Pie charts & waffle diagrams
🎯 In this topic you will
- Draw and interpret pie charts and waffle diagrams
🧠 Key Words
- label
- pie chart
- proportions
- sector
- waffle diagram
Show Definitions
- label: A word or number used to identify parts of a diagram or chart.
- pie chart: A circular chart divided into sectors to show proportions of a whole.
- proportions: The relative size or ratio of parts compared to the whole.
- sector: A slice of a circle in a pie chart that represents a proportion of the whole.
- waffle diagram: A grid of squares used to represent percentages or proportions visually.
You can use a pie chart to display data showing how an amount is divided or shared. It shows proportions, not actual amounts.
You draw a pie chart as a circle divided into sections called sectors. The angles at the centres of all the sectors add up to $360^\circ$. When you draw a pie chart, you must make sure that you label each sector and draw the angles accurately.
❓ EXERCISES
1. The table shows the number of different makes of car in a car park.
| Make of car | Frequency |
|---|---|
| Ford | 12 |
| Vauxhall | 18 |
| Toyota | 10 |
| Nissan | 20 |
a. Copy and complete the calculations below to work out the number of degrees for each sector of a pie chart, to show the information given in the table.
👀 Show answer
Total number of cars = $12+18+10+20=60$.
Number of degrees per car = $360 \div 60 = 6$°.
Number of degrees for each sector:
- Ford = $12 \times 6 = 72$°
- Vauxhall = $18 \times 6 = 108$°
- Toyota = $10 \times 6 = 60$°
- Nissan = $20 \times 6 = 120$°
b. Draw a pie chart to show the information in the table. Remember to label each sector and to give the pie chart a title.
👀 Show answer
Draw a circle and divide it into sectors with the following angles:
- Ford → 72°
- Vauxhall → 108°
- Toyota → 60°
- Nissan → 120°
Label each sector clearly with the car make. Title: Car Park – Car Makes.
2. A group of 40 people are asked which type of music they prefer. The table shows the results. Draw a pie chart to show the information in the table.
| Type of music | Frequency |
|---|---|
| Soul | 5 |
| Classical | 20 |
| Pop | 8 |
| Other | 7 |
👀 Show answer
Total = 40 people → degrees per person = $360 \div 40 = 9°$.
- Soul = $5 \times 9 = 45°$
- Classical = $20 \times 9 = 180°$
- Pop = $8 \times 9 = 72°$
- Other = $7 \times 9 = 63°$
Pie chart sectors: Soul 45°, Classical 180°, Pop 72°, Other 63°.
3. A supermarket sells five types of milk made from plants. The pie chart shows the proportion of the different plant milks the supermarket sold one day.
a. Which milk was the most popular?
b. What fraction of the different plant milks sold was almond?
c. What percentage of the different plant milks sold was oat?
d. Altogether, the supermarket sold 180 litres on this day. How many litres of soya milk was sold on this day?
👀 Show answer
3a. Almond (largest sector: 120°).
3b. Almond fraction = $120 \div 360 = \tfrac{1}{3}$.
3c. Oat = 60° → $60 \div 360 = \tfrac{1}{6} = 16.7\%$.
3d. Soya = 90° → $90 \div 360 = \tfrac{1}{4}$.
$\tfrac{1}{4} \times 180 = 45$ litres.
🧠 Think like a Mathematician
Task: Work out the missing frequencies and totals from Alexi’s pie chart survey and justify your reasoning.
Scenario: Alexi asked people their favourite type of film and recorded the results in a table. Some numbers are missing:
| Favourite type of film | Frequency | Number of degrees |
| Action | 2 | 40 |
| Romantic | 7 | ? |
| Science fiction | ? | 80 |
| Comedy | ? | 100 |
Questions:
👀 show answer
- Each frequency corresponds to $\dfrac{360}{\text{total people}}$ degrees. First, find degrees per person using Action: - 2 people = 40° → 1 person = 20°.
- Romantic: 7 people × 20° = 140°.
- Science fiction: 80° ÷ 20° = 4 people.
- Comedy: 100° ÷ 20° = 5 people.
- Completed table:
| Favourite type of film | Frequency | Number of degrees |
| Action | 2 | 40 |
| Romantic | 7 | 140 |
| Science fiction | 4 | 80 |
| Comedy | 5 | 100 |
| Total | 18 | 360 |
- b i) Yes – to complete the pie chart you need the missing values.
- b ii) Use the fact that 1 person = 20°.
- b iii) Total = 18 people.
❓ EXERCISES
5. The waffle diagram shows the colours of the cars in a school’s staff car park.
a. Copy the table and use the waffle diagram to complete it, showing the number of each colour car.
| Colour of car | Number of cars |
|---|---|
| Red | 3 |
| Blue | 4 |
| Green | 5 |
| Yellow | 2 |
| White | 6 |
👀 Show answer
Total cars = $3 + 4 + 5 + 2 + 6 = 20$.
