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# 6.8: Circle Graphs

Difficulty Level: At Grade Created by: CK-12

## Introduction

Candy Data

One day while Taylor was in the candy store, she saw a chart that her Dad had made sitting on the counter.

“What’s this mean?” she asked, looking at the chart.

“That is a chart that shows our best sellers. Every other candy sells less than 10%, so I don’t usually include them. These are the top sellers. I keep track of our inventory each month and determine which candies were the top sellers. Then I create a graph of the data,” he explained.

“Where is the graph?”

“I could do that,” Taylor said smiling.

Taylor was so excited. She could finally put all of her math to work. She knew that a circle graph would be the best way to show the percentages. Here is the chart.

Lollipops - 55%

Licorice - 10%

Chocolates - 20%

Gummy Bears - 15%

Taylor started to work on the circle graph and she thought that she knew what she was doing, but then she got stuck. She couldn’t remember how to change each percentage into a number of degrees.

This is where you come in. It is your turn to help Taylor. Pay attention to this lesson and you will know how to create the circle graph in the end.

What You Will Learn

By the end of the lesson, you will be able to utilize the following skills:

• Interpret circle graphs given actual data or data expressed as fractions or percents of the whole.
• Make circle graphs given actual data.
• Make circle graphs given data as percents.
• Display and interpret real-world survey data using circle graphs.

Teaching Time

I. Interpret Circle Graphs Given Actual Data or Data Expressed as Fractions or Percents of the Whole

In a circle graph, the circle represents the whole. A circle graph can be used to compare the parts with the whole. It is a useful way to visually display data. Each of the parts is called a sector.

Let’s look at how data is expressed in a circle graph.

Example

The circle graph shows how the students at Grandville Middle School voted for a school mascot. Which mascot got the least number of votes?

Since there are no values shown on the circle graph, you need to visually determine which sector is the smallest. The smallest sector is the one for the Panther.

The Panther got the least number of votes for mascot.

Example

The circle graph shows the method of transportation used by students to get to Grandville Middle School. What percent of the students use the school bus to get to school?

The sectors of a circle graph must add up to 100%. Find the sum of the three given percents and then subtract from 100%.

\begin{align*}15 \% + 20 \% + 25 \% = 60 \%\!\\ 100 \% - 60 \% = 40 \%\end{align*}

40% of the students use the school bus to get to school.

Example

The circle graph shows the results of a music survey. What fraction of the people surveyed said country was their favorite type of music?

The fractions in the sectors of a circle graph must add up to 1. Find the sum of the three given fractions and then subtract from 1.

\begin{align*}\frac{1}{4} + \frac{1}{2} + \frac{1}{10} & = \frac{5}{20} + \frac{10}{20} + \frac{2}{20} = \frac{17}{20}\\ 1 - \frac{17}{20} & = \frac{20}{20} - \frac{17}{20} = \frac{3}{20}\end{align*}

\begin{align*}\frac{3}{20}\end{align*} of the people surveyed said country was their favorite type of music.

We can show the same circle graph with its percents or with the measures of its central angles. The sum of the measures of the central angles in a circle graph is \begin{align*}360^ \circ\end{align*}.

6V. Lesson Exercises

Use the two graphs above to answer the following questions.

1. Which number of degrees is equal to 40%?
2. True or false. 25% is the same as a \begin{align*}90^\circ\end{align*} angle?
3. How many degrees is equal to 15%?

Take a few minutes to check your work with a partner.

II. Make Circle Graphs Given Actual Data

Creating a circle graph may seem tricky, but if you think about the last examples it can become easier to figure out. First, notice that in the graphs at the end of the last section, each percentage was converted to a specific number of degrees. When you know the number of degrees that a percentage is equal to, you can use a protractor and a circle to draw it in exactly.

To figure this out, we have to figure out each percentage in terms of degrees. How do we do this?

First, we do this by creating a proportion. A percent is out of 100, so we 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 \begin{align*}360^ \circ\end{align*}. Since we are trying to figure out the number of degrees in a particular portion of the circle, we 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*}

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

\begin{align*}100x & = 25(360)\\ 100x & = 9000\\ x & =90\\ 25 \% &= 90^\circ\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 \begin{align*}90^\circ\end{align*} angle. That would equal 25% of the graph.

