6.23: Circle Graphs to Display Data
One day while Taylor was in the candy store, she saw a chart that her Dad had made sitting on the counter.
“What’s this mean?” she asked looking at the chart.
“That is a chart that shows our best sellers. Every other candy sells less than 10%, so I don’t usually include it. These are the top sellers. I keep track of our inventory each month and determine which candies were the top sellers. Then I create a graph of the data,” he explained.
“Where is the graph?”
“I haven’t made it yet.”
“I could do that,” Taylor said smiling.
“Terrific! Go right ahead.”
Taylor was so excited. She could finally put all of her math to work. She knew that a circle graph would be the best way to show the percentages. Here is the chart.
Lollipops - 55%
Licorice - 10%
Chocolates - 20%
Gummy Bears - 15%
Taylor started to work on the circle graph and she thought that she knew what she was doing, but then she got stuck. She couldn’t remember how to change each percentage into a number of degrees.
This is where you come in. It is your turn to help Taylor. Pay attention to this Concept and you will know how to create the circle graph in the end.
Guidance
Creating a circle graph may seem tricky, but if you think about circle graphs it can become easier to figure out. First, notice that in the graphs at the end of the last Concept, that each percentage was converted to a specific number of degrees.
When you know the number of degrees that a percentage is equal to, you can use a protractor and a circle to draw it in exactly.
To figure this out, we have to figure out each percentage in terms of degrees. How do we do this?
First, we do this by creating a proportion. A percent is out of 100, so we can make a ratio out of any percent.
25% becomes \begin{align*}\frac{25}{100}\end{align*}
15% becomes \begin{align*}\frac{15}{100}\end{align*}
A circle is out of \begin{align*}360^ \circ\end{align*}. Since we are trying to figure out the number of degrees, we use a variable over 360 for the second ratio.
Here is a proportion for converting 25% to degrees.
\begin{align*}\frac{25}{100} = \frac{x}{360}\end{align*}
Now we cross multiply and solve for the variable \begin{align*}x\end{align*}. That will be the number of degrees.
\begin{align*}100x & = 25(360)\\ 100x & = 9000\\ x & =90\\ 25 \% &= 90^\circ\end{align*}
Now if you were going to draw this on a circle graph, you could take a circle and your protractor and measure in a \begin{align*}90^\circ\end{align*} angle. That would equal 25% of the graph.
Now let's apply this.
The table shows the number of students in the seventh grade who are studying each foreign language. Make a circle graph that shows the data.
Foreign Language | Number of Students Studying Language |
---|---|
Spanish | 88 |
French | 48 |
Italian | 16 |
German | 8 |
Step 1: Find the total number of seventh grade students studying a foreign language. Then find the percent of students studying each language.
\begin{align*}88 + 48 + 16 + 8 = 160\end{align*}
Foreign Language | Number of Students Studying Language | Percent of Students Studying Language |
---|---|---|
Spanish | 88 | \begin{align*}\frac{88}{160} = \frac{11}{20} = 55 \%\end{align*} |
French | 48 | \begin{align*}\frac{48}{160} = \frac{3}{10} = 30 \%\end{align*} |
Italian | 16 | \begin{align*}\frac{16}{160} = \frac{1}{10} = 10 \%\end{align*} |
German | 8 | \begin{align*}\frac{8}{160} = \frac{1}{20} = 5 \%\end{align*} |
Step 2: Find the measure of the central angle by multiplying \begin{align*}360^\circ\end{align*} by the percent.
Foreign Language | Number of Students Studying Language | Percent of Students Studying Language | Degrees in Central Angle |
---|---|---|---|
Spanish | 88 | 55% | 55% of \begin{align*}360^\circ = 0.55 \times 360^\circ = 198^\circ\end{align*} |
French | 48 | 30% | 30% of \begin{align*}360^\circ = 0.30 \times 360^\circ = 108^\circ\end{align*} |
Italian | 16 | 10% | 10% of \begin{align*}360^\circ = 0.10 \times 360^\circ = 36^\circ\end{align*} |
German | 8 | 5% | 5% of \begin{align*}360^\circ = 0.05 \times 360^\circ = 18^\circ\end{align*} |
Step 3: 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 4: Label each sector with a title and percent and give a title to the entire circle graph.
Here is the final graph.
Convert each percent into degrees.
Example A
20%
Solution: \begin{align*}72^\circ\end{align*}
Example B
40%
Solution:\begin{align*}144^\circ\end{align*}
Example C
75%
Solution:\begin{align*}270^\circ\end{align*}
Here is the original problem once again. Use what you have learned to help Taylor make the circle graph.
One day while Taylor was in the candy store, she saw a chart that her Dad had made sitting on the counter.
“What’s this mean?” she asked looking at the chart.
“That is a chart that shows our best sellers. Every other candy sells less than 10%, so I don’t usually include it. These are the top sellers. I keep track of our inventory each month and determine which candies were the top sellers. Then I create a graph of the data,” he explained.
“Where is the graph?”
“I haven’t made it yet.”
“I could do that,” Taylor said smiling.
“Terrific! Go right ahead.”
Taylor was so excited. She could finally put all of her math to work. She knew that a circle graph would be the best way to show the percentages. Here is the chart.
Lollipops - 55%
Licorice - 10%
Chocolates - 20%
Gummy Bears - 15%
Taylor started to work on the circle graph and she thought that she knew what she was doing, but then she got stuck. She couldn’t remember how to change each percentage into a number of degrees.
First, we need to convert each percentage to a number of degrees. We can do this by multiplying each decimal by 360.
Lollipops \begin{align*}.55 \times 360 = 198^\circ\end{align*}
Licorice \begin{align*}.10 \times 360 = 36^\circ\end{align*}
Chocolates \begin{align*}.20 \times 360 = 72^\circ\end{align*}
Gummy Bears \begin{align*}.15 \times 360 = 54^\circ\end{align*}
Next, Taylor can use a protractor and a circle to create the circle graph. Here is her final work.
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 the original problem once again.
Convert 30% into degrees.
Answer
First, we write a proportion.
\begin{align*}\frac{30}{100} = \frac{x}{360}\end{align*}
Next, we cross multiply and solve for the variable.
\begin{align*}10x &= 30(360)\\ 100x &= 10800\\ x &= 108\\ 30 \% &= 108^\circ\end{align*}
This is our answer.
Video Review
Here is a video for review.
- This is a James Sousa video on constructing a pie chart.
Practice
Directions: Use what you have learned to tackle each problem.
1. 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 |
2. 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.
3. Use a newspaper to locate a circle graph of some data. Then write five questions about the data.
Directions: Look at each percentage and then use a proportion to find the equivalent number of degrees. You may round your answer when necessary.
4. 12%
5. 25%
6. 28%
7. 42%
8. 19%
9. 80%
10. 90%
11. 34%
12. 15%
13. 5%
14. 10%
15. 78%
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Area
Area is the space within the perimeter of a two-dimensional figure.Diameter
Diameter is the measure of the distance across the center of a circle. The diameter is equal to twice the measure of the radius.Pi
(Pi) is the ratio of the circumference of a circle to its diameter. It is an irrational number that is approximately equal to 3.14.Radius
The radius of a circle is the distance from the center of the circle to the edge of the circle.Squaring
Squaring a number is multiplying the number by itself. The exponent 2 is used to show squaring.Image Attributions
Here you'll learn to make circle graphs given data.