MAT 102: Intro to Statistics
The Greatest Last-Place Finish Ever!
Mexico, 1968
John Stephen Akhwari of Tanzania
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The Greatest Last-Place Finish Ever!
Mexico, 1968
Out of the cold darkness he came. John Stephen
Akhwari of Tanzania entered at the far end of the
stadium, pain hobbling his every step, his leg bloody
and bandaged. The winner of the marathon had been
declared over an hour earlier. Only a few spectators
remained. But the lone runner pressed on.
As he crossed the finish line, the small crowd
roared out its appreciation. Afterward, a reporter
asked the runner why he had not retired from the
race, since he had no chance of winning. He seemed
confused by the question. Finally, he answered:
"My country did not send me to Mexico City to
start the race. They sent me to finish."
A Statistical Short Story!
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Have you heard the story about
Malcom Forbes, who once got lost
floating for miles in one of his
famous balloons, and finally landed
in the middle of a cornfield?
He spotted a man coming toward
him and asked, “Sir, can you tell me
where I am?”
The man said, “Certainly, you are in
a basket in a field of corn.”
Forbes said, “You must be a
statistician.”
 The man replied, “That’s
amazing, how did you know
that?”
 “Easy,” said Forbes, “your
information is concise, precise,
and absolutely useless!”
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The purpose of this course
is to convince you that
information resulting from
a good statistical analysis
is always concise, often
precise, but NEVER
USELESS!
Why Study Statistics?
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So why is statistics required in
so many majors?
One reason is that numerical information is
everywhere. Look in the newspapers (USA
Today), news magazines (Time, Newsweek,
U.S. News and World Report), business
magazines (BusinessWeek, Forbes), or general
interest magazines (People), women’s
magazines (Ladies Home Journal or Elle), or
sports magazines (Sports Illustrated, ESPN
The Magazine), and you will be bombarded
with numerical information!
Yes, Data are everywhere!
 Let’s take a look at some
interesting statistics I
found on the Internet!
Before we answer the
question: What is
Statistics?
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Internet Statistical Examples
 40% of women have hurled
footwear at a man.
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27% admit to cheating on an
exam or quiz.
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When nobody else is around,
47% drink straight from the
carton.
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10% of us claim to have seen a ghost.
Last semester, my students had the
same reaction the first day of stat
class!
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2008 Opening Day salary for Major
League Baseball Players is
$3.15 million!
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Average Major League Baseball
Career Is 5.6 Years!
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The average career of a Major League Baseball
player is 5.6 years, according to a new study by a
University of Colorado at Boulder research team.
The study examined the career statistics of
baseball players who started their careers between
1902 and 1993. Pitchers were excluded because
of their unique positions, career volatility and
propensity for injuries. Between 1902 and 1993,
5,989 position players started their careers and
played 33,272 person years of Major League
Baseball. Using voluminous baseball statistics,
the authors then developed an average career
length for the players.
Chapter One
Definition : Statistics
 Statistics involves the procedures associated
with the data collection process, the
summarizing and interpretation of data, and
the drawing of inferences or conclusions based
upon the analysis of the data.
Branches of Statistics
Essentially the study of statistics involves:
describing the main characteristics of raw
data
as well as
drawing conclusions from the data based
upon the analysis of the data.
From this point of view, statistics can thus be
subdivided into two branches:
1)
Descriptive Statistics
and
2) Inferential Statistics
Descriptive Statistics
 Descriptive Statistics: uses
numerical and/or visual
techniques to summarize or
describe the data in a clear and
effective manner.
 Let’s look at an example of
Descriptive Statistics.
Descriptive Statistics Example
Descriptive Statistics describes the
basic features of a data set.
 In the NHL: a growth industry, the
large amounts of data pertaining to
height and weight of every NHL
player was described in a sensible
way. The descriptive statistic reduced
lots of data into a simpler summary:
one number for the height & one
number representing the weight of
the NHL players.
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Some Example of Descriptive Statistics
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Batting Average:
a simple number used to summarize how well a
batter is performing in baseball. This single number
is simply the number of hits divided by the number
of times at bat (reported to three significant digits).
A batter who is hitting .333 is getting a hit one time
in every three at bats. One batting .250 is hitting one
time in four. The single number describes a large
number of discrete events.
Grade Point Average (GPA).
This single number describes the general
performance of a student across a potentially wide
range of course experiences.
Caution!
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When describing a large data set of observations
with a single statistic runs the risk of distorting
the original data or losing important detail.
For example:
The batting average doesn't tell you whether the
batter is hitting home runs or singles. It doesn't
tell whether she's been in a slump or on a streak.
