CHAPTER 1
The Nature of Probability and
Statistics
© Copyright McGraw-Hill 2004
1-1
Objectives

Demonstrate knowledge of statistical terms.

Differentiate between the two branches of
statistics.

Identify types of data.

Identify the measurement level for each
variable.
© Copyright McGraw-Hill 2004
1-2
Objectives (cont’d.)

Identify the four basic sampling techniques.

Explain the difference between an
observational and an experimental study.

Explain how statistics can be used and
misused.

Explain the importance of computers and
calculators in statistics.
© Copyright McGraw-Hill 2004
1-3
Introduction

Statistics is the
science of
conducting studies
to collect, organize,
summarize, analyze,
and draw
conclusions from
data.
© Copyright McGraw-Hill 2004
1-4
Descriptive and Inferential Statistics

Descriptive statistics

Inferential statistics
consists of generalizing
consists of the
from samples to
collection,
populations, performing
organization,
summarization, and
presentation of data.
estimations hypothesis
testing, determining
relationships among
variables, and making
predictions.
© Copyright McGraw-Hill 2004
1-5
Basic Vocabulary

Probability is the chance of an event
occurring.

A population consists of all subjects that are
being studied.

A sample is a group of subjects selected from
a population.
© Copyright McGraw-Hill 2004
1-6
Variables and Data

In order to gain knowledge about seemingly
haphazard events, statisticians collect
information for variables that describe the
events.

A variable is a characteristic or attribute that
can assume different values.

Data are the values that variables can
assume.
© Copyright McGraw-Hill 2004
1-7
Variables and Data (cont’d.)

A data set is a collection of data values.

Each value in the data set is called a data
value or a datum.

Random variables have values that are
determined by chance.
© Copyright McGraw-Hill 2004
1-8
Random Variation

Insurance companies set their rates based on
random variables. Over a long period of time,
the rate of the occurrence of accidents tends
to be constant.
© Copyright McGraw-Hill 2004
1-9
Variables and Types of Data

Qualitative variables can be placed into
distinct categories according to some
characteristic or attribute.

Quantitative variables are numerical in nature
and can be ordered or ranked.
© Copyright McGraw-Hill 2004
1-10
Variables and Types of Data (cont’d.)
Quantitative variables can be further classified
into two groups.

Discrete variables assume values that can be
counted.

Continuous variables can assume all values
between any two specific values.
© Copyright McGraw-Hill 2004
1-11
Levels of Measurement

Nominal—classifies data into mutually
exclusive (nonoverlapping), exhausting
categories in which no order or ranking can
be imposed on the data.

Ordinal—classifies data into categories that
can be ranked; however, precise differences
between the ranks do not exist.
© Copyright McGraw-Hill 2004
1-12
Levels of Measurement (cont’d.)

Interval—ranks data, and precise differences
between units of measure do exist; however,
there is no meaningful zero.

Ratio—possesses all the characteristics of
interval measurement, and there exists a true
zero.
© Copyright McGraw-Hill 2004
1-13
Classification of Data
Nominallevel data
Zip code
OrdinalInterval-level Ratio-level
level data data
data
Grade
SAT score
Height
Gender
Rating
IQ
Eye color
Ranking
Temperature Time
© Copyright McGraw-Hill 2004
Weight
1-14
Data Collection and Sampling Techniques

Surveys are the most common method of
collecting data. Three methods of surveying
are:
 Telephone
 Mailed
surveys
questionnaire surveys
 Personal
interviews
© Copyright McGraw-Hill 2004
1-15
Sampling Methods

Random samples are selected using chance
methods or random methods.

Researchers obtain systematic samples by
numbering each subject of the populations
and then selecting every kth number.
© Copyright McGraw-Hill 2004
1-16
Sampling Methods

Researchers select stratified samples by
dividing the population into groups according
to some characteristic that is important to the
study, then sampling from each group.

Researchers select cluster samples by using
intact groups called clusters.
© Copyright McGraw-Hill 2004
1-17
Observational and Experimental Studies

In an observational

In an experimental
study, the researcher
study, the researcher
merely observes what is
manipulates one of the
happening or what has
variables and tries to
happened in the past
determine how the
and tries to draw
manipulation influences
conclusions based on
other variables.
these observations.
© Copyright McGraw-Hill 2004
1-18
Uses and Misuses of Statistics

Suspect samples
 Very
small samples
 Bias
sample selection
 Volunteer
samples

Ambiguous averages

Changing the subject
© Copyright McGraw-Hill 2004
1-19
Uses and Misuses of Statistics (cont’d)

Detached statistics

Implied connections

Misleading graphs

Faulty survey questions
© Copyright McGraw-Hill 2004
1-20
Computers and Calculators

In the past, statistical
calculations were done
with pencil and paper.
However, with the
advent of calculators,
numerical computations
became easier.
© Copyright McGraw-Hill 2004
1-21
Statistical Packages

Excel, MINITAB, and the TI-83 graphing
calculator can be used to perform statistical
computations.

Students should realize that the computer
and calculator merely give numerical answers
and save time and effort of doing calculations
by hand.
© Copyright McGraw-Hill 2004
1-22
Summary

The two major areas of statistics are
descriptive and inferential.

When the populations to be studied are large,
statisticians use subgroups called samples.

The four basic methods for obtaining samples
are: random, systematic, stratified, and
cluster.
© Copyright McGraw-Hill 2004
1-23
Summary (cont’d.)

Data can be classified as qualitative or
quantitative.

The four basic types of measurement are
nominal, ordinal, interval, and ratio.

The two basic types of statistical studies are
observational and experimental.
© Copyright McGraw-Hill 2004
1-24
Conclusion

The applications of statistics are many
and varied. People encounter them in
everyday life, such as in reading
newspapers or magazines, listening to
the radio, or watching television.
© Copyright McGraw-Hill 2004
1-25
Homework

Chapter 1, Page 26
 6,

7,8,9,12,14,15
Critical Thinking Challenges Page 30
 6-
Hostile Children ….
© Copyright McGraw-Hill 2004
1-26