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.