National Council of Teachers of MathematicsSan Diego,

April 21 – 24, 2010

“E St d t ith R l“Engage Students with Real World Data Analysis”World Data Analysis

Dr. Janet M WinterPenn State University

Reading PAReading, PA.jmw11@psu.edu

General InformationGeneral Information

• 3000 students at Penn State Berks3000 students at Penn State Berks• Located in Reading PA, which is 50 miles

north west of Philadelphianorth west of Philadelphia• Most students complete 2 years at Berks

d t f t U i it P kand transfer to University Park• Less than 20% live on campus• Approximately 250 statistics/ year at Berks• Approximately 35 students/sectionApproximately 35 students/section

Background of Students:Background of Students:

Understand basic algebra

Miscellaneous non-technical majors

Celebrate Earth DayCelebrate Earth Day

Power point will be available shortly at:Power point will be available shortly at:http://www.bk.psu.edu

Use link : Faculty StaffUse link: Faculty DirectoryJanet WinterJanet Winter

Why Real Data?Why Real Data?• Higher interest levelg

• Engage Students• Engage Students

• Make Connections

• Reinforce current events or historically important eventsimportant events

Simple Ways to Collect Data:

• Collect it from your class!Collect it from your class!

Fi d it! (W b i )• Find it! (Web, newspaper, magazine)

• Look it up! (Data worth remembering)

Spontaneous Data CollectionSpontaneous Data Collection

• SurveysSurveys• Hand raising

St d t d t iti• Students record answers to non-sensitive questions on the board

• Conduct an experiment and record the results

• Students record answers on cards

Surveys:Surveys:• How many hours did you sleep last night?How many hours did you sleep last night?• How many hours did you watch TV last

night?g• Do you drink soda daily?• How many hours did you study this week?y y y• How much do you pay for your cell phone ?• Do you have access to a car?Do you have access to a car?• Do you have an i-phone?• How much did you spend on your books?How much did you spend on your books?

Hand Raisers for Proportion Questions!

– Did you ever attend an opening season ballDid you ever attend an opening season ball game?

– Do you have a car on campus?

– Did you get the flu this year?

– Do you exercise 5 or more hours each week?

Hand Raisers for Chi SquareHand Raisers for Chi Square

Select your favorite flavor of ice cream:Select your favorite flavor of ice cream: vanilla, chocolate, strawberry, peach, cookies & cream? (Chi-Square)cookies & cream? (Chi Square)

S l t f it f t f d t tSelect your favorite fast food restaurant:MacDonald’s, Wendy’s, Arby’s, Red Robin,(Chi Square)

Compare Class Data to Stated percents

Place Your Mark: First Twenty Students

Are you registered to vote?Are you registered to vote?Male Female

Y N Y NYes No Yes No

Difference in Two Proportions: M WMen vs Women

Place Your Mark: First Twenty Students

Are you taking summer classes?Are you taking summer classes?Freshmen Upper Classmen

Y N Y NYes No Yes No

Difference in Two Proportions: M WMen vs Women

Place Your Mark: First Twenty Students

Did you get a flu shot?Did you get a flu shot?Male Female

Y N Y NYes No Yes No

Difference in Two Proportions: M WMen vs Women

Place Your Mark: First Twenty Students

Do you wear a seat belt?Do you wear a seat belt?Male Female

Y N Y NYes No Yes No

Difference in Two Proportions: M WMen vs Women

Place Your Mark: First Twenty Students

Are you employed more than 20Are you employed more than 20 hrs/week?

Dorm Student Living off CampusDorm Student Living off CampusYes No Yes No

Difference in Two Proportions: Men vs WomenMen vs Women

Record an AnswerFirst 10 Students

• How many credits are you taking?How many credits are you taking?• How many miles are on the car you

regularly drive?regularly drive?• How much money are you carrying?• How long did you sleep last might?• What is your BMI?y

Average for One Sample

Use gender living arrangementsUse gender, living arrangements, employment, etc to divide the class into two groups to have data for the Difference in Twodata for the Difference in Two Averages

Tell Me your Difference• Find your pulse• Time 1 minute; students count their pulseTime 1 minute; students count their pulse• Every one jumps three times

Fi d l i• Find your pulse again• Time 1 minute; students count again• Tell me the difference : your after jumping

pulse minus your before jumping pulse p y j p g prate

• Paired Difference Test or Confidence Interval

Ways to Cut Back the DataWays to Cut Back the Data …

• Use data from a systematic sample withUse data from a systematic sample with about 10 students for the math

• First students in the room

• First folks finished with a problemp

First 10 students: Plot a Dot and Record your Ordered Pair

• Hrs studied and grade on last testHrs studied and grade on last test• Height /weight

F t L th h i ht• Foot Length vs height

Regression/Correlation Problems

Data from the Web, Newspapers, orother printed sources :

Printed Graphs and Statistics Worth Using

USA Today Snapshots

Misleading Graph Assignment:Misleading Graph Assignment:

Use newspapers magazines and otherUse newspapers, magazines, and other printed matter. Find three misleading graphs Provide a copy of each graph andgraphs. Provide a copy of each graph and at least one reason it is misleading.

