This document defines key concepts in statistics including: - Descriptive statistics which organizes and summarizes data, and inferential statistics which makes predictions about populations based on samples. - Qualitative vs. quantitative variables, and discrete vs. continuous quantitative variables. - Different levels of measurement for variables including nominal, ordinal, interval, and ratio scales. - The concepts of mutually exclusive and exhaustive categories.

1. 1. Define what is meant by statistics.
2. Explain what is meant by descriptive statistics and inferential
statistics.
3. Distinguish between a qualitative variable and a quantitative
variable.
4. Distinguish between a discrete variable and a continuous
variable.
5. Distinguish among the nominal, ordinal, interval, and ratio levels
of measurement.
6. Define the terms mutually exclusive and exhaustive.
GOALS
When you have completed this chapter, you will be able to:
Chapter One: Introduction
Important: This file is a modified electronic version of Statistical Techniques in Business and Economics
© The McGraw-Hill Companies, Inc., 1999

2. What is Meant by Statistics?
 Statistics is the science of
collecting, organizing, presenting, ana
lyzing, and interpreting numerical data
for the purpose of assisting in making
a more effective decision.
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3. Who Uses Statistics?
 In today’s information
society, decisions are made on the
basis of data. A family checks the
neighborhood before purchasing a
house, a company checks the labor
and transportation conditions before
opening a new branch, an engineer
tests the tensile strength of a wire
before winding it into a cable, and so
on.
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4. Types of Statistics
 Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative way.
 EXAMPLE 1: A survey found that 49% of the people knew
the name of the first book of the Bible. The statistic 49
describes the number out of every 100 persons who knew
the answer.
 EXAMPLE 2: According to Consumer Reports, Whirlpool
washing machine owners reported 9 problems per 100
machines during 2005. The statistic 9 describes the
number of problems out of every 100 machines.
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5. Types of Statistics
 Inferential Statistics: A
decision, estimate, prediction, or
generalization about a
population, based on a sample.
 A population is a collection of all
possible individuals, objects, or
measurements of interest.
 A sample is a portion, or part, of the
population of interest.
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6. Types of Statistics
(examples of inferential statistics)
 EXAMPLE 1: Measuring lifetimes of
transistors
 EXAMPLE 2: Classifying air as healthy
or unhealthy based on the Air Quality
Index (AQI)
 EXAMPLE 3: Collecting data on the
volume of traffic flow in a busy street of
Manila.
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7. Types of Variables
 Qualitative or Attribute variable: data
in the form of classifications into
different groups or categories. The
characteristic or variable being studied
is nonnumeric.
 EXAMPLES: Gender, religious
affiliation, type of automobile
owned, place of birth, eye color.
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8. Types of Variables
 Quantitative variable: data in the form
of numerical measurements or counts.
The variable can be reported
numerically.
 EXAMPLE: ozone level of the air,
minutes remaining in class, number of
children in a family.
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9. Types of Variables
 Quantitative variables can be classified as
either discrete or continuous.
 Discrete variables:Variables which assume a
finite or countable number of possible values.
Usually obtained by counting.
 EXAMPLE: the number of bedrooms in a
house. (1,2,3,..., etc...).
 Continuous variables: Variables which
assume an infinite number of possible values.
Usually obtained by measurement.
 EXAMPLE: The time it takes to fly from
Manila to Cebu.
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10. Summary of Types of Variables
Qualitative or attribute
(type of car owned)
discrete
(number of children)
continuous
(time taken for an exam)
Quantitative or numerical
DATA
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11. Sources of Statistical Data
 Researching problems usually
requires published data. Statistics on
these problems can be found in
published articles, journals, and
magazines.
 Published data is not always available
on a given subject. In such
cases, information will have to be
collected and analyzed.
 One way of collecting data is via
questionnaires.
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12. Levels of Measurement
 Nominal level (scaled): Data that can
only be classified into categories and
cannot be arranged in an ordering
scheme.
 EXAMPLES: eye color, gender,
religious affiliation.
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13. Levels of Measurement
 Mutually exclusive: An individual or
item that, by virtue of being included in
one category, must be excluded from
any other category.
 EXAMPLE: eye color.
 Exhaustive: each person, object, or
item must be classified in at least one
category.
 EXAMPLE: religious affiliation.
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14. Levels of Measurement
 Ordinal level: involves data that may
be arranged in some order, but
differences between data values
cannot be determined or are
meaningless.
 EXAMPLE: During a taste test of 4
colas, cola C was ranked number
1, cola B was ranked number 2, cola A
was ranked number 3, and cola D was
ranked number 4.
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15. Levels of Measurement
 Interval level: similar to the ordinal
level, with the additional property that
meaningful amounts of differences
between data values can be
determined. There is no natural zero
point.
 EXAMPLE: Temperature on the
Fahrenheit scale.
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16. Levels of Measurement
 Ratio level: the interval level with an
inherent zero starting point.
Differences and ratios are meaningful
for this level of measurement.
 EXAMPLES: money, heights of NBA
players.
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17. Assessment:
1.A statistic is
a. collection of values b. single value.
c. The sum of several values. d. The largest value in a set of observations
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2. In descriptive statistics our main objective is to
a. Describe the population. b. Describe the data we
collected.
c. Infer something about the population. d.Compute an average.
3. Which of the following statements is true regarding a population?
a. It must be a large number of values. b. It must refer to people.
c. It is a collection individuals, objects, or measurements.
d. None of the above.
4. Which of the following statements is true regarding a sample?
a. It is a part of population. b. It must contain at least five
observations.
c. It refers to descriptive statistics. d. All of the above are correct.
5. A qualitative variable
a. Always refers to a sample. b. Is nonumeric.
c. Always has only two possible outcomes. d. All of the above are correct.

18. Assessment:6. A discrete variable
a. Is an example of a qualitative variable. b.Can assume only whole number
values.
c. Can assume only certain clearly separated values.
d. Cannot be negative.
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7. A nominal scale variable is
a. Usually the result of counting something. b. Has a meaningful zero
point.
c. May assume negative values.
d. Cannot have more than two categories.
8. The ratio scale of measurement
a. Usually involves ranking. b. Cannot assume negative
values.
c. Has a meaningful zero point. d. Is usually based on counting.
9. The ordinal scale of measurement
a. Has a meaningful zero point. b. Is based on ranks.
c. Cannot assume negative values. d. All of the above.
10. Categories are exhaustive when
a. There is a meaningful zero point. b. The objects can be
ranked.
c. Each object must appear in at least one category.
d. Each object can be included in only one category.