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2.7: Circle Graphs and Choosing Displays

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Introduction

Vegetable Totals

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

Alex wishes that she had put the information in a bar graph because he finds them so much easier to read.

What conclusions can Alex draw from the circle graph?

Can you make a bar graph from the circle graph?

If Alex and Tania double their production next year, how many vegetables will that be?

Now it is your turn to work. Learn everything that you need to about circle graphs and you will be able to help Alex with his dilemma.

What You Will Learn

In this lesson you will learn the following skills:

  • Interpret given circle graphs
  • Use circle graphs to make predictions
  • Use data from a circle graph to make a bar graph
  • Select among frequency tables, line plots, bar graphs and line graphs for best displays of given data.

Teaching Time

I. Interpreting Given Circle Graphs

Alex has been given a circle graph that he isn’t sure how to read. That is where this section of the lesson begins. In this first section, we are going to look at how to interpret the results that we see in a circle graph.

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.

Here is a circle graph for you to interpret. Use it to answer the following questions.

  1. What does this graph measure?
  2. Which type of movie is the most popular?
  3. Which is the least popular?
  4. What percentage of students would choose a romance movie?

Take a minute and discuss your answers with a neighbor.

II. Using a Circle Graph to Make Predictions

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 it is your turn to make some predictions. Use the circle graph below to answer the following questions.

  1. Based on the graph, what is the most popular student activity?
  2. If 55% of the students have this as their favorite activity, what percent of the students don’t have sports as their favorite activity?
  3. What is the least popular activity?

Take a minute to check your answers with a neighbor.

III. Use Data from a Circle Graph to Make a Bar Graph

Circle graphs are just one of many different displays we can use to organize and present data in a form that is easy to interpret. As we have said, circle graphs are most useful when we are comparing parts of a whole or total. We can easily see which part is the biggest or smallest.

Bar graphs also allow us to make comparisons easily. Unlike most circle graphs, bar graphs let us compare exact amounts.

We usually use circle graphs when dealing with percentages, and the percents of the pieces add up to 100 percent. In a bar graph, however, we use a scale to show the exact amount of each category. Take a look at the two graphs below.

Both graphs show how Trey spends the \$40 he earns each month delivering papers.

The circle graph gives this information in percents. We can see that Trey spends 40 percent of his money on food and 10 percent on buying baseball cards. He saves the other 50% for his new bike.

The bar graph shows the same results but in a different format. The “pieces” in the circle graph are represented by bars on the bar graph. We show the categories of how Trey spends his money across the bottom. Along the side, a scale gives actual amounts of money. The height of each category bar tells exactly how much money Trey spends on that category. The food bar shows that Trey spent $16 on food and $4 on baseball cards. He saves $20 each week to put towards the new bike.

How did we get from a percentage to an actual amount of money?

When we have a circle graph, the data is presented in percentages. When we have a bar graph, the data is presented using the actual amounts that the percentages represent.

To figure out a number from a percentage, we have to do a little arithmetic.

Let’s look at the first piece of data-Trey spent 40% of $40.00 on food.

We need to figure out how much that 40% of 40.00 is. To do that, we can write a proportion. A proportion compares two fractions, so first we convert our percentage to a fraction:

40 \% = \frac{40}{100}

Notice that the fraction shows the partial value on top, and the total on the bottom. Next, we want to know how much of the $40.00 is 40%. We write a second fraction with the total number of dollars Trey has to spend on the bottom, and a variable on top to represent the part of his total money we want to know:

\frac{x}{40}

Here is our proportion.

\frac{40}{100}& = \frac{x}{40}\\1600 &= 100x\\x&=16

You can see that we cross multiplied and divided to get our answer.

Trey spent $16 of his $40.00 on food.

If you look back at the bar graph, you can see that this is the actual amount from the bar graph.

Once you have converted all of the percentages to actual numbers, you can build a bar graph just as you did in an earlier lesson.

Now it is time to practice. Practice converting these percentages into numbers.

  1. John spent 15% of $20.00 on candy. How much did he spend?
  2. Susan ate 45% of 20 carrots. How many did she eat?

IV. Select the Best Way to Display Data

Now we have learned all about the different ways to display data. Each method has its pros and cons. When assessing a situation, you will need to select the best choice for displaying your data.

Here are some notes on each of the ways that we have learned about to display data.

  1. Frequency Table-shows how often an event occurs.
  2. Line plot-shows how often an event occurs-useful when there are a lot of numbers over a moderate range.
  3. Bar graphs-useful when comparing one or more pieces of data
  4. Line graph-shows how information changes over time
  5. Circle graph-a visual way to show percentages of something out of a whole.

Take a minute to write these notes down in your notebooks.

Choose the best data display given each description below.

  1. A tally of how many people ate ice cream cones in one week.
  2. The number of people who attended Red Sox games for 2002, 2003 and 2004.
  3. Percentages showing where people choose to go on vacation.

Real Life Example Completed

Vegetable Totals

Now that you have learned all about circle graphs, you are ready to help Alex with his dilemma.

Let’s look at the problem again before we begin.

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

Squash = 100

Zuchini = 60

Potatoes = 40

Carrots = 120

Tomatoes = 80

Alex wishes that she had put the information in a bar graph because he finds them so much easier to read.

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.

  1. What is the largest group of vegetables grown?
    1. According to the graph, the carrots were the largest group grown.
  2. If they were to double production next year, how many of each type of vegetable would be grown?
    1. Carrots = 120 to 240, tomatoes = 80 to 160, zucchini = 60 to 120, squash = 100 to 200, potatoes = 40 to 80.
  3. Which vegetable was the smallest group?
    1. 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.

Alex prefers bar graphs to circle graphs. Let’s use the data from the circle graph to build a bar graph.

  • The first thing to see is that the range of growth is from 40 to 120. We can make our axis on the left hand side have a range from 0 to 120 in intervals of 20. This will include each category of vegetable.
  • Here is our bar graph.

Alex and Tania now have two different ways to examine the same data. Planning for next year’s garden is a lot simpler now.

Vocabulary

Here are the vocabulary words that you will find in this section.

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.

Technology Integration

Khan Academy Reading Pie Graphs (Circle Graphs)

James Sousa, Constructing a Circle Graph Part 1

James Sousa, Constructing a Circle Graph Part 2

Other Videos:

http://www.youtube.com/watch?v=jFg-e51Rhv4 – This is an excellent video on the basics of creating a circle graph.

Time to 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 and 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?

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