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Interpretation of Circle Graphs

Connect circle graph percents to degrees of a circle.

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Interpretation of Circle Graphs
Credit: CK-12 Foundation
License: CC BY-NC 3.0

Monica is opening a restaurant. She wants to offer at least two kinds of ice cream flavors for dessert. She uses a data collection company to find out what flavors people prefer. The company uses this circle graph to show the results of the survey. Of the four flavors, which two flavors would most people prefer?

In this concept, you will learn how to interpret circle graphs.

Interpreting Circle Graphs

A circle graph is a visual way of displaying data that is written in percents. The circle represents 100%. The circle is divided into sections. Each section shows what part of 100 that item represents. The circle graph uses different colors for each category being described. The legend on the right shows what each color corresponds to.

License: CC BY-NC 3.0

This circle graph describes a student’s spending habits.Each color represents what his money is spent on. Blue is savings, red is baseball cards, and green is food. By looking at this graph, you may determine that this student saves half (or 50%) of all his money. He spends a smaller fraction on baseball cards and the rest on food.

Notice that all three percents add up to 100%. A circle graph shows information out of 100.

Examples

Example 1

Earlier, you were given a problem about Monica and her ice cream flavors.

Monica needs to pick two flavors that would satisfy the most people. Monica needs to use the circle graph to make her decision.

First, Monica needs to find the two flavors with biggest section or the largest percents.

She sees that the red and blue sections make up most of the circle graph.

Then, she looks at the legend to see what the colors represent.

Red represents chocolate and blue represents vanilla.

Monica should pick chocolate and vanilla to satisfy the most people.

Example 2

Use the circle graph to answer the questions.

License: CC BY-NC 3.0

Based on this graph, which foreign language is the most popular?

First, look at the circle graph. Find the largest wedge. The percent is also written each wedge.

The pink wedge with 55% is the largest wedge.

Then, look at the legend to find what language pink represents.

Pink represents Spanish.

Spanish has the largest percent, 55%. This means 55% of all the students have studied Spanish.

Spanish is the most popular foreign language studied.

Example 3

License: CC BY-NC 3.0

Looking at the graph above, about what percent is not spent on saving?

First, look at the wedge that represents savings.

The blue wedge represents the amount spent on savings.

Then, determine about how much of the total is spent on savings.

The blue wedge takes up about half or 50% of the circle.

Example 4

True or false: the following percents could be part of one circle graph: 25%, 10%, and 65%.

First, add the given percents.

\begin{align*}25\% + 10\% + 65\% = 100\%\end{align*}

A circle graph represents 100%.

True, 25%, 10% and 65% can be part of one circle graph.

Example 5

True or false: the following percents could be part of the same circle graph: 35%, 70%, and 5%.

First, add the given percents.

35% + 70% + 5% = 110%

A circle graph cannot be more than 100%.

False, 35%, 70% and 5% cannot be part of the same circle graph.

Review

Use the circle graph to answer the following questions.

License: CC BY-NC 3.0

  1. Which foreign language is the least popular?
  2. If 30% of the students chose French, what percent did not choose French?
  3. What percent of the students chose Italian?
  4. What percent of the students did not chose Italian?
  5. What percent of the students chose Latin?
  6. What percent of the students did not choose Latin or French?
  7. What percent of the students did not choose French or Spanish?
  8. What percent of the students did not choose German?

License: CC BY-NC 3.0

  1. What percent of Patrick’s budget is spent of transportation?
  2. What percent of the budget is spent on food?
  3. What percent of the budget is not spent on food or savings?
  4. If 35% of the budget is spent on rent and utilities, what percent is not spent on this?
  5. True or false. Patrick does not spend any money on clothing.
  6. What percent is spent on savings and food together?
  7. If Patrick was going to increase his savings by 15% what would the new percent of savings be?

Review (Answers)

To see the Review answers, open this PDF file and look for section 8.13. 

Resources

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Vocabulary

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 one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

Percent

Percent means out of 100. It is a quantity written with a % sign.

Sector

A sector of a circle is a portion of a circle contained between two radii of the circle. Sectors can be measured in degrees.

sector angle formula

The sector angle formula is used to calculate how many degrees of the circle should be allocated to a given value and is calculated by dividing the frequency of the data in the sector by the total frequency of the data all multiplied by 360.

Image Attributions

  1. [1]^ Credit: CK-12 Foundation; License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ License: CC BY-NC 3.0
  5. [5]^ License: CC BY-NC 3.0
  6. [6]^ License: CC BY-NC 3.0

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