. The value of zero cannot be
arbitrarily assigned because it represents a fixed point. This definition enables the statistician
to create ratios with the data.
Examples of ratio data are height, mass, time, volume, and Kelvin temperature.
With ratio data, an analyst can state that 180 kg of mass is twice as much as 90 kg or, in
other words, make a ratio of 180:90. Many of the data gathered by machines in industry are
ratio data.
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1.2
Variables, Data, and Data Measurement
1-9
Other examples in the business world that are ratio level in measurement are production
cycle time, work measurement time, passenger distance, number of trucks sold, complaints
per 10,000 flyers, and number of employees. With ratio-level data, no b factor is required in
converting units from one measurement to another, that is, y = ax. As an example, in converting height from metres to feet, 1 m = 3.28 ft.
Because interval- and ratio-level data are usually gathered by precise instruments often used
in production and engineering processes, in standardized testing, or in standardized accounting
procedures, they are called metric data and are sometimes referred to as quantitative data.
Comparison of the Four Levels of Data
Figure 1.4 shows the relationships of the usage potential among the four levels of data
measurement. The concentric squares denote that each higher level of data can be analyzed
by any of the techniques used on lower levels of data but, in addition, can be used in other
statistical techniques. Therefore, ratio data can be analyzed by any statistical technique
applicable to the other three levels of data plus some others.
Nominal data are the most limited data in terms of the types of statistical analysis that can
be used with them. Ordinal data allow the statistician to perform any analysis that can be done
with nominal data and some additional ones. With ratio data, a statistician can make ­ratio
comparisons and appropriately do any analysis that can be performed on nominal, ordinal,
or interval data. Some statistical techniques require ratio data and cannot be used to analyze
other levels of data.
Statistical techniques can be separated into two categories: parametric statistics and nonparametric statistics. Parametric statistics require that data be interval or ratio. If the data
are nominal or ordinal, nonparametric statistics must be used. Nonparametric statistics
can also be used to analyze interval or ratio data. This text focuses largely on parametric statistics, with the exception of Chapter 16 and Chapter 17, which contain nonparametric techniques. Thus, much of the material in this text requires interval or ratio data. Figure 1.5
contains a summary of metric data and nonmetric data.
Metric
data
Nonmetric
data
• Higher-level data
• Interval and ratio
• Quantitative data
• Can use parametric statistics
• Lower-level data
• Nominal and ordinal
• Qualitative data
• Must use nonparametric statistics
FIGURE 1.5 Metric vs. Nonmetric Data
Concept Check
Match the level with the correct measurement.
1. Nominal
a. Measures with a fixed zero that means “no quantity”; a constant interval
(distance on the scale)
2. Ordinal
b. Measures require a fixed distance, but the zero point is arbitrary
3. Interval
c. Measures classified by shared attributes (characteristics)
4. Ratio
d. Measures by orderings (ranks)
Ratio
Interval
Ordinal
Nominal
FIGURE 1.4 Usage Potential
of Various Levels of Data
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C h a pte r 1
Introduction to Statistics and Business Analytics
D E MONST RAT I O N P R O B L EM 1 . 1
Many changes continue to occur in the health-care system. Because of the increasing pressure to
deliver a high level of service at increasingly low costs and the need to determine how providers
can better serve their patients, hospital administrators sometimes administer a quality satisfaction
survey to their patients after release from hospital. The following types of questions are sometimes
asked on such a survey. These questions will result in what level of data measurement?
1. How long ago were you released from the hospital?
2. Which type of unit were you in for most of your stay?
___Coronary care unit
___Intensive care unit
___Maternity care unit
___Medical unit
___Pediatric/children’s unit
___Surgical unit
3. How serious was your condition when you were first admitted to the hospital?
__Critical __Serious __Moderate __Minor
4. Rate the skill of your doctor:
__Excellent __Very Good __Good __Fair __Poor
5. On the following scale from one to seven, rate the nursing care:
Poor 1 2 3 4 5 6 7 Excellent
Solution Question 1 is a time measurement with an absolute zero and is therefore a ratio-level
measurement. A person who has been out of the hospital for two weeks has been out twice as long
as someone who has been out of the hospital for one week.
Question 2 yields nominal data because the patient is asked only to categorize the type of
unit he or she was in. This question does not require a hierarchy or ranking of the type of unit.
Questions 3 and 4 are likely to result in ordinal-level data. Suppose a number is assigned to each
descriptor in each of these two questions. For question 3, “critical” might be assigned a 4, “serious”
a 3, “moderate” a 2, and “minor” a 1. Certainly, the higher the number, the more serious is the
patient’s condition. Thus, these responses can be ranked by selection. However, the increases in
importance from 1 to 2 to 3 to 4 are not necessarily equal. This same logic applies to the numeric
values assigned in question 4.
Question 5 displays seven numeric choices with equal distances between the numbers shown
on the scale and no adjective descriptors assigned to the numbers. Many analysts would declare
this to be interval-level measurement because of the equal distance between numbers and the
absence of a true zero on this scale. Other analysts might argue that because of the imprecision of
the scale and the vagueness of selecting values between “poor” and “excellent,” the measurement
is only ordinal in level.
1.3
Big Data
LEARNING OBJECTIVE 1.3
Explain the differences between the four dimensions of big data.
In the current world of business, there is exponential growth in the data available to
­decision-makers to help them produce better business outcomes. Growing sources of data are
available from the Internet, social media, governments, transportation systems, health care,
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1.3
environmental organizations, and a plethora of business data sources, among others. Business
data include, but are not limited to, consumer information, labour statistics, financials, product and resource tracking information, supply chain information, operations information, and
human resource information. According to vCloud, 2.5-quintillion bytes of data are created
every day. As a business example, from its millions of products and hundreds of millions of
customers, Walmart alone collects multi-terabytes of new data every day, which are then added to its petabytes of historical data.4
The advent of such growth in the amount and types of data available to analysts, data
scientists, and business decision-makers has resulted in a new term, “Big Data.” Big data has
been defined as a collection of large and complex datasets from different sources that are difficult
to process using traditional data management and processing applications.5 In addition, big
data can be seen as a large amount of either organized or unorganized data that is analyzed to
make an informed decision or evaluation.6 All data are not created in the same way, nor do they
represent the same things. Thus, analysts recognize that there are at least four characteristics
or dimensions associated with big data.7 These are:
1. Variety
2. Velocity
3. Veracity
4. Volume
Variety refers to the many different forms of data based on data sources. A wide variety of data is available from such sources as mobile phones, videos, text, retail scanners,
Internet searches, government documents, multimedia, empirical research, and many others. Data can be structured (such as databases or Excel sheets) or unstructured (such as
writing and photographs). Velocity refers to the speed at which the data is available and
can be processed. The velocity characteristic of data is important in ensuring that data is
current and updated in real time.8 Veracity of data has to do with data quality, correctness, and accuracy.9 Data lacking veracity may be imprecise, unrepresentative, inferior,
and ­untrustworthy. In using such data to better understand business decisions, it might be
said that the result is “Garbage In, Garbage Out.” Veracity indicates reliability, authenticity,
legitimacy, and validity in the data. Volume has to do with the ever-increasing size of the
data and databases. Big data produces vast amounts of data, as exemplified by the Walmart
example mentioned above. A fifth characteristic or dimension of data that is sometimes
considered is Value. Analysis of data that does not generate value makes no contribution
to an organization.10
Along with this unparalleled explosion of data, major advances have been made
in computing performance, network functioning, data handling, device mobility, and
other areas. When businesses capitalize on these developments, new opportunities become
available for discovering greater and deeper insights that could produce significant improvements in the way businesses operate and function. So how do businesses go about capitalizing
on this potential?
4
“How Walmart Makes Data Work for Its Customers,” SAS.com, 2016, at www.sas.com/en_us/insights/­
articles/ analytics/how-walmart-makes-data-work-for-its-customers.html.
5
Shih-Chia Huang, Suzanne McIntosh, Stanislav Sobolevsky, and Patrick C. K. Hung, “Big Data Analytics
and Business Intelligence in Industry,” Information Systems Frontiers 19 (2017): 1229–32.
6
Ibid.
7
Hans W. Ittmann, “The Impact of Big Data and Business Analytics on Supply Chain Management,” Journal
of Transport and Supply Chain Management 9, no. 1 (2015).
8
Huang et al., “Big Data Analytics and Business Intelligence in Industry.”
9
Ittmann, “The Impact of Big Data and Business Analytics on Supply Chain Management.”
10
Roger H. L. Chiang, Varun Grover, Ting-Peng Lian, and Zhang Dongsong, “Special Issue: Strategic Value of
Big Data and Business Analytics,” Journal of Management Information Systems 35, no. 2: 383–87.
Big Data
1-11
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Introduction to Statistics and Business Analytics
1.4
Business Analytics
LEARNING OBJECTIVE 1.4
Compare and contrast the three categories of business analytics.
To benefit from the challenges, opportunities, and potentialities presented to business
­decision-makers by big data, the new field of “business analytics” has emerged. There are
different definitions of business analytics in the literature. However, one that most accurately describes the intent of the approach here is that business analytics is the application
of processes and techniques that transform raw data into meaningful information to improve
­decision-making.11 Because big data sources are so large and complex, new questions have
arisen that cannot always be effectively answered with traditional methods of analysis.12 In
light of this, new methodologies and processing techniques have been developed, giving birth
to a new era in decision-making referred to as the “business analytics period.”13 Other names
sometimes used to refer to business analytics are business intelligence, data science, data
­analytics, analytics, and even big data, but the goal in all cases is to convert data into ­actionable
insight for more timely and accurate decision-making.14 For example, when applied to the
business environment, data analytics becomes synonymous with business analytics.15
Business analytics provides added value to data, resulting in deeper and broader business
insights that can be used to improve decision-makers’ insights and understanding in all
aspects of business, as shown in Figure 1.6.
Value added
FIGURE 1.6 Business Analytics
Add Value to Data
Big
data
Business
analytics
Better
decisionmaking
There are many new opportunities for employment in business analytics, yet there is
presently a shortage of available talent in the field. In fact, an IBM survey of 900 business and
information technology executives cited the lack of business analytics skills as a top business
challenge.16 Today’s executives say that they are seeking data-driven leaders. They are looking
for people who can work comfortably with both data and people—managers who can build
useful models from data and also lead the team that will put it into practice.17 A paper on
“Canada’s Big Data Talent Gap” estimated that this country will face a shortage of “between
10,500 and 19,000 professionals with deep data and analytical skills, such as those required
11
Coleen R. Wilder and Ceyhun O. Ozgur, “Business Analytics Curriculum for Undergraduate Majors,”
Informs 15, no. 2 (January 2015): 180–87, doi.org/10.1287/ited.2014.0134.
12
Dursun Delen and Hamed M. Zolbanin, “The Analytics Paradigm in Business Research,” Journal of
­Business Research 90 (2018): 186–95.
13
M. J. Mortenson, N. F. Doherty, and S. Robinson, “Operational Research from Taylorism to Terabytes: A
Research Agenda for the Analytic Sage,” European Journal of Operational Research 241, no. 3 (2015): 583–95.
14
R. Sharda, D. Delen, and E. Turban, Business Intelligence Analytics and Data Science: A Managerial
­Perspective (Upper Saddle River, NJ: Pearson, 2017).
15
C. Aasheim, S. Williams, P. Rutner, and A. Gardner, “Data Analytics vs. Data Science: A Study of
­ imilarities and Differences in Undergraduate Programs Based on Course Descriptions,” Journal of
S
­Information Systems Education 26, no. 2 (2015): 103–15.
16
G. Finch, C. Reese, R. Shockley, and R. Balboni, “Analytics: A Blueprint for Value: Converting Big Data and
Analytics Insights into Results,” IBM Institute for Business Value, 2013, www-935.ibm.com/services/us/gbs/
thoughtleadership/ninelevers/.
17
Dan LeClair, “Integrating Business Analytics in the Marketing Curriculum: Eight Recommendations,”
Marketing Education Review 28, no. 1 (2018): 6–13.
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1.4 Business Analytics
for roles like Chief Data Officer, Data Scientist, and Data Solutions Architect.” An additional
150,000 professionals with solid data and analytical skills will be needed to fill managerial
positions such as Business Manager and Business Analyst.18
Categories of Business Analytics
It might be said that the mission of business analytics is to apply processes and techniques to
transform raw data into meaningful information. There is a plethora of such techniques available, drawing from such areas as statistics, operations research, mathematical modelling, data
mining, and artificial intelligence, to name a few. The various techniques and approaches provide different information to decision-makers. Accordingly, the business analytics community
has organized and classified business analytic tools into three main categories: Descriptive
Analytics, Predictive Analytics, and Prescriptive Analytics.
Descriptive Analytics The simplest and perhaps the most commonly used of the three
categories of business analytics is descriptive analytics. Often the first step in the analytics
process, descriptive analytics takes traditional data and describes what has happened or is
happening in a business. It can be used to condense big data into smaller, more useful data.19
Also referred to as reporting analytics, descriptive analytics can be used to discover hidden
­relationships in the data and identify undiscovered patterns.20 Descriptive analytics drills
down in the data to uncover useful and important details, and mines data for trends.21 At this
step, visualization can be a key technique for presenting information.
