Chapter 1:
Introduction to
Statistics
Learning Objectives
LO1
LO2
LO3
LO4
Define statistics and list example applications of
statistics in business.
Define important statistical terms, including
population, sample, and parameter, as they relate to
descriptive and inferential statistics.
Explain the difference between variables,
measurement, and data.
Compare the four different levels of data: nominal,
ordinal, and ratio.
What is Statistics?
• The gathering, (organizing, summarizing) analyzing,
interpreting, and presenting data
• The science of numbers
• Branch of mathematics
• Course of study or way of thinking
• The recording of numerical facts and figures
• The recording or registration of a death
• Measurement(s) on characteristics associated with objects
(things, elements) included in a sample
• Type of distribution being used to analyze data
Applications in Business
• 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.
• In a 2008 survey of 14 countries conducted by GlobeScan for
the National Geographic Society, Canada ranked 13 out of 14
when it came to environmentally friendly consumption
patterns. This was due mostly to Canadian preferences for
bigger houses and an established culture of using privately
owned cars as opposed to transit.
Descriptive vs. Inferential Statistics
• Descriptive Statistics:
– Using data gathered on a group to describe or reach conclusions
about that same group and that group alone: The average for your
statistics class.
• Inferential Statistics:
– Using sample data to reach conclusions or make general
statement(s) about the population from which the sample was
taken: The average litres per 100 km based on four cars selected
from a parking lot.
Population Versus Sample
• Population:
– Webster’s Third New International Dictionary defines population as a
collection of persons, objects, or items of interest.
• Census:
– When researchers gather data from the whole population for a given
measurement of interest, they call it a census.
• Sample:
– A sample is a portion of the whole and, if properly taken, is
representative of the whole.
Parameter vs. Statistic
• Parameter — a descriptive measure (s) of the population with
respect to some characteristic of interest.
• Usually values representing the tendency for things to be
alike(converge to a norm); and the tendency for things to
differ (diverge) from that norm.
– Parameters are usually represented by Greek letters
• Statistic — a descriptive measure(s) of the population with
respect to some characteristic but using sample data.
– Sample statistics are usually represented by Roman letters
Population
All The Cars in the Parking Space Of Interest
The Population and Census Data
Identifier
Color
MPG
RD1
RD2
RD3
RD4
RD5
BL1
BL2
GR1
GR2
GY1
GY2
GY3
Red
Red
Red
Red
Red
Blue
Blue
Green
Green
Gray
Gray
Gray
12
10
13
10
13
27
24
35
35
15
18
17
Representativeness of the Sample
• The accuracy of the sample statistic depends on how
representative the sample is.
• Is the sample in the next slide representative of the twelve cars in
the parking lot?
• There are 2 blue, 2 green, 3 grey, and 5 red cars.
• In the sample there are no blue cars. The sample is biased in terms
of consumer choice attributes, green, grey and red.
Sample and Sample Data
Characteristics
• Each member of the population may have several
characteristics associated with it.
• Cars in a parking lot may have characteristics such colour,
speed, design, manufacturer, fuel consumption rates, price,
performance ranking by AAA, etc
• The various characteristics are measured using nominal,
ordinal, interval or ratio measures.
• The type of statistical analysis that is appropriate depends on
the level of data measurement used.
Variables and Data
• A variable is a characteristic of any entity being studied that is
capable of taking on different values.
• A measurement occurs when a standard process is used to
assign numbers to particular attributes or characteristics of a
variable.
• 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.
Hierarchy of Levels of Data
Examples of Levels of Data Measures
• Nominal. Player number 10. Identifies the player but does not
assign a value to the player. “John is an educator” assigns John
to a category, coded as 5. This number assigns no value to john.
• Ordinal ranks. The ranking in the Canadian dance skating
competition; 1, 2, 3, 4… The order is clear but the difference
between the performances cannot be inferred by the numeric
values.
• Interval. Measures of temperature have no natural or fixed zero
point. Zero is just a reference point.
• Ratio scale measures: height, weight, time, etc. Here zero is not
arbitrary. It is fixed. It means the absence of the characteristic.
Usage Potential of Various
Levels of Data
Nominal Level Data
• Using numbers or codes to classify or categorize the characteristic
or attribute
Ordinal Level Data
• Numbers are used to indicate rank or order
– Relative magnitude of numbers is meaningful
– Differences between numbers are not comparable
• Example: Ranking productivity of employees
• Example: Taste test ranking of three brands of soft drink
• Example: Positions within an organization where
–
–
–
–
–
1 used for President
2 used for Vice President
3 for Plant Manager
4 for Department Supervisor
5 for Employee
Ordinal Data as Indicators of Preference or
Degrees of Agreement
• Coding of Responses on a Questionnaire:
• “Faculty and staff should receive preferential treatment for
parking space”.
• Rank Your response from 1 (least important) to 5 (most
important)
Ordinal measures require special statistical techniques
Example of Ordinal Measurement
Position at the Finish Line
Interval Level Data
• Distance between consecutive integers (1,2,3,4 or 20o , 21o,
and 22o ) are equal.
• Differences between consecutive numbers have meaning
• 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.
• Examples:
• Fahrenheit Temperature: zero does not mean the absence of
temperature
• Calendar Time, Percentage Change
Ratio Level Data
• Characteristics of measure
–
–
–
–
Relative magnitude of numbers is meaningful
Differences between numbers are comparable
Location of origin, zero, is absolute (natural)
Vertical intercept of unit of measure transform function is zero
• Examples:
– Height, Weight, and Volume
– Monetary variables: Profit and Loss, Revenues, and Expenses;
unemployment insurance, subsidies
– Financial ratios, such as P/E Ratio, Inventory Turnover, and Quick Ratio.
Statistical Techniques
• 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.
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