WARM UPJAKE IS A CAR BUFF WHO WANTS TO FIND OUT MORE ABOUT THE VEHICLES THAT STUDENTS AT HIS SCHOOL DRIVE. HE GETS PERMISSION TO GO TO THE STUDENT PARKING LOT AND RECORD SOME DATA. LATER, HE DOES SOME RESEARCH ABOUT EACH MODEL OF CAR ON THE INTERNET. FINALLY, JAKE MAKES A SPREADSHEET THAT INCLUDES EACH CAR’S MODEL, YEAR, COLOR, NUMBER OF CYLINDERS, GAS MILEAGE, WEIGHT, AND WHETHER IT HAS A NAVIGATION SYSTEM.

1.WHO ARE THE INDIVIDUALS IN JAKE'S STUDY?

2.WHAT VARIABLES DID JAKE MEASURE?

1.The individuals are the cars in the student parking lot.

He measured:2. the car's model (categorical)3.Year (Quantitative)4.Color (categorical)5.Number of cylinders (quantitative)6.Gas mileage (quantitative)7.Weight (quantitative)8.Whether it has a navigation system

(categorical)

OBJECTIVE

Today you will learn how to display categorical data with a bar graph. Decide if it would be appropriate to make a pie chart.

Identify what makes some graphs of categorical data deceptive.

Calculate and display the marginal distribution of a categorical variable from a two-way table.

Frequency TablesClass Counts

FirstSecondThirdCrew

325285706885

Records the totals and the category names

Relative Frequency TablesClass Counts

FirstSecondThirdCrew

14.77%12.95%32.08%40.21%

Displays percentages

6003000

Crew

Third

Second

First

900

The Area Principle says that the area occupied by a part of the graph should correspond to the magnitude of the value it represents.

First Second Third Crew0

100

200

300

400

500

600

700

800

900

1000

Bar ChartFr

equ

enc

y

Class

Pie Chart

First Second Third Crew

Third Class706

Second Class285

First Class325

Crew885

Bar Charts-Should have small spaces between the bars. Bars are lined up along a common base.

Pie Charts- Gives a quick impression of how a whole group is partitioned. Only use pie charts when you want to show the whole group of cases as a WHOLE.

Use a pie chart only when you want to emphasize each category’s relation to the whole.

Type of information

Percent who post

Photo of themselvesSchool nameCity or town where they liveEmail addressCell phone number

91

71

71

53

20

Here are the percentages of 12 to 17 year olds who post various types of personal information on their social media profiles, according the Pew Internet Parent/Teen Privacy Survey in 2012.

A pie chart would not be appropriate for these data because each percent in the table refers to a different type of information, not to parts of a whole.

Type of information

Percent who post

Photo of themselvesSchool nameCity or town where they liveEmail addressCell phone number

91

71

71

53

20

Make a well-labeled bar graph to display the data:

Photo of them-selves

School Name

City or town

where they live

Email address

Cell phone

number

0102030405060708090

100

Age group (years) Percent owning an

MP3 Player 12 to 17 54 18 to 24 30 25 to 34 30 35 to 54 13 55 and older 5

Ages 12-17

Ages 18-24

Ages 25-34

Ages 35-54

Ages 55 and older

0

10

20

30

40

50

60

Make a chart of the data. Would you use a bar chart or a pie chart?

Marginal Distribution- The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among ALL individuals described by the table.

Opinion Female Male Total

Almost no chance

96 98 194

Some chance 426 286 712

A 50-50 chance

696 720 1416

A good chance

663 758 1421

Almost certain

486 597 1083

Total 2367 2459 4826

Gender1.Use the data

in the two-way table to calculate the marginal distribution in percent.

2.Make a graph

You do: The Pew Research Center asked a random sample of 2024 adult cell phone owners from the United States which type of cell phone they own: iPhone, Android, or other (including non-smart phones). Her are the results by category.

18-34 35-54 55+ Total

iPhone 169 171 127 467

Android 214 189 100 503

Other 134 277 643 1054

Total 517 637 870 2024

Use the cell phone data to calculate the marginal distribution (in percents) of type of cell phone.

Make a graph to display the marginal distribution.iPhone: 467/2024=23.1%

Android: 503/2024= 24.9%Other: 1054/2024= 52.1%

iPhone Android Other0

10

20

30

40

50

60

Blue Brown Green/Hazel/Other

Total

Males 6 20 6 32

Females 4 16 12 32

Total 10 36 18 64

A statistics class reports the following data on Sex and Eye Color for students in the class:1. What percent of females are

brown-eyed?2. What percent of brown-eyed

students are female?3. What percent of students are

brown-eyed females 4. What’s the distribution of the

Eye Color?

5. What’s the conditional distribution of Eye Color for the males?

6. Compare the percent who are female among the blue-eyed students to the percent of all students who are female.

Sex

Eye Color

Superpower

U.K. U.S.

Fly 54 45

Freeze 52 44

Invisibility

30 37

Super strength

20 23

Telepathy 44 66

Country1. Find the conditional distributions

of superpower preferences among students from the United Kingdom and the United States.

2. Make an appropriate graph to compare the conditional distributions.

3. Is there an association between country or origin and superpower preference? Give appropriate evidence to support your answer.