MAT 102: Intro to StatisticsMAT 102: Intro to Statistics

The Greatest Last-Place Finish Ever!The Greatest Last-Place Finish Ever! Mexico, 1968 Mexico, 1968

John Stephen Akhwari of Tanzania

The Greatest Last-Place Finish Ever!The Greatest Last-Place Finish Ever! Mexico, 1968 Mexico, 1968

      Out of the cold darkness he came. John Stephen Out of the cold darkness he came. John Stephen Akhwari of Tanzania entered at the far end of the Akhwari of Tanzania entered at the far end of the stadium, pain hobbling his every step, his leg bloody stadium, pain hobbling his every step, his leg bloody and bandaged. The winner of the marathon had been and bandaged. The winner of the marathon had been declared over an hour earlier. Only a few spectators declared over an hour earlier. Only a few spectators remained. But the lone runner pressed on.remained. But the lone runner pressed on.

      As he crossed the finish line, the small crowd As he crossed the finish line, the small crowd roared out its appreciation. Afterward, a reporter roared out its appreciation. Afterward, a reporter asked the runner why he had not retired from the asked the runner why he had not retired from the race, since he had no chance of winning. He seemed race, since he had no chance of winning. He seemed confused by the question. Finally, he answered:confused by the question. Finally, he answered:

      "My country did not send me to Mexico City to "My country did not send me to Mexico City to start the race. They sent me to finish."start the race. They sent me to finish."

A Statistical Short Story!A Statistical Short Story! Have you heard the story about Have you heard the story about

Malcom Forbes, who once got lost Malcom Forbes, who once got lost floating for miles in one of his floating for miles in one of his famous balloons, and finally famous balloons, and finally landed in the middle of a landed in the middle of a cornfield? cornfield?

He spotted a man coming toward He spotted a man coming toward him and asked, “Sir, can you tell him and asked, “Sir, can you tell me where I am?” me where I am?”

The man said, “Certainly, you are The man said, “Certainly, you are in a basket in a field of corn.” in a basket in a field of corn.”

Forbes said, “You must be a Forbes said, “You must be a statistician.” statistician.”

The man replied, “That’s The man replied, “That’s amazing, how did you know amazing, how did you know that?” that?”

““Easy,” said Forbes, “your Easy,” said Forbes, “your information is concise, information is concise, precise, and absolutely precise, and absolutely useless!”useless!”

The purpose of this The purpose of this course is to convince course is to convince you that information you that information resulting from a good resulting from a good statistical analysis is statistical analysis is always concise, often always concise, often precise, but NEVER precise, but NEVER USELESS!USELESS!

Why Study Statistics?Why Study Statistics? So why is statistics required in so So why is statistics required in so

many majors? many majors? One reason is that numerical information is One reason is that numerical information is

everywhere. Look in the newspapers everywhere. Look in the newspapers (USA (USA Today),Today), news magazines news magazines (Time, Newsweek, U.S. (Time, Newsweek, U.S. News and World Report),News and World Report), business magazines business magazines (BusinessWeek, Forbes),(BusinessWeek, Forbes), or general interest or general interest magazines magazines (People),(People), women’s magazines women’s magazines (Ladies Home Journal(Ladies Home Journal or or Elle),Elle), or sports or sports magazines magazines (Sports Illustrated, ESPN The (Sports Illustrated, ESPN The Magazine),Magazine), and you will be bombarded with and you will be bombarded with numerical information!numerical information!

Yes, Data are Yes, Data are everywhere! everywhere!

Let’s take a look at some Let’s take a look at some interesting statistics I interesting statistics I found on the Internet! found on the Internet! Before we answer the Before we answer the question: What is question: What is Statistics?Statistics?

Internet Statistical ExamplesInternet Statistical Examples 40% of women have hurled 40% of women have hurled

footwear at a man.footwear at a man.

27% admit to cheating on an exam 27% admit to cheating on an exam or quiz.or quiz.

When nobody else is around, 47% When nobody else is around, 47% drink straight from the carton.drink straight from the carton.

10% of us claim to have seen a ghost.10% of us claim to have seen a ghost.

Last semester, my students had the same Last semester, my students had the same reaction the first day of stat class!reaction the first day of stat class!

