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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

Let’s Think About It

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.

Guidance

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*}25100

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

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

25100=x360

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}x. 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*}

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. 

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

30100=x360

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*}

10x100xx30%====30(360)10,800108108

The answer is 30% is equal to 108°.

Guided Practice

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*}

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 \begin{align*}\frac{88}{160}=0.55=55\%\end{align*}88160=0.55=55%
French 48 \begin{align*}\frac{48}{160}=0.30=30\%\end{align*}48160=0.30=30%
Italian 16 \begin{align*}\frac{16}{160}=0.10=10\%\end{align*}16160=0.10=10%
German 8 \begin{align*}\frac{8}{160}=0.05=5\%\end{align*}8160=0.05=5%

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

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

Here is the final graph.

Examples

Example 1

Convert 20% into degrees.

First, set up the proportion.

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

20100=x360

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}x. 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*}

100x100xx20%====20(360)7,2007272

The answer is 20% equals 72°.

Example 2

Convert 40% into degrees.

First, set up the proportion. 

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

40100=x360

Next, cross multiply and solve for the variable \begin{align*}x\end{align*}x. 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*}

100x100xx40%====40(360)14,400144144

The answer is 40% equals 144°.

Example 3

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°.

Follow Up

Remember 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.

Video Review

https://www.youtube.com/watch?v=ZlDkk_fpW3Q&feature=youtu.be

Explore More

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

2. 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.

3. 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.

4. 12%

5. 25%

6. 28%

7. 42%

8. 19%

9. 80%

10. 90%

11. 34%

12. 15%

13. 5%

14. 10%

15. 78%

Vocabulary

Sector

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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