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© Copyright McGraw-Hill 20041-1
CHAPTER 1
The Nature of Probability and Statistics
© Copyright McGraw-Hill 20041-2
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 20041-3
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 20041-4
Introduction
Statistics is the
science of
conducting studies
to collect, organize,
summarize, analyze,
and draw
conclusions from
data.
© Copyright McGraw-Hill 20041-5
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.
© Copyright McGraw-Hill 20041-6
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 20041-7
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 20041-8
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 20041-9
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 20041-10
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 20041-11
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 20041-12
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 20041-13
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
© Copyright McGraw-Hill 20041-14
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
© Copyright McGraw-Hill 20041-15
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 20041-16
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 20041-17
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.
© Copyright McGraw-Hill 20041-18
Uses and Misuses of Statistics
Suspect samples
Very small samples
Bias sample selection
Volunteer samples
Ambiguous averages
Changing the subject
© Copyright McGraw-Hill 20041-19
Uses and Misuses of Statistics (cont’d)
Detached statistics
Implied connections
Misleading graphs
Faulty survey questions
© Copyright McGraw-Hill 20041-20
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 20041-21
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 20041-22
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 20041-23
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 20041-24
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.