Displaying Categorical Data

CH. 3 Day 1 NotesAP Statistics

EQ: How do we display categorical data?

Warm UpIdentify the W’s, name the variables and

specify if it should be treated as categorical or quantitative.

A listing posted by the Arby’s restaurant chain gives, for each of the sandwiches it

sells, the type of meat in the sandwich, the number of calories, and the serving size in ounces. The data might be used to assess

the nutritional value of the different sandwiches.

Warm Up - Answer• Who (are we studying): Arby’s

sandwiches• What (characteristics are we using): oType of meat (categorical)onumber of calories (quantitative)

(calories)oserving size (quantitative) (ounces)

• When: Not specified• Where: Arby’s restaurants• How: We are using the list posted by the

restaurant

Tell whether the variable is categorical,

quantitative, or an identifier.

1.Shoe size

2.VIN number of a car

3.Number of pages in a book

4.Class rank

5.Length of your arm

QI

QI or C

Q

ExtraIn what way might Age be

considered to be a quantitative variable?

What about as a categorical variable?

Ways to Represent Data

Today we will focus on:

Frequency Tables

RelativeFrequency

Tables

Bar ChartsBar Charts

Pie Charts

Frequency Tables• Helps organize data

• Records totals and categories

• Relative frequency table-displays the percentages(proportions) of the values in each category.

Make a frequency table and a relative frequency

table of the following averages for previous AP

Stats students.

A C BF A BC D DF B CC C BB D AB D C

A

B

C

D

F

A

B

C

D

F

36642

.1428

.2857

.2857

.1905

.0952

Why make a picture?

• It may reveal things you can’t see in the table

• It shows important features• It helps you tell about the data to

others

Things to Remember…• Context• Appropriate Scale• Area Principle• Label!oInclude units where applicable

Make a bar chart of the previous

AP Stats averages by letter grade.

You may also see it like this…

A

B

C

D

F

0 1 2 3 4 5 6 7

What do we see in the graph?

Make a relative frequency bar chart of

the previous AP Stats averages.

Pie Charts

Doesn’t add up to 100%50% does not look like halfPercentages of what whole?

Respondents could be in more than one category

Make a pie chart of the previous AP Stats averages.

A

B

C

D

F

A

B

C

D

F

.1428

.2857

.2857

.1905

.0952

How can we be sure it’s divided proportionally?

What do we see in the graph?

• A should look bigger than F• B and C should look the same• B and C should look twice the size of A• D should appear larger than A

• Can approximate areas• Can also use Geometry to calculate Central Angle

measures (cross-curricular)

Important Disclaimer:CAN ONLY USE BAR

CHARTS AND PIE CHARTS AS LONGS AS INDIVIDUALS

BEING STUDIED DO NOT FALL INTO MORE

THAN ONE CATEGORY.

The table below gives the distribution by

region of the population in the United

States in 1996.

58.5West

93.1South

62.1Midwest

51.6Northeast

Population(in millions)Region

Make a pie chart of the population data.

NE

MW

S

W

Homeworkp. 36-44 # 5, 7, 8, 10, 11, 13, 14

(due Monday)

Reminder:Due tomorrow-

1) p.16 Homework from Textbook 2) Reading Questions Ch.2-3