DEPARTMENT OF QUANTITATIVE METHODS & INFORMATION
SYSTEMS
Introduction to Business Statistics
QM 120
Chapter 1
Spring 2008
Dr. Mohammad Zainal – Dr. Jafar Ali
Chapter 1
2
What is statistics ?
¾
¾
¾
¾
¾
A group of methods used to collect, organize, present, analyze,
and interpret data to make more effective decisions (educated
guess vs. pure guess).
¾
¾
Numerical facts:‐
Average income of Kuwaiti families.
Your monthly expenses.
Wedding cost.
cost
Opening a business without assessing the need for it may affect its
success.
Two fields of study:‐
¾
¾
Mathematical statistics.
Applied statistics.
Types of statistics
¾ Applied statistics can be divided into two areas: descriptive
statistics and inferential statistics.
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Types of statistics
¾
A population is a collection of all possible individuals,
objects, or measurements of interest.
A parameter is a summary measure computed to describe a
characteristic of the population
¾
¾
A sample is a portion, or part, of the population of interest.
A statistic is a summary measure computed to describe a characteristic
of the sample
¾
¾
Descriptive
p
statistics consists of methods for organizing,
g
g
displaying, and describing data in an informative way by
using tables, graphs, and summary measures.
¾
According to bank reports, 20% of the investors in the KSE declared
bankruptcy during 2007. The statistic 20 describes the number of
bankruptcies out of every 100 KSE investors.
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Types of statistics
A Gallup poll found that 49% of the people in a survey knew the
name of the first president of the USA. The statistic 49 describes the
number
u be out of every
e e y 100 persons
e o who
ho knew
k e the answer.
a
e
¾
¾
Inferential statistics consists of methods that use sample
results to help make decisions or predictions about a
population.
One can make some decisions about the political view of all KU
students
stude
ts (a
(around
ou d 15000)
5000) based o
on a sa
sample
p eo
of 500 stude
students.
ts.
¾ The accounting department of a large firm will select a sample of
invoices to check the accuracy of all the invoices of the company.
¾
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Descriptive Statistics
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Collect data
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Present data
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¾
e g Survey Observation, Experiments
e.g., Survey,
Observation Experiments
e.g., Charts and graphs
Characterize data
¾
e.g., Sample average= ∑x
i
n
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Inferential Statistics
¾
Making statements about a population by examining sample results
sample results
Sample statistics
(known) Population parameters
Inference (unknown, but can be estimated from sample evidence)
Sample
Population
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Remember
¾Descriptive statistics
¾Collecting, presenting, and describing data
¾Inferential statistics
¾Drawing conclusions and/or making decisions concerning a population based only
on sample data
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Estimation
¾
¾
e.g., Estimate the population mean weight using the sample mean weight
Hypothesis Testing
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e.g., Use sample evidence to test the claim that the population mean weight is 120 pounds
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Population versus sample
¾
Suppose a statistician is interested in knowing:
¾
The 2004 gross sale of all companies in Kuwait.
The 2004 gross sale of all
companies in Kuwait
¾
The prices of all houses in Mishrif.
¾
All companies and all houses are the target population for each case.
¾
We can make our decision based on a portion of the
population
p
p
((sample).
p )
¾
USA presidential election polls are based on few hundred voters instead of 205,018,000 voters.
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Population versus sample
¾
Why we sample?
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Less time consuming than a census
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Less costly to administer than a census
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It is possible to obtain statistical results of a sufficiently high precision based on samples.
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Population versus sample
¾
Census and sample survey
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Representative sample
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A survey that includes every member of the population is called a
census. The technique of collecting information from a portion of
the population is called a sample survey.
A sample that represents the characteristics of the population as
closely as possible is called a representative sample.
Random Sample
p
¾
A sample drawn in such a way that each element of the population
has the same chance of being selected is called a random sample.
¾
If the chance of being selected is the same for each element of the
population, it is called a simple random sample (SRS)
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Applications in business and economics
¾
Successful managers and decision‐makers should understand and use statistics effectively.
y
¾
Examples of the uses of statistics in business and economics are:‐
¾Accounting: Sample of balance sheets to audit.
¾Finance: Comparing stocks.
¾Marketing: Understanding the relationship between promotions and sales.
sales
¾Production: Quality control charts.
¾Economics: Forecasting unemployment rate.
¾Insurance: Finding premiums of a policy QM-120, M. Zainal
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Basic terms
¾
Element, Variable, observation, and data set.
¾
An element or member of a sample
p or p
population
p
is a specific
p
subject
j
or object (person, firm, item, country…etc.).
¾
A variable is a characteristic under study that assumes different
values for different element.
¾
The value of a variable for an element is called observation or
measurement.
Variable
2001 Sales of three U.S. Companies
An element
Company
2001 Sales (million of dollars)
IBM
85,866
Dell Computer
31,168
GM
177,260
Data
set
An
observation
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Types of variables
¾
Quantitative Variable:
¾
When the characteristic being studied can be reported numerically,
it is called a quantitative variable.
¾
¾
Example: The number of students in each section of the Business
Statistics course; the distance students travel from home to CBA;
the number of children in a family.
Qualitative or categorical Variable:
¾
When the characteristic being studied is nonnumeric, it is called a
qualitative variable.
q
¾
Example: A classification of university students by gender or by
program (Business, Education, Arts, etc.) is an example of a
qualitative variable. Type of automobile owned, and eye color
are also qualitative.
