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Chapter 1
The Nature of Probability
and Statistics
Introduction
1-1 Descriptive and Inferential Statistics
1-2 Variables and Types of Data
1-3 Data Collection and Sampling Techniques
1-4 Observational and Experimental Studies
1-5 Uses and Misuses of Statistics
1-6 Computers and Calculators
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Introduction
Statistics is the science of conducting studies to
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1-1 Descriptive and Inferential Statistics
A variable is a characteristic or attribute that can assume
different values.
Data are the values (measurements or observations) that
the variables can assume.
Variables with values that are determined by chance are
called random variables.
A collection of data values from a data set.
Each value in the data set is called a data value or a
datum.
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1-1 Descriptive and Inferential Statistics
Data value or Datum
Variables
Model
Number sold
Cost
Sunscraper
9
$427,000
Skycoaster
6
365,000
High-flyer
12
725,000
Data set
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1-1 Descriptive and Inferential Statistics
Collection
Organization
Summarization
Presentation of data
Generalizing from
samples to populations
Performing estimations
and hypothesis tests
Determining
relationships among
variables
Making predictions
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1-1 Descriptive and Inferential Statistics
A population
consists of all
subjects (human or
otherwise) that are
studied.
A sample is a subset
of the population.
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1-1 Descriptive and Inferential Statistics
Hypothesis testing is a decision-making process for
evaluating claims about a population, based on
information obtained from samples.
Two
groups
Heart Attacks
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Men over 70
years old
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1-2 Variables and Types of Data
Numerical, can be
ordered or ranked
i.e. ages, heights,
weights
can be place into categories
i.e. gender (male or female)
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can be counted
i.e. 5, 29, 8000
often include fractions and decimals
i.e. 2.59, 312.1
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1-2 Variables and Types of Data
Table 1-1
Recorded Values and Boundaries
Variable
Recorded value
Boundaries
Length
15 centimeters (cm)
14.5-15.5cm
Temperature
86 degrees Fahrenheit (℉)
85.5-86.5℉
Time
0.43 second (sec)
0.425-0.435sec
Mass
1.6 grams (g)
1.55-1.65g
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1-2 Variables and Types of Data
categorical
(names)
i.e. subject
(English,
Mathematics,
History,
Psychology)
nominal, plus
can be ranked
(order)
i.e. grades (A, B,
C, D, F)
ordinal, plus
intervals are
consistent, no
true zero
i.e. temperature,
IQ
interval, plus
ratios are
consistent, true
zero
i.e. height,
weight, salary
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1-2 Variables and Types of Data
Determine the measurement level.
Variable
Nominal
Ordinal
Hair Color
Yes
No
Nominal
Zip Code
Yes
No
Nominal
Letter Grade
Yes
Yes
No
ACI Score
Yes
Yes
Yes
No
Interval
Height
Yes
Yes
Yes
Yes
Ratio
Age
Yes
Yes
Yes
Yes
Ratio
Temperature (℉)
Yes
Yes
Yes
No
Interval
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Interval
Ratio
Level
Ordinal
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1-3 Data Collection and Sampling Techniques
Data Collection
 Less costly
 Not answer when the
calls are made
 Have unlisted
numbers and cell
phones
 Wider geographic
area
 Less expensive
 Anonymous
 Inappropriate
answers
 Difficulty reading
 In-depth responses
 More costly
(interviewers must be
trained in asking
questions and recording
responses)
 Interviewers may be
biased in his or her
selection of
respondents
Other ways: surveying records or direct observation of situations
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1-3 Data Collection and Sampling Techniques
Sampling Techniques －Random Sampling (1/4)
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Goal: 15 subjects out of 85 subjects
→number from 01 to85
Step 1: Select a starting number.
(closing your eyes and placing
your finger on a number in the table)
Subjects are selected
Step
2: Proceed
downward until
by
random
numbers.
you have selected 15 different
numbers between 01 and 85.
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1-3 Data Collection and Sampling Techniques
Sampling Techniques －Systematic Sampling (2/4)
Subjects are selected by using every kth number after the first
subject is random selected from 1 through k.
Goal: Suppose there were 15 subjects in the population and a sample of 3
subjects were needed. →15/3=5, then k =5
5
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1-3 Data Collection and Sampling Techniques
Sampling Techniques －Stratified Sampling (3/4)
Subjects are selected by dividing up the population into groups
(strata), and subjects are randomly selected within groups.
strata
First-year students
sample
The president of a twoyear college students
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Second-year students
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1-3 Data Collection and Sampling Techniques
Sampling Techniques －Cluster Sampling (4/4)
Subjects are selected by using an intact group that is
representative of the population.
cluster
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sample
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1-4 Observational and Experimental Studies
The researcher merely
observes what is
happening or what has
happened in the past and
tries to draw conclusions
based on these
observations.
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The researcher
manipulates one of the
variables and tries to
determine how the
manipulation influences
other variables.
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1-4 Observational and Experimental Studies
The independent variables in an experimental study
is the one that is being manipulated by the researcher.
The independent variable is also called the
explanatory variable.
The resultant variable is called the dependent
variable or the outcome variable.
A confounding variable is one of that influences the
dependent or outcome variable but was not separated
from the independent variable.
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1-4 Observational and Experimental Studies
Two
groups
Heart Attacks
Men over 70
years old
The group that given the drug is called the treatment
group.
The group that given the drug is called the control
group.
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1-5 Uses and Misuses of Statistics
Suspect Samples
Is the sample large enough?
How was the sample selected?
Is the sample representative of the population?
Ambiguous Averages
What particular measure of average was used
and why?
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1-5 Uses and Misuses of Statistics
Changing the Subject
Are different values used to represent the same
data?
Detached Statistics
One third fewer calories…….than what?
Implied Connections
Studies suggest that some people may understand
what this statement means.
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1-5 Uses and Misuses of Statistics
Misleading Graphs
Are the scales for the x-axis and y-axis
appropriate for the data?
Faulty Survey Questions
Do you feel that statistics teachers should be
paid higher salaries?
Do you favor increasing tuition so that colleges
can pay statistics teachers higher salaries?
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1-6 Computers and Calculators
Microsoft Excel
Microsoft Excel with MegaStat
TI-83/84
Minitab
SAS
SPSS
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