A school survey asked students to respond to the statement, “If a friend recommends music to me and supplies a link I always have a listen.” The percentages of responses are shown below. A total of 400 students were surveyed. How can this information be represented as a circle graph?

Completely False – 2%

False – 5%

Neither – 15%

True – 38%

Completely True – 40%

In this concept, you will learn how to read and understand circle graphs.

### Interpreting Circle Graphs

In a **circle graph**, the circle represents the whole. A circle graph can be used to compare the parts with the whole. It is a useful way to visually display data. Each of the parts is called a **sector**.

Let’s look at how data is expressed in a circle graph.

The circle graph below shows how the students at Grandville Middle School voted for a school mascot. Which mascot got the least number of votes?

Since there are no values shown on the circle graph, you need to visually determine which sector is the smallest. The smallest sector is the one for the Panther.

The answer is the Panther got the least number of votes for mascot.

Let’s look at another example.

The circle graph shows the method of transportation used by students to get to Grandville Middle School. What percent of the students use the school bus to get to school?

The sectors of a circle graph must add up to 100%. Find the sum of the three given percents and then subtract that total from 100%.

The answer is 40% of the students use the school bus to get to school.

Let’s look at another example.

This circle graph shows the results of a music survey. What fraction of the people surveyed said country was their favorite type of music?

The fractions in the sectors of a circle graph must add up to 1. Find the sum of the three given fractions and then subtract from 1.

\begin{align*}\begin{array}{rcl}
\frac{1}{4}+ \frac{1}{2}+ \frac{1}{10} & = & \frac{5}{20}+ \frac{10}{20}+ \frac{2}{20}= \frac{17}{20}\\ \\
1- \frac{17}{20} & = & \frac{3}{20}
\end{array}\end{align*}

The answer is \begin{align*}\frac{3}{20}\end{align*}

### Examples

#### Example 1

Earlier, you were given a problem about the music recommendation survey, that asked if you felt the need to listen to a link a friend sent you.

The percentages of the 400 student responses are shown below.

Response |
Percent |

Completely False | 2% |

False | 5% |

Neither | 15% |

True | 38% |

Completely True | 40% |

How many degrees in the circle do each of the answers take up? How many students selected each response?

First, change the percents to decimals.

\begin{align*}\begin{array}{rcl}
2\% &=& 0.02 \\
5\% &=& 0.05 \\
15\% &=& 0.15 \\
38\% &=& 0.38 \\
40\% &=& 0.40
\end{array}\end{align*}

Then, multiply by 360 to get the degrees.

The answer is in the table below.

Response |
Degrees of the Circle |

Completely False | 7.2° |

False | 18° |

Neither | 54° |

True | 136.8° |

Completely True | 144° |

To figure out how many students selected each response, you also need to consider the decimal form of each percent.

Then, multiply by the total number of students, which is 400.

The answer is in the table below.

Response |
Number of students |

Completely False | 8 |

False | 20 |

Neither | 60 |

True | 152 |

Completely True | 160 |

#### Example 2

You can show the same circle graph with its percents or with the measures of its central angles. The sum of the measures of the central angles in a circle graph is 360°.

Notice that you can take the percent, change it to a decimal, and then multiply it by 360 to find the number of degrees. Check this out with the following example.

The table shows the results of the favorite school lunch of students in the seventh grade at Grandville Middle School. Make a circle graph for the results of the survey.

Favorite Food |
% of Students Surveyed |

Pizza | 30% |

Grilled Cheese | 35% |

Hamburger | 10% |

Chicken Fingers | 25% |

First, find the measure of the central angle by multiplying 360° by the percent.

Favorite Food |
% of Students Surveyed |
Degrees in Central Angle |

Pizza | 30% | |

Grilled Cheese | 35% | 35% of \begin{align*}360^\circ = 0.35 \times 360^\circ = 126^\circ\end{align*} |

Hamburger | 10% | 10% of |

Chicken Fingers | 25% | 25% of \begin{align*}360^\circ = 0.25 \times 360^\circ = 90^\circ\end{align*} |

Next, 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.

Now, label each sector with a title and percent and give a title to the entire circle graph.

If you have actual data, you first need to find the percent for each sector of the circle graph. Then you can find the measures of the central angles of the circle and make the circle graph.

**Use the two graphs from the school transportation example above to answer the following questions.**

#### Example 3

Which number of degrees is equal to 40%?

First, change the percent to a decimal.

\begin{align*}40\% = 0.40\end{align*}

Next, multiply by 360.

The answer is 40% is equal to 144°.

#### Example 4

True or false: 25% of a circle graph is the same as a 90° angle?

First, change the percent to a decimal.

Next, multiply by 360.

The answer is true.

#### Example 5

How many degrees is equal to 15%?

First, change the percent to a decimal.

Next, multiply by 360.

The answer is 15% is equal to 54°.

### Review

Use the survey to answer each question.

A survey of 300 people asked them to name their favorite spectator sport. The results are shown in the circle graph below.

- What was the most favorite spectator sport of the people surveyed?
- What was the least favorite spectator sport of the people surveyed?
- What percent of the people surveyed said that football was their favorite spectator sport?
- How many people said that basketball was their favorite spectator sport?
- How many more people said that soccer was their favorite sport than ice hockey?
- The table shows 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 |

- 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.
- Use a newspaper to locate a circle graph of some data. Then write five questions about the data.

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.

- What percent of the students enjoy soup as a lunch?
- What is the favorite choice of students for school lunch?
- What is the least favorite choice?
- What percent of the students enjoy salad?
- What percent of the students did not choose salad as a favorite choice?
- What percent of the students chose either pizza or tacos as their favorite choice?
- What percent of the students chose chicken sandwich or pizza as their favorite choice?
- What percent of the students did not choose chicken or pizza?
- What is your favorite choice for lunch?
- If you could add a food choice to this survey, what would it be?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.22.