Example

Convert 30% into degrees.

First, we write a proportion.

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

Next, we cross multiply and solve for the variable.

\begin{align*}10x &= 30(360)\\ 100x &= 10800\\ x &= 108\\ 30 \% &= 108^\circ\end{align*}

6W. Lesson Exercises

Convert each percent into degrees.

1. 20%
2. 40%
3. 75%

Take a few minutes to check your work with a friend.

III. Make Circle Graphs Given Data as Percents

Now let’s look at taking this one step further. If we know the percents for a circle graph, we can find the measures of the central angles of the circle. Then we can use a compass, a protractor, and a straight edge to make the circle graph.

Example

The table shows the results of the favorite school lunch of students in the seventh grade at Grandville Middle School. Make a circle graph for the results of the survey.

Favorite Food % of Students Surveyed
Pizza 30%
Grilled Cheese 35%
Hamburger 10%
Chicken fingers 25%

Step 1: Find the measure of the central angle by multiplying \begin{align*}360^\circ\end{align*} by the percent.

Favorite Food % of Students Surveyed Degrees in Central Angle
Pizza 30% 30% of \begin{align*}360^\circ = 0.30 \times 360^\circ = 108^\circ\end{align*}
Grilled Cheese 35% 35% of \begin{align*}360^\circ = 0.35 \times 360^\circ = 126^\circ\end{align*}
Hamburger 10% 10% of \begin{align*}360^\circ = 0.10 \times 360^\circ = 36^\circ\end{align*}
Chicken fingers 25% 25% of \begin{align*}360^\circ = 0.25 \times 360^\circ = 90^\circ\end{align*}

Step 2: 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.

Step 3: Label each sector with a title and percent and give a title to the entire circle graph.

What about if we have actual data?

If we have actual data, we first need to find the percent for each sector of the circle graph. Then we can find the measures of the central angles of the circle and make the circle graph.

Example

The table 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

Step 1: 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*}

Foreign Language Number of Students Studying Language Percent of Students Studying Language
Spanish 88 \begin{align*}\frac{88}{160} = \frac{11}{20} = 55 \%\end{align*}
French 48 \begin{align*}\frac{48}{160} = \frac{3}{10} = 30 \%\end{align*}
Italian 16 \begin{align*}\frac{16}{160} = \frac{1}{10} = 10 \%\end{align*}
German 8 \begin{align*}\frac{8}{160} = \frac{1}{20} = 5 \%\end{align*}

Step 2: 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% 55% of \begin{align*}360^\circ = 0.55 \times 360^\circ = 198^\circ\end{align*}
French 48 30% 30% of \begin{align*}360^\circ = 0.30 \times 360^\circ = 108^\circ\end{align*}
Italian 16 10% 10% of \begin{align*}360^\circ = 0.10 \times 360^\circ = 36^\circ\end{align*}
German 8 5% 5% of \begin{align*}360^\circ = 0.05 \times 360^\circ = 18^\circ\end{align*}

Step 3: 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.

Step 4: Label each sector with a title and percent and give a title to the entire circle graph.

Here is the final graph.

IV. Display and Interpret Real-World Survey Data Using Circle Graphs

Now you can make and interpret circle graphs for real-world data.