2008 Opening Day salary for Major 2008 Opening Day salary for Major League Baseball Players isLeague Baseball Players is

$3.15 million!$3.15 million!

Average Major League Baseball Average Major League Baseball Career Is 5.6 Years!Career Is 5.6 Years!

The average career of a Major League Baseball The average career of a Major League Baseball player is 5.6 years, according to a new study by a player is 5.6 years, according to a new study by a University of Colorado at Boulder research team. University of Colorado at Boulder research team.

The study examined the career statistics of baseball The study examined the career statistics of baseball players who started their careers between 1902 and players who started their careers between 1902 and 1993. Pitchers were excluded because of their 1993. Pitchers were excluded because of their unique positions, career volatility and propensity unique positions, career volatility and propensity for injuries. Between 1902 and 1993, 5,989 position for injuries. Between 1902 and 1993, 5,989 position players started their careers and played 33,272 players started their careers and played 33,272 person years of Major League Baseball. Using person years of Major League Baseball. Using voluminous baseball statistics, the authors then voluminous baseball statistics, the authors then developed an average career length for the players. developed an average career length for the players.

Chapter OneChapter One

Definition :Definition : StatisticsStatistics StatisticsStatistics involves the procedures associated involves the procedures associated

with the data collection process, the with the data collection process, the summarizing and interpretation of data, and summarizing and interpretation of data, and the drawing of inferences or conclusions based the drawing of inferences or conclusions based upon the analysis of the data.upon the analysis of the data.

Branches of StatisticsBranches of StatisticsEssentially the study of statistics involves:Essentially the study of statistics involves: describing the main characteristics of raw describing the main characteristics of raw

datadata as well as as well as drawing conclusions from the data based drawing conclusions from the data based upon the analysis of the dataupon the analysis of the data. .

From this point of view, statistics can thus be From this point of view, statistics can thus be subdivided into subdivided into two branchestwo branches::

1)1) Descriptive StatisticsDescriptive Statistics and and

2) Inferential Statistics2) Inferential Statistics

Descriptive StatisticsDescriptive Statistics Descriptive StatisticsDescriptive Statistics: uses : uses

numerical and/or visual techniques numerical and/or visual techniques to summarize or describe the data to summarize or describe the data in a clear and effective manner.in a clear and effective manner.

Let’s look at an example of Let’s look at an example of Descriptive Statistics.Descriptive Statistics.

Descriptive Statistics ExampleDescriptive Statistics Example

Descriptive Statistics describes the Descriptive Statistics describes the basic features of a data set. basic features of a data set.

In the NHL: a growth industry, the In the NHL: a growth industry, the large amounts of data pertaining to large amounts of data pertaining to height and weight of every NHL height and weight of every NHL player was described in a sensible player was described in a sensible way. The descriptive statistic reduced way. The descriptive statistic reduced lots of data into a simpler summary: lots of data into a simpler summary: one number for the height & one one number for the height & one number representing the weight of number representing the weight of the NHL players. the NHL players.

Some Example of Descriptive StatisticsSome Example of Descriptive Statistics Batting Average:Batting Average: a simple number used to summarize how well a a simple number used to summarize how well a

batter is performing in baseball. This single number batter is performing in baseball. This single number is simply the number of hits divided by the number is simply the number of hits divided by the number of times at bat (reported to three significant digits). of times at bat (reported to three significant digits). A batter who is hitting .333 is getting a hit one time A batter who is hitting .333 is getting a hit one time in every three at bats. One batting .250 is hitting one in every three at bats. One batting .250 is hitting one time in four. The single number describes a large time in four. The single number describes a large number of discrete events. number of discrete events.

Grade Point Average (GPA).Grade Point Average (GPA). This single number describes the general This single number describes the general

performance of a student across a potentially wide performance of a student across a potentially wide range of course experiences. range of course experiences.

Caution!Caution! When describing a large data set of observations When describing a large data set of observations

with a single statistic runs the risk of distorting the with a single statistic runs the risk of distorting the original data or losing important detail. original data or losing important detail.

