© copyright mcgraw-hill 2004 1-1 chapter 1 the nature of probability and statistics

© Copyright McGraw-Hill 20041-1

CHAPTER 1

The Nature of Probability and Statistics


Objectives

Demonstrate knowledge of statistical terms.

Differentiate between the two branches of

statistics.

Identify types of data.

Identify the measurement level for each

variable.


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.


Introduction

Statistics is the

science of

conducting studies

to collect, organize,

summarize, analyze,

and draw

conclusions from

data.


Descriptive and Inferential Statistics

Descriptive statistics

consists of the

collection,

organization,

summarization, and

presentation of

data.

Inferential statistics

consists of generalizing

from samples to

populations, performing

estimations hypothesis

testing, determining

relationships among

variables, and making

predictions.


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.


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.


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.


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.


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.


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.


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.


Classification of Data

Nominal-level data

Ordinal-level data

Interval-leveldata

Ratio-leveldata

Zip code

Gender

Eye color

Grade

Rating

Ranking

SAT score

IQ

Temperature

Height

Weight

Time


Data Collection and Sampling Techniques

Surveys are the most common method of

collecting data. Three methods of surveying

are:

Telephone surveys

Mailed questionnaire surveys

Personal interviews


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.


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.


Observational and Experimental Studies

In an observational

study, the researcher

merely observes what

is happening or what

has happened in the

past and tries to draw

conclusions based on

these observations.

In an experimental

study, the researcher

manipulates one of the

variables and tries to

determine how the

manipulation influences

other variables.


Uses and Misuses of Statistics

Suspect samples

Very small samples

Bias sample selection

Volunteer samples

Ambiguous averages

Changing the subject


Uses and Misuses of Statistics (cont’d)

Detached statistics

Implied connections

Misleading graphs

Faulty survey questions


Computers and Calculators

In the past, statistical

calculations were done

with pencil and paper.

However, with the

advent of calculators,

numerical

computations became

easier.


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.


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.


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.


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 1-1 chapter 1 the nature of probability and statistics

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