6.23: Circle Graphs to Display 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 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.
This is where you come in. It is your turn to help Taylor. Pay attention to this Concept and you will know how to create the circle graph in the end.
Guidance
Creating a circle graph may seem tricky, but if you think about circle graphs it can become easier to figure out. First, notice that in the graphs at the end of the last Concept, that 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
15% becomes
A circle is out of
Here is a proportion for converting 25% to degrees.
Now we cross multiply and solve for the variable
Now if you were going to draw this on a circle graph, you could take a circle and your protractor and measure in a
Now let's apply this.
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.
Foreign Language  Number of Students Studying Language  Percent of Students Studying Language 

Spanish  88 

French  48 

Italian  16 

German  8 

Step 2: Find the measure of the central angle by multiplying
Foreign Language  Number of Students Studying Language  Percent of Students Studying Language  Degrees in Central Angle 

Spanish  88  55% 
55% of 
French  48  30% 
30% of 
Italian  16  10% 
10% of 
German  8  5% 
5% of 
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.
Convert each percent into degrees.
Example A
20%
Solution:
Example B
40%
Solution:
Example C
75%
Solution:
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
Licorice
Chocolates
Gummy Bears
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 in this Concept.
 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 degrees which are created out of
360∘ .
 Sector
 the section of a circle graph. Each section is known as a sector. Each sector can be measured in degrees and given a percentage.
Guided Practice
Here is the original problem once again.
Convert 30% into degrees.
Answer
First, we write a proportion.
Next, we cross multiply and solve for the variable.
This is our answer.
Video Review
Here is a video for review.
 This is a James Sousa video on constructing a pie chart.
Practice
Directions: Use what you have learned to tackle each problem.
1. 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 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.
Directions: 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%
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Image Attributions
Here you'll learn to make circle graphs given data.