Much of what is taught in a traditional introductory statistics course could be classified
as descriptive analytics, including descriptive statistics, frequency distributions, discrete distributions, continuous distributions, sampling distributions, and statistical inference.22 We
could probably add correlation and various clustering techniques to the mix, along with data
mining and data visualization techniques.
Predictive Analytics The next step in data reduction is predictive analytics, which
finds relationships in the data that are not readily apparent with descriptive analytics.23 With
predictive analytics, patterns or relationships are extrapolated forward in time, and the past
is used to make predictions about the future.24 Predictive analytics also provides answers
that move beyond using the historical data as the principal basis for decisions.25 It builds
and ­assesses algorithmic models that are intended to make empirical rather than theoretical
predictions, and are designed to predict future observations.26 Predictive analytics can help
managers develop ­likely scenarios.27
Topics in predictive analytics can include regression, time-series, forecasting, simulation,
data mining (see Section 1.5), statistical modelling, machine-learning techniques, and others. They can also include classifying techniques, such as decision-tree models and neural
networks.28
18
“Closing Canada’s Big Data Talent Gap,” report by Canada’s Big Data Consortium, October 2015.
19
Jeff Bertolucci, “Big Data Analytics: Descriptive vs. Predictive vs. Prescriptive,” Information Week,
­December 31, 2018, www.informationweek.com/big-data/big-data.
20
C. K. Praseeda and B. L. Shivakumar, “A Review of Trends and Technologies in Business Analytics,”
­International Journal of Advanced Research in Computer Science 5, no. 8 (November-December 2014): 225–29.
21
Watson ioT, “Descriptive, Predictive, Prescriptive: Transforming Asset and Facilities Management with
Analytics,” IBM paper, 2017, www-01.ibm.com/common/ssi/cgi-bin/ssialias?infotype=SA&subtype=WH&­
htmlfid=TIW14162USEN.
22
Wilder and Ozgur, “Business Analytics Curriculum for Undergraduate Majors.”
23
B. Daniel, “Big Data and Analytics in Higher Education: Opportunities and Challenges,” British Journal of
Educational Technology 46, no. 5 (2015): 904–920, onlinelibrary.wiley.com/doi/abs/10.1111/bjet.12230.
24
Praseeda and Shivakumar, “A Review of Trends and Technologies in Business Analytics.”
25
Ibid.
26
Delen and Zolbanin, “The Analytics Paradigm in Business Research.”
27
Watson ioT, “Descriptive, Predictive, Prescriptive.”
28
Sharda, Delen, and Turban, Business Intelligence Analytics and Data Science.
1-13
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1-14
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Introduction to Statistics and Business Analytics
Prescriptive Analytics The final stage of business analytics is prescriptive analytics,
which is still in its early stages of development.29 Prescriptive analytics follows descriptive
and predictive analytics in an attempt to find the best course of action under certain circumstances.30 The goal is to examine current trends and likely forecasts and use that information
to make better decisions.31 Prescriptive analytics takes uncertainty into account, recommends
ways to mitigate risks, and tries to see what the effect of future decisions will be in order to adjust
the decisions before they are actually made.32 It does this by exploring a set of possible actions
based on descriptive and predictive analyses of complex data, and then suggesting courses
of action.33 Prescriptive analytics evaluates data and determines new ways to operate while
balancing all constraints,34 at the same time continually and automatically processing new
data to improve recommendations and provide better decision options.35 It not only foresees
what will happen and when, but also suggests why it will happen and recommends how to act
in order to take advantage of the predictions.36 Predictive analytics uses a set of mathematical
techniques that computationally determine an optimal action or decision given a complex set
of objectives, requirements, and constraints.37
Topics in prescriptive analytics come from the fields of management science or operations research and are generally aimed at optimizing the performance of a system, using tools
such as mathematical programming, simulation, network analysis, and others.38
1.5
Data Mining and Data Visualization
LEARNING OBJECTIVE 1.5
Describe the data mining and data visualization processes.
The dawning of the big data era has given rise to new and promising prospects for improving
business decisions and outcomes. Two main components in the process of transforming the
mountains of data now available into useful business information are data mining and data
visualization.
Data Mining
In the field of business, data mining is the process of collecting, exploring, and analyzing
large volumes of data in an effort to uncover hidden patterns and/or relationships that can be
used to enhance business decision-making. In short, data mining is a process used by companies to turn raw data into meaningful information that can potentially lead to some business
advantage. Data mining allows business people to discover and interpret useful information
29
Praseeda and Shivakumar, “A Review of Trends and Technologies in Business Analytics.”
30
Delen and Zolbanin, “The Analytics Paradigm in Business Research.”
31
Sharda, Delen, and Turban, Business Intelligence Analytics and Data Science.
32
Praseeda and Shivakumar, “A Review of Trends and Technologies in Business Analytics.”
33
Watson ioT, “Descriptive, Predictive, Prescriptive.”
34
Daniel, “Big Data and Analytics in Higher Education.”
35
A. Basu, “Five Pillars of Prescriptive Analytics Success,” Analytics (March/April 2013), pp. 8–12, analytics-­
magazine.org/executive-edge-five-pillars-of-prescriptive-analytics-success/.
36
Praseeda and Shivakumar, “A Review of Trends and Technologies in Business Analytics.”
37
I. Lusting, B. Dietrich, C. Johnson, and C. Dziekan, “The Analytics Journey,” Analytics Magazine 3, no. 6
(2010): 11–13.
38
Sharda, Delen, and Turban, Business Intelligence Analytics and Data Science.
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1.5 Data Mining and Data Visualization
that will help them make more knowledgeable decisions and better serve their customers
and clients.
Figure 1.7 displays the process of data mining, which involves finding the data, converting the data into useful forms, loading the data into a holding or storage location, managing
the data, and making the data accessible to business analytics’ users. Data scientists often
refer to the first three steps of this process as ETL (extract, transform, and load). Extracting
involves locating the data by asking the question “Where can it be found?” Countless pieces
of data are unearthed the world over in a great variety of forms and from multiple disparate
sources. Because of this, extracting data can be the most time-consuming step.39 After a set of
data has been located and extracted, it must be transformed or converted into a usable form.
Included in this transformation may be a sorting process that determines which data are
useful and which are not. In addition, data are typically “cleaned” by removing corrupt or
­incorrect records and identifying incomplete, incorrect, or irrelevant parts of the data.40 Often
the data are sorted into columns and rows to improve usability and searchability.41 After the
set of data is extracted and transformed, it is loaded into an end target, which is often a database. Data are often managed through a database management system, which is a software
system that enables users to define, create, maintain, and control access to the database.42
­Lastly, the ultimate goal of the process of data mining is to make the data accessible and
­usable to the business analyst.
Data Visualization
As business organizations amass large reservoirs of data, one swift and easy way to
obtain an overview of the data is through data visualization, which has been described as
perhaps the most useful component of business analytics, and the element that makes it
truly unique.43 So what is data visualization? Generally, data visualization is any attempt
made by data analysts to help individuals better understand data by putting it in a visual
context. Specifically, data visualization is the study of the visual representation of data
and is employed to convey data or information by imparting it as visual objects ­displayed in
graphics.
Interpretation of data is vital to unlocking the potential value it holds and to ­making
the most informed decisions.44 Using visual techniques to convey information hidden
in data allows for a broader audience with a wider range of backgrounds to view and
understand its meaning. Data visualization tools help make data-driven insights accessible
to people at all levels throughout an organization and can reveal surprising patterns and
connections, resulting in improved decision-making. To communicate information clearly
and efficiently, data visualization uses statistical graphics, plots, information graphics, and
other tools. Numerical data may be encoded, using dots, lines, or bars, to visually communicate a quantitative message, thereby making complex data more accessible, understandable,
and usable.45
39
Shirley Zhao, “What Is ETL? (Extract, Transform, Load),” paper from Experian Data Quality, October 20,
2017, www.edq.com/blog/what-is-etl-extract-transform-load/.
40
S. Wu, “A Review on Coarse Warranty Data and Analysis,” Reliability Engineering and System Safety 114
(2013): 1–11, doi.org/10.1016/j.ress.2012.12.021.
41
Zhao, “What Is ETL?”
42
Thomas M. Connolly and Carolyn E. Begg, Database Systems: A Practical Approach to Design
­Implementation and Management, 6th ed. (Harlow, UK: Pearson, 2014), 64.
43
James R. Evans. Business Analytics: Methods, Models, and Decisions, 2nd ed. (Boston: Pearson, 2016), 7.
44
R. Roberts, R. Laramee, P. Brookes, G.A. Smith, T. D’Cruze, and M.J. Roach, “A Tale of Two Visions—­
Exploring the Dichotomy of Interest between Academia and Industry in Visualisation,” in Proceedings of
the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and
Applications, vol. 3 (Setúbal, Portugal: SciTePress, 2018), 319–26.
45
Stephen Few, “Eenie, Meenie, Minie, Moe: Selecting the Right Graph for Your Message,” paper from
­Perceptual Edge, 2004, www.perceptualedge.com/articles/ie/the_right_graph.pdf.
1-15
Extract data
Transform data
Load data
Manage data
Make data accessible
to business analyst
FIGURE 1.7 Process of Data
Mining
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C h a pte r 1
Introduction to Statistics and Business Analytics
Visualization Example
As an example of data visualization, consider the top five
­ rganizations in the manufacturing industry to receive Canadian government funding and
o
their respective amount funded (in dollars) in a recent year, displayed in Table 1.1.46
TA B L E 1. 1
Top Five Manufacturing Firms to Receive Canadian
Government Funding
Company Name
Dollars Funded
FCA Canada Inc. (Chrysler)
$85,800,000
Bombardier Inc.
$54,150,000
Produits Kruger
$39,500,000
Sonaca Montréal Inc.
$23,250,000
Hanwha L&C Canada Inc.
$15,000,000
One of the leading companies to develop data visualization software is Tableau©.
Figure 1.8 is a bubble chart of the Table 1.1 data, developed using Tableau©. One of the
advantages of using visualization to display data is the variety of types of graph or charts.
Figure 1.9 contains a Tableau©-produced bar chart of the same information to give the user
a different perspective.
FIGURE 1.8 Bubble Chart of
the Top Five Manufacturing
Firms to Receive Canadian
Government Funding
Sonaca
Montréal
Inc.
FCA Canada Inc.
(Chrysler)
Hanwha
L&C
Canada
Inc.
Bombardier
Inc.
Produits
Kruger
FCA Canada
Inc.(Chrysler)
Company name
FIGURE 1.9 Bar Chart of
the Top Five Manufacturing
Firms to Receive Canadian
Government Funding
Bombardier Inc.
Produits Kruger
Sonaca
Montréal Inc.
Hanwha L & C
Canada Inc.
0M
46
10M
20M
30M
40M
50M
Dollars funded
60M
70M
80M
90M
“Top 50 Companies That Received Canadian Government Funding,” The Globe and Mail, July 19, 2017,
www.theglobeandmail.com/report-on-business/top-50-report-on-business-the-funding-portal/article19192109/.
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Why Statistics Is Relevant
1-17
End-of-Chapter Review
Decision Dilemma Solved
Statistics Describe the State of Business
in India’s Countryside
Several statistics were reported in the Decision Dilemma about
rural India. The authors of the sources from which the Decision
Dilemma was drawn never stated whether the reported statistics
were based on actual data drawn from a census of rural India
households or on estimates taken from a sample of rural households. If the data came from a census, then the totals, averages, and
percentages presented in the Decision Dilemma are ­parameters. If,
on the other hand, the data were gathered from samples, then they
are statistics. Although governments do conduct censuses and at
least some of the reported numbers could be parameters, more
often than not such data are gathered from samples of people or
items. For example, in rural India, the government, academicians,
or business analysts could have taken random samples of households, gathering consumer statistics that are then used to estimate
population parameters, such as percentage of households with
televisions, and so forth.
In conducting research on a topic like consumer consumption in rural India, a wide variety of statistics can be gathered that
represent several levels of data. For example, ratio-level measurements on items such as income, number of children, age of household heads, number of heads of livestock, and grams of toothpaste
consumed per year might be obtained. On the other hand, if
analysts use a Likert-type scale (1-to-5 measurements) to gather
responses about the interests, likes, and preferences of rural Indian consumers, an ordinal-level measurement would be obtained,
as with the ranking of products or brands in market research studies. Other variables, such as geographic location, sex, occupation,
or religion, are usually measured with nominal data.
The decision to enter the rural India market is not just a
marketing decision. It involves production and operations capacity, scheduling issues, transportation challenges, financial commitments, managerial growth or reassignment issues, accounting issues
(accounting for rural India may differ from techniques used in
urban markets), information systems, and other related areas. With
so much on the line, company decision-makers need as much relevant information available as possible. In this Decision Dilemma, it is
obvious to the decision-maker that rural India is still quite poor and
illiterate. Its capacity as a market is great. The statistics on the increasing sales of a few personal-care products look promising. What are the
future forecasts for the earning power of people in rural India? Will
major cultural issues block the adoption of the types of products that
companies want to sell there? The answers to these and many other
interesting and useful questions can be obtained by the appropriate
use of statistics. The approximately 800-million people living in rural
India certainly make it a market segment worth studying further.