Vocabulary Applications from USA Today Snapshots

• State a definitionState a definition– Students can memorize it

• Apply a definition– Students must understand it

List the population, sampling method, sample, at least one variable, andp , ,

two statistics.

List the population, sampling method, sample, at least one variable, andsample, at least one variable, and

two statistics.

List the population, sampling method, sample, at least one variable, andsample, at least one variable, and

two statistics.

If students have trouble withIf students have trouble with snapshots, use an p ,intermediate set of examples

Officials at the Golden State Performing Arts Center are concerned about theArts Center are concerned about the patrons’ perception of air quality in the center. Using a table of random numbers gand seat numbers, officials identify 30 people attending an event and ask them to rate air quality in the center using a scale 1-5 with 1 being the best and 5 the

t Th f th 30 ti iworst. The average of the 30 ratings is 3.7. For this situation list: the population, the sample the sampling method datathe sample, the sampling method, data, a parameter, and a statistic.

The registrar is concerned about registration problems Using a list of allregistration problems. Using a list of all registered students and a table of random numbers she randomly selectsrandom numbers, she randomly selects 15 freshmen, 12 sophomores, 10 juniors, and 5 seniors. She interviews these students asking them detailed questions about their registration experience for

O 2this semester. Only 2 students reported any difficulties. For this situation list: the population the sample the samplingpopulation, the sample, the sampling method, data, a parameter, and a statisticstatistic.

Assignment:Assignment:

Find a USA Today snapshots in the newspaper orFind a USA Today snapshots in the newspaper or online.

List the population, sampling method, sample, at least one variable, and two statistics.,

Historical ConnectionsHistorical Connections

Leonardo da VinciLeonardo da Vinci• "Renaissance man”Renaissance man

f th t t i t f ll ti• one of the greatest painters of all time

the most diversely talented person ever to have lived

The Last SupperThe Last Supper

Vitruvian ManVitruvian Man

The Vitruvian Man on the EuroThe Vitruvian Man on the Euro

The Skylab 3 patch shows a Vi i M i h l b dVitruvian Man, with a globe and

sun in rear

ANDAND…….

• Correlation and Regression data gatheringCorrelation and Regression data gathering opportunities………

The Perfect Person:The Perfect Person:• a palm is the width of four fingers

• a foot is the width of four palms (i.e. 12 inches) p ( )

• the length of a man's outspread arms is equal to his height

• the distance from the hairline to the bottom of the chin is one-tenth of a man's height

• the distance from the top of the head to the bottom of the chin is one-eighth of a man's height

• the maximum width of the shoulders is a quarter of a man's heightthe maximum width of the shoulders is a quarter of a man s height

• the distance from the elbow to the tip of the hand is one-fifth of a man's height

• the distance from the elbow to the armpit is one-eighth of a man's height p g g

• the length of the hand is one-tenth of a man's height

• the distance from the bottom of the chin to the nose is one-third of the length of the head

• the distance from the hairline to the eyebrows is one-third of the length of the face

• the length of the ear is one-third of the length of the face

Historical ProblemsHistorical Problems

• In initial tests of the Salk vaccine 33 ofIn initial tests of the Salk vaccine, 33 of 200,000 vaccinated children later developed polio Of 200 000 children givendeveloped polio. Of 200,000 children given the placebo, 115 later developed polio. At the 0 01 significance level test the claimthe 0.01 significance level, test the claim that the Salk vaccine is effective in lowering the polio ratelowering the polio rate.

News connection:News connection:

• 2010 Report: n = 6100 adults2010 Report: n = 6100 adults 16% of adults total daily caloric intake was from added sugarsfrom added sugars

• 1977-1978 Report: 11% of adults total daily caloric intake was yfrom added sugars

Not Enough informationNot Enough information

• Unless we make an assumption about theUnless we make an assumption about the sample size for the for the 1977-78

• Or look up the previous study

Groups of 4/5: add a question: • Survey question- Miscellaneous• Hand Raiser Yeah or nay questions• Hand Raiser – Yeah or nay questions,

qualitative variables (one proportion)Pl Y M k S t i t t• Place Your Mark – Separate into two or more groups then yeah or nay questions

• Record an answer – quantitative variable questions (Mean, Variance, ANOVA)

• Plot a dot- bi-variate quantitative data (Regression/correlation)( g )

• Tell me your difference (Matched pairs)

All work will be postedAll work will be posted

Power point will be available shortly at:Power point will be available shortly at:http://www.bk.psu.edu

Use link : Faculty StaffUse link: Faculty DirectoryJanet WinterJanet Winter

Our Common GoalOur Common Goal

• Use data from class, the web, the newspaper to involve students and getnewspaper to involve students and get them connected to statistics and the data that has changed the worldthat has changed the world.

