10.5 A Slice of the Pie

A pie chart displays how a whole splits into proportions, using slices of a circle. Each slice’s angle is proportional to the quantity it stands for, and the full circle measures 360°.

Here is a table of grades earned by 40 students:

Grade A B C D E
Students 14 10 8 6 2

To draw the chart, we share 360° in the ratio 14 : 10 : 8 : 6 : 2. First simplify the ratio by dividing each term by their HCF, which is 2:

14 : 10 : 8 : 6 : 2 \;=\; 7 : 5 : 4 : 3 : 1.

These terms add to 7 + 5 + 4 + 3 + 1 = 20, so every “part” is worth 360° \div 20 = 18°. The slice angles are:

\begin{aligned} \text{Grade A} &= 7 \times 18° = 126°, & \text{Grade B} &= 5 \times 18° = 90°,\\ \text{Grade C} &= 4 \times 18° = 72°, & \text{Grade D} &= 3 \times 18° = 54°,\\ \text{Grade E} &= 1 \times 18° = 18°. \end{aligned}

A reassuring check: 126° + 90° + 72° + 54° + 18° = 360°.

Math Talk To draw the chart: using a protractor, mark off the first slice (126°) from a starting radius, then mark 90° from the new edge for the next slice, then 72°, and so on, each slice measured from the boundary of the one before. Why must 126° + 90° + 72° + 54° + 18° come to exactly 360°? What would it mean if your slices failed to close the circle?

Use the interactive pie-chart maker below to turn any small data set into slice angles, then watch the chart draw itself.

Pie-Chart Angle Maker
Enter up to five category values (e.g. number of students). The widget shares 360 degrees in proportion and draws the pie.

Figure it Out: Pie Charts

Practice

  1. 480 people voted for a favourite season. 120 liked summer, 160 liked rainy, and the rest liked winter. Find the slice angles and draw a pie chart.
  2. Draw a pie chart for favourite app categories: Games 40\%, Music 30\%, Learning 20\%, News 10\%.
  3. Collect the favourite sports of students in your class (each student picks one), then construct a pie chart from your data.
  1. Winter = 480 - 120 - 160 = 200 people. Each person is worth 360° \div 480 = 0.75°, so the angles are summer = 120 \times 0.75 = 90°, rainy = 160 \times 0.75 = 120°, winter = 200 \times 0.75 = 150° (90+120+150 = 360 ✓).
  2. A percentage is a share of the whole, so multiply each by 360°: Games = 40\% \times 360° = 144°, Music = 30\% \times 360° = 108°, Learning = 20\% \times 360° = 72°, News = 10\% \times 360° = 36° (144+108+72+36 = 360 ✓).
  3. (Activity, answers depend on your class’s data. Confirm that all your slice angles add to 360°.)