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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

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*}

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.

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

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.

Next, cross multiply and solve for the variable.

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.

 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.

 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.

 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.

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.

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

The answer is 20% equals 72°.

#### Example 2

Convert 40% into degrees.

First, set up the proportion.

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

The answer is 40% equals 144°.

#### Example 3

Convert 75% into degrees.

First, set up the proportion.

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

The answer is 75% equals 270°.

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.

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.

### Explore More

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.

 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 Language: English

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.