Key Considerations
With the abundance and proliferation of statistical data, ­potential
misuse of statistics in business dealings is a concern. It is, in
­effect, unethical business behaviour to use statistics out of context. ­Unethical business people might use only selective data from
studies to underscore their point, omitting statistics from the same
studies that argue against their case. The results of statistical studies can be misstated or overstated to gain favour.
This chapter noted that, if data are nominal or ordinal, then
only nonparametric statistics are appropriate for analysis. The use
of parametric statistics to analyze nominal and/or ordinal data is
wrong and could be considered under some circumstances to be
unethical.
In this text, each chapter contains a section on ethics that
discusses how businesses can misuse the techniques presented in
the chapter in an unethical manner. As both users and producers,
business students need to be aware of the potential ethical pitfalls
that can occur with statistics.
Why Statistics Is Relevant
In the contemporary business world, good decisions are driven by data. In all areas of business, amazing
amounts of diverse data are available for interpretation and quantitative insight. Business managers and
professionals are increasingly required to justify decisions on the basis of data analysis. Thus, the ability
to extract useful information from data is one of the most important, and marketable, skills business
managers and professionals can acquire. This text is an introduction to the theory and, more importantly,
the methods used to intelligently collect, analyze, and interpret data relevant to business ­decision-making.
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1-18
C h a pte r 1
Introduction to Statistics and Business Analytics
Summary of Learning Objectives
LE A R N I N G O BJ E CT I VE 1 . 1 Define important statistical
terms, including population, sample, and parameter, as they
relate to descriptive and inferential statistics.
Statistics is an important decision-making tool in business and is used in
virtually every area of business. In this text, the word statistics is defined
as the science of gathering, analyzing, interpreting, and presenting data.
The study of statistics can be subdivided into two main areas:
­descriptive statistics and inferential statistics. Descriptive statistics
­result from gathering data from a body, group, or population and
reaching conclusions only about that group. Inferential statistics are
generated from the process of gathering sample data from a group,
body, or population and reaching conclusions about the larger group
from which the sample was drawn.
LEARNING OBJECTIVE 1.2 Explain the difference
­between variables, measurement, and data, and compare the
four different levels of data: nominal, ordinal, interval, and ratio.
Most business statistics studies contain variables, measurements, and
data. A variable is a characteristic of any entity being studied that is
capable of taking on different values. Examples of variables might
include monthly household food spending, time between arrivals at
a restaurant, and patient satisfaction rating. A measurement is when
a standard process is used to assign numbers to particular attributes
or characteristics of a variable. Measurements of monthly household
food spending might be taken in dollars, time between arrivals might
be measured in minutes, and patient satisfaction might be measured
using a 5-point scale. Data are recorded measurements. It is data that
are analyzed by business statisticians in order to learn more about the
variables being studied.
The appropriate type of statistical analysis depends on the
level of data measurement, which can be (1) nominal, (2) ordinal,
(3) ­interval, or (4) ratio. Nominal is the lowest level, representing the
classification of only data, such as geographic location, sex, or social
insurance number. The next level is ordinal, which provides rank
ordering measurements in which the intervals between consecutive
numbers do not necessarily represent equal distances. Interval is
the next highest level of data measurement, in which the distances
represented by consecutive numbers are equal. The highest level of
data measurement is ratio. This has all the qualities of interval measurement, but ratio data contain an absolute zero, and ratios between
numbers are meaningful. Interval and ratio data are sometimes called
metric or quantitative data. Nominal and ordinal data are sometimes
called nonmetric or qualitative data.
Two major types of inferential statistics are (1) parametric
statistics and (2) nonparametric statistics. Use of parametric statistics
requires interval or ratio data and certain assumptions about the distribution of the data. The techniques presented in this text are largely
parametric. If data are only nominal or ordinal in level, nonparametric statistics must be used.
LEARNING OBJECT IV E 1.3 Explain the differences between the four dimensions of big data.
The emergence of exponential growth in the number and type of data
existing has resulted in a new term, big data, which is a collection of
large and complex datasets from different sources that are difficult to process using traditional data management and process applications. There
are four dimensions of big data: (1) variety, (2) velocity, (3) veracity,
and (4) volume. Variety refers to the many different forms of data,
velocity refers to the speed at which the data are available and can
be processed, veracity has to do with data quality and accuracy, and
volume has to do with the ever-increasing size of data.
LEARNING OBJECT IV E 1.4 Compare and contrast the
three categories of business analytics.
Business analytics is a relatively new field of business dealing with
the challenges, opportunities, and potentialities available to ­business
­analysts through big data. Business analytics is the application of
processes and techniques that transform raw data into meaningful
­information to improve decision-making. There are three categories of
business analytics: (1) descriptive analytics, (2) predictive analytics,
and (3) prescriptive analytics.
LEARNING OBJECT IV E 1.5
and data visualization processes.
Describe the data mining
Two main components in the process of transforming the mountains
of data now available are data mining and data visualization. Data
mining is the process of collecting, exploring, and analyzing large
volumes of data in an effort to uncover hidden patterns and/or relationships that can be used to enhance business decision-making. One
effective way of communicating data to a broader audience of people
is data visualization. Data visualization is any attempt made by data
analysts to help individuals better understand data by putting it in a
visual context. Specifically, data visualization is the study of the visual
representation of data and is employed to convey data or information
by imparting it as visual objects displayed in graphics.
Key Terms
big data 1-11
business analytics 1-12
census 1-4
data 1-6
data mining 1-14
data visualization 1-15
descriptive analytics 1-13
descriptive statistics 1-4
inferential statistics 1-4
interval-level data 1-8
measurement 1-6
metric data 1-9
nominal-level data 1-7
nonmetric data 1-8
nonparametric statistics 1-9
ordinal-level data 1-7
parameter 1-4
parametric statistics 1-9
population 1-4
predictive analytics 1-13
prescriptive analytics
ratio-level data 1-8
sample 1-4
statistic 1-4
statistics 1-3
variable 1-6
variety 1-11
velocity 1-11
veracity 1-11
volume 1-11
1-14
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Exploring the Databases with Business Analytics
1-19
Supplementary Problems
1.1 Give a specific example of data that might be gathered from each
of the following business disciplines: accounting, finance, human
resources, marketing, operations and supply chain management,
information systems, production, and management. An example in
the marketing area might be “number of sales per month by each
salesperson.”
g. An employee’s identification number
h. The response time of an emergency unit
1.8 Classify each of the following as nominal, ordinal, interval, or
ratio data.
a. The ranking of a company by Report on Business magazine’s
Top 1000
1.2 State examples of data that can be gathered for decision-making
purposes from each of the following industries: manufacturing,
insurance, travel, retailing, communications, computing, agriculture,
banking, and health care. An example in the travel industry might be
the cost of business travel per day in various European cities.
b. The number of tickets sold at a movie theatre on any given
night
c. The identification number on a questionnaire
d. Per capita income
1.3 Give an example of descriptive statistics in the recorded music
industry. Give an example of how inferential statistics could be used
in the recorded music industry. Compare the two examples. What
makes them different?
e. The trade balance in dollars
f. Profit/loss in dollars
g. A company’s tax identification number
h. The Standard & Poor’s bond ratings of cities based on the following scales:
1.4 Suppose you are an operations manager for a plant that manufactures batteries. Give an example of how you could use descriptive
statistics to make better managerial decisions. Give an example of
how you could use inferential statistics to make better managerial
decisions.
Rating
Highest quality
High quality
Upper medium quality
Medium quality
Somewhat speculative
Low quality, speculative
Low grade, default possible
Low grade, partial recovery possible
Default, recovery unlikely
1.5 There are many types of information that might help the man­
ager of a large department store run the business more efficiently
and better understand how to improve sales. Think about this in such
areas as sales, customers, human resources, inventory, suppliers, and
so on. List five variables that might produce information that could
aid the manager in his or her job. Write a sentence or two describing
each variable, and briefly discuss some numerical observations that
might be generated for each variable.
1.6 Suppose you are the owner of a medium-sized restaurant in a
small city. What are some variables associated with different aspects
of the business that might be helpful to you in making business
decisions about the restaurant? Name four of these variables. For each
variable, briefly describe a numerical observation that might be the
result of measuring the variable.
1.7 Video Classify each of the following as nominal, ordinal,
interval, or ratio data.
a. The time required to produce each tire on an assembly line
b. The number of litres of milk a family drinks in a month
c. The ranking of four machines in your plant after they have
been designated as excellent, good, satisfactory, and poor
AAA
AA
A
BBB
BB
B
CCC
CC
C
1.9 Video The Mapletech Manufacturing Company makes electric wiring, which it sells to contractors in the construction industry.
Approximately 900 electrical contractors purchase wire from Mapletech
annually. Mapletech’s director of marketing wants to determine electrical contractors’ satisfaction with Mapletech’s wire. She develops a
questionnaire that yields a satisfaction score of between 10 and 50 for
participant responses. A random sample of 35 of the 900 contractors
is asked to complete a satisfaction survey. The satisfaction scores for
the 35 participants are averaged to produce a mean satisfaction score.
a. What is the population for this study?
d. The telephone area code of clients in Canada
b. What is the sample for this study?
e. The age of each of your employees
c. What is the statistic for this study?
f. The dollar sales at the local pizza house each month
d. What would be a parameter for this study?
Exploring the Databases with Business Analytics
Six major databases constructed for this text can be used to apply
the business analytics and statistical techniques presented in this
course. These databases are located in WileyPLUS, and each one is available in a few electronic formats for your convenience. These six databases represent a wide variety of business areas: the stock market,
international labour, finance, energy, and agri-business. The data are
Grade
see the databases on the Student Website and in WileyPLUS
gathered from such reliable sources as Statistics Canada, the Toronto
Stock Exchange, Yahoo Finance, the Fraser Institute, and the Global
Environment Outlook (GEO) Data Portal. Four of the six databases
contain time-series data that can be especially useful in forecasting
and regression analysis. Here is a description of each database, along
with information that may help you to interpret outcomes.
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1-20
C h a pte r 1
Introduction to Statistics and Business Analytics
Canadian Stock Market Database
The stock market database contains seven variables on the Toronto
Stock Exchange. Weekly observations for a period of five years yield
a total of 257 observations per variable. The variables are Composite
Index, Energy Index, Financial Index, Health Index, Utility Index,
I.T. Index, and Gold Index. These data were obtained directly from
TMX Inc.
Canadian RRSP Contribution Database
The registered retirement savings plan database contains five variables: Number of Tax Filers, Total RRSP Contributors, Average Age of
RRSP Contributors, Total RRSP Contributions ($ × 1,000), and Median RRSP Contributions ($). There are 156 entries for each variable in
this database, representing 10 years of data for each of 10 provinces
and 3 territories in Canada. The data in this database were obtained
from Statistics Canada.
International Labour Database
This time-series database contains the civilian unemployment rates
in percent from seven countries (G7) presented yearly over a 30-year
period. The data are published by the Bureau of Labor Statistics of the
U.S. Department of Labor. The countries are Canada, France, Germany,
Italy, Japan, the United Kingdom, and the United States.
Financial Database
The financial database contains observations on 12 variables for
100 companies. The variables are Industry Group, Type of Industry,
Total Revenues, Price, Average Yield, Dividend Growth, Average
Price/Earnings (P/E) Ratio, Dividends per Share, Total Debt/Total
Equity, Price/Cash Flow, Price/Book, and One-Year Total Return. The
data were gathered from the Toronto Stock Exchange. The companies
represent seven different types of industries. The variable “Type” displays a company’s industry type as follows:
1 = Real Estate
2 = Financial Institutes
3 = Chemicals
4 = Mining, Electric, Oil & Gas, Pipelines
5 = Telecommunications, Retail, Commercial Services, Auto
Parts & Equipment, Transportation
6 = Insurance
7 = Food, Pharmaceuticals, Electronics, Media, Aerospace/
Defence, Hand/Machine Tools, Agriculture, Iron/Steel, Holding Companies, Engineering and Construction, Machinery—
Diversified, Forest Products and Paper
Energy Resource Database
The energy resource database consists of data for North America
and Europe on nine variables related to energy supply and emission
of carbon dioxide over a period of 35 years. The database is adapted
from the Global Environment Outlook (GEO) Data Portal. The nine
variables are the seven total primary energy supplies of Solar, Wind,
Tide, and Wave; Nuclear; Natural Gas; Coal and Coal Products; Crude
Oil; Hydro; and Petroleum Products, plus the two sources of emissions of CO2: Manufacturing Industries and Construction, and
Transportation.
Agri-Business Canada Database
The agri-business time-series database contains the monthly weight
(in thousands of pounds) of seven different grains over an eight-year
period. Each of the seven variables represents 94 months of data. The
seven grains are Wheat; Wheat, Excluding Durum; Durum Wheat;
Oats; Barley; Flaxseed; and Canola. The data are published by Statistics Canada under Agri-business.
