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2.2.4: Circle Graphs to Display Data

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  • Circle Graphs to Display Data

    Screen Shot 2020-04-29 at 9.50.51 PM.png

    Capture Queen - 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

    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.

    Screen Shot 2020-04-29 at 9.58.48 PM.png

    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.

    7th Graders Studying Foreign Languages
    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

    Percent of 7th Graders Studying Foreign Language
    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.

    Sector Degrees of 7th Graders Studying Foreign Language
    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.

    Screen Shot 2020-04-29 at 9.59.24 PM.png

    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.

    Screen Shot 2020-04-29 at 9.59.57 PM.png

    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.

    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.
    7th Grade Fundraising
    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%

    Review (Answers)

    To see the Review answers, open this PDF file and look for section 6.23.


    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