Example

The chart shows the Patrick family’s monthly budget. Make a circle graph to display their budget. Then find how much the family budgets for in each category if their monthly income is 2,500. Rent and utilities - 35% Food - 25% Savings - 10% Transportation - 15% Clothing - 10% Other - 5% First find the number of degrees in the central angle for each category. Rent and utilities - 35% - \begin{align*}0.35 \times 360^\circ = 126^\circ\end{align*} Food - 25% - \begin{align*}0.25 \times 360^\circ = 90^\circ\end{align*} Savings - 10% - \begin{align*}0.10 \times 360^\circ = 36^\circ\end{align*} Transportation - 15% - \begin{align*}0.15 \times 360^\circ = 54^\circ\end{align*} Clothing - 10% - \begin{align*}0.10 \times 360^\circ = 36^\circ\end{align*} Other - 5% - \begin{align*}0.05 \times 360^\circ = 18^\circ\end{align*} Next make a circle graph. Then find how much the Patrick family budgets for in each category. Rent and utilities - 35% - \begin{align*}0.35 \times \ 2,500 = \ 875\end{align*} Food - 25% - \begin{align*}0.25 \times \ 2,500 = \ 625\end{align*} Savings - 10% - \begin{align*}0.10 \times \ 2,500 = \ 250\end{align*} Transportation - 15% - \begin{align*}0.15 \times \ 2,500 = \ 375\end{align*} Clothing - 10% - \begin{align*}0.10 \times \ 2,500 = \ 250\end{align*} Other - 5% - \begin{align*}0.05 \times \ 2,500 = \ 125\end{align*} The Patrick family budgets875 for rent and utilities, $625 for food,$250 for saving, $375 for transportation,$250 for clothing, and 125 for other. ## Real Life Example Completed Candy Data Here is the original problem once again. Use what you have learned to help Taylor make the circle graph. One day while Taylor was in the candy store, she saw a chart that her Dad had made sitting on the counter. “What’s this mean?” she asked, looking at the chart. “That is a chart that shows our best sellers. Every other candy sells less than 10%, so I don’t usually include it. These are the top sellers. I keep track of our inventory each month and determine which candies were the top sellers. Then I create a graph of the data,” he explained. “Where is the graph?” “I haven’t made it yet.” “I could do that,” Taylor said smiling. “Terrific! Go right ahead.” Taylor was so excited. She could finally put all of her math to work. She knew that a circle graph would be the best way to show the percentages. Here is the chart. Lollipops - 55% Licorice - 10% Chocolates - 20% Gummy Bears - 15% Taylor started to work on the circle graph and she thought that she knew what she was doing, but then she got stuck. She couldn’t remember how to change each percentage into a number of degrees. First, we need to convert each percentage to a number of degrees. We can do this by multiplying each decimal by 360. Lollipops \begin{align*}.55 \times 360 = 198^\circ\end{align*} Licorice \begin{align*}.10 \times 360 = 36^\circ\end{align*} Chocolates \begin{align*}.20 \times 360 = 72^\circ\end{align*} Gummy Bears \begin{align*}.15 \times 360 = 54^\circ\end{align*} Next, Taylor can use a protractor and a circle to create the circle graph. Here is her final work. ## Vocabulary Here are the vocabulary words that are found in this lesson. Circle Graph a visual display of data in a circle. A circle graph is created from percentages with the entire circle representing the whole. The sectors of the circle graph are divided according to the number of degrees they represent out of \begin{align*}360^\circ\end{align*}. Sector a section of a circle graph. Each section is known as a sector. Each sector can be measured in degrees and given a percentage. ## Technology Integration Other Videos: 1. http://www.schooltube.com/video/3569a4aea02846e18614/Circle-Graph-with-Protractor – This is a school tube video on how to make a circle graph using a protractor. ## Time to Practice Directions: Use the survey to answer each question. A survey of 300 people asked them to name their favorite spectator sport. The results are shown in the circle graph below. 1. What was the most favorite spectator sport of the people surveyed? 2. What was the least favorite spectator sport of the people surveyed? 3. What percent of the people surveyed said that football was their favorite spectator sport? 4. How many people said that basketball was their favorite spectator sport? 5. How many more people said that soccer was their favorite sport than ice hockey? 6. The table shows the 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 wash150
Book sale $175 Bake sale$100
Plant sale \$75

7. 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.

8. Use a newspaper to locate a circle graph of some data. Then write five questions about the data.

Directions: Look at each percentage and then use a proportion to find the equivalent number of degrees. You may round your answer when necessary.

9. 12%

10. 25%

11. 28%

12. 42%

13. 19%

14. 80%

15. 90%

16. 34%

17. 15%

18. 5%

19. 10%

20. 78%

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