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Interpret circle graphs

A circle graph represents a whole data set as a circle divided into sectors, with each sector’s central angle, fraction of the circle, and percentage corresponding to a category’s share of the total. Interpretation includes comparing category proportions, determining a category’s count when the total is known, and finding the total or missing share from given information, while recognizing that sector size—not position or radius—communicates the data.

Detailed Explanation: Interpret circle graphs

A circle graph shows how a whole group is divided into categories. The entire circle represents:

  • 360∘360^\circ
  • 11 whole
  • 100%100\%

A larger sector represents a larger share. The sector’s position in the circle does not matter.

Example: A circle graph shows how 40 students spend their free time.

  • Sports: 144∘144^\circ
  • Reading: 90∘90^\circ
  • Music: 54∘54^\circ
  • Art: the remaining part

Step 1: Find a sector’s fraction of the circle.

Use

fraction=sector angle360∘\text{fraction}=\frac{\text{sector angle}}{360^\circ}

For sports:

144360=25\frac{144}{360}=\frac{2}{5}

So sports represents 25\frac{2}{5} of the students.

Step 2: Change the fraction to a percentage.

25=40%\frac{2}{5}=40\%

Sports represents 40%40\% of the circle.

Step 3: Find the number of students.

Multiply the percentage by the total:

40%×40=0.40×40=1640\%\times 40=0.40\times 40=16

So, 16 students chose sports.

For reading:

90360=14=25%\frac{90}{360}=\frac14=25\% 25%×40=1025\%\times 40=10

So, 10 students chose reading.

For music:

54360=320=15%\frac{54}{360}=\frac{3}{20}=15\% 15%×40=615\%\times 40=6

So, 6 students chose music.

Step 4: Find the missing art sector.

First subtract the known angles from the whole circle:

360∘−(144∘+90∘+54∘)=72∘360^\circ-(144^\circ+90^\circ+54^\circ)=72^\circ

Art represents 72∘72^\circ of the circle.

Its percentage is

72360=20%\frac{72}{360}=20\%

The number of students is

20%×40=820\%\times 40=8

So, 8 students chose art.

Step 5: Compare categories.

Sports is 40%40\%, while music is 15%15\%. Therefore, sports represents the larger share. The difference is

40%−15%=25%40\%-15\%=25\%

So, sports represents 25 percentage points more of the students than music.

Learn by doing: Interpret circle graphs

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    Graphing - Circle Graph (Fractions) - Read Value

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