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.
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