Use the databases to answer the following question.
1. In the Financial Database, what is the level of data for each of the
following variables?
a. Type of Industry
b. Average Price
c. Price/Cash Flow
Case
Canadian Farmers Dealing with Stress
Farming is an extremely demanding job whose success depends largely on the dedication of the farmers. In order to tackle the rigorous
tasks of the trade, farmers must be in good physical and mental condition. The University of Guelph conducted a study in 2017/18 which
showed that Canadian farmers experienced higher levels of anxiety
and depression and displayed lower levels of help-seeking behaviour
compared to the general Canadian populace. The study indicated that
Canadian farmers were at a heightened risk of suicide compared to
the rest of the population. The Canadian Agricultural Safety Association (CASA) also recently sponsored research on the stress level of
Canadian farmers.
Western Opinion Research Inc. conducted the research study,
which was completed by 1,100 farmers across Canada. The survey asked farmers to rate their stress level, ranging from “stressed”
to “somewhat stressed” to “very stressed.” The results varied and
revealed the following: two-thirds of farmers indicated feeling “stressed,”
45% indicated feeling “somewhat stressed,” and one in five indicated
feeling “very stressed.” The results of the survey also revealed that
the major causes of stress among farmers were (a) financial concerns
related to prices of commodities, (b) diseases affecting livestock,
and (c) finances regarding general farm expenses. The results also
revealed that a large percentage of farmers (35%) were interested in
having access to more stress-related resources in order to help alleviate their stress level.
This study allowed CASA to realize that stress within the farming industry is a major issue, therefore making it imperative to take
action and offer stress counselling resources to farmers. These
­resources include (a) confidential meeting with a health care
professional, (b) over-the-phone consultation with a health care professional, and (c) attending workshops such as retreats that focus on
relaxation techniques and role playing with other farmers.
Over the last few years, CASA has made great progress to help
reduce the stress level of Canadian farmers. For example, successful
counselling services that deal with farmers and their problems were
established using phone, email, and online chat help lines. These
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Using the Computer
include the Manitoba Farm, Rural & Northern Support Services and
the Saskatchewan Farm Stress Line. These services are well recognized
and are having great success in helping farmers, mainly because they
are staffed by paid professional counsellors who all have farming backgrounds, making the farmers feel more comfortable because they are
connecting with someone who understands their work-related issues.
Discussion
Think of the market research that was conducted by CASA.
1. What are some of the populations that CASA might have been
interested in measuring for these studies? Did CASA attempt to
contact entire populations? What samples were taken? In light of
these two questions, how was the inferential process used by CASA
in its market research? Can you think of any descriptive statistics
that might have been used by CASA in its decision-making process?
2. In the various market research efforts made by CASA to deter-
mine stress experienced by farmers, some of the possible measurements appear in the following list. Categorize these by level
of data. Think of some other measurements that CASA analysts
might have taken to help them in this research effort and categorize them by level of data.
a. Ranking of the level of stress on a stress test
b. Number of farmers that ask for professional help
c.Number of farmers that are aware of professional help
resources
1-21
d. Number of farmers that try to manage stress on their own
e.Number of farmers that are interested in having access to
more stress-related resources
f. Number of farmers that are close to being out of business
g.Number of farmers that would prefer dealing with stress
on their own
h.Number of farmers that would prefer dealing with stress
with a professional over the telephone
i.Number of farmers that would prefer dealing with stress
with a professional in person
j. Age of survey respondent
k. Gender of survey respondent
l. Geographical region of survey respondent
m. Amount of time farmers spend dealing with their stress
n.Rating of the most stress-related factors on a scale from 1
to 10, where 1 is the least stress-related factor and 10 is the
most stress-related factor
o.Rating of the reasons why farmers do not seek more help
for stress on a scale from 1 to 10, where 1 is the least important reason and 10 is the most important reason
Sources: Klinic Community Health, “Annual Report 2017/18,” klinic.
mb.ca/wp-content/uploads/2018/06/AnnualReport1718.pdf; Manitoba
Farm and Rural Stress Line, “Annual Report,” 2008, 2010, www.
ruralsupport.ca/index.php?pageid=22; Saskatchewan Farm Stress Line,
www.mobilecrisis.ca/farm-stress-line-rural-sask; Canadian Agricultural
Safety Association, “National Stress and Mental Survey of Canadian
Farmers,” February 11, 2005, www.casa-acsa.ca/en/safetyshop-library/
national-stress-and-mental-survey-of-canadian-farmers/.
Big Data Case
Virtually every chapter in this text will end with a big data case.
Unlike the chapter cases, which feature a wide variety of companies
and business scenarios, the big data case will be based on data from
a single industry, U.S hospitals. Drawing from the American Hospital Association database of over 2,000 hospitals, we will use business
analytics to mine data on these hospitals in different ways for each
chapter based on analytics presented in that chapter.
The hospital database features data on twelve variables, thereby
offering over 24,000 observations to analyze. Hospital data for each
of the 50 states are contained in the database with qualitative data
representing state, region of the country, type of ownership, and
type of hospital. Quantitative measures include Number of Beds,
Number of Admissions, Census, Number of Outpatients, Number of
Births, Total Expenditures, Payroll Expenditures, and Personnel.
Using the Computer
Statistical Analysis Using Excel
The advent of the modern computer opened many new opportunities for statistical analysis. The computer allows for storage,
­retrieval, and transfer of large data sets. Furthermore, computer software has been developed to analyze data by means of
­sophisticated statis­tical techniques. Some widely used statistical
­techniques, such as multiple regression, are so tedious and cumbersome to compute manually that they were of little practical use
to analysts before computers were developed. In this textbook, the
end-of-chapter “Using the Computer” feature will show you how
you can use software to apply the statistical techniques you learn
in each chapter.
• Business statisticians use many popular statistical software
packages, including MINITAB, SAS, and SPSS. Many computer
spreadsheet software packages can also analyze data statistically.
In this text, when it is appropriate to use a computer, we will use
Microsoft Excel for data analysis.
• Excel is by far the most commonly used spreadsheet for PCs,
making it the obvious choice for basic statistical analysis. Excel
can perform a variety of calculations and includes a large collection of statistical functions. The Data Analysis ToolPak provides
a further suite of statistical macro-functions.
• We note, however, that although Excel is a fine spreadsheet, it
is not a professional statistical data analysis package: there are
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1-22
C h a pte r 1
Introduction to Statistics and Business Analytics
some important limitations. Key limitations to keep in mind
include the following: missing values in Excel are difficult to
handle when performing data analysis; data organization differs according to analysis, sometimes forcing you to reorganize
your data; some output and charts produced by Excel are of poor
quality from a statistical point of view and are sometimes inadequately labelled; and there is no record of how an analysis was
done if the Data Analysis ToolPak is used.
• Despite these limitations, Excel is the most commonly used
package in the business environment and is the package you are
most likely to use in your professional life.
• It is important to remember that a statistical software package
is not a replacement for a thorough understanding of correct
statistical methods. The business analyst is responsible for determining the most appropriate statistical methods for a given business problem. Simply relying on convenient software tools that
may be at hand without thinking through the most appropriate
approach can lead to errors, oversights, and poor decisions.
One of the goals of this text is to show you when and how to use
sta­tistical methods to provide information that can be used in
business decisions.
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CHAPTER 2
Visualizing Data with
Charts and Graphs
LEARNING OBJECTIVES
The overall objective of Chapter 2 is for you to master several techniques for summarizing
and visualizing data, thereby enabling you to:
2.1
Explain the difference between grouped and
ungrouped data and construct a frequency
distribution from a set of data. Explain what the
distribution represents.
2.2 Describe and construct different types of quantitative
data graphs, including histograms, frequency
polygons, ogives, and stem-and-leaf plots. Explain
when these graphs should be used.
2.3
Describe and construct different types of qualitative
data graphs, including pie charts, bar charts, and Pareto
charts. Explain when these graphs should be used.
2.4
Display and analyze two variables simultaneously
using cross tabulation and scatter plots.
2.5 Describe and construct a time-series graph. Visually
identify any trends in the data.
Decision Dilemma
iStock.com/instamatics
As most people suspect, the United States is the number one
consumer of oil in the world, followed by China, India, Japan,
Saudi Arabia, and the Russian Federation. (Canada ranks tenth,
with a consumption that is below that of Germany and above
that of Mexico.) China, however, is the world’s largest consumer
of coal, with India coming in at number two, followed by the
United States, Japan, and the Russian Federation. (Canada
ranks 18th, below Malaysia and above Thailand.) The annual
oil and coal consumption figures for six of the top total energyconsuming nations in the world, according to figures released
by the BP Statistical Review of World Energy for a recent year,
are as follows.
© istockphoto.com/instamatics
Energy Consumption Around the World
2-1
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2-2
Ch apter 2
Visualizing Data with Charts and Graphs
Country
Oil
Consumption
(thousands of
barrels)
Coal
Consumption
(million tonnes
oil equivalent)
U.S.
19,880
332.1
China
12,799
1,892.6
India
4,690
424.0
Japan
3,988
120.5
Russian Federation
3,224
92.3
Brazil
3,017
16.5
Managerial, Statistical, and Analytical Questions
Suppose you are an energy industry analyst and you are
asked to prepare a brief report showing the leading energyconsumption countries in both oil and coal.
1. What is the best way to display the data on energy consumption in a report? Are the raw data enough? Can you effectively
display the data graphically?
2. Is there a way to graphically display oil and coal figures
­together so that readers can visually compare countries on
their consumptions of the two different energy sources?
Source: BP Statistical Review of World Energy, June 2018. www.bp.com/
content/dam/bp/en/corporate/pdf/energy-economics/statistical-review/
bp-stats-review-2018-full-report.pdf.
Introduction
In this era of seemingly boundless big data, the application of business analytics has great
potential to unearth business knowledge and intelligence that can substantially improve business decision-making. A key objective of business analytics is to convert data into deeper and
broader actionable insights and understandings for all aspects of business. One of the first
steps is to visualize the data through graphs and charts, thereby providing business analysts
with an overview of the data and a glimpse into any underlying relationships.
In this chapter, we will study how to visually represent data in order to convey information that can unlock potentialities for making better business decisions. Remember, using
visuals to convey information hidden in the data allows for a broader audience with a wide
range of backgrounds to understand its meaning. Data visualization tools can reveal surprising patterns and connections, making data-driven insights accessible to people at all levels
of an organization. Graphical depictions of data are often much more effective communication tools than tables of numbers in business meetings. In addition, key characteristics of
graphs often suggest appropriate choices among potential numerical methods (discussed in
later chapters) for analyzing data.
A first step in exploring and analyzing data is to reduce important and sometimes
expansive data to a graphic picture that is clear, concise, and consistent with the message of
the original data. Converting data to graphics can be creative and artful. This chapter focuses on graphical tools for summarizing and presenting data. Charts and graphs discussed in
detail in Chapter 2 include histograms, frequency polygons, ogives, dot plots, stem-and-leaf
plots, bar charts, pie charts, and Pareto charts for one-variable data, and cross-tabulation
tables and scatter plots for two-variable numerical data. In addition, there is a section on
time-series graphs for displaying data gathered over time. Box-and-whisker plots are discussed in Chapter 3.
A non-inclusive list of other graphical tools includes the line plot, area plot, bubble
chart, treemap, map chart, Gantt chart, bullet chart, doughnut chart, circle view, highlight
table, matrix plot, marginal plot, probability distribution plot, individual value plot, and
contour plot.
Recall the four levels of data measurement discussed in Chapter 1: nominal, ordinal,
interval, and ratio. The lowest levels of data, nominal and ordinal, are referred to as qualitative data, while the highest levels of data, interval and ratio, are referred to as quantitative data. In this chapter, Section 2.2 will present quantitative data graphs and Section 2.3
will present qualitative data graphs. Note that the data visualization software Tableau©
divides data variables into measures and dimensions based on whether data are qualitative
or quantitative.
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2.1
2.1
Frequency Distributions
LEARNING OBJECTIVE 2.1
Explain the difference between grouped and ungrouped data and construct a frequency
distribution from a set of data. Explain what the distribution represents.
Raw data, or data that have not been summarized in any way, are sometimes referred to as
­ungrouped data. As an example, Table 2.1 contains raw data showing 60 years of unemployment rates for Canada. Data that have been organized into a frequency distribution are
called grouped data. Table 2.2 presents a frequency distribution for the data displayed in
Table 2.1. The distinction between ungrouped and grouped data is important because statistics
are calculated differently for each type of data. Several of the charts and graphs presented in
this chapter are constructed from grouped data.
