3. Learning Objectives
Explain why knowledge of statistics is important.
Define statistics and provide an example of how statistics
is applied.
Differentiate between descriptive and inferential statistics.
Classify variables as qualitative or quantitative, and
discrete or continuous.
Distinguish between nominal, ordinal, interval, and ratio
levels of measurement.
Understand the values associated with the practice of
statistics.
LO1-1
LO1-2
LO1-3
LO1-4
LO1-5
LO1-6
5. There are at least three reasons for
studying statistics:
1. Numerical information is everywhere
– newspapers, magazines, online, etc.
Statistics will help you understand this
information.
2. Statistical techniques are used to
make decisions that affect our lives, from
insurance rates to medical treatments.
3. The knowledge of statistical methods
will help you understand why decisions
are made and give you a better
understanding of how they affect you.
Why Study Statistics?
6. To make an informed decisions, you need to be able to:
1. Determine whether the existing information is adequate or
additional information is required.
2. Gather additional information, if it is needed, in such a way
that it does not provide misleading results.
3. Summarize the information in an informative manner.
4. Analyze the available information.
5. Draw conclusions and make inferences while assessing the
risk of an incorrect conclusion.
Statistical methods will provide you with a framework for the
decision-making process.
Why Study Statistics?
8. A statistic is a number used to communicate a piece of
information. For example, your grade point average is 3.5.
Statistics is the science of collecting, organizing, presenting,
analyzing, and interpreting data to assist in making more
effective decisions.
Example:
Your grade point average is 3.5. By collecting data and applying
statistics, you can determine the required average to be
admitted to a college and the likelihood that you will be admitted.
What Is Meant By Statistics
10. The study of statistics is divided into two categories: descriptive
statistics and inferential statistics.
Descriptive statistics involves methods of organizing,
summarizing, and presenting data in an informative way. This
involves graphical summaries as well as measures of central
tendency and dispersion.
Inferential statistics involves the methods used to estimate a
property of a population based on a sample. You might think of
inferential statistics as a “best guess” of a population value
based on sample information.
Types of Statistics
11. Examples of Descriptive Statistics:
1. Past census data.
2. Past weekly earnings of hospitality workers.
Examples of Inferential Statistics:
3. 46% of all high school students can solve problems involving
fractions.
4. 77% of all high school students can correctly total the cost of
a burger and fries on a restaurant menu.
Types of Statistics
12. A population is the entire set of individuals or objects of interest
or the measurements obtained from all individuals or objects of
interest.
A sample is a portion, or part, of the population of interest.
Populations and Samples
13. It is often necessary to take a sample instead of studying every
member of a population due to one or more of the following
reasons:
1. The prohibitive cost of surveying the whole population.
2. The destructive nature of some tests.
3. The physical impossibility of capturing the population.
Types of Statistics
14. In-Class Exercise
The Wooden Furniture Company asked a sample of 2564
consumers to try out a newly developed living room set in a
showroom. Of the 2564 sampled, 2126 said they would
purchase the furniture if it were marketed.
(a) What should the Wooden Furniture Company report to its
Board of Directors regarding the percentage of acceptance of
the living room set?
(b) Is this an example of descriptive statistics or inferential
statistics? Explain.
16. Qualitative
With a qualitative variable,
the characteristic being
studied is non-numeric.
Examples:
Gender, religious affiliation,
type of automobile owned,
country of birth, eye colour.
Quantitative
With a Quantitative
variable, the characteristic
being studied is numeric.
Examples:
Age, Height, Number of
automobile owned, Monthly
Income.
Types of Variables
17. Discrete
A discrete variable can
only assume certain values
and there are usually “gaps”
between values.
Examples:
Number of bedrooms in a
house, number of cars
arriving at a shopping
centre, number of students
in a statistics course
section.
Continuous
A continuous variable can
assume any value within a
specified range.
Examples:
Tire pressure, weight of
shipment of grain, amount
of cereal in a box, duration
of a flight.
Quantitative Variables: Classification
20. Data can be classified according to one of four levels of
measurement:
1. Nominal
2. Ordinal
3. Interval
4. Ratio (natural 0)
The lowest level of measurement is the nominal level. The
highest level of measurement is the ratio level.
Levels of Measurement
21. At the nominal level of measurement, observations of a
qualitative variable can only be classified and counted.
The nominal level has the following properties:
1. The variable of interest is divided into categories or outcomes.
2. There is no natural order to the outcomes.
Examples: Colour of M&Ms, gender.
