Skill: Interpret circle graphs

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

• $360^\circ$
• $1$ whole
• $100\%$

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

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

Use

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

For sports:

$$\frac{144}{360}=\frac{2}{5}$$

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

Step 2: Change the fraction to a percentage.

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

Sports represents $40\%$ of the circle.

Step 3: Find the number of students.

Multiply the percentage by the total:

$$40\%\times 40=0.40\times 40=16$$

So, 16 students chose sports.

For reading:

$$\frac{90}{360}=\frac14=25\%$$ $$25\%\times 40=10$$

So, 10 students chose reading.

For music:

$$\frac{54}{360}=\frac{3}{20}=15\%$$ $$15\%\times 40=6$$

So, 6 students chose music.

Step 4: Find the missing art sector.

First subtract the known angles from the whole circle:

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

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

Its percentage is

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

The number of students is

$$20\%\times 40=8$$

So, 8 students chose art.

Step 5: Compare categories.

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

$$40\%-15\%=25\%$$

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