TA B L E 2.1
Unemployment Rates for Canada over 60 Years (Ungrouped Data)
6.0
6.4
12.0
9.5
6.0
7.0
6.3
11.3
9.6
6.1
7.1
5.6
10.5
9.1
8.3
5.9
5.4
9.6
8.3
8.1
5.5
7.1
8.8
7.6
7.5
4.7
7.1
7.8
6.8
7.3
3.9
8.0
7.5
7.2
7.1
3.6
8.4
8.1
7.7
6.9
4.1
7.5
10.3
7.6
6.9
4.8
7.5
11.2
7.2
7.0
4.7
7.6
11.4
6.8
6.3
5.9
11.0
10.4
6.3
5.8
TAB L E 2. 2
Frequency Distribution of 60 Years of
Unemployment Data for Canada (Grouped Data)
Class Interval
Frequency
2–under 4
2
4–under 6
10
6–under 8
29
8–under 10
11
10–under 12
7
12–under 14
1
One particularly useful tool for grouping data is the frequency distribution, which is
a summary of data presented in the form of class intervals and frequencies. How is a frequency
distribution constructed from raw data? That is, how are frequency distributions like the one
displayed in Table 2.2 constructed from raw data like those presented in Table 2.1? Frequency
distributions are relatively easy to construct. Although some guidelines help in their construction, frequency distributions vary in final shape and design, even when the original raw data
are identical. In a sense, frequency distributions are constructed according to individual business analysts’ tastes.
Frequency Distributions
2-3
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2-4
Ch apter 2
Visualizing Data with Charts and Graphs
When constructing a frequency distribution, the business analyst should first determine
the range of the raw data. The range is often defined as the difference between the largest and
smallest numbers. The range for the data in Table 2.1 is 8.4 (12.0 − 3.6).
The second step in constructing a frequency distribution is to determine how many classes it will contain. One guideline is to select between 5 and 15 classes. If the frequency distribution contains too few classes, the data summary may be too general to be useful. Too many
classes may result in a frequency distribution that does not aggregate the data enough to be
helpful. The final number of classes is arbitrary. The business analyst arrives at a number by
examining the range and determining a number of classes that will span the range adequately
and be meaningful to the user. The data in Table 2.1 were grouped into six classes for Table 2.2.
After selecting the number of classes, the business analyst must determine the width of
the class interval. An approximation of the class width can be calculated by dividing the range
by the number of classes. For the data in Table 2.1, this approximation is 8.4/6, or 1.4. Normally, the number is rounded up to the next whole number, which in this case is 2. The frequency
distribution must start at a value equal to or lower than the lowest number of the ungrouped
data and end at a value equal to or higher than the highest number. The lowest unemployment
rate is 3.6 and the highest is 12.0, so the business analyst starts the frequency distribution at 2
and ends it at 14. Table 2.2 contains the completed frequency distribution for the data in Table
2.1. Class endpoints are selected so that no value of the data can fit into more than one class.
The class interval expression “under” in the distribution of Table 2.2 avoids this problem.
Class Midpoint
The midpoint of each class interval is called the class midpoint and is sometimes referred to
as the class mark. It is the value halfway across the class interval and can be calculated as the
average of the two class endpoints. For example, in the distribution of Table 2.2, the midpoint
of the class interval 4–under 6 is 5, or (4 + 6)/2.
Class Beginning Point = 4
Class Width = 2
Class Midpoint = 4 +
1
(2) = 5
2
The class midpoint is important because it becomes the representative value for each class in
most group statistics calculations. The third column in Table 2.3 contains the class midpoints
for all classes of the data from Table 2.2.
TAB L E 2. 3
Class Midpoints, Relative Frequencies, and Cumulative Frequencies
for Unemployment Data
Interval
Frequency
Class
Midpoint
Relative
Frequency
Cumulative
Frequency
2–under 4
2
3
0.0333
2
4–under 6
10
5
0.1667
12
6–under 8
29
7
0.4833
41
8–under 10
11
9
0.1833
52
10–under 12
7
11
0.1167
59
12–under 14
1
13
0.0167
60
Totals
60
1.0000
Relative Frequency
Relative frequency is the proportion of the total frequency that is in any given class interval
in a frequency distribution. Relative frequency is the individual class frequency divided by
the total ­frequency. For example, from Table 2.3, the relative frequency for the class interval
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2.1
6–under 8 is 29/60 = 0.4833. We consider the relative frequency here to prepare for the study
of probability in Chapter 4. Indeed, if values are selected randomly from the data in Table 2.1,
the probability of drawing a number that is 6–under 8 is 0.4833, the relative frequency for that
class interval. The fourth column of Table 2.3 lists the relative frequencies for the frequency
distribution of Table 2.2.
Cumulative Frequency
The cumulative frequency is a running total of frequencies through the classes of a frequency
distribution. The cumulative frequency for each class interval is the frequency for that class
interval added to the preceding cumulative total. In Table 2.3, the cumulative frequency for
the first class is the same as the class frequency: 2. The cumulative frequency for the second
class interval is the frequency of that interval (10) plus the frequency of the first interval (2),
which yields a new cumulative frequency of 12. This process continues through the last interval, at which point the cumulative total equals the sum of the frequencies (60). The concept
of cumulative frequency is used in many areas, including sales cumulated over a fiscal year,
sports scores during a contest (cumulated points), years of service, points earned in a course,
and costs of doing business over a period of time. Table 2.3 gives cumulative frequencies for
the data in Table 2.2.
D E MO NSTRATIO N P R OB LEM 2 . 1
The following data are the average weekly interest rates for a 60-week period.
7.29
7.03
7.14
6.77
6.35
7.16
6.78
6.79
7.07
7.03
6.69
7.02
7.40
7.16
6.96
6.87
6.80
7.10
7.13
6.95
6.98
7.56
6.75
6.87
7.11
7.08
7.24
7.34
7.47
7.31
7.39
7.28
6.97
6.90
6.57
6.96
6.70
6.57
6.88
6.84
7.11
6.95
7.23
7.31
7.00
7.02
7.40
7.12
7.16
7.16
7.30
7.17
6.96
6.78
7.30
6.99
6.94
7.29
7.05
6.84
Construct a frequency distribution for these data. Calculate and display the class midpoints, relative frequencies, and cumulative frequencies for this frequency distribution.
Solution How many classes should this frequency distribution contain? The range of the data is
1.21 (7.56 − 6.35). If seven classes are used, each class width is approximately:
Range
​Class Width = ​ ________________
​= ____
​ 1.21
​= 0.173​
7
Number of Classes
If a class width of 0.20 is used, a frequency distribution can be constructed with endpoints
that are more uniform looking and allow presentation of the information in categories more
­familiar to interest rate users.
The first class endpoint must be 6.35 or lower to include the smallest value; the last endpoint
must be 7.56 or higher to include the largest value. In this case, the frequency distribution begins
at 6.30 and ends at 7.70. The resulting frequency distribution, class midpoints, relative frequencies,
and cumulative frequencies are listed in the following table.
Class Interval
Frequency
Class Midpoint
6.30–under 6.50
6.50–under 6.70
6.70–under 6.90
6.90–under 7.10
7.10–under 7.30
7.30–under 7.50
7.50–under 7.70
Totals
1
3
12
18
16
9
1
60
6.40
6.60
6.80
7.00
7.20
7.40
7.60
Relative
Frequency
Cumulative
Frequency
0.0167
0.0500
0.2000
0.3000
0.2666
0.1500
0.0167
1.0000
1
4
16
34
50
59
60
Frequency Distributions
2-5
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2-6
Ch apter 2
Visualizing Data with Charts and Graphs
The frequencies and relative frequencies of these data reveal the interest rate classes that are likely
to occur during the period. Most of the interest rates (55 of the 60) are in the classes starting with
(6.70–under 6.90) and going through (7.30–under 7.50). The rates with the greatest frequency, 18,
are in the 6.90–under 7.10 class.
Concept Check
Fill in the blanks.
The value halfway across the class interval (calculated as the average of the two class endpoints) is called
the class __________. For each class, the individual class frequency divided by the total frequency is
called the __________ frequency. Moreover, a running total of frequencies through the classes of a
­frequency distribution is called the __________ frequency.
2.1 Problems
2.1 The following data represent the afternoon high temperatures for
50 construction days during a year in Toronto.
6
13
‒9
3
‒1
21
29
4
26
3
18
‒12
27
2
11
8
‒4
‒9
2
‒9
19
7
2
‒5
27
21
‒1
‒8
18
‒11
23
17
4
24
16
3
8
2
12
6
9
17
7
‒1
‒1
‒4
29
‒8
16
1
Class Interval
b. Construct a frequency distribution for the data using 10 class
intervals.
c. Examine the results of (a) and (b) and comment on the usefulness of the frequency distribution in terms of temperature summarization capability.
2.2 A packaging process is supposed to fill small boxes of raisins with
approximately 50 raisins so that each box will have the same mass.
However, the number of raisins in each box will vary. Suppose 100
boxes of raisins are randomly sampled, the raisins counted, and the
following data are obtained.
51
53
49
52
48
46
53
59
53
52
53
45
44
49
55
51
50
57
45
48
52
57
54
54
53
48
47
47
45
50
50
39
46
57
55
53
57
61
56
45
60
53
52
52
47
56
49
60
40
56
51
58
55
52
53
48
43
49
46
47
51
47
54
53
43
47
58
53
49
47
52
51
47
49
48
49
52
41
50
48
Frequency
0–under 5 6
a. Construct a frequency distribution for the data using five class
intervals.
57
44
49
49
51
54
55
46
59
47
2.3 The owner of a fast-food restaurant ascertains the ages of a sample of customers. From these data, the owner constructs the frequency
distribution shown. For each class interval of the frequency distribution, determine the class midpoint, the relative frequency, and the
­cumulative frequency.
52
48
53
47
46
57
44
48
57
46
Construct a frequency distribution for these data. What does the frequency distribution reveal about the box fills?
5–under 10 8
10–under 15
17
15–under 20
23
20–under 25
18
25–under 30
10
30–under 35 4
What does the relative frequency tell the fast-food restaurant owner
about customer ages?
2.4 The human resources manager for a large company commissions
a study in which the employment records of 500 company employees
are examined for absenteeism during the past year. The business analyst conducting the study organizes the data into a frequency distribution to assist the human resources manager in analyzing the data.
The frequency distribution is shown. For each class of the frequency
distribution, determine the class midpoint, the relative frequency, and
the cumulative frequency.
Class Interval
Frequency
0–under 2
218
2–under 4
207
4–under 6 56
6–under 8 11
8–under 10 8
2.5 List three specific uses of cumulative frequencies in business.
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2.2
Quantitative Data Graphs
Quantitative Data Graphs
2.2
LEARNING OBJECTIVE 2.2
Describe and construct different types of quantitative data graphs, including histograms,
frequency polygons, ogives, and stem-and-leaf plots. Explain when these graphs should
be used.
Data graphs can generally be classified as quantitative or qualitative. Quantitative data graphs
are plotted along a numerical scale, and qualitative graphs are plotted using non-numerical
categories. In this section, we will examine four types of quantitative data graphs: (1) histogram, (2) frequency polygon, (3) ogive, and (4) stem-and-leaf plot.
Histograms
One of the more widely used types of graphs for quantitative data is the histogram. A histogram
is a series of contiguous rectangles that represents the frequency of data in given class intervals. If
the class intervals used along the horizontal axis are equal, then the heights of the rectangles represent the frequency of values in a given class interval. If the class intervals are unequal, then the
areas of the rectangles can be used for relative comparisons of class frequencies. Construction of
a histogram involves labelling the x-axis with the class endpoints and the y-axis with the frequencies, drawing a horizontal line segment from class endpoint to class endpoint at each frequency
value, and connecting each line segment vertically from the frequency value to the x-axis to form
a series of rectangles. Figure 2.1 is a histogram of the frequency distribution in Table 2.2.
A histogram is a useful tool for differentiating the frequencies of class intervals. A quick
glance at a histogram reveals which class intervals produce the highest frequency totals. Figure 2.1 clearly shows that the class interval 6–under 8 yields by far the highest frequency count
(29). Examination of the histogram reveals where large increases or decreases occur between
classes, such as from the 2–under 4 class to the 4–under 6 class, an increase of 8, and from the
6–under 8 class to the 8–under 10 class, a decrease of 18.
Note that the scales used along the x and y axes for the histogram in Figure 2.1 are almost identical. However, because ranges of meaningful numbers for the two variables being
graphed often differ considerably, the histogram may have different scales on the two axes.
