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2.16: Circle Graphs

Difficulty Level: At Grade Created by: CK-12
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Sue collected data over an entire year to show how many vegetables she grew. 

Total vegetables = 400

Carrots = 120

Potatoes = 40

Tomatoes = 80

Zucchini = 60

Squash = 100

She displays it in a circle graph to visually see which vegetables grew best in her garden and which vegetables grew the least.

Sue can now analyze the circle graph to draw conclusions based on her data. She wants to rank her vegetables from least amount grown to most grown.

In this concept, you will learn how to read circle graphs to answer questions. 

Circle Graphs

Like bar graphs, line graphs, and other data displays, circle graphs are a visual representation of data.

In particular, a circle graphs are used to show the relationships between a whole and its parts. The whole might be a total number of people or items. It can also be decimals that add up to 1. Decimals are related to percentages, they are both parts of a whole. A circle graph will often show percents that add up to 100 percent.

Take a look at the circle graph below. It shows which pets the students in the sixth grade have.

In order to interpret circle graphs, you first need to understand what “whole” and “parts” it represents. This information can be found in the graph’s title and labels of the parts.

Each section is labeled according to a percentage. Each percentage is a part of a whole. The whole is the whole class or 100% of the students. The largest group would have the greatest percentage. In this case, dogs are the most popular pet with 40% of the kids in the sixth grade having dogs. The smallest group would have the smallest percentage. In this case, there are two groups that are the smallest or the least popular pet. In this circle graph, rabbits and birds are the smallest group. Since this is a graph about popularity, you can say that the least popular pets are rabbits and birds. The most popular pet is a dog.

Here is another example:

Circle graphs display data so that you can make generalizations about different components of the data. Circle graphs are also used to make predictions.

This information can help to understand the likelihood that other people will choose the same categories based on the percentages that are greatest and least. Suppose, for instance, that a student was absent from the class when the poll was taken to see which kind of movie the students preferred. Which category would the absent student most likely choose based on the data shown in the graph?

Because most of the students selected comedy as their favorite type of movie, it would be more likely that the absent student would also choose comedy. That is not a certain answer, just a prediction. Remember, a prediction is made based on an assumption or pattern but it is not an exact answer.

Examples

Example 1

Earlier, you were given a problem about Sue and her vegetable garden. This is the data that Sue has collected over an entire year of growth in her garden:

Total vegetables = 400

Squash = 100

Zucchini = 60

Potatoes = 40

Carrots = 120

Tomatoes = 80

Sue created a circle graph to display her data visually.

Now, Sue wants to rank her vegetables from least amount grown to greatest amount grown. In order to do this, she needs to read and interpret her circle graph.

First, Sue will rank the percentages of each vegetable from least to greatest. This gives her a start on ranking them correctly.

10%

15%

20%

25%

30%

Next, Sue matches up each percentage with the color that percentage represents.

10% Light Blue

15% Green

20% Red

25% Purple

30% Blue

Then, Sue uses her key to match the sections in the circle graph with each of the vegetables in her garden. This will display her rank of least amount grown to greatest amount grown.

10% Light Blue- Potatoes

15% Green- Zucchini

20% Red- Tomatoes

25% Purple- Squash

30% Blue- Carrots

The answer is from least to greatest amount grown: Potatoes, Zucchini, Tomatoes, Squash, Carrots. 

Sue can also conclude that Potatoes grew the least in her garden which Carrots grew the most.

Example 2

Look at this graph and answer the following question.

Based on the graph, what is the most popular student activity? 

First, look for the largest colored section of the graph. It is represented in blue.

Next, look for the percentage next to that section to make sure it is the greatest percentage represented in the graph. This section represents 55%, which is the greatest section in the graph.

Then, look at the key to determine which activity is represented by the 55% blue section. The blue section represents sports.

The answer is that sports is the most popular activity.

Use the circle graph on movie data to answer the following questions.

Example 3

Which type of movie is the most popular?

First, look for the colored section that is the greatest section of the graph. It is blue. 

Next, check the percentage to see if it also represents the greatest percentage in the graph.

Then, look at the key to determine which movie type is represented by the blue section.

The answer is comedy movies are the most popular.

Example 4

Which type of movie is the least popular?

First, look for the section of the graph that is the smallest section. It is green.

Next, check the percentage to make sure that is the least percentage represented in the graph as well.

Then, look at the key to determine which movie type is represented by green in the graph.

The answer is horror movies are the least popular.

Example 5

What percentage of students would choose a romance movie?

First, look at the key to see which color represents romance movies.

Next, find that colored section on the graph.

Then, look at the percentage that labels that part of the graph.

The answer is 15% of students choose romance movies.

Review

Use the circle graph to answer the following questions.

This circle graph shows the results of a survey taken of sixth graders about their favorite things to do in the summer. Use the graph to answer the following questions.

1. What percent of the students enjoy the pool in the summer?

2. What percent of the students enjoy camping?

3. What percent of the students enjoy hiking?

4. What percent of the students enjoy going to the beach?

5. What percent of the students do not enjoy camping?

6. What percent of the students enjoy being near or in the water?

7. What percent of the students enjoy camping and hiking?

8. What percent of the students did not choose hiking as a summer activity?

9. Which section has the majority of the votes?

10. If a new student’s opinion was added to the survey, which category would the new student most likely choose?

This circle graph shows the results of a survey taken among students about their favorite school lunches. Use the graph to answer the following questions.

11. What percent of the students enjoy soup as a lunch?

12. What is the favorite choice of students for school lunch?

13. What is the least favorite choice?

14. What percent of the students enjoy salad?

15. What percent of the students did not choose salad as a favorite choice?

16. What percent of the students chose either pizza or tacos as their favorite choice?

17. What percent of the students chose chicken sandwich or pizza as their favorite choice?

18. What percent of the students did not choose chicken or pizza?

19. What is your favorite choice for lunch?

20. If you could add a food choice to this survey, what would it be?

Answers for Review Problems

To see the Review answers, open this PDF file and look for section 2.16. 

Resources

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Date Created:
Sep 24, 2015
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Jul 12, 2016
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