# 6.23: Circle Graphs to Display Data

Difficulty Level: At Grade Created by: CK-12
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Practice Circle Graphs to Display Data

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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

15% becomes

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.

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

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.

Next, cross multiply and solve for the variable.

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.

Next, divide each response color by the total.

 Favorite color % of Responses Orange Blue Green Pink Turquoise Red Black

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 Blue Green Pink Turquoise Red Black

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.

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

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

 Foreign Language Number of Students Studying Language Percent of Students Studying Language Degrees in Central Angle Spanish 88 55% French 48 30% Italian 16 10% German 8 5%

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.

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

The answer is 20% equals 72°.

#### Example 4

Convert 40% into degrees.

First, set up the proportion.

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

The answer is 40% equals 144°.

#### Example 5

Convert 75% into degrees.

First, set up the proportion.

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

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%

### Notes/Highlights Having trouble? Report an issue.

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### Vocabulary Language: English

TermDefinition
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.

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