# 6.23: Circle Graphs to Display Data

**At Grade**Created by: CK-12

**Practice**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 \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*}

\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.

#### 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.

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

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*}

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.

#### 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*}

\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*}

\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*}

\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.

- 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%

### Review (Answers)

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

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In this concept, you will learn to create your own circle graphs with data.

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