The GPA doesn't tell you whether the student was
in difficult courses or easy ones, or whether they
were courses in their major field or in other
disciplines.
Given these limitations, descriptive statistics still
provides a powerful summary that may enable
comparisons across people or other units.
Inferential Statistics
Inferential Statistics: is the branch of
statistics that involves drawing
conclusions about a large group,
called a population, based on the
analysis of a smaller group of data,
called a sample, collected from the
population.
 Let’s look at an example of
Inferential Statistics.
Inferential Statistics Example
According to a CNN/Gallup Poll
nationwide phone survey of 1,000 Adults
regarding leisure time:
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Inferential statistics is used to try to infer from a
portion of a data set what the entire data set
might think.
In the CNN/Gallup Poll, the pollsters are
inferring that 52% of the ALL (population)
adults living in the U.S. believe they do not
have enough leisure time. This inference is
based on the opinions of the 1,000 (sample)
adults in the phone poll. This is the essence of
inferential statistics. That is, the pollsters are
drawing a conclusion or inference about the
ALL (or population) of adults using the opinion
of a portion (or sample) of the population.
Population and Sample
Definition: Population
The Population is the entire collection
of all individuals or objects of
interest.
 Definition: Sample
The Sample is the portion of the
population that is selected for study.
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Researchers, pollsters and/or decision makers use
Inferential Statistics to draw conclusions or
inferences about a population.
Examples:
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A medical researcher wants to determine if large
doses of vitamin C are effective in combating colds.
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A market researcher wants to know in what
quantities the American consumer is willing to
purchase a new product.
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Pollsters want to estimate what percentage of the
American public approve of the death penalty to
curb crime.
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Researchers use a sample because it is usually
impractical or impossible to obtain all the population
observations or measurements.
Example: an electrical company wants to determine the
average life of their new 40 watt light bulb
Population: All the 40 watt bulbs the company
manufactures
Objective: To obtain the average life of the population
of light bulbs
Problem: To compute the population average life of
each bulb is impractical since they would not have
any bulbs left to sell!
Solution: It is necessary to select a representative
sample.
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Representative Sample
Similar to the "toothpick" technique used to determine if
a cake is completely baked. A toothpick is inserted in
several areas of the cake, and if the toothpick comes
out free of cake batter each time, it is concluded that
the entire cake is done.
Thus, the bulb manufacturer needs to select a sample
with similar characteristics as all the new 40 watt
light bulbs that can be used to make inferences about
the entire population.
Objective of Inferential Statistics
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To use sample information to estimate a population
characteristic. Thus it is imperative that the
researcher try to design a procedure to select a
sample which is representative of the population.
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DEFINITION: Representative sample
is a sample that has the pertinent characteristics of the
population in the same proportion, as they are
included in that population.
Let’s Summarize The Differences
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With descriptive statistics you are simply
describing the data set.
With inferential statistics, you are trying
to reach conclusions that extend beyond
the immediate data set.
Thus, we use inferential statistics to make
inferences from our data to more general
conditions; we use descriptive statistics
simply to describe what's going on in a
data set.
Is this an example of Descriptive
or Inferential Statistic?
Time for our own survey!
Are you enjoying this Stat class?
Before you answer, keep this in mind!
Parameter and Statistic
In the light bulb example, a sample was
selected and the sample average was
used to estimate the average life for all
the new 40 watt light bulbs.
When a number is used to describe a
characteristic of a sample, such as sample
average, this number is called a statistic.
The population average is an example of
a parameter since it describes a
population characteristic.
Definition: Statistic
A statistic is a number that describes a
characteristic of a sample.
 Definition : Parameter
A parameter is a number that describes a
characteristic of a population.
Thus, we can say that the concept of
inferential statistics is to use a sample
statistic (sample average of the bulbs) to
make inferences about a population
parameter (population average of the
bulbs).
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Example
An opinion poll of 1500 potential voters was
taken to estimate how all the 20,000 voters in
an election district will vote in the upcoming
election. The opinion poll results indicate that
52% will vote for the politician A in the
upcoming election.
 Population: The 20,000 voters
 Sample: 1500 potential voters polled
 Statistic: 52% is a statistic since it describes a
characteristic of the sample.
Bus Tour Traveler
NFL Weigh In
Money for big kids!
Who teens turn to with pressures
and problems!
Infertility Incidence
Women vote more!
Study in the Journal of the AMA states
teenage girls who supplement their diet with
extra serving of Calcium daily built stronger
bones!
Soyjoy Ad
Eating Jelly Beans causes an Unhealthy
Spike & Drop in Blood Sugar!