For example:For example:The The batting averagebatting average doesn't tell you whether the doesn't tell you whether the batter is hitting home runs or singles. It doesn't batter is hitting home runs or singles. It doesn't tell whether she's been in a slump or on a streak. tell whether she's been in a slump or on a streak. The The GPAGPA doesn't tell you whether the student was doesn't tell you whether the student was in difficult courses or easy ones, or whether they in difficult courses or easy ones, or whether they were courses in their major field or in other were courses in their major field or in other disciplines. disciplines.

Given these limitations, descriptive statistics still Given these limitations, descriptive statistics still provides a powerful summary that may enable provides a powerful summary that may enable comparisons across people or other units.comparisons across people or other units.

Inferential StatisticsInferential StatisticsInferential Statistics:Inferential Statistics: is the branch of is the branch of

statistics that involves drawing statistics that involves drawing conclusions about a large group, called conclusions about a large group, called a a populationpopulation, based on the analysis of a , based on the analysis of a smaller group of data, called a smaller group of data, called a samplesample, , collected from the population. collected from the population.

Let’s look at an example of Inferential Let’s look at an example of Inferential Statistics.Statistics.

Inferential Statistics ExampleInferential Statistics ExampleAccording to a CNN/Gallup Poll nationwide phone

survey of 1,000 Adults regarding leisure time:

Inferential statistics is used to try to infer from a Inferential statistics is used to try to infer from a portion of a data set what the entire data set portion of a data set what the entire data set might think. might think.

In the CNN/Gallup Poll, the pollsters are In the CNN/Gallup Poll, the pollsters are inferring that 52% of the ALL (population) inferring that 52% of the ALL (population) adults living in the U.S. believe they do not adults living in the U.S. believe they do not have enough leisure time. This inference is have enough leisure time. This inference is based on the opinions of the 1,000 (sample) based on the opinions of the 1,000 (sample) adults in the phone poll. This is the essence of adults in the phone poll. This is the essence of inferential statistics. That is, the pollsters are inferential statistics. That is, the pollsters are drawing a conclusion or inference about the drawing a conclusion or inference about the ALL (or population) of adults using the opinion ALL (or population) of adults using the opinion of a portion (or sample) of the population.of a portion (or sample) of the population.

Population and SamplePopulation and Sample

Definition:Definition: PopulationPopulation

The The PopulationPopulation is the entire collection is the entire collection of all individuals or objects of of all individuals or objects of interest.interest.

Definition:Definition: SampleSample

The The SampleSample is the portion of the is the portion of the population that is selected for study.population that is selected for study.

Researchers, pollsters and/or decision makers use Researchers, pollsters and/or decision makers use Inferential Statistics to draw conclusions or Inferential Statistics to draw conclusions or inferences about a population. inferences about a population.

Examples:Examples: A medical researcher wants to determine if large A medical researcher wants to determine if large

doses of vitamin C are effective in combating doses of vitamin C are effective in combating colds.colds.

A market researcher wants to know in what A market researcher wants to know in what quantities the quantities the American consumer is willing to American consumer is willing to purchase a new product.purchase a new product.

Pollsters want to estimate what percentage of the Pollsters want to estimate what percentage of the American public approve of the death penalty to American public approve of the death penalty to curb crime.curb crime.

Researchers use a sample because it is usually Researchers use a sample because it is usually impractical or impossible to obtain all the population impractical or impossible to obtain all the population observations or measurements. observations or measurements.

Example:Example: an electrical company wants to determine the an electrical company wants to determine the average life of their new 40 watt light bulb average life of their new 40 watt light bulb

Population:Population: All the 40 watt bulbs the company All the 40 watt bulbs the company manufactures manufactures

Objective:Objective: To obtain the average life of the population To obtain the average life of the population of light bulbsof light bulbs

Problem:Problem: To compute the population average life of To compute the population average life of each bulb is impractical since they would not have each bulb is impractical since they would not have any bulbs left to sell! any bulbs left to sell!

Solution:Solution: It is necessary to select a It is necessary to select a representative representative sample.sample.

Representative SampleRepresentative Sample

Similar to the "toothpick" technique used to determine Similar to the "toothpick" technique used to determine if a cake is completely baked. A toothpick is inserted if a cake is completely baked. A toothpick is inserted in in several areasseveral areas of the cake, and if the toothpick of the cake, and if the toothpick comes out free of cake batter each time, it is comes out free of cake batter each time, it is concluded that the concluded that the entireentire cake is done. cake is done.

