# 2.2.4: Circle Graphs to Display Data

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## Circle Graphs to Display Data

A massive online survey asked almost 100 million people to identify their favorite color from seven options: blue, green, red, black, turquoise, orange, and pink. Once they had the data, the survey company needed to find a visually engaging way to present the data, and decided to use a circle graph.

In this concept, you will learn to create your own circle graphs with data.

## Creating Circle Graphs to Display Data

When creating a circle graph, each percentage can be converted to a specific number of degrees. When you know the number of degrees a percentage is equal to, you can use a protractor and a circle to draw it in exactly.

To figure this out, you have to figure out each percentage in terms of degrees.

First, create a proportion. A percent is out of 100, so you can make a ratio out of any percent.

25% becomes 25100

15% becomes 15100

A circle is made up of 360°. Since you are trying to figure out the number of degrees, you use a variable over 360 for the second ratio.

Here is a proportion for converting 25% to degrees.

25100=x360

Next, cross multiply and solve for the variable x. That will be the number of degrees.

100x100xx25%====25(360)9,0009090∘

Now if you were going to draw this on a circle graph, you could take a circle and your protractor and measure in a 90° angle. That would equal 25% of the graph.

Let’s look at another example.

Convert 30% into degrees.

First, write a proportion.

30100=x360

Next, cross multiply and solve for the variable.

10x100xx30%====30(360)10,800108108∘

The answer is 30% is equal to 108°.

## Examples

### Example 1

Earlier, you were given a problem about the color survey.

The responses from the almost 100 million respondents are shown in the table below.

 Favorite Color # of Responses Orange 30 Million Blue 26 million Green 15 million Pink 7 million Turquoise 7 million Red 5 million Black 4.5 million

First, convert each color to a decimal and find the total number of responses by adding.

30+26+15+7+7+5+4.5=94.5 million

Next, divide each response color by the total.

 Favorite color % of Responses Orange 30÷94.5=0.3175=31.75% Blue 26÷94.5=0.2751=27.51% Green 15÷94.5=0.1587=15.87% Pink 7÷94.5=0.0741=7.41% Turquoise 7÷94.5=0.0741=7.41% Red 5÷94.5=0.0529=5.29% Black 4.5÷94.5=0.0476=4.76%

Next, convert each percent to a number of degrees. You can do this by changing each percent to a decimal and then multiplying each decimal by 360.

 Favorite Color Degrees in Central Angle Orange 0.3175×360∘=114.3∘ Blue 0.2751×360∘=99.1∘ Green 0.1587×360∘=57.1∘ Pink 0.0741×360∘=26.7∘ Turquoise 0.0741×360∘=26.7∘ Red 0.0529×360∘=19∘ Black 0.0476×360∘=17.1∘

Finally, create the circle graph.

### Example 2

The table below shows the number of students in the seventh grade who are studying each foreign language. Make a circle graph that shows the data.

 Foreign Language Number of Students Studying Language Spanish 88 French 48 Italian 16 German 8

First, find the total number of seventh grade students studying a foreign language. Then find the percent of students studying each language.

88+48+16+8=160

 Language Number   of   Students Studying Language Percent of Students Studying Language Spanish 88 88160=0.55=55% French 48 48160=0.30=30% Italian 16 16160=0.10=10% German 8 8160=0.05=5%

Next, find the measure of the central angle by multiplying 360∘ by the percent.

 Foreign Language Number of Students Studying Language Percent of Students Studying Language Degrees in Central Angle Spanish 88 55% 0.55×360∘=198∘ French 48 30% 0.30×360∘=108∘ Italian 16 10% 0.10×360∘=36∘ German 8 5% 0.05×360∘=18∘

Now, draw a circle with a compass. Draw one radius. Use that radius as a side of one central angle. Measure and draw the other central angles using a protractor.

Then, label each sector with a title and percent and give a title to the entire circle graph.

Here is the final graph.

### Example 3

Convert 20% into degrees.

First, set up the proportion.

20100=x360

Next, cross multiply and solve for the variable x. That will be the number of degrees.

100x100xx20%====20(360)7,2007272∘

The answer is 20% equals 72°.

### Example 4

Convert 40% into degrees.

First, set up the proportion.

40100=x360

Next, cross multiply and solve for the variable x. That will be the number of degrees.

100x100xx40%====40(360)14,400144144∘

The answer is 40% equals 144°.

### Example 5

Convert 75% into degrees.

First, set up the proportion.

75100=x360

Next, cross multiply and solve for the variable x. That will be the number of degrees.

100x100xx75%====75(360)27,000270270∘

The answer is 75% equals 270°.

## Review

1. The table shows how much money the students in the seventh grade have raised so far for a class trip. Make a circle graph that shows the data.
 Fundraiser Amount Car wash $150 Book sale$175 Bake sale $100 Plant sale$75
1. Make a list of 5 popular ice cream flavors. Then survey your classmates asking them which of the 5 flavors is their favorite ice cream flavor. Use the data to make a circle graph.
2. Use a newspaper to locate a circle graph of some data. Then write five questions about the data.

Look at each percentage and then use a proportion to find the equivalent number of degrees. You may round your answer when necessary.

1. 12%
2. 25%
3. 28%
4. 42%
5. 19%
6. 80%
7. 90%
8. 34%
9. 15%
10. 5%
11. 10%
12. 78%

## Vocabulary

Term Definition
Sector A sector of a circle is a portion of a circle contained between two radii of the circle. Sectors can be measured in degrees.