Statistics

Section 10.1 Book

Unit 6.1

Relative Frequency Graphs

Essential Question : What is a relative frequency?

Relative Frequency graphs summarize data in categories, but instead of including the actual number for each category, they compare the number in that category to the total for all categories.

Relative frequency graphs can be bar graphs or circle graphs, and they show fractions or percents, not values.

In this lesson you will see how to make relative frequency circle graphs and relativefrequency bar graphs.

Complete the investigation on page 550.

Continent Land area

(thousands of km2)

Australia 7

Europe 9

Antarctica 14

South America 18

North America 24

Africa 30

Asia 45

Total 147

Now, we will convert the data into a circle graph.

We need to determine the angle measure for each section of the graph. To do this, use the fact that there are 360 degrees in a circle.

For example, to find the number of degrees in thesection representing Australia, solve this proportion:

360147

7 x

360147

7 x

Land area of AustraliaAngle measure for Australia section

Total land area Total degrees in a circle

147x = 2520 x ≈ 17

Continent Angle Measure

Australia 17º

Europe

04.22

3240147360147

9

x

x

x

22º

Continent Angle Measure

Australia 17º

Europe 22º

Antarctica

29.34

5040147360147

14

x

x

x

34º

Continent Angle Measure

Australia 17º

Europe 22º

Antarctica 34º

South America

08.44

6480147360147

18

x

x

x

44º

Continent Angle Measure

Australia 17º

Europe 22º

Antarctica 34º

South America 44º

North America

77.58

8640147360147

24

x

x

x

59º

Continent Angle Measure

Australia 17º

Europe 22º

Antarctica 34º

South America 44º

North America 59º

Africa

47.73

10800147360147

30

x

x

x

74º

Continent Angle Measure

Australia 17º

Europe 22º

Antarctica 34º

South America 44º

North America 59º

Africa 74º

Asia

21.110

16200147360147

45

x

x

x

110º

360ºTotal

Label the circle graph on the bottom left of your notes handout with frequencies.

You can find these counts in the first table you completed.

79

141824

3045

To find the percent of the total area Australia contains, solve the proportion:

100147

7 p

147p = 700 p ≈ 5

Set up a proportion and solve to find the percentages for each continent. (Be sure all percentages add to 100%.)

Europe: Antarctica:

12.6

900147100147

7

p

p

p

52.9

1400147100147

14

p

p

p

South America: North America:

24.12

1800147100147

18

p

p

p

33.16

2400147100147

24

p

p

p

Africa: Asia:

41.20

3000147100147

30

p

p

p

61.30

4500147100147

45

p

p

p

Label the relative frequency circle graph on the bottom right of your notes handout with the values you just found.

5%

6%10%12%

16%

20% 31%

In both circle graphs the relative size of each section indicates the portion of the total areathat the continent contains.

A relative frequency bar graph for this data showspercents of the total land area rather than the land area itself.

Australia

Europe

Antarctica

South America

North America

Africa

Asia

Notice that like box plots, relative frequency plotsdo not show actual data values.

For example, both of the relative frequency graphs show that Asia makes up 31% of the total land area of the continents, but neither graph indicates what the land area of Asia is.

Example A: The table shows the number of students enrolled in each grade at RHHS.

9th grade

10th grade

11th grade

12th grade

407 396 328 299

Percentages

Angle Measure

a) How many students are enrolled in RHHS?

1430 students

b) Set up a proportion to find what percent of the school is represented in each grade.

Ninth Grade Tenth Grade

46.28

4070014301001430

407

x

x

x

69.27

3960014301001430

396

x

x

x

b) Set up a proportion to find what percent of the school is represented in each grade.

Eleventh Grade Twelfth Grade

94.22

3280014301001430

328

x

x

x

91.20

2990014301001430

299

x

x

x

9th grade

10th grade

11th grade

12th grade

407 396 328 299

Percentages 28% 28% 23% 21%

Angle Measure

c) Now, create a frequency circle graph. First, compute the angle measure for each section of the graph. Set up a proportion to find these values.

Ninth Grade Tenth Grade

102

14652014303601430

407

x

x

x

69.99

14256014303601430

396

x

x

x

c) Now, create a frequency circle graph. First, compute the angle measure for each section of the graph. Set up a proportion to find these values.

Eleventh Grade Twelfth Grade

57.82

11808014303601430

328

x

x

x

27.75

10764014303601430

299

x

x

x

9th grade

10th grade

11th grade

12th grade

407 396 328 299

Percentages 28% 28% 23% 21%

Angle Measure 102º 100º 83º 75º

Create the circle graph of RHHS enrollment using a protractor and the angle measures just computed. Label each sector and include the percentage for the sector.

RHHS Enrollment 2008-2009

9th grade10th grade

12th grade

28%28%

21%

11th grade

23%

RHHS Enrollment 2008-2009

GRADE

LEVELS

9th Grade

10th Grade

11th Grade

12th Grade

Create a relative frequency bar graph of enrollment at RHHS.