# 2.2.4: Circle Graphs to Display Data

- Page ID
- 5754

## 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.

Umberto Salvagnin; Capture Queen - https://www.flickr.com/photos/kaibara/4950289155/in/photolist-8xrwv2-oHPMU3-edYFnV-dKK1oM-c4Aqj-38n1EA-47DPma-6RHwHn-QBCDd-6SFCeP-2hztQQ-DtQSs-4Wm3Xx-6PijHK-7jKLUK-o7xxzf-sjRVt-6VC6PL-4BpfkL-4nbDC7-bz7P6t-JXs4Z-4ocTxd-5nBMFN-2qBxub-4VNHT7-pYB29B-jbNnE3-E7Bwm-rb6un-opJte2-a15LTb-mxKgRT-6Ld4kq-7iXYLy-pibBd6-nDusfB-e1FnCE-5BJ1rx-7AXCvH-2Jw7QW-9LfgXx-hCMnta-dRrZhp-8wAPXn-9mD6Hr-6Ucrrm-vooGvf-bVCLZ-mCznX;https://www.flickr.com/photos/uaeincredible/231011361/in/photolist-mpZCv-54kbk6-uKek2t-oeipFZ-C5DcP-sejdDJ-qvs4R9-npMCE-5x8hhh-4it75W-bDeKCS-68B7wS-efj8ND-rYL9nn-sM9r5-vqaGMb-9tjxcy-3agcN1-5YGWy2-6bdM4J-6aESrV-vtHyyn-9dQiY7-7Ls5GD-6Hm12q-de8gVT-2M6Tf-p8Fk2r-5WkDRw-5jLpAC-8wAQDB-7XUm8L-aBP1F6-4wJnUd-pXConv-8ymrXZ-5qJx6i-bGVtdg-aaB23d-5zFYt1-5RRt3r-qEHUuU-iGAJ6-fge1rL-eR4zu-7khEyF-ok9RAq-6t8WcV-7X3FuK-o8qGjU

### 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.

Umberto Salvagnin; Capture Queen - https://www.flickr.com/photos/kaibara/4950289155/in/photolist-8xrwv2-oHPMU3-edYFnV-dKK1oM-c4Aqj-38n1EA-47DPma-6RHwHn-QBCDd-6SFCeP-2hztQQ-DtQSs-4Wm3Xx-6PijHK-7jKLUK-o7xxzf-sjRVt-6VC6PL-4BpfkL-4nbDC7-bz7P6t-JXs4Z-4ocTxd-5nBMFN-2qBxub-4VNHT7-pYB29B-jbNnE3-E7Bwm-rb6un-opJte2-a15LTb-mxKgRT-6Ld4kq-7iXYLy-pibBd6-nDusfB-e1FnCE-5BJ1rx-7AXCvH-2Jw7QW-9LfgXx-hCMnta-dRrZhp-8wAPXn-9mD6Hr-6Ucrrm-vooGvf-bVCLZ-mCznX;https://www.flickr.com/photos/uaeincredible/231011361/in/photolist-mpZCv-54kbk6-uKek2t-oeipFZ-C5DcP-sejdDJ-qvs4R9-npMCE-5x8hhh-4it75W-bDeKCS-68B7wS-efj8ND-rYL9nn-sM9r5-vqaGMb-9tjxcy-3agcN1-5YGWy2-6bdM4J-6aESrV-vtHyyn-9dQiY7-7Ls5GD-6Hm12q-de8gVT-2M6Tf-p8Fk2r-5WkDRw-5jLpAC-8wAQDB-7XUm8L-aBP1F6-4wJnUd-pXConv-8ymrXZ-5qJx6i-bGVtdg-aaB23d-5zFYt1-5RRt3r-qEHUuU-iGAJ6-fge1rL-eR4zu-7khEyF-ok9RAq-6t8WcV-7X3FuK-o8qGjU

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

Here is the final graph.

Umberto Salvagnin; Capture Queen - https://www.flickr.com/photos/kaibara/4950289155/in/photolist-8xrwv2-oHPMU3-edYFnV-dKK1oM-c4Aqj-38n1EA-47DPma-6RHwHn-QBCDd-6SFCeP-2hztQQ-DtQSs-4Wm3Xx-6PijHK-7jKLUK-o7xxzf-sjRVt-6VC6PL-4BpfkL-4nbDC7-bz7P6t-JXs4Z-4ocTxd-5nBMFN-2qBxub-4VNHT7-pYB29B-jbNnE3-E7Bwm-rb6un-opJte2-a15LTb-mxKgRT-6Ld4kq-7iXYLy-pibBd6-nDusfB-e1FnCE-5BJ1rx-7AXCvH-2Jw7QW-9LfgXx-hCMnta-dRrZhp-8wAPXn-9mD6Hr-6Ucrrm-vooGvf-bVCLZ-mCznX;https://www.flickr.com/photos/uaeincredible/231011361/in/photolist-mpZCv-54kbk6-uKek2t-oeipFZ-C5DcP-sejdDJ-qvs4R9-npMCE-5x8hhh-4it75W-bDeKCS-68B7wS-efj8ND-rYL9nn-sM9r5-vqaGMb-9tjxcy-3agcN1-5YGWy2-6bdM4J-6aESrV-vtHyyn-9dQiY7-7Ls5GD-6Hm12q-de8gVT-2M6Tf-p8Fk2r-5WkDRw-5jLpAC-8wAQDB-7XUm8L-aBP1F6-4wJnUd-pXConv-8ymrXZ-5qJx6i-bGVtdg-aaB23d-5zFYt1-5RRt3r-qEHUuU-iGAJ6-fge1rL-eR4zu-7khEyF-ok9RAq-6t8WcV-7X3FuK-o8qGjU

### 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

Answer the following questions.

- 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 |

- 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.
- 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.

- 12%
- 25%
- 28%
- 42%
- 19%
- 80%
- 90%
- 34%
- 15%
- 5%
- 10%
- 78%

## Resources

## 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. |

## Additional Resources

PLIX: Play, Learn, Interact, eXplore - Interpretations of Circle Graphs: Northwest Region in millions

Video: Reading Pie Graphs

Practice: Circle Graphs to Display Data

Real World: Favorite Films