2.16: Pie Charts
Have you ever looked at a circle graph? Do you know that you can learn a lot from circle graphs?
Alex and Tania have had a wonderful time planting and growing vegetables in their garden. They have learned a lot and have been keeping track of all of the vegetables that they have grown all summer long. They have collected a total of 400 vegetables. Not bad for their first attempt at a garden. They did not have much luck with the vegetable stand though. They found that because they gave so many vegetables away to their workers, that there wasn’t very much to sell in the end.
“Next year, we want to double our production,” said Alex to his sister.
“That’s a good idea. I made a circle graph showing our results from this year,” Tania handed a copy of the circle graph to Alex as she left the room.
Alex looked at the graph. It clearly shows all of the categories of vegetables that they grew with percentages next to them. Alex can’t seem to make heads or tails of all of the information. Here is the graph.
Alex looks back at the data again.
Total vegetables = 400
Carrots = 120
Tomatoes = 80
Zucchini = 60
Squash = 100
Potatoes = 40
What conclusions can Alex make by looking at the circle graph? Can he make any predictions? To understand this, you will need to know how to read a circle graph.
Guidance
Like bar graphs, line graphs, and other data displays, circle graphs are a visual representation of data.
In particular, we use circle graphs 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. We haven’t learned about percentages yet, but we can still use them if we think of them as 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, we first need to understand what “whole” and “pieces” it represents. We can gather this information from the graph’s title and the labels of the pieces.
Think about the graph above.
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. Here we have the numbers for who has what kind of pet. 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 them. The smallest group would have the smallest percentage. In this case, there are two groups that are the smallest or the least popular. In this circle graph, rabbits and birds are the smallest group. Since this is a graph about popularity, we can say that the least popular pets are rabbits and birds. The most popular pet is a dog.
We have seen that circle graphs display data so that we can make generalizations about different components of the data. They make it easy for us to interpret and analyze data. We can also use circle graphs to make predictions.
In the last example, the circle graph showed us which kind of movies were most popular (comedy) and which were least popular (horror). This information helps us understand the likelihood that other people will choose the same categories. 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. Can we make any assumptions about which category the absent student might choose?
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. We could be wrong too. Remember a prediction is made based on an assumption or pattern but it is not an exact answer.
Now let's practice by using the circle graph shown above to answer questions.
Example A
Which type of movie is the most popular?
Solution: Comedy
Example B
Which is the least popular?
Solution: Horror
Example C
What percentage of students would choose a romance movie?
Solution: 15%
Remember Alex and the circle graph? Now back to the original problem.
“Next year, we want to double our production,” said Alex to his sister.
“That’s a good idea. I made a circle graph showing our results from this year,” Tania handed a copy of the circle graph to Alex as she left the room.
Alex looked at the graph. It clearly shows all of the categories of vegetables that they grew with percentages next to them.
Here is the graph.
Alex looks back at the data again.
Total vegetables = 400
Squash = 100
Zuchini = 60
Potatoes = 40
Carrots = 120
Tomatoes = 80
To help Alex, the first thing that we need to do is to underline all of the important information.
Next, we can draw some conclusions about the data to help Alex make sense of the graph. Let’s look at a few questions to help us make sense of the vegetable growth.

What is the largest group of vegetables grown?
 According to the graph, the carrots were the largest group grown.

If they were to double production next year, how many of each type of vegetable would be grown?
 Carrots = 120 to 240, tomatoes = 80 to 160, zucchini = 60 to 120, squash = 100 to 200, potatoes = 40 to 80.

Which vegetable was the smallest group?
 The smallest group is potatoes.
Alex and Tania can look at two things as they work to increase vegetable growth. Our graph doesn’t tell us why they only grew 40 potatoes. They can analyze whether insects hurt their crop or whether or not they planted enough. The circle graph gives them a great starting point for future planning.
Vocabulary
Here are the vocabulary words in this Concept.
 Circle graph
 a visual display of data that uses percentages and circles.
 Decimals
 a part of a whole represented by a decimal point.
 Percentages
 a part of a whole written out of 100 using a % sign
 Predictions
 to examine data and decide future events based on trends.
Guided Practice
Here is one for you to try on your own.
Look at this graph and answer the following questions.
Based on the graph, what is the most popular student activity? If 55% of the students have this as their favorite activity, what percent of the students don’t have sports as their favorite activity?
Answer
If you look at the graph, the largest section of the graph is 55% which is sports. Sports is the most popular activity.
If 55% of the students chose sports, then 45% did not choose it as their favorite activity.
Video Review
Here are videos for review.
Khan Academy Reading Pie Graphs (Circle Graphs)
James Sousa, Constructing a Circle Graph Part 1
James Sousa, Constructing a Circle Graph Part 2
Practice
Directions: 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?
Circle graph
A circle graph is a visual display of data that illustrates data as percentages.Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Misleading Statistics
Statistics designed to falsely show an increase or decrease in the data.Percent
Percent means out of 100. It is a quantity written with a % sign.pie chart
A pie chart shows the relationship of the parts to the whole by visually comparing the sizes of the sections (slices) of a circle.Prediction
A prediction is a statement one makes about the likelihood of a future event.whole relationship
The whole relationship is represented by the entire circle.Image Attributions
Here you'll learn to interpret a circle graph and make predictions based on the data.
Concept Nodes:
Circle graph
A circle graph is a visual display of data that illustrates data as percentages.Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Misleading Statistics
Statistics designed to falsely show an increase or decrease in the data.Percent
Percent means out of 100. It is a quantity written with a % sign.pie chart
A pie chart shows the relationship of the parts to the whole by visually comparing the sizes of the sections (slices) of a circle.Prediction
A prediction is a statement one makes about the likelihood of a future event.whole relationship
The whole relationship is represented by the entire circle.