Pie Charts

20 min

Let's begin

Mugisha's class asked 40 pupils how they come to school. This time they do not just want to compare the ways of travelling. They want to show what share of the whole school uses each one.

For "parts of a whole", the best picture is a pie chart: a circle cut into slices, like a cake.

What a pie chart shows

The whole circle stands for all the data: 100%, which is 360° at the centre.
Each slice, called a sector, stands for one category. A bigger share gets a bigger slice.
Pie charts are best with a few categories. With many tiny slices they become hard to read.

Easy shares to remember: half = 50% = 180°; a quarter = 25% = 90°; an eighth = 12.5% = 45°.

Working out the angles

Each category gets the same fraction of 360° as it has of the data:

sector angle = frequency ÷ total × 360°

Way of travel	Pupils	Working	Angle
Walk	20	20 ÷ 40 × 360°	180°
Bicycle	10	10 ÷ 40 × 360°	90°
Moto	6	6 ÷ 40 × 360°	54°
Bus	4	4 ÷ 40 × 360°	36°
Total	40		360°

Always check that the angles add up to 360°: 180 + 90 + 54 + 36 = 360. ✔

Drawing the pie chart

Draw a circle with your compasses and mark the centre.
Draw one radius, straight up from the centre.
Put your protractor on the centre and measure the first angle (180°) from that radius. Draw the next radius.
Measure each following angle from the last line you drew.
Label every sector (or add a key) and give the chart a title.

Reading a pie chart

To go back from an angle to an amount, use: amount = angle ÷ 360 × total.

Worked example

a family spends 120 000 Frw a month. Their pie chart shows food 150°, school fees 90°, rent 60°, transport 30° and savings 30°.

Food: 150 ÷ 360 × 120 000 = 50 000 Frw.
School fees: 90° is a quarter of the circle, so ¼ × 120 000 = 30 000 Frw.
Rent: 60 ÷ 360 × 120 000 = 20 000 Frw.
Transport and savings: 30 ÷ 360 × 120 000 = 10 000 Frw each.
Check: 50 000 + 30 000 + 20 000 + 10 000 + 10 000 = 120 000 Frw. ✔

Bar chart or pie chart?

Use a bar chart to compare the sizes of categories with each other. Use a pie chart to show how one whole is shared into parts.

Tip

Everything is "out of 360". Angle = frequency ÷ total × 360°, and every pie chart's angles add up to exactly 360°.

✦

Try it yourself

In a class of 30 pupils, 10 like football best. What angle is the football sector?
A pie chart shows the favourite sports of 50 people. The netball sector is 72°. How many people chose netball?
What percentage of the data is a sector of 180°?
A pie chart has three sectors. Two are 150° and 120°. What is the third?

Answers

10 ÷ 30 × 360° = 120°.
72 ÷ 360 × 50 = 10 people.
180° is half the circle: 50%.
360° − 150° − 120° = 90°.

Quick check

60 pupils were asked their favourite sport, and 15 chose football. What is the angle of the football sector in a pie chart?

What you learned today

In a pie chart the whole circle (360°) is all the data, and each sector is one category.
Sector angle = frequency ÷ total × 360°; amount = angle ÷ 360 × total.
Pie charts show parts of a whole; bar charts compare categories.

Sources and credits

Mathematics Grade 8, 19.3 Pie charts by Siyavula Education, licensed under CC BY 3.0. Adapted by Ganzaa.

The school-travel and family-budget examples, the pie chart drawing and the table of angles were written by Ganzaa.

1What a pie chart shows

2Working out the angles

3Drawing the pie chart

4Reading a pie chart

5Bar chart or pie chart?