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Types of variables
¾
¾
Quantitative Variables (data that can be reported numerically) can be classified as either Discrete or Continuous.
Discrete Variable
¾
¾
A quantitative variable that can only assume certain values.
¾ Example: The number of bedrooms in a house, the number of
hamburgers sold at Burger King today, the number of children in
a family. Usually discrete variables result from counting. The
u
e o
of children
i e iin a family
a i y can
a bee 2 o
or 3 but
u not
o 2.45
number
Continuous Variable
¾
A quantitative variable that can assume any value within a specified range.
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Types of variables
¾
Example: The amount of rain in Kuwait last winter (it could be 20.55 cm), the height of students in a class, tire pressure, time to do an assignment, a persons weight.
Variable
Quantitative
Qualitative
Discrete
Continuous
(e.g., number of
houses, car
accidents)
(e.g., length, age,
height, weight)
(e.g., make of a
computer, hair
color,
l gender)
d )
Types of Variable
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Levels of variables
¾
Another way to classify data is by the way it is measured.
¾
Nominal level of measurement
Nominal level of measurement
¾
A nominal level of measurement data strictly with qualitative data.
¾
Observations are simply assigned to predetermined categories.
¾
This data type does not allow us to perform any mathematical operations, such as adding or multiplying.
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Number can be used at the nominal level but they canʹt be added or placed in a meaningful order of greater than or less than. ¾
This type is considered the lowest level of data.
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Levels of variables
¾
Ordinal level of measurement
¾
ordinal is the next level up. ¾
It has all the properties of nominal data with the added feature that we can rank‐order the values from highest to lowest. ¾
An example is if you were to have a cooking race. Letʹs say the finishing order was Scott, Tom, and Bob. We still canʹt perform mathematical operations on this data, but we can say that Scottʹs cooking was faster than Bobʹs. ¾
However, we cannot say how much faster.
¾
Ordinal data does not allow us to make measurements between the categories and to say, for instance, that Scottʹs cooking is twice as good as Bob‘s.
¾
Ordinal data can be either qualitative or quantitative
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Levels of variables ¾
Interval level of measurement
¾
Moving up the scale of data, we find ourselves at the interval level, which is strictly quantitative data.
which is strictly quantitative data.
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Now we can get to work with the mathematical operations of addition and subtraction when comparing values.
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For this data, the difference between the different categories can be measured with actual numbers and also provides meaningful information.
¾
Temperature measurement in degrees Fahrenheit is a common example here. For instance, 70 degrees is 5 degrees warmer than 65
example here. For instance, 70 degrees is 5 degrees warmer than 65 degrees.
¾
However, multiplication and division canʹt be performed on this data. Why not? Simply because we cannot argue that 100 degrees is twice as warm as 50 degrees.
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Levels of variables
¾
Ratio level of measurement
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The king of data types is the ratio level.
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This is as good as it gets as far as data is concerned.
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Now we can perform all four mathematical operations to compare values with absolutely no feelings of guilt.
¾
Examples of this type of data are age, weight, height
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Data Measurement Levels
Measurements
Highest Level
g
R ti /I t
Ratio/Interval Data
lD t
Rankings Ordered Categories
Complete Analysis
Higher Level
Ordinal Data
Mid‐level Analysis
Categorical Codes ID Numbers Category Names
Lowest Level
Nominal Data
Basic Analysis
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Cross‐section versus time‐series data
¾
Cross‐section data:
¾
Data collected on different elements at the same point of time Data
collected on different elements at the same point of time
or for the same period of time are called cross‐section data.
2001 Sales of three U.S. Companies
Company
2001 Sales (million of dollars)
IBM
85,866
Dell Computer
31,168
GM
177,260
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Cross‐section versus time‐series data
¾
Time‐series data:
¾
Data collected on the same element for the same variable at
different points in time or for different periods of time are
called time‐series data.
Price of a 30‐seoncd TV commercial during super bowl telecast
Year
Super Bowl
Price of a 30-second TV commercial
(million of dollars)
1999
XXXIII
1.60
2000
XXIV
2.10
2001
XXXV
2.05
2002
XXXVI
1.90
2003
XXXVII
2.20
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Cross‐section versus time‐series data
Sales (in $1000’s)
Time Series Data: Ordered data values observed over time
2003
2004
2005
2006
Atlanta
435
460
475
490
Boston
320
345
375
395
Cleveland
405
390
410
395
Denver
260
270
285
280
Cross Section Data: Data values observed at a fixed point in time
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Sources of data
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Internal sources.
¾
Company’ss own personnel file.
Company
own personnel file
¾
Accounting records.
¾
¾
¾
Example: A company that wants to forecast the future sale of its
product may use the data of past periods from its own record.
External sources.
¾
Governmental publications.
¾
Private publications.
Survey or experiment.
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Sources of data
S
Survey or experiment
i
t
Experiments
Written questionnaires
Telephone surveys
Direct observation and personal interview QM-120, M. Zainal
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Statistics and Ethics
¾
People often use statistics to persuade others to their
opinions,
p
it can lead to the misuse of statistics in several
ways:
¾
Choosing a sample that ensures results in favoring your desired
outcome (biased sample)
¾
Making the differences seems greater than they actually look in
graphs
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Statistics and Ethics
¾
Internet polls are unreliable because those websites have no
control over the respondents or how many times they respond.
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