ap statistics semester i ago-dic 2009 ii

8/14/2019 AP Statistics Semester i Ago-dic 2009 II

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APAP

SEMESTER I AGO-DICSEMESTER I AGO-DIC

20092009I il rtizISC Gil Ortiz


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SOCRATES469 / 470 BC - 399 BC

Socratic Ignorance

"I know that I know nothing"


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STATISTICS HISTORYSome scholars pinpoint the origin of

statistics to 1662, with the publicati

onofNatural and Political Observations

upon the Bills of Mortalityby JohnGraunt.Its mathematical foundations were

laid in the 17th century with thedevelopment of probability theory by

Blaise Pascal and Pierre de Fermat.Probability theory arose from the

study of games of chance. Themethod of least squares was firstdescribed by Carl Friedrich Gauss


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STATISTICS

Early applications of statisticalthinking revolved around the needsof states to base policy ondemographic and economic data,

hence its stat- etymology. The scopeof the discipline of statisticsbroadened in the early 19th centuryto include the collection and analysisof data in general.

The term statistics is ultimately

derived from the New Latinstatisticum collegium ("council ofstate") and the Italian word statista("statesman" or "politician").

Today, statistics is widely employedin government, business, and the


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INTRO TO STATISTICSWHAT IS STATISTICS ? VID


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Resources

www.collegeboard.com

www.whfreeman.com/tps3e

Register to take Online Quizzes Send me the result

[email protected]

www.ti.com


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"Imagination is more important thanknowledge."


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Einsteins RiddleALBERT EINSTEIN WROTE THISRIDDLE EARLY DURING THE 19thCENTURY. HE SAID THAT 98% OF

THE WORLD POPULATION WOULDNOT BE ABLE TO SOLVE IT.ARE YOU IN THE TOP 2% OFINTELLIGENT PEOPLE IN THEWORLD?

SOLVE THE RIDDLE AND FIND OUT.


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There are no tricks, just pure logic,so good luck and don't give up.

1. In a street there are five houses,painted five different colours.

2. In each house lives a person ofdifferent nationality3. These five homeowners each drinka different kind of beverage, smoke

different brand of cigar and keep adifferent pet.

THE QUESTION: WHO OWNS THE

FISH?


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HINTS1. The Brit lives in a red house.

2. The Swede keeps dogs as pets.

3. The Dane drinks tea.4. The Green house is next to, and on the left ofthe White house.

5. The owner of the Green house drinks coffee.6. The person who smokes Pall Mall rears birds.

7. The owner of the Yellow house smokes Dunhill.8. The man living in the centre house drinks milk.9. The Norwegian lives in the first house.10. The man who smokes Blends lives next to the onewho keeps

cats.

11. The man who keeps horses lives next to the manwho smokes

Dunhill.12. The man who smokes Blue Master drinks beer.13. The German smokes Prince.

14. The Norwegian lives next to the blue house.15. The man who smokes Blends has a neighbourwho


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Einstein's Riddle - ANSWER

The German owns the fish.


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"Do not worry about your difficulties in

Mathematics.I can assure you mine are still greater."


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Fundamental DefinitionsStatistics

Population

Sample


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STATISTICS:STATISTICS:

FundamentalFundamentalDEFINITIONS

Like any new field, you have to learn thevocabulary in order to understand what isgoing on. In the beginning it seems like alot because the terms may be unfamiliar or

they may be words that you know but theyare used in a different way. There is no wayaround it but to memorize the meanings.Its like with a foreign language. You justhave to learn what the new words mean.


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Definition: Statistics refers to a set ofmethods and rules for organizing ,summarizing and interpreting information.


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POPULATIONS AND SAMPLES

In research, we are trying to find outgeneral information about a class of people.(e. g. why do people commit crimes?) As a

researcher, I want to know something aboutpeople in general. This group of people ingeneral is called a population.

Definition: A population is the set of allindividuals of interest in a particular study.E. g. All people in the United StatesAll students in schoolStudents in 3rd Semester


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Population

You want to know how many people in Mexicoprefer Coke over Pepsi Define the Population:

Give another example of population:


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All individuals in the U. S. is not only a largesample, it is a very diverse sample hard to findfactors that relate to them all.I could not include every individual from the

group in my study. So I want to take a samplefrom the population and hope it would represent

the whole group.

Definition: A sample is a set of individualsselected from a population, usually intended to

represent the population in a research study


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Definition: A sample is a set of individualsselected from a population, usually intended torepresent the population in a research study.

How would you Sample all people in the US?

Sample for Cola drinkers in Mexico?

Sample your own example:


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When we describe information, we usedifferent terms to represent populations andsamples.

Definition: A parameter is a value which

describes a population.Define a parameter in the Cola drinkers in

Mexico:

Define a parameter in your example:

Definition: A statistic is a value whichdescribes a sample.

Define a statistic in the Cola drinkers inMexico:


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Once we have data, there are two things we cando with it. We can describe it and we can use itto make generalizations from it. These are thetwo different roles of statistics.

Definition: Descriptive statistics are statistical

procedures that summarize, organize andsimplify data. Write an example:

Definition: Inferential statistics are techniques

that allow us to study samples and then makegeneralizations about the populations fromwhich they were selected.

Write an example:


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There is usually some difference between the

way the sample looks and the way thepopulation looks. This difference is known assampling error

Definition: Sampling erroris the discrepancythat exists between the sample statistic and thepopulation parameter. (e. g. margin of errorin voters polls).