Figure 2.2 shows what the histogram of unemployment rates would look like if the scale on
35
35
30
30
25
20
Frequency
15
20
15
10
10
5
5
Unemployment Rates for Canada
FIGURE 2.1 Histogram of Canadian
Unemployment Data
r1
4
12
–
un
de
de
r
un
10
–
8–
un
de
r
12
10
r8
nd
e
6–
u
r6
nd
e
4–
u
6–
u
nd
e
6
nd
er
8–
8
un
de
10
r1
–u
0
nd
er
12
1
–u
nd 2
er
14
4
nd
er
nd
er
4–
u
2–
u
r4
0
0
2–
u
Frequency
25
Unemployment Rates for Canada
FIGURE 2.2 Histogram of Canadian Unemployment Data
(y-axis compressed)
2-7
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2-8
Ch apter 2
Visualizing Data with Charts and Graphs
the y-axis were more compressed than that on the x-axis. Notice that less difference in the
height of the rectangles appears to represent the frequencies in Figure 2.2. It is important that
the user of the graph clearly understand the scales used for the axes of a histogram. Otherwise,
a graph’s creator can lie with statistics by stretching or compressing a graph to make a point.1
50
45
40
35
30
25
20
15
10
5
0
le
12 ss t
2– ha
16 un n 1
6– de 22
21 un r 1
0– de 66
25 un r 2
4– de 10
29 un r 2
9– de 54
34 un r 2
3– de 99
38 un r 3
7– de 43
43 un r 3
1– de 87
47 un r 4
5– de 31
51 un r 4
9– de 75
56 un r 5
3– de 19
60 un r 5
7– de 63
65 un r 6
1– de 07
69 un r 6
5– de 51
74 un r 6
0– de 95
78 un r 7
4– de 40
82 un r 7
8– de 84
87 un r 8
2– de 28
m un r 8
or de 72
e r
th 91
an 6
91
6
Frequency
Using Histograms to Get an Initial Overview of the Data Because of the
widespread availability of computers and statistical software packages to business decisionmakers, the histogram continues to grow in importance for yielding information about the
shape of the distribution of a large database, the variability of the data, the central location
of the data, and outlier data. Although most of these concepts are presented in Chapter 3, the
notion of the histogram as an initial tool to access these data characteristics is presented here.
For example, suppose a financial decision-maker wants to use data to reach some conclusions about the stock market. Figure 2.3 shows a histogram of 324 stock volume observations. What can we learn from this histogram? Virtually all stock market volumes fall
between 78-million and 1-billion shares. The distribution takes on a shape that is high on
the left end and tapered to the right. In Chapter 3, we will learn that the shape of this distribution is skewed toward the right end. In statistics, it is often useful to determine whether data are approximately normally distributed (bell-shaped curve), as shown in Figure 2.4.
We can see by examining the histogram in Figure 2.3 that the stock market volume data are
not normally distributed. Although the centre of the histogram is located near 500-million
shares, a large portion of stock volume observations falls in the lower end of the data, somewhere between 100-million and 400-million shares. In addition, the histogram shows some
outliers in the upper end of the distribution. Outliers are data points that appear outside the
main body of observations and may represent phenomena that differ from those represented
by other data points. By looking closely at the histogram, we notice a few data observations
near 1 billion. One could conclude that on a few stock market days an unusually large volume
of shares are traded. These and other insights can be gleaned by examining the histogram and
show that histograms play an important role in the initial analysis of data.
Stock Volumes (in millions)
FIGURE 2.3 Histogram of Stock Volumes
FIGURE 2.4 Normal
Distribution
Frequency Polygons
A frequency polygon, like the histogram, is a graphical display of class frequencies. However,
instead of using rectangles like a histogram, in a frequency polygon each class frequency is
plotted as a dot at the class midpoint, and the dots are connected by a series of line segments.
1
It should be pointed out that Excel uses the term histogram to refer to a frequency distribution. However, if
you check Chart Output in the Excel histogram dialogue box, a graphical histogram is also created.
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2.2
Quantitative Data Graphs
Construction of a frequency polygon begins, as with a histogram, by scaling class endpoints
along the x-axis and frequency values along the y-axis. A dot is plotted for the associated frequency value at each class midpoint. Connecting these midpoint dots completes the graph.
Figure 2.5 shows a frequency polygon of the distribution data from Table 2.2 produced in
Excel. The information gleaned from frequency polygons and histograms is similar. As with
the histogram, changing the scales of the axes can compress or stretch a frequency polygon,
which affects the user’s impression of what the graph represents.
35
FIGURE 2.5 Frequency
Polygon of the
Unemployment Data
30
Frequency
25
20
15
10
5
0
3
5
7
9
Class Midpoints
11
13
Ogives
An ogive (o-jive) is a cumulative frequency polygon. Construction begins by labelling the x-axis
with the class endpoints and the y-axis with the frequencies. However, the use of cumulative
frequency values requires that the scale along the y-axis be great enough to include the frequency total. A dot of zero frequency is plotted at the beginning of the first class, and construction proceeds by marking a dot at the end of each class interval for the cumulative value.
Connecting the dots then completes the ogive. Figure 2.6 presents an ogive produced in Excel
for the data in Table 2.2.
Ogives are most useful when the decision-maker wants to see running totals. For example,
if a comptroller is interested in controlling costs, an ogive could depict cumulative costs over
a fiscal year.
Steep slopes in an ogive can be used to identify sharp increases in frequencies. In Figure 2.6,
a particularly steep slope occurs in the 6–under 8 class, signifying a large jump in class
frequency totals.
FIGURE 2.6 Ogive of the
Unemployment Data
70
Cumulative Frequency
60
50
40
30
20
10
0
2
4
6
8
Class Endpoints
10
12
14
2-9
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2-10
C h apter 2
Visualizing Data with Charts and Graphs
Stem-and-Leaf Plots
Another way to organize raw data into groups is by a stem-and-leaf plot. This technique is simple and provides a unique view of the data. A stem-and-leaf plot is constructed by separating the
digits for each number of the data into two groups, a stem and a leaf. The leftmost digits are the stem
and consist of the higher-valued digits. The rightmost digits are the leaves and contain the lower
values. If a set of data has only two digits, the stem is the value on the left and the leaf is the value
on the right. For example, if 34 is one of the numbers, the stem is 3 and the leaf is 4. For numbers
with more than two digits, division of stem and leaf is a matter of analyst preference.
Table 2.4 contains scores from an examination on plant safety policy and rules given to
a group of 35 job trainees. A stem-and-leaf plot of these data is displayed in Table 2.5. One
advantage of such a distribution is that the instructor can readily see whether the scores are
in the upper or lower end of each bracket and also determine the spread of the scores. A second advantage of stem-and-leaf plots is that the values of the original raw data are retained
(whereas most frequency distributions and graphic depictions use the class midpoint to represent the values in a class).
TAB L E 2. 4
86
77
91
60
55
76
92
47
88
67
23
59
72
75
83
77
68
82
97
89
81
75
74
39
67
79
83
70
78
91
68
49
56
94
81
TAB L E 2. 5
Stem
Safety Examination Scores for Plant Trainees
Stem-and-Leaf Plot for Plant Safety Examination Data
Leaf
2
3
3
9
4
7
9
5
5
6
9
6
0
7
7
8
8
7
0
2
4
5
5
6
7
7
8
1
1
2
3
3
6
8
9
9
1
1
2
4
7
8
9
D E MONST RAT I O N P R O B L EM 2 . 2
The following data represent the costs (in dollars) of a sample of 30 postal mailings by a company.
3.67
1.83
6.72
3.34
5.10
2.75
10.94
7.80
4.95
6.45
9.15
1.93
5.47
5.42
4.65
5.11
3.89
4.15
8.64
1.97
3.32
7.20
3.55
4.84
2.84
Using dollars as a stem and cents as a leaf, construct a stem-and-leaf plot of the data.
2.09
2.78
3.53
4.10
3.21
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2.2 Quantitative Data Graphs
Solution
Stem
Leaf
1
83
93
97
2
09
75
78
84
3
21
32
34
53
55
4
10
15
65
84
95
5
10
11
42
47
6
45
72
7
20
80
8
64
9
15
10
94
67
89
Concept Check
1. What is the first step in constructing a graph of statistical data?
2. Draw the outline of a histogram for each of the following descriptions.
a. A set of quiz scores where the quiz was very easy
b. The last digit of the winning lottery numbers for a year
c. The average mass of a healthy adult measured monthly over the course of two years
3. When are ogives most useful to decision-makers?
4. What is the key advantage of stem-and-leaf plots over histograms?
2.2 Problems
2.6 Assembly times in minutes for components must be understood
in order to “level” the stages of a production process. Construct both
a histogram and a frequency polygon for the following assembly time
data, and comment on the key characteristics of the distribution.
Class Interval
Frequency
30–under 32 5
32–under 34 7
34–under 36
15
36–under 38
21
38–under 40
34
40–under 42
24
42–under 44
17
44–under 46 8
2.7 A call centre is trying to better understand staffing requirements.
It records the number of calls received during the evening shift for
78 evenings and obtains the information given below. Construct a
histogram of the data and comment on the key characteristics of the
distribution. Construct a frequency polygon and compare it with
the histogram. Which do you prefer, and why?
Class Interval
Frequency
10–under 20 9
20–under 30 7
30–under 40
10
40–under 50 6
50–under 60
13
60–under 70
18
70–under 80
15
2.8 Construct an ogive for the following data.
Class Interval
Frequency
3–under 6 2
6–under 9 5
9–under 12
10
12–under 15
11
15–under 18
17
18–under 21 5
2-11
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2-12
C h apter 2
Visualizing Data with Charts and Graphs
2.9 A real estate group is investigating the price for condominiums of
a given size. The following sales prices (in $ thousands) were obtained
in one region of a city. Construct a stem-and-leaf plot for the following
data using two digits for the stem. Comment on the key characteristics
of the distribution.
212
257
243
218
253
273
239
271
261
238
227
220
255
226
240
266
249
254
270
226
218
234
230
249
257
239
222
239
246
250
261
258
249
219
263
263
238
259
265
255
235
229
240
230
224
260
229
221
239
262
2.10 The following data represent the number of passengers per flight
in a sample of 50 flights from Toronto, Ontario, to Detroit, Michigan.
23
25
69
48
45
46
20
34
46
47
66
47
35
23
49
67
28
60
38
19
13
16
37
52
32
58
38
52
50
64
19
44
80
17
27
17
29
59
57
61
65
48
51
41
70
17
29
33
77
19
ACI data on the number of passengers that emplaned and deplaned
in a recent year. As an example, Atlanta’s Hartsfield-Jackson International Airport was the busiest airport in the world, with 107,394,029
passengers. Toronto’s Pearson International Airport was the busiest
airport in Canada with 49,507,418 passengers. What are some observations that you can make from the graph? Describe the top 30 airports in the world using this histogram.
2.12 Every year, a hundred or so boats go fishing for Alaskan king
crabs for three or four weeks off the Bering Strait. To catch these
king crabs, large pots are baited and left on the sea bottom, often
a few hundred metres deep. Because of the investment in boats,
equipment, personnel, and supplies, fishing for such crabs can be
financially risky if not enough crabs are caught. Thus, as pots are
pulled and emptied, there is great interest in how many legal king
crabs (males of a certain size) there are in any given pot. Suppose the
number of legal king crabs is reported for each pot during a season
and recorded. In addition, suppose that 200 of these pots are randomly selected and the numbers per pot are used to create the ogive
shown below. Study the ogive and comment on the number of legal
king crabs per pot.
200
Construct a stem-and-leaf plot for these data. What does the stemand-leaf plot tell you about the number of passengers per flight?
180
2.11 The Airports Council International (ACI) publishes data on the
world’s busiest airports. Shown below is a histogram constructed from
140
12
Number of Pots
14
160
100
80
60
40
10
Frequency
120
20
0
8
6
10 20 30 40 50 60 70 80 90 100 110 120
Number of Legal King Crabs per Pot
4
2
10
r1
de
un
10
5–
–u
nd
er
10
5
95
85
er
nd
95
85
–u
er
75
er
–u
75
nd
nd
65
65
–u
er
nd
–u
55
45
–u
nd
er
55
0
Annual Number of Passengers (millions)
2.3
Qualitative Data Graphs
LEARNING OBJECTIVE 2.3
Describe and construct different types of qualitative data graphs, including pie charts,
bar charts, and Pareto charts. Explain when these graphs should be used.
In contrast to quantitative data graphs that are plotted along a numerical scale, qualitative
graphs are plotted using non-numerical categories. In this section, we will examine three
types of qualitative data graphs: (1) pie charts, (2) bar charts, and (3) Pareto charts.
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2.3
Qualitative Data Graphs
2-13
Pie Charts
A pie chart is a circular depiction of data where the area of the whole pie represents 100% of the
data and slices represent a percentage breakdown of the sublevels. Pie charts show the relative
magnitudes of parts to a whole. They are widely used in business, particularly to depict such
things as budget categories, market share, and time and resource allocations. However, the
use of pie charts is minimized in the sciences and technology because they can lead to less
accurate judgments than are possible with other types of graphs.2 Generally, it is more difficult
for the viewer to interpret the relative size of angles in a pie chart than to judge the length of
rectangles in a histogram or the relative distance of a frequency polygon dot from the x-axis. In
the feature Thinking Critically About Statistics in Business Today 2.1, “Where Are Soft Drinks
Sold?,” graphical depictions of the percentage of sales by place were displayed by both a pie
chart and a vertical bar chart.
Thinking Critically About Statistics in Business Today 2.1
Where Are Soft Drinks Sold?
Place of Sales
Percentage
Supermarkets
44
Soda fountains
24
Convenience stores/gas stations
16
Vending machines
11
These data can be displayed graphically in several ways. Displayed here are a pie chart and a bar chart of the data. Some
statisticians prefer the histogram or the bar chart over the pie
chart because they believe it is easier to compare categories that
are similar in size with the histogram or the bar chart rather than
the pie chart.