Enjoy the Conference!Enjoy the Conference!

• I hope you leave San Diego with a barrelI hope you leave San Diego with a barrel of ideas to motivate and engage students

• It is not a matter of choice. Our students’ f t d t ’ f t d dfuture and our country’s future depends on us!

Questions for Class Data Collection Introductory Survey Questions

Applications: Identifying types of variables; Descriptive data projects How many hours did you sleep last night? How many hours did you watch TV last night? Do you drink soda daily? How many hours did you study this week? How much do you pay for your cell phone? Do you have access to a car? Do you have an i-phone? How much did you spend on your books? How many hours do you work in a week? How many text messages did you send yesterday? How many text messages did you receive yesterday? How many phone calls did you make yesterday? How many different places have you lived? Are you left or right handed? Have you purchased the required textbook? How much did you pay for your last haircut? Did you eat breakfast this morning? How many face book friends do you have? How many college applications did you complete? How many college acceptances did you receive? Do you text while driving?

Hand Raisers for One Proportion or two Proportions; Categorical Data with two or more levels Applications: One Proportion, Two proportions, Chi-Square Tests or Graphing qualitative variables One Proportion; use gender, handedness, etc to separate the data into two groups Did you ever attend an opening season ball game? Do you have a car on campus? Did you get the flu this year? Do you exercise 5 or more hours each week? Are you registered to vote? Are you taking summer classes? Did you get the flu shot? Do you wear a safety belt? Do you like to swim? Have you ever skied? Have you ever gone fishing? Did you ever paddle a canoe? Does anyone in your family hike? Do you play an instrument? Do you have allergies? Do you get poison ivy? Can you ice skate?

Have you ever surfed? Have you been to Europe? Do you want to travel to Europe? “Place Your Mark” Chi Square Goodness of fit test: What is your favorite ice cream? (Vanilla, chocolate, strawberry, cookies & cream, peach) What is your favorite flavor jello? (Cherry, lime, orange, strawberry) Which pizza do you prefer? (Pizza Hut, Dominos, Papa Murphy’s) What is your favorite music? (Jazz, Rapp, Country,) Where you born in the spring, summer, fall, or winter? Who is the best outfielder in baseball? (Juan Rivera, Torrey Hunter, etc) What month were you born? What is your favorite subject? (Math, science, English, history) Did you ever attend an opening season ball game? Compare class data to the USA today Snapshots. How do your parents commute to work?

Plot- a-Dot ( bivariate continuous quantitative data) Applications: Scatter plots; regression/correlation Hours worked, hours studied /week Hours studied/grade on last test Foot length/height Height/weight Arm span/height Palm length/Width of four fingers Hairline to the bottom of your chin/height Top of head to the bottom of the chin/height Maximum width of your shoulders/height Measurement of your elbow to the tip of your hand/height Distance from your elbow to your armpit/height Length of your hand/height Distance from the bottom of your chin to your nose/length of your head Distance from your hairline to your eyebrows/ length of your face Length of your ear/length of your face

Record Your Answer Applications: Mean, variance/standard deviation How many times do you eat a home cooked meal eat week? How many nights each week does your family sit around the dinner table together? How many AP classes are you taking? How many different houses or apartments have you ever lived? How many people are in your immediate family? What is your height? What is your shoe size? How much do you earn each week? How many texts did you send last night? How many tattoos do you have? How many piercings do you have? How many credits are you taking? How many miles are on the car you regularly drive? How much money are you carrying? How long did you sleep last night? What is your BMI? Tell Me Your Difference - Paired Answers Squeeze a bathroom scale with left and right hand Toss and item into a target with left/right hand Pulse Before/after jumping

Process: • Find your pulse • Teacher times 1 minute while students count their pulse • Every one jumps three times • Students find their pulse again. • Time 1 minute; students count their pulse gain • Tell me the difference : your after jumping pulse minus your before jumping pulse rate

Ways to separate the class into two groups Gender Left/right handed Upper Classmen/Lower Classmen Employed/Unemployed Even/odd last digit of cell phone number Employed 20 or fewer hours each week/employed more than 20 hours each week

Ways to Cut Back the Data • Use data from a systematic sample with data from about 10 students for the math • Use the First 10 students in the room • Select the first folks finished with a problem

Historical Problems

• In initial tests of the Salk vaccine, 33 of 200,000 vaccinated children later developed polio. Of 200,000 children given the placebo, 115 later developed polio. At the 0.01 significance level, test the claim that the Salk vaccine is effective in lowering the polio rate.

April 22, 2010 News

2010 Report: n = 6100 adults 16% of adult’s total daily caloric intake was from added sugars

1977-1978 Report: 11% of adult’s total daily caloric intake was from added sugars Since this information is missing the sample size for the 1977-1978 report, it would not be useful for class. Assume both studied has the same sample size for class work.