6.22: Interpretation of Circle Graphs
The chart shows the Patrick family’s monthly budget. Make a circle graph to display their budget. Then find how much the family budgets for in each category if their monthly income is $2,500.
Rent and utilities - 35%
Food - 25%
Savings - 10%
Transportation - 15%
Clothing - 10%
Other - 5%
What does the family budget look like? Can you interpret where and how they spend their money?
This Concept is all about interpreting circle graphs. Use it to answer these questions at the end of the Concept.
Guidance
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 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 Panther got the least number of votes for mascot.
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 from 100%.
\begin{align*}15 \% + 20 \% + 25 \% &= 60 \%\\ 100 \% - 60 \% &= 40 \%\end{align*}
40% of the students use the school bus to get to school.
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*}\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{20}{20} - \frac{17}{20} = \frac{3}{20}\end{align*}
\begin{align*}\frac{3}{20}\end{align*} of the people surveyed said country was their favorite type of music.
We 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 \begin{align*}360^ \circ\end{align*}.
Notice that you can take the percent, change it to a decimal and multiply it by 360 to find the number of degrees. Check this out with the following examples.
Use the two graphs above to answer the following questions.
Example A
Which number of degrees is equal to 40%?
Solution:\begin{align*}144^\circ\end{align*}
Example B
True or false. 25% is the same as a \begin{align*}90^\circ\end{align*} angle?
Solution: True
Example C
How many degrees is equal to 15%?
Solution:\begin{align*}54^\circ\end{align*}
Here is the original problem once again.
The chart shows the Patrick family’s monthly budget. Make a circle graph to display their budget. Then find how much the family budgets for in each category if their monthly income is $2,500.
Rent and utilities - 35%
Food - 25%
Savings - 10%
Transportation - 15%
Clothing - 10%
Other - 5%
What does the family budget look like? Can you interpret where and how they spend their money?
Patrick's family spends most of their money on rent, utilities and food. They spend the least amount of money on other things and clothing. These are a couple of statements that we can make about their monthly budget.
Vocabulary
Here are the vocabulary words in this Concept.
- Circle Graph
- a visual display of data in a circle. A circle graph is created from percentages with the entire circle representing the whole. The sectors of the circle graph are divided according to degrees which are created out of \begin{align*}360^\circ\end{align*}.
- Sector
- the section of a circle graph. Each section is known as a sector. Each sector can be measured in degrees and given a percentage.
Guided Practice
Here is one for you to try on your own.
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% |
Answer
Step 1: Find the measure of the central angle by multiplying \begin{align*}360^\circ\end{align*} by the percent.
Favorite Food | % of Students Surveyed | Degrees in Central Angle |
---|---|---|
Pizza | 30% | 30% of \begin{align*}360^\circ = 0.30 \times 360^\circ = 108^\circ\end{align*} |
Grilled Cheese | 35% | 30% of \begin{align*}360^\circ = 0.35 \times 360^\circ = 126^\circ\end{align*} |
Hamburger | 10% | 10% of \begin{align*}360^\circ = 0.10 \times 360^\circ = 36^\circ\end{align*} |
Chicken fingers | 25% | 25% of \begin{align*}360^\circ = 0.25 \times 360^\circ = 90^\circ\end{align*} |
Step 2: 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.
Step 3: Label each sector with a title and percent and give a title to the entire circle graph.
What about if we have actual data?
If we have actual data, we first need to find the percent for each sector of the circle graph. Then we can find the measures of the central angles of the circle and make the circle graph.
Video Review
Here is a video for review.
- This is a Khan Academy video on reading circle graphs.
Practice
Directions: 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.
1. What was the most favorite spectator sport of the people surveyed?
2. What was the least favorite spectator sport of the people surveyed?
3. What percent of the people surveyed said that football was their favorite spectator sport?
4. How many people said that basketball was their favorite spectator sport?
5. How many more people said that soccer was their favorite sport than ice hockey?
6. The table shows the 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 |
7. 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.
8. 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.
9. What percent of the students enjoy soup as a lunch?
10. What is the favorite choice of students for school lunch?
11. What is the least favorite choice?
12. What percent of the students enjoy salad?
13. What percent of the students did not choose salad as a favorite choice?
14. What percent of the students chose either pizza or tacos as their favorite choice?
15. What percent of the students chose chicken sandwich and pizza as their favorite choice?
16. What percent of the students did not choose chicken or pizza?
17. What is your favorite choice for lunch?
18. If you could add a food choice to this survey, what would it be?
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
Here you'll learn to interpret circle graphs using given data.
Concept Nodes:
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.