50
40
Percent
Beverages that contain more than 1% by weight of flavours are
considered to be soft drinks, including flavoured bottled water,
soda water, seltzer water, and tonic water. Based on data from
Statista, the value of Canadian domestic retail sales for flavoured
soft drinks in 2018 contributed around $1.67 billion to the country’s gross domestic product. Aside from Pepsi and Coca Cola, popular soft drinks in Canada include Canada Dry, Crush, Big 8, and
Clearly Canadian.
Where are soft drinks sold? The following data from Bernstein Research indicate that the four leading places for soft drink
sales in the U.S. are supermarkets, soda fountains or snack bars,
convenience stores/gas stations, and vending machines.
30
20
10
0
Mass merchandisers 3
SuperSoda
Conven- Vending Mass Drugstore
market fountain ience/Gas
merch.
Drugstores 2
Place
Mass merch.
3%
Vending
11%
Drugstore
2%
Supermarket
44%
Things to Ponder
1. How might this information be useful to large soft drink companies?
2. How might the packaging of soft drinks differ according to
the top four places where soft drinks are sold?
Convenience/Gas
16%
3. How might the distribution of soft drinks differ between the
various places where soft drinks are sold?
Soda fountain
24%
2
William S. Cleveland, The Elements of Graphing Data (Monterey, CA: Wadsworth Advanced Books and Software, 1985).
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2-14
C h apter 2
Visualizing Data with Charts and Graphs
Construction of the pie chart is done by determining the proportion of the subunit to
the whole. Table 2.6 contains annual sales for the top petroleum-refining companies in the
U.S. in a recent year. To construct a pie chart from these data, convert the raw sales figures to
proportions by dividing each sales figure by the total sales figure. This proportion is analogous
to the relative frequency computed for frequency distributions. The pie chart in Figure 2.7
depicts the data from Table 2.6.
Leading U.S. Petroleum-Refining Companies
TAB L E 2. 6
Company
Annual Sales
(US$ millions)
Proportion
ExxonMobil
270,772
0.4232
Chevron Texaco
147,967
0.2313
ConocoPhillips
121,663
0.1902
Valero Energy
53,919
0.0843
Marathon Petroleum
45,444
0.0710
639,765
1.0000
Totals
FIGURE 2.7 Pie Chart of
Petroleum-Refining Sales by
Brand
Valero Energy
8.43%
ConocoPhillips
19.02%
Marathon Petroleum
7.10%
ExxonMobil
42.32%
Chevron Texaco
23.13%
Bar Charts
Another widely used qualitative data graphing technique is the bar chart or bar graph.
A bar graph or chart contains two or more categories along one axis and a series of bars, one for
each category, along the other axis. Typically, the length of the bar represents the magnitude of
the measure (amount, frequency, money, percentage, etc.) for each category. The bar chart is
qualitative because the categories are non-numerical, and it may be either horizontal or vertical. A bar chart generally is constructed from the same type of data that are used to produce
a pie chart. However, an advantage of using a bar chart over a pie chart for a given set of data
is that for categories that are close in value, it is considered easier to see the difference in the
bars of bar charts than to discriminate between pie slices.
As an example, consider the data in Table 2.7 regarding how much the average university
student spends on back-to-school items. Constructing a bar chart from these data, the categories are electronics, clothing and accessories, residence furnishings, school supplies, and
miscellaneous. Bars for each of these categories are made using the dollar figures given in the
table. The resulting bar chart is shown in Figure 2.8.
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2.3
TA B LE 2.7
Qualitative Data Graphs
Back-to-School Spending by the Average University Student
Category
Amount Spent ($)
Electronics
211.89
Clothing and accessories
134.40
Residence furnishings
90.90
School supplies
68.47
Miscellaneous
93.72
FIGURE 2.8 Bar Chart of
Back-to-School Spending
Misc.
School
supplies
Residence
furnishings
Clothing and
accessories
Electronics
50.00
100.00
150.00
Amount Spent ($)
200.00
250.00
DE MO NSTRATIO N P R O B LEM 2 . 3
According to the National Retail Federation and Center for Retailing Education at the University
of Florida, the four main sources of inventory shrinkage are employee theft, shoplifting, administrative error, and vendor fraud. The estimated annual dollar amount in shrinkage (in US$ millions) associated with each of these sources is shown below.
Construct a pie chart to depict these data.
Employee theft
$17,918.6
Shoplifting
15,191.9
Administrative error
7,617.6
Vendor fraud
Total
2,553.6
$43,281.7
Solution Convert each raw dollar amount to a proportion by dividing each individual amount
by the total.
Employee theft
17,918.6/43,281.7
=
0.414
Shoplifting
15,191.9/43,281.7
=
0.351
Administrative error
7,617.6/43,281.7
=
0.176
Vendor fraud
2,553.6/43,281.7
=
0.059
Total
1.000
2-15
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2-16
C h apter 2
Visualizing Data with Charts and Graphs
Vendor fraud
6%
Employee theft
41%
Administrative
error
18%
Shoplifting
35%
Using the raw data above, we can produce the following bar chart.
Vendor fraud
Administrative error
Shoplifting
Employee theft
5,000
10,000
Shrinkage (US$ millions)
15,000
20,000
Pareto Charts
A third type of qualitative data graph is a Pareto chart, which could be viewed as a particular
application of the bar chart. One of the important aspects of the quality movement in business
is the constant search for causes of problems in products and processes. A graphical technique
for displaying problem causes is Pareto analysis. Pareto analysis is a quantitative tallying of
the number and types of defects that occur with a product or service. Analysts use this tally to
produce a vertical bar chart that displays the most common types of defects, ranked in order of
occurrence from left to right. The bar chart is called a Pareto chart.
Pareto charts were named after an Italian economist, Vilfredo Pareto, who observed more
than 100 years ago that most of Italy’s wealth was controlled by a few families who were the
major drivers behind the Italian economy. Quality expert J. M. Juran applied this notion to
the quality field by observing that poor quality can often be addressed by attacking a few major
causes that result in most of the problems. A Pareto chart enables decision-makers responsible
for quality management to separate the most important defects from trivial defects, which
helps them set priorities for needed quality improvement work.
Suppose the number of electric motors being rejected by inspectors for a company has been
increasing. Company officials examine the records of several hundred motors in which at least
one defect was found, to determine which defects occurred more frequently. They find that 40%
of the defects involved poor wiring, 30% involved a short in the coil, 25% involved a defective
plug, and 5% involved seizing of bearings. Figure 2.9 is a Pareto chart constructed from this information. It shows that the three main problems with defective motors—poor wiring, a short in
the coil, and a defective plug—account for 95% of the problems. From the Pareto chart, decisionmakers can formulate a logical plan for reducing the number of defects.
Company officials and workers would probably begin to improve quality by examining
the segments of the production process that involve the wiring. Next, they would study the
construction of the coil, then examine the plugs used and the plug-supplier process.
Figure 2.10 is a different rendering of this Pareto chart. In addition to the bar chart
analysis (primary axis), the Pareto analysis contains a cumulative percentage line graph
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45
40
40
35
35
30
30
25
20
100
90
80
70
60
50
40
30
20
10
0
25
20
15
15
10
10
5
5
0
Qualitative Data Graphs
0
Poor
wiring
Short in
coil
Defective Bearings
plug
seized
FIGURE 2.9 Pareto Chart for Electric Motor Problems
Poor
wiring
Short in
coil
2-17
Cumulative Percentage
45
Count
Percentage of Total
2.3
Defective Bearings
plug
seized
FIGURE 2.10 Pareto Chart for Electric Motor Problems
(secondary axis). Observe the slopes on the line graph. The steepest slopes represent the more
frequently occurring problems. As the slopes level off, the problems occur less frequently. The
line graph gives the decision-maker another tool for determining which problems to solve first.
Concept Check
1. True or false?
Pie charts are an effective way of displaying data if the intent is to compare the size of a slice with
the whole pie, rather than comparing the slices among themselves.
2. What type of chart do you think could be used to help answer the following questions?
a. What are the main issues that our business is facing?
b. What 20% of sources are causing 80% of our quality control problems?
c. Where should we focus our efforts to achieve the largest improvement?
3. What is the key difference between histograms and bar charts?
2.3 Problems
2.13 The top seven airlines in the world by passengers carried in a recent year were Delta Airlines with 164.6 million, United Airlines with
140.4 million, Southwest Airlines with 134.0 million, American Airlines with 107.9 million, China Southern Airlines with 86.5 million,
Ryanair with 79.6 million, and Lufthansa with 74.7 million. Construct
a pie chart and a bar chart to depict this information.
2.14 The following is a list of the six largest pharmaceutical and biotech companies in the world ranked by health-care revenue (in US$
millions). Use this information to construct a pie chart and a bar chart
to represent these six companies and their revenues.
Pharmaceutical Firm
Revenue (US$ millions)
Pfizer
67,809
Novartis
53,324
Merck & Co.
45,987
Bayer
44,200
GlaxoSmithKline
42,813
Johnson and Johnson
37,020
2.15 Initial public offerings (IPOs) can be a risky investment; thus, in
an IPO, the issuer may obtain the assistance of an underwriting firm.
Shown here is a list of the top five Canadian underwriting firms with
the amount of money they raised in a recent year. Construct a bar
chart to display these data. Construct a pie chart to represent these
data and label the slices with the appropriate percentages. Comment
on the effectiveness of using a pie chart to display the total amount
raised by these top underwriting firms.
Underwriting Firm
Total Amount ($ millions)
RBC Capital Markets
29,172
TD Securities
25,193
CIBC World Markets
19,875
National Bank Financial
17,653
BMO Capital Markets
16,958
Source: Barry Critchley, “ ‘Out of Sync’ Canadian Markets Dampen
Dealmaking in First Half,” Financial Post, August 2, 2018. Material
reprinted with the express permission of National Post, a division of
Postmedia Network Inc.
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2-18
C h apter 2
Visualizing Data with Charts and Graphs
2.16 The Canada Beef Export Federation reports that the top six destinations for Canadian beef in a recent year were the U.S. with $1,697
million, Mexico with $269 million, Japan with $171 million, South
Korea with $28 million, Taiwan with $16 million, and China with $4
million. Construct a pie chart to depict this information.
2.17 An airline uses a call centre to take reservations. It has been receiving an unusually high number of customer complaints about its
reservation system. The company conducted a survey of customers,
asking them whether they had encountered any of the following problems in making reservations: busy signal, disconnection, poor connection, too long a wait to talk to someone, could not get through to an
agent, or transferred to the wrong person. Suppose a survey of 744
complaining customers resulted in the following frequency tally.
2.4
Number of Complaints
184
Complaint
Too long a wait
10
Transferred to the wrong person
85
Could not get through to an agent
37
Got disconnected
420
Busy signal
8
Poor connection
Construct a Pareto chart from this information to display the various
problems encountered in making reservations.
Charts and Graphs for Two Variables
LEARNING OBJECTIVE 2.4
Display and analyze two variables simultaneously using cross tabulation and scatter
plots.
It is very common in business statistics to want to analyze two variables simultaneously in
an effort to gain insight into a possible relationship between them. For example, business
analysts might be interested in the relationship between years of experience and amount of
productivity in a manufacturing facility or in the relationship between a person’s technology
usage and their age. Business analysts have many techniques for exploring such relationships.
Two of the more elementary tools for observing the relationships between two variables are
cross tabulation and scatter plot.
Cross Tabulation
Cross tabulation is a process for producing a two-dimensional table that displays the ­frequency
counts for two variables simultaneously. As an example, suppose a job satisfaction survey of a
randomly selected sample of 177 bankers is taken in the banking industry. The bankers are
asked how satisfied they are with their job using a 1 to 5 scale where 1 denotes very dissatis­
fied, 2 denotes dissatisfied, 3 denotes neither satisfied nor dissatisfied, 4 denotes satisfied, and
5 denotes very satisfied. In addition, each banker is asked to report his or her age by using one
of three categories: under 30 years, 30 to 50 years, and over 50 years. Table 2.8 displays
how some of the data might look as they are gathered. Note that age and level of job satisfaction are recorded for each banker. By tallying the frequency of responses for each combination of categories between the two variables, the data are cross tabulated according to the
two variables. For instance, in this example there is a tally of how many bankers rated their
level of satisfaction as 1 and were under 30 years of age, there is a tally of how many bankers
rated their level of satisfaction as 2 and were under 30 years of age, and so on until frequency
tallies are determined for each possible combination of the two variables. Table 2.9 shows the
completed cross-tabulation table for the banker survey. A cross-tabulation table is sometimes
referred to as a contingency table, and Excel calls such a table a PivotTable.
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2.4
Banker Data Observations by Job Satisfaction and Age
TAB L E 2. 8
Level of Job
Satisfaction
Age
1
4
53
2
3
37
3
1
24
4
2
28
5
4
46
6
5
62
7
3
41
8
3
32
9
4
29
.
.
.
.
.
.
.
.
.