Levels of Measurement
22. At the ordinal level of measurement, data classifications are
ranked or ordered according to the particular trait they possess
but we are not able to distinguish the magnitude of the
differences between groups.
The properties of the ordinal level of measurement are:
1. Data are represented by an attribute.
2. The data can only be ranked or ordered because the ordinal
level of measurement assigns relative values.
Examples: Professor ratings, terrorist attack risk levels.
Levels of Measurement
23. The interval level of measurement includes all the
characteristics of the ordinal level but, in addition, the
difference between values is a constant size.
The properties of interval level data are as follows:
1. Data classifications are ordered according to the amount
of the characteristic they possess.
2. Equal differences in the characteristic are represented by
equal differences in the levels
Examples: Temperature in degrees Celsius, shoe size, IQ
scores.
Levels of Measurement
24. The ratio level of measurement has all the characteristics of
the interval level but, in addition, the 0 point is meaningful
and the ratio between two numbers is meaningful.
The properties of ratio level data are as follows:
1. Data classifications are ordered according to the amount of
the characteristics they possess.
2. Equal differences in the characteristic are represented by
equal differences in the numbers assigned to the classifications.
3. The zero point is the absence of the characteristic and the
ratio between two numbers is meaningful.
Examples: Wages, weight, height.
Levels of Measurement
25. Interval scales hold no true zero and can
represent values below zero. For example,
you can measure temperatures below 0 degrees
Celsius, such as -10 degrees.
Ratio variables, on the other hand, never fall
below zero. Height and weight measure from 0
and above but never fall below it.
27. In-Class Exercise
What level of measurement is reflected in the following data?
(a) A sample number of books read in a year by 50 readers is
given below:
(b) In a survey of 300 television viewers, 100 were from a low
income group, 150 from a middle income group, and 50 from
a high income group.
15 4 3 11 17 3 1 7 14 14
10 6 6 10 18 13 4 17 16 11
5 13 8 16 9 4 5 18 16 12
7 11 9 14 11 12 5 12 17 13
8 12 12 6 2 1 6 13 15 9
29. There is a saying that has been around for a long time that
illustrates our point:
“Figures don’t lie, but liars figure”
This refers to the misuse of statistics whereby data is presented
in ways that are misleading.
Examples:
1. Different values are used to represent the same data.
2. Implying connections between variables that may not exists.
3. Misleading graphs.
Ethics and Statistics
30. Business analytics is used to process and analyze data and
information to support a story or narrative of a company’s
business, such as:
1. What makes us profitable?
2. How will our customers respond to a change in marketing?
An ability to use computer software to summarize, organize,
analyze, and present the findings of statistical analysis is
essential.
Basic Business Analytics
31. Chapter Summary
I. Statistics is the science of collecting, organizing, presenting,
analyzing, and interpreting data to assist in making more
effective decisions.
II. There are two types of statistics.
A. Descriptive statistics are procedures used to organize
and summarize data.
B Inferential statistics involve taking a sample from a
population and making estimates about a population
based on the sample results.
1. A population is an entire set of individuals or objects of
interest or the measurements obtained from all
individuals or objects of interest.
2. A sample is a part of the population.
32. Chapter Summary
III. There are two types of variables.
A. A qualitative variable is categorical or non-numeric.
1. Usually, we are interested in the number or percent of
the observations in each category.
2. Qualitative data are usually summarized in graphs and
bar charts.
B. There are two types of quantitative variables, and they
are usually reported numerically.
1. Discrete variables can assume only certain values,
and there are usually gaps between values.
2. A continuous variable can assume any value within a
specified range.
33. Chapter Summary
IV. There are four levels of measurement.
A. With the nominal level, the data are sorted into categories
with no particular order to the categories.
B. The ordinal level of measurement presumes that one
classification is ranked higher than another.
C. The interval level of measurement has the ranking
characteristic of the ordinal level of measurement plus the
characteristic that the distance between values is a
constant size.
D. The ratio level of measurement has all the characteristics
of the interval level, plus there is a meaningful zero point
and the ratio of two values is meaningful.
Editor's Notes
#14: Solution:
(a) On the basis of the sample of 2564 customers, we estimate that, if it is marketed, or of all customers will purchase the living room set.
(b) Inferential statistics, because a sample was used to draw a conclusion about how all customers in the population would react if Wooden Furniture Company marketed a newly developed living room set.
#27: Solution:
(a) Number of books read is a ration scale variable. Zero books read is a true 0 and 20 books read is twice as many as 10 books.
(b) Ordinal scale. There is no meaningful difference between values so it can only be classified. It can be ordered.