Thus, the bulb manufacturer needs to select a sample Thus, the bulb manufacturer needs to select a sample with similar characteristics as all the new 40 watt with similar characteristics as all the new 40 watt light bulbs that can be used to make inferences about light bulbs that can be used to make inferences about the entire population.the entire population.

Objective of Inferential StatisticsObjective of Inferential Statistics

To use sample information to estimate a population To use sample information to estimate a population characteristic. Thus it is imperative that the characteristic. Thus it is imperative that the researcher try to design a procedure to select a researcher try to design a procedure to select a sample which is representative of the populationsample which is representative of the population. .

DEFINITION: DEFINITION: Representative sampleRepresentative sampleis a sample that has the pertinent characteristics of the is a sample that has the pertinent characteristics of the population in the same proportion, as they are population in the same proportion, as they are included in that population.included in that population.

Let’s Summarize The DifferencesLet’s Summarize The Differences With descriptive statistics you are simply With descriptive statistics you are simply

describing the data set.describing the data set. With inferential statistics, you are trying With inferential statistics, you are trying

to reach conclusions that extend beyond to reach conclusions that extend beyond the immediate data set. the immediate data set.

Thus, we use inferential statistics to make Thus, we use inferential statistics to make inferences from our data to more general inferences from our data to more general conditions; we use descriptive statistics conditions; we use descriptive statistics simply to describe what's going on in a simply to describe what's going on in a data set.data set.

Is this an example of Descriptive Is this an example of Descriptive or Inferential Statistic?or Inferential Statistic?

Time for our own survey!Time for our own survey!Are you enjoying this Stat class?Are you enjoying this Stat class?

Before you answer, keep this in mind!Before you answer, keep this in mind!

Parameter and StatisticParameter and Statistic

In the light bulb example, a sample was In the light bulb example, a sample was selected and the selected and the sample averagesample average was was used used to estimateto estimate the the average lifeaverage life for for allall the new 40 watt light bulbsthe new 40 watt light bulbs. .

When a number is used to describe a When a number is used to describe a characteristic of a sample, such as sample characteristic of a sample, such as sample average, this number is called a average, this number is called a statisticstatistic. . The population average is an example of The population average is an example of a a parameterparameter since it describes a since it describes a population characteristic.population characteristic.

Definition: Definition: StatisticStatisticA A statisticstatistic is a number that describes a is a number that describes a

characteristic of a sample.characteristic of a sample. Definition : Definition : ParameterParameterA A parameterparameter is a number that describes a is a number that describes a

characteristic of a population.characteristic of a population.Thus, we can say that the concept of Thus, we can say that the concept of

inferential statistics is to use a sample inferential statistics is to use a sample statistic (sample average of the bulbs) to statistic (sample average of the bulbs) to make inferences about a population make inferences about a population parameter (population average of the parameter (population average of the bulbs). bulbs).

ExampleExampleAn opinion poll of 1500 potential voters was An opinion poll of 1500 potential voters was

taken to estimate how all the 20,000 voters in taken to estimate how all the 20,000 voters in an election district will vote in the upcoming an election district will vote in the upcoming election. The opinion poll results indicate that election. The opinion poll results indicate that 52% will vote for the politician A in the 52% will vote for the politician A in the upcoming election. upcoming election.

Population:Population: The 20,000 voters The 20,000 voters Sample:Sample: 1500 potential voters polled 1500 potential voters polled Statistic:Statistic: 52% is a statistic since it describes a 52% is a statistic since it describes a

characteristic of the sample.characteristic of the sample.

Bus Tour TravelerBus Tour Traveler

NFL Weigh InNFL Weigh In

Money for big kids!Money for big kids!

Who teens turn to with pressures Who teens turn to with pressures and problems!and problems!

Infertility IncidenceInfertility Incidence

Women vote more!Women vote more!

Study in the Journal of the AMA states Study in the Journal of the AMA states teenage girls who supplement their diet with teenage girls who supplement their diet with extra serving of Calcium daily built stronger extra serving of Calcium daily built stronger

bones!bones!

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Eating Jelly Beans causes an Unhealthy Eating Jelly Beans causes an Unhealthy Spike & Drop in Blood Sugar!Spike & Drop in Blood Sugar!