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Circle Graphs to Display Data

Use percents to calculate the number of degrees needed for a circle graph.

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Circle Graphs to Display Data
License: CC BY-NC 3.0

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 \begin{align*}\frac{25}{100}\end{align*}

15% becomes \begin{align*}\frac{15}{100}\end{align*}

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. 

\begin{align*}\frac{25}{100}= \frac{x}{360}\end{align*}

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}. That will be the number of degrees.

\begin{align*}\begin{array}{rcl} 100x &=& 25(360)\\ 100x &=& 9,000\\ x &=& 90\\ 25\% &=& 90^\circ \end{array}\end{align*}

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. 

\begin{align*}\frac{30}{100}= \frac{x}{360}\end{align*}

Next, cross multiply and solve for the variable.

\begin{align*}\begin{array}{rcl} 10x &=& 30(360)\\ 100x &=& 10,800\\ x &=& 108\\ 30\% &=& 108^\circ \end{array}\end{align*}

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. 

\begin{align*}30 + 26 + 15 + 7 + 7 + 5 + 4.5 = 94.5 \ \text{million}\end{align*}

Next, divide each response color by the total.

Favorite color % of Responses
Orange \begin{align*}30 \div 94.5 = 0.3175 = 31.75\%\end{align*}
Blue \begin{align*}26 \div 94.5 = 0.2751 = 27.51\%\end{align*}
Green \begin{align*}15 \div 94.5 = 0.1587 = 15.87\%\end{align*}
Pink \begin{align*}7 \div 94.5 = 0.0741 = 7.41\%\end{align*}
Turquoise \begin{align*}7 \div 94.5 = 0.0741 = 7.41\%\end{align*}
Red \begin{align*}5 \div 94.5 = 0.0529 = 5.29\%\end{align*}
Black \begin{align*}4.5 \div 94.5 = 0.0476 = 4.76\%\end{align*}

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 \begin{align*}0.3175 \times 360^\circ = 114.3^\circ\end{align*}
Blue \begin{align*}0.2751 \times 360^\circ = 99.1^\circ\end{align*}
Green \begin{align*}0.1587 \times 360^\circ = 57.1^\circ\end{align*}
Pink \begin{align*}0.0741 \times 360^\circ = 26.7^\circ\end{align*}
Turquoise \begin{align*}0.0741 \times 360^\circ = 26.7^\circ\end{align*}
Red \begin{align*}0.0529 \times 360^\circ = 19^\circ\end{align*}
Black \begin{align*}0.0476 \times 360^\circ = 17.1^\circ\end{align*}

Finally, create the circle graph.

License: CC BY-NC 3.0

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.

\begin{align*}88 + 48 + 16 + 8 = 160\end{align*}

Percent of 7th Graders Studying Foreign Language
Language Number   of   Students Studying Language Percent of Students Studying Language
Spanish 88 \begin{align*}\frac{88}{160}=0.55=55\%\end{align*}
French 48 \begin{align*}\frac{48}{160}=0.30=30\%\end{align*}
Italian 16 \begin{align*}\frac{16}{160}=0.10=10\%\end{align*}
German 8 \begin{align*}\frac{8}{160}=0.05=5\%\end{align*}

Next, find the measure of the central angle by multiplying \begin{align*}360^\circ\end{align*} 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% \begin{align*}0.55 \times 360^\circ = 198^\circ\end{align*}
French 48 30% \begin{align*}0.30 \times 360^\circ = 108^\circ\end{align*}
Italian 16 10% \begin{align*}0.10 \times 360^\circ = 36^\circ\end{align*}
German 8 5% \begin{align*}0.05 \times 360^\circ = 18^\circ\end{align*}

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.

License: CC BY-NC 3.0

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

Here is the final graph.

License: CC BY-NC 3.0

Example 3

Convert 20% into degrees.

First, set up the proportion.

\begin{align*}\frac{20}{100}= \frac{x}{360}\end{align*}

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}. That will be the number of degrees.

\begin{align*}\begin{array}{rcl} 100x &=& 20(360)\\ 100x &=& 7,200\\ x &=& 72\\ 20\% &=& 72^\circ \end{array}\end{align*}

The answer is 20% equals 72°.

Example 4

Convert 40% into degrees.

First, set up the proportion. 

\begin{align*}\frac{40}{100}= \frac{x}{360}\end{align*}

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}. That will be the number of degrees.

\begin{align*}\begin{array}{rcl} 100x &=& 40(360)\\ 100x &=& 14,400\\ x &=& 144\\ 40\% &=& 144^\circ \end{array}\end{align*}

The answer is 40% equals 144°.

Example 5

Convert 75% into degrees.

First, set up the proportion. 

\begin{align*}\frac{75}{100}= \frac{x}{360}\end{align*}

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}. That will be the number of degrees.

\begin{align*}\begin{array}{rcl} 100x &=& 75(360)\\ 100x &=& 27,000\\ x &=& 270\\ 75\% &=& 270^\circ \end{array}\end{align*}

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

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Vocabulary

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.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
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