Write an example:

We want to reduce sampling error whenever


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One way that we use to try to insure that our

sample is representative is to use randomselection

Definition: Random selection or random

samplingis a process for obtaining a samplefrom a population that requires that everyindividual in the population have the samechance of being selected for the sample. A

sample obtained by this method is called arandom sample.


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he Scientific Method

The scientific method is a process for studyingbehavior that relies on objectivity. It requiresthat we try to eliminate personal biases frominfluencing the outcome of our studies.

Theory - Hypothesis data collection


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Definition: Theory an integrated andoverarching set of principles that explain and

predicts phenomena

Definition: Hypothesis a specific testableprediction (usually) derived from a theory


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Mean, Median, Mode, and

The "mean" is the "average" you're used to,where you add up all the numbers and thendivide by the number of numbers.

The "median" is the "middle" value in the list ofnumbers. To find the median, your numbershave to be listed in numerical order, so youmay have to rewrite your list first.

The "mode" is the value that occurs mostoften. If no number is repeated, then there isno mode for the list.The "range" is just the difference between the

lar est and smallest values.


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Example for Mean, Median, Mode, andRange

Find the mean, median, mode, and range for

the following list of values:13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 +

13) 9 = 15

The median is the middle value, so we have to

rewrite the list in order:13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so themiddle one will be the (9 + 1) 2 = 10 2 =

5th number:


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The mode is the number that is repeated more

often than any other, so 13 is the mode.

The largest value in the list is 21, and thesmallest is 13, so the range is 21 13 = 8.

mean: 15median: 14mode: 13

range: 8


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M&Ms Activity


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DATA PRODUCTION


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Producing dataSurveySurveys are popular ways to gauge public opinionThe idea of a survey: Select a sample of people to represent a larger population. Ask the individuals in the sample some questions and

record their responses. Use sample results to draw some conclusions about the

population.

Observational study

In an observational study, we observe individuals andmeasure variables of interest but do not attempt toinfluence the responses.

ExperimentIn an experiment, we deliberately do something to

individuals in order to observe their responses.


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Example Observational

Census

Phone survey

Vaccines

Interview

Comparing two drugs

Exam

PAAR students


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Exercise Observational-

Design an Observational Study.Question?

Population?

Sample?

Data production?

Analisys?

Conclusion?

Design an Experiment.Question?


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Homework Exercises(from pg 11)P1

P2

P3

P4

P5


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DATA ANALYSIS


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Individuals and VariablesIndividuals are the objects described by a set of data

(people, animals, things).

Variables are any characteristics of an individual. Avariable can take different values for differentindividuals.Categorical variable. Places an individual into one of

several groups or categories.

Quantitative variable. Takes numerical values forwhich arithmetic operations (adding, average) makesense.

Id: Individuals, Variables (Categorical/Quantitative)


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Distribution

The Distribution of a variable tells us whatvalues the variable takes and how often it takesthese values.

Describing Categorical variables


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Describing Categorical variables

Bar graph

Side-by-side Bar graph

Do you wear your seat belt?


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Describing Quantitative variablesDotplot

Use your TI 84 plus

Find Mode:

Mean:

Median:

Range:

Graph the distribution


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Exploring Relationships between variables


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Many relationships between two variablesare influenced by other variables lurking in the


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Comparing the percents of delayed flightsfor the two airlines at five airports.


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EXERCISESP.7

P.8

P.9

P.10

P.12

Class Exercises(from pg 19)


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PROBABILITY

P b bilit Wh t th


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Probability: What are the

When you toss a coinWhat is the probability of getting heads?

Probability: what happens in the long run.Number of

ProportionofH


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The Big idea of

Chance behavior is unpredictable in the shortrun,

but has a regular and predictable pattern inthe long run.


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Games of Chance:

Texas Hold em Black jack RouletteDice

Probability quantifies the pattern of chance


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Basic Probability

The probability for a given event can be thought ofas the ratio of the number of ways that event canhappen divided by the number of ways that anypossible outcome could happen. If we identify theset of all possible outcomes as the "sample space"and denote it by S, and label the desired event asE, then the probability for event E can be written

How Likely? = What is the Probability?

Rolls in Craps


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Rolls in Craps

iE: BettingWhat is theProbability?


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The following chart shows the dice combinations needed to roll


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Exploring Probability.

Playing Cards, Dice, Spinners,


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STATISTICAL INFERENCE


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Drawing Conclusions

Have you ever cheated on a test or exam?Yes 48%

Internet survey of 1200 students, aged 13 to 17,between January 23 and February 10, 2003.

If all 13 to 17 year-old students were asked thesame question, would exactly 48% have answeryes?

What about with a second sample or a thirdsample?


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Probability provides a description of how the Sampleresults will vary in relation to the true Population

percent.We rely on Probability to help us answer research

questions with a known degree of confidence.

Based in the Sampling method in the previous example,we can say the estimate of 48% is very likely to be withinthe 3% of the true Population percent.

That is, we can be confident that between 45% and 51%of all teenage students would say that they have cheatedon a test.

Statistical Inference allows us to use the results ofproperly designed experiments and observetional


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REVIEW EXERCISESExercises. P13, P14, P17, P18Chapter Exs. P19,P20, P22, P23, P26

On-line Quiz. *20% First Period gradeChapter P: What is Statistics?www. whfreeman.com/tps3eRegister as a Student

Instructor e-mail

ap statistics semester i ago-dic 2009 ii

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