Elementary Statistics
Chapter 1
Introduction to Statistics
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Statistics
 Method of analysis
a collection of methods for planning
experiments, obtaining data, and then
then organizing, summarizing, presenting,
analyzing, interpreting, and drawing
conclusions based on the data
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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What is Statistics?
• USA Today, December 10, 1997--The biggest study
ever of the health effects of alcohol concludes that a
drink a day can cut your risk of death by 20%…The
researchers gave questionnaires to 490,000 men and
women and then followed up nine years later, after
46,000 of them had died…[However], the benefits
decreased as people drank more. Among those who
averaged four or five drinks a day, the risk of death
among men was 10% lower, while among women it
was 7% lower.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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What is Statistics?
• New York Times, September 17, 1996--Millions of
Americans routinely ignore one of mom’s most
important pieces of advice: Wash your hands after
you go to the bathroom. This unsettling item of news
was gathered in the only way possible--by actually
watching what people do (or don’t do) in public
restrooms. The researchers--if that’s what they
should be called--hid in stalls or pretended to comb
their hair while observing 6,333 men and women do
their business in five cities…Just 60% of those using
restrooms in Penn Station (New York City)washed up
afterward.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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• Statistics is the science of data. It involves
collecting, classifying, summarizing, organizing,
analyzing, and interpreting data.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Population
• A population is the complete collection of all
elements (scores, people, measurements, and so
on) to be studied. The collection is complete in
the sense that it includes all subjects to be
studied.
• A population is the totality of all subjects
possessing certain common characteristics that
are being studied.
• In a statistical study, the researcher must define
the population being studied.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Sample
• A sample is a subgroup or subset of the
population.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Population and Sample
• Potential advertisers value television’s wellknown Nielsen ratings as a barometer of a TV
show’s popularity among viewers. The Nielsen
rating of a certain TV program is an estimate of
the proportion of viewers, expressed as a
percentage, who tune their sets to the program
on a given night at a given time. A typical Nielsen
survey consists of 165 families selected
nationwide who regularly watch television.
Suppose we are interested in the Nielsen ratings
for the latest episode of ER.
• Identify the population of interest.
• Describe the sample.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Census
the collection of data from every
element in a population
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Parameters and Statistics
• A parameter is a numerical measurement
describing some characteristic of the population.
– Example: when Lincoln was first elected to the presidency, he
received 39.82% of he 1,865,908 votes cast. If we consider the
collection of all of those votes to be the population being
considered, then 39.82% is a parameter, not a statistic.
• A statistic is a numerical measurement
describing some characteristic of the sample.
– Example: Based on a sample of 877 surveyed executives, it
was found that 45% of them would not hire anyone whose job
application contained a typographical error.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Parameter
a numerical measurement describing
some characteristic of a population
population
parameter
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copy right 2001. Addison Wesley Longman
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Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Statistic
a numerical measurement describing
some characteristic of a sample
sample
statistic
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Population, Sample, and Inference
• Are state lottery winners who win big payoffs likely to quit
their jobs within one year of winning? No, according to a
study published in the Journal of the Institute for
Socioeconomic Studies (Sept. 1985). The researcher mailed
questionnaires to over 2,000 lottery winners who won at
least $50,000 between 1975 and 1985. Of the 576 who
responded, only 11% had quit their jobs during the first year
after striking it rich. In this study, identify
• The population
• The sample
• The inference made about the population
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Data
• Data are obtained by measuring some
characteristic or property of the objects (usually
people or things) of interest to us.
• A variable is a characteristic (Property) that
differs or varies from one observation from the
next.
• All data (and, consequently, the variables we
measure) are either quantitative or qualitative.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Qualitative/Quantitative Data
• Quantitative data are observations measured on
a natural numerical scale.
• Nonnumeric data that can only be classified into
one of a group of categories are qualitative data.
• State whether each of the following variables
measured on graduating high school students is
quantitative or qualitative.
–
–
–
–
National Honor Society member or not
Scholastic Assessment Test (SAT) score
Number of colleges applied to
Part-time job status
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Quantitative data
numbers representing counts or
measurements
 Qualitative (or categorical or
attribute) data
can be separated into different categories
that are distinguished by some nonnumeric
characteristics
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Quantitative data
the incomes of college graduates
 Qualitative (or categorical or
attribute) data
the genders (male/female) of college
graduates
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Discrete vs Continuous Data
• Discrete data result when the number of possible
values is either a finite number or a “countable”
number.
• Continuous (numerical) data result from infinitely
many possible values that correspond to some
continuous scale hat covers a range of values
without gaps, interruptions, or jumps.
Continuous data is measurable.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Discrete
data result when the number of possible values is
either a finite number or a ‘countable’ number of
possible values
0, 1, 2, 3, . . .
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
Discrete
data result when the number of possible values is
either a finite number or a ‘countable’ number of
possible values
0, 1, 2, 3, . . .
 Continuous
(numerical) data result from infinitely many possible
values that correspond to some continuous scale
that covers a range of values without gaps,
interruptions, or jumps
2
3
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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• Determine whether the given values are from a
discrete or continuous data set.
– A statistics professor counts 3 absent students.
– A statistics professor finds that on the first test, the first paper
is turned in 39.627 minutes after the test began.
– In a survey of 1068 Americans, 73 state that they own
answering machines.
– A manufacturer of rechargeable calculator batteries finds that
one batch consists of 850 good batteries and 7 that are
defective.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 nominal level of measurement
•
characterized by data that consist of
names, labels, or categories only. The data
cannot be arranged in an ordering scheme
(such as low to high)
• Example: survey responses yes, no,
undecided
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 ordinal level of measurement
•
involves data that may be arranged in some
order, but differences between data values
either cannot be determined or are meaningless
• Example: Course grades A, B, C, D, or F
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 interval level of measurement
•
like the ordinal level, with the additional
property that the difference between any two data
values is meaningful. However, there is no
natural zero starting point (where none of the
quantity is present)
• Example: Years 1000, 2000, 1776, and 1492
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 ratio level of measurement
•
the interval level modified to include the
natural zero starting point (where zero indicates
that none of the quantity is present). For values
at this level, differences and ratios are
meaningful.
• Example: Prices of college textbooks
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Levels of Measurement
 Nominal - categories only
 Ordinal - categories with some order
 Interval - differences but no natural
starting point
 Ratio - differences and a natural starting
point
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Uses of Statistics
 Almost
all fields of study benefit
from the application of statistical
methods
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Abuses of Statistics
 Bad Samples
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
self-selected survey
• (or voluntary response sample)
•
one in which the respondents themselves decide whether
to be included
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Abuses of Statistics
 Bad Samples
 Small Samples
 Loaded Questions
 Misleading Graphs
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Figure 1-1 Salaries of People with Bachelor’s Degrees and with
High School Diplomas
$40,500
$40,500
$40,000
$40,000
35,000
30,000
30,000
20,000
$24,400
25,000
20,000
$24,400
10,000
0
Bachelor High School
Degree Diploma
(a)
Bachelor High School
Degree Diploma
(b)
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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We should analyze the
numerical information given
in the graph instead of being
mislead by its general shape.
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Abuses of Statistics




Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
 Pictographs
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Double the length, width, and height of a cube,
and the volume increases by a factor of eight
Figure 1-2
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Abuses of Statistics
 Bad Samples
 Small Samples
 Loaded Questions
 Misleading Graphs
 Pictographs
 Precise Numbers
 Distorted Percentages
 Partial Pictures
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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“Ninety percent of all our cars
sold in this country in the last 10
years are still on the road.”
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Abuses of Statistics








Bad Samples
Small Samples
Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
 Deliberate Distortions
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Observational Study
observing and measuring specific
characteristics without attempting to modify
the subjects being studied
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Experiment
apply some treatment and then observe its
effects on the subjects
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Designing an Experiment
 Identify your objective
 Collect sample data
 Use a random procedure that
avoids bias
 Analyze the data and form
conclusions
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Confounding
occurs in an experiment when the effects
from two or more variables cannot be
distinguished from each other
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Replication
used when an experiment is repeated on a
sample of subjects that is large enough so that
we can see the true nature of any effects
(instead of being misled by erratic behavior of
samples that are too small)
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Random Sample
members of the population are selected in
such a way that each has an equal chance of
being selected
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions
 Random Sample
members of the population are selected in
such a way that each has an equal chance of
being selected
 Simple Random Sample (of size n)
subjects selected in such a way that every
possible sample of size n has the same
chance of being chosen
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Random Sampling - selection so that
each has an equal chance of being selected
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Systematic Sampling - Select some
starting point and then select every K th element in
the population
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Convenience Sampling - use results
that are readily available
Hey!
Do you believe
in the death
penalty?
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Stratified Sampling - subdivide the
population into subgroups that share the same
characteristic, then draw a sample from each
stratum
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Cluster Sampling - divide the population
into sections (or clusters); randomly select some of
those clusters; choose all members from selected
clusters
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Methods of Sampling
 Random
 Systematic
 Convenience
 Stratified
 Cluster
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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Definitions

•

•
Sampling Error
the difference between a sample result and the true population
result; such an error results from chance sample fluctuations.
Nonsampling Error
sample data that are incorrectly collected, recorded, or analyzed
(such as by selecting a biased sample, using a defective instrument,
or copying the data incorrectly).
Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
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