177
3
51
Banker
TA B L E 2.9
Charts and Graphs for Two Variables
Cross-Tabulation Table of Banker Data
Age Category
Level of Job
Satisfaction
Under 30
30–50
Over 50
Total
1
7
3
0
10
2
19
14
3
36
3
28
17
12
57
4
11
22
16
49
5
2
9
14
25
Total
67
65
45
177
Scatter Plot
A scatter plot is a two-dimensional graph plot of pairs of points from two numerical variables. The scatter plot is a graphical tool that is often used to examine possible relationships
between two variables.
As an example of two numerical variables, consider the data in Table 2.10. Displayed are
the base salary and total compensation (cash bonuses, stock-based bonuses, options-based bonuses, pension value, and any other payments aside from base salary) for the 25 highest-paid
Canadian CEOs in a recent year. Do these two numerical variables exhibit any relationship?
It might seem logical that when the base salary is high, the total CEO compensation would be
high as well. However, the scatter plot of these data, displayed in Figure 2.11, shows somewhat mixed results. The apparent tendency is that total CEO compensations occur mostly in
the range between $10,000 and $30,000 (in $ thousands) for the entire range of base salaries,
with a single exception that takes the highest total CEO compensation for a rather average
base salary.
2-19
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2-20
C h apter 2
Visualizing Data with Charts and Graphs
TA B L E 2. 10
Total Compensation and Base Salary for the
25 Highest-Paid Canadian CEOs
Total Compensation
($ thousands)
83,131
Base Salary
($ thousands)
1,300
28,614
431
24,603
1,030
21,427
267
18,830
2,905
17,777
2,110
17,592
1,371
17,370
1,314
15,872
887
15,855
1,284
15,381
1,803
14,641
618
14,193
86
12,905
1,375
12,752
525
12,578
1,381
12,245
1,467
12,132
1,193
11,998
446
11,894
0 ($1.00)
11,822
1,373
11,816
1,373
11,764
1,000
11,580
1,457
11,522
1,496
Source: Adapted from Canadian Business staff, “Canadaʼs Top 100 Highest-Paid
CEOs,” Canadian Business, January 2, 2018. www.canadianbusiness.com/
lists-and-rankings/richest-people/canada-100-highest-paid-ceos/.
3,000
2,500
Base Salary ($ thousands)
FIGURE 2.11 Scatter Plot of
Total Compensation and Base
Salary for the 25 Highest-Paid
Canadian CEOs
2,000
1,500
1,000
500
0
0
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
Total Compensation ($ thousands)
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2.4
Charts and Graphs for Two Variables
2-21
Concept Check
1. Draw the outline of a scatter plot for each of the following sets of two numerical variables.
a. The mass and height of 30 people selected at random
b. The mass and IQ of 30 people selected at random
c. The number of advertising dollars spent by a company and the total sales revenue
2.4 Problems
2.18 The U.S. National Oceanic and Atmospheric Administration,
National Marine Fisheries Service, publishes data on the quantity
and value of domestic fishing in the U.S. The quantity (in millions
of kilograms) of fish caught and used for human food and for industrial products (oil, bait, animal food, etc.) over a decade follows. Is a
relationship evident between the quantity used for human food and
the quantity used for industrial products for a given year? Construct a
scatter plot of the data. Examine the plot and discuss the strength of
the relationship of the two variables.
Human Food
Industrial Product
1,661
1,285
1,612
1,105
1,493
1,401
1,472
1,455
1,509
1,417
1,497
1,347
1,542
1,199
1,794
1,341
2,085
1,184
2,820
1,027
2.20 It seems logical that the number of days per year that an employee is late for work is at least somewhat related to the employee’s job satisfaction. Suppose 10 employees are asked to record how
satisfied they are with their job on a scale from 0 to 10, with 0 denoting completely unsatisfied and 10 denoting completely satisfied.
Suppose also that through human resource records, it is determined
how many days each of these employees was tardy last year. The
scatter plot below graphs the job satisfaction scores of each employee against the number of days he or she was tardy. What information
can you glean from the scatter plot? Does there appear to be any
relationship between job satisfaction and tardiness? If so, how might
they appear to be related?
12
Job Satisfaction
10
2.19 Are the advertising dollars spent by a company related to
­total sales revenue? The following data represent the advertising
­dollars and the sales revenues for various companies in a given
­industry during a recent year. Construct a scatter plot of the data
from the two variables and discuss the relationship between the
two variables.
Advertising ($ millions)
Sales ($ millions)
4.2
155.7
1.6
87.3
6.3
135.6
2.7
99.0
10.4
168.2
7.1
136.9
5.5
101.4
8.3
158.2
8
6
4
2
0
0
2
4
6
8
Tardiness
10
12
14
2.21 The human resources manager of a large chemical plant was
interested in determining what factors might be related to the number of non-vacation days that workers were absent during the past
year. One of the factors the manager considered was the distance
the worker commutes to work. She wondered if longer commutes
result in stress and whether increases in the likelihood of transportation failure might result in more worker absences. The manager
studied company records, randomly selected 532 plant workers, and
recorded the number of non-vacation days the workers were absent
the previous year and how far their place of residence was from the
plant. She then recoded the raw data in categories and created the
cross-tabulation table shown below. Study the table and comment
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2-22
C h apter 2
Visualizing Data with Charts and Graphs
on any relationship that may exist between distance to the plant and
number of absences.
One-Way Commute Distance (in km)
Number of
0–2
Annual Non3–5
Vacation-Day
More than 5
Absences
Customer
Level of Education
Rating of Service
1
high school only
acceptable
2
university degree
unacceptable
3
university degree
acceptable
0–3
4–10
More than 10
4
high school only
acceptable
95
184
117
5
university degree
unacceptable
21
40
53
6
high school only
acceptable
12
7
high school only
unacceptable
8
university degree
acceptable
9
university degree
unacceptable
10
university degree
unacceptable
11
high school only
acceptable
12
university degree
acceptable
13
university degree
unacceptable
14
high school only
acceptable
15
university degree
acceptable
16
high school only
acceptable
17
high school only
acceptable
18
high school only
unacceptable
19
university degree
unacceptable
20
university degree
acceptable
21
university degree
unacceptable
22
high school only
acceptable
23
university degree
acceptable
24
high school only
acceptable
25
university degree
unacceptable
3
7
2.22 A customer relations expert for a retail tire company is interested in determining if there is any relationship between a customer’s
level of education and his or her rating of the quality of the tire company’s service. The tire company administers a very brief survey to
each customer who buys tires and has them installed at the store. The
customer is asked to describe the quality of the service rendered as
either “acceptable” or “unacceptable.” In addition, each respondent
is asked the level of education attained from the categories of “high
school only” or “university degree.” These data are gathered on 25
customers and are given at right. Use this information to construct a
cross-tabulation table. Comment on any relationships that may exist
in the table.
2.5
Visualizing Time-Series Data
LEARNING OBJECTIVE 2.5
Describe and construct a time-series graph. Visually identify any trends in the data.
As part of big data and the business analytics process, business analysts sometimes use historical data—measures taken over time—to estimate what might happen in the future. One type
of data that is often used in such analysis is time-series data, defined as data gathered on
a particular characteristic over a period of time at regular intervals. Such a time period might
be hours, days, weeks, months, quarters, years, or some other unit. To be useful to analysts,
time-series data need to be “cleaned,” such that measurements are taken at regular time intervals and arranged according to time of occurrence. Some examples of time-series data are five
years of monthly retail trade data, weekly Treasury bill rates over a two-year period, and one
year of daily household consumption data.
As an example, Table 2.11 shows time-series data for motor vehicles produced from 1999
through 2018 for both Canada and Japan.
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2.5
TA B LE 2.11
Visualizing Time-Series Data
2-23
Motor Vehicles Produced from 1999 through 2018 for both Canada
and Japan
Year
Motor Vehicles Produced in
Canada (thousands)
Motor Vehicles Produced in Japan
(thousands)
1999
3,059
9,895
2000
2,962
10,141
2001
2,533
9,777
2002
2,629
10,257
2003
2,553
10,286
2004
2,712
10,512
2005
2,688
10,800
2006
2,572
11,484
2007
2,579
11,596
2008
2,082
11,576
2009
1,490
7,934
2010
2,068
9,629
2011
2,135
8,399
2012
2,463
9,943
2013
2,380
9,630
2014
2,394
9,775
2015
2,283
9,278
2016
2,370
9,205
2017
2,200
9,694
2018
2,021
9,729
By visualizing these time-series data using a line chart, a business analyst can make it
easier for a broader audience to see any trends or directions in the data. Figure 2.12 is an
Excel-produced line graph of the data. Looking at this graph, the business analyst can see
that motor vehicle production in Canada began a downward slide in 2008 that has continued until 2018.
FIGURE 2.12 Excel-Produced
Line Graph of the Motor
Vehicle Data for Canada
3,000
2,500
2,000
1,500
1,000
500
–
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
20
18
Motor Vehicles Produced (thousands)
3,500
Year
in Canada
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2-24
C h apter 2
Visualizing Data with Charts and Graphs
Suppose we want to compare motor vehicle production for Canada to that of Japan during
this same period of time. Figure 2.13 is an Excel-produced line graph showing the data in
­Table 2.11. By looking at the visualization (graph) rather than just the raw data, it is easier
to see that both countries had a dip in production in the middle years. In contrast to Canada,
Japan has recently reached levels close to those in the early 2000s.
14,000
12,000
10,000
8,000
6,000
4,000
09
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
20
18
08
20
07
20
06
20
05
20
04
20
03
20
02
20
01
20
00
20
20
99
2,000
19
Motor Vehicles Produced (thousands)
FIGURE 2.13 Excel-Produced
Line Graph of the Motor
Vehicle Data for both Canada
and Japan
Year
in Canada
in Japan
D E MO NST RAT I O N P R O B L EM 2 . 4
Consider the time-series data given below displaying the number of passengers per year for the
major airport of each of seven cities over a period of seven years. How could a business analyst
display the data in a visual way that would add interest to the data and help decision-makers more
readily see trends for each city and differences between cities?
Number of Passengers per Airport of Seven Cities Over a Seven-Year Period (millions)
Year
Atlanta
Beijing
Dubai
London
Shanghai
Bangkok
Madrid
1
92.389
78.675
50.978
69.434
41.448
47.911
49.653
2
94.957
81.929
57.685
70.037
44.88
53.002
45.176
3
94.431
83.712
66.432
72.368
47.19
51.364
39.729
4
96.179
86.128
70.476
73.409
51.688
46.423
41.823
5
101.491
89.939
78.015
74.99
60.053
52.808
46.78
6
104.172
94.394
83.654
75.716
66.002
55.892
50.398
7
103.903
95.786
88.242
78.015
70.001
60.861
53.386
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2.5
Solution
Visualizing Time-Series Data
2-25
Make a time-series graph of the data using multiple lines. The resulting graph is:
120
Passengers (millions)
100
80
60
40
20
0
1
Atlanta
2
Beijing
3
Dubai
4
Year
London
5
6
Shanghai
Bangkok
7
Madrid
Studying this visual, we can see that the Atlanta airport was the largest, followed by ­Beijing,
for the entire seven-year period. We can also see that while London remained fairly constant,
the Dubai airport continually increased at a near constant rate, resulting in it becoming the
­number-three airport in passengers by year 7. Meanwhile, Shanghai maintained a steady growth,
but Madrid’s airport was down and up, as was the Bangkok airport.
While most visualizations are considered to be descriptive business analytics, in Chapter 15
we will explore ways to use time-series data such as these as predictive business analytics, to develop future forecasts.
Concept Check
Time-series data represent data gathered for a particular characteristic over a period of time at regular
­intervals. Draw the outline of a time-series graph for each of the following variables.
a. Canada’s yearly CO2 emissions for a period of 20 consecutive years
b. USD/CAD daily average exchange rate for a period of 30 consecutive days (Exchange rates are
expressed as 1 unit of the foreign currency converted into Canadian dollars.)
c. Live births by month in Canada for a period of 12 consecutive months
2.5 Problems
2.23 Shown here are the sales data (in $ millions) for furniture and
home furnishing stores over a recent period of five years. Using this
data:
a. Construct a time-series graph for one year of the data. Looking
at your graph, what are some of your insights and conclusions
regarding this industry in that year?
b. Construct one graph that displays the data from each of the
five years separately but in the same graph so that you can compare the five years. What insights and/or conclusions might you
reach about this industry now that you can see the five years in
one graph?
c. Place the data together in order (perhaps one long column)
and construct one graph (similar to part a) with all the data. Seeing one graph with all 60 data points lined up, what insights and
understanding can you gain that perhaps you didn’t see in part b?
Month
January
February
March
April
May
June
July
August
September
October
November
December
1
6,866
7,169
7,787
6,872
7,682
7,378
7,551
8,065
7,438
7,260
8,259
9,215
2
7,296
7,088
7,873
7,312
7,831
7,556
7,979
8,463
7,851
8,060
8,843
9,197
Year
3
7,203
7,227
8,105
7,791
8,385
7,881
8,403
8,735
8,371
8,440
8,949
10,228
4
7,974
7,537
8,647
8,298
8,934
8,613
9,147
9,174
8,983
9,110
9,471
10,891
5
8,166
8,363
9,233
8,632
8,964
9,067
9,124
9,513
9,483
9,031
9,967
10,966
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