Interpreting results
Pie charts and waffle diagrams
A pie chart shows how a whole is divided up. It tells you the proportions, not the amounts — which is exactly why it works so well for percentages.
What a pie chart shows
A PIE CHART shows how an amount is divided or shared. It shows PROPORTIONS, not actual amounts. The circle is split into SECTORS, and the angles at the centre add up to 360°. A WAFFLE DIAGRAM does the same job with a 10 × 10 grid of squares — each square is 1%, which makes percentages very easy to read.
Drawing one: degrees per person
Ninety people were asked about their holiday. First work out the degrees for ONE person: 360° ÷ 90 = 4° per person Then multiply for each sector: activity 32 × 4° = 128° beach 27 × 4° = 108° city break 24 × 4° = 96° other 7 × 4° = 28° Always check: 128 + 108 + 96 + 28 = 360 ✓
Reading a sector back
A sector of 30° out of 360° is 30/360 = 1/12 of the people. A sector of 72° is 72/360 = 1/5 = 20%. Simplify the fraction, then convert if the question asks for a percentage.
Finding a missing sector
The sectors must total 360°, so a missing one is whatever is left. If four sectors measure 30°, 133°, 72° and 45°: 30 + 133 + 72 + 45 = 280° 360 − 280 = 80° And 80/360 = 2/9, so with 90 people that is 2/9 × 90 = 20 people.
Worked examples
Degrees per person for 90 people
- A full circle is 360°.
- 360 ÷ 90 = 4.
Answer: 4° per person
The sector for 27 beach holidays
- Each person is 4°.
- 27 × 4 = 108.
Answer: 108°
27 out of 90 as a percentage
- 27 ÷ 90 = 0.3.
- 0.3 × 100 = 30.
Answer: 30%
A 72° sector as a fraction
- 72 out of 360.
- 72/360 simplifies to 1/5.
Answer: 1/5, which is 20%
Sectors of 30°, 133°, 72° and 45° — what is left?
- 30 + 133 + 72 + 45 = 280.
- 360 − 280 = 80.
Answer: 80°
Checking a pie chart is correct
- Add every sector angle.
- The total must be exactly 360°.
Answer: They must add to 360°
Where you see this in real life
- Election results are shown as pie charts because the share of the vote matters more than the raw count.
- A phone's storage screen is a waffle or bar of 100 units, so each square is one per cent of the space.
Key words
- Pie chart
- a circle divided into sectors to show proportions
- Sector
- a slice of a pie chart
- Waffle diagram
- a 10 by 10 grid where each square is 1%
- Proportion
- how big a part is compared with the whole
- Label
- the text saying what each sector represents