Red: 3
Blue: 4
Green: 5
Yellow: 2
White: 6
b. Draw a pie chart to show the information given in the completed table.
👀 Show answer
Each car represents $360 \div 20 = 18°$ in the pie chart.
- Red = $3 \times 18 = 54°$
- Blue = $4 \times 18 = 72°$
- Green = $5 \times 18 = 90°$
- Yellow = $2 \times 18 = 36°$
- White = $6 \times 18 = 108°$
Draw a circle, divide into the above angles, and label each sector with the car colour.
🧠 Think like a Mathematician
Task: Use the waffle diagram to draw a pie chart showing the number of people at a tennis tournament.
Scenario: The waffle diagram has 50 squares in total. Each square represents 1 person. The key shows: - Women (purple) = 20 squares - Men (green) = 10 squares - Girls (white) = 6 squares - Boys (orange) = 14 squares
Questions:
👀 show answer
- Total squares = 50, so each square = $\tfrac{360}{50} = 7.2^\circ$.
- Angles: - Women: 20 × 7.2 = 144° - Men: 10 × 7.2 = 72° - Girls: 6 × 7.2 = 43.2° - Boys: 14 × 7.2 = 100.8°
- b i) Method: find degrees per person (360 ÷ 50), then multiply by each group’s frequency.
- b ii) Yes – the same method works for any number of squares, since you always divide 360° by the total number of people.
- b iii) The best method is the degrees-per-person method because it is systematic, always works, and avoids estimation errors.
❓ EXERCISES
7. The waffle diagram shows the number of hot drinks sold in a café on one day.
a. Copy the table and use the diagram to complete it.
| Hot drink | Number of drinks | Percentage of total | Number of degrees |
|---|---|---|---|
| Tea | 45 | 30% | 108° |
| Coffee | 90 | 60% | 216° |
| Hot chocolate | 15 | 10% | 36° |
| Total | 150 | 100% | 360° |
b. Sofia says: “Instead of working out the percentages and then the degrees, I think it is easier to work out the degrees straight away, like this: Tea = $\dfrac{45}{150} \times 360 = 108°$.” Do you agree with Sofia or would you rather work out the percentages and then the degrees? Explain why.
👀 Show answer
Both methods are valid:
- Sofia’s method (direct to degrees) is quicker, because it goes straight from fraction to sector angle.
- The percentage method is useful if you also want to compare proportions in percentage terms.
It depends on whether you need percentages as well as degrees. If not, Sofia’s method is simpler.
c. Draw a pie chart to show the information given in the waffle diagram.
👀 Show answer
Pie chart sectors should be drawn with:
- Tea → 108°
- Coffee → 216°
- Hot chocolate → 36°
Label each sector clearly with the drink name.
8. The pie chart shows the results of a survey of students’ favourite subject. 180 students chose Maths. Show that 105 students chose ‘other’.
👀 Show answer
Step 1: The Maths sector = 120°.
Step 2: If 120° corresponds to 180 students, then:
$\text{Scale} = 180 \div 120 = 1.5$ students per degree.
Step 3: The ‘other’ sector = 70° (since total = 360°, and $360 - (120 + 42 + 90 + 38) = 70$).
Step 4: Number of students for ‘other’ = $70 \times 1.5 = 105$.
✅ Therefore, 105 students chose ‘other’.
⚠️ Be careful!
- Always use the total: compute fractions with $T=\text{sum of all categories}$; angles are $(\text{category}/T)\times 360^\circ$.
- Angles must sum to $360^\circ$: due to rounding, adjust the last sector slightly so totals match exactly.
- Label every sector: include category name and value (count or %) and add a clear title/legend.
- Don’t read by arc length/area: compare central angles (or percentages), not just how long the edge looks.
- Percent ↔ angle checks:$1\% = 3.6^\circ$, so $25\% = 90^\circ$, $50\% = 180^\circ$, $10\% = 36^\circ$.
- From pie to counts: use $\text{count} = (\text{angle}/360^\circ)\times T$; don’t guess by eye.
- Waffle diagrams: each square is equal; use $\%\!=\text{squares}/\text{total squares}\times 100\%$ and $\text{angle}=(\text{squares}/\text{total})\times 360^\circ$.
- Count squares carefully: tick as you count, and be consistent about half-squares; totals must equal the full grid.
- Use consistent units: don’t mix raw counts from waffles with percentages from pies without converting via the same total $T$.
- Common slip: using $360/T$ incorrectly—compute “degrees per one” first ($\text{dp1}=360^\circ/T$), then multiply by each category.