Pie charts
🎯 In this topic you will
- Compare pie charts
🧠 Key Words
- categorical data
- pie chart
- proportions
- sector
Show Definitions
- categorical data: Data that can be sorted into groups or categories (e.g., colors, types of food).
- pie chart: A circular chart divided into sectors to show parts of a whole.
- proportions: The relative size or amount of one part compared to the whole.
- sector: A section of a circle representing part of the data in a pie chart.
You already know how to draw and interpret a pie chart.
You can use pie charts to compare different sets of categorical data, but remember that a pie chart shows proportions, not actual amounts.
❓ EXERCISES
1. The pie charts show the proportion of boys and girls in two swimming clubs.
There are 120 children in the Dolphins swimming club. There are 72 children in the Seals swimming club.
a. Which swimming club has the greater proportion of girls?
b. Which swimming club has the greater number of girls? Copy and complete the working.
👀 Show answer
Step 1: Proportion of girls in each club
- Dolphins: Girls sector = 150° out of 360° = $\tfrac{150}{360} = \tfrac{5}{12} \approx 41.7\%$
- Seals: Girls sector = 240° out of 360° = $\tfrac{240}{360} = \tfrac{2}{3} \approx 66.7\%$
✅ The Seals club has the greater proportion of girls.
Step 2: Number of girls in each club
- Dolphins: $\tfrac{150}{360} \times 120 = 50$ girls
- Seals: $\tfrac{240}{360} \times 72 = 48$ girls
✅ The Dolphins club has the greater number of girls (50 compared to 48).
Final Answer:
• Greater proportion of girls → Seals club • Greater number of girls → Dolphins club
2. The pie charts show the proportion of Ivan’s income that he made from gardening, washing windows, and painting houses in 2009 and 2019.
a. What fraction of Ivan’s income came from gardening in:
i) 2009 ii) 2019
b. Copy and complete these sentences. Choose from the words in the rectangle: doubled, stayed the same, tripled, halved, more than tripled.
- In 2019 the proportion of Ivan’s income that came from gardening had … compared to 2009.
- In 2019 the proportion of Ivan’s income that came from painting houses had … compared to 2009.
- In 2019 the proportion of Ivan’s income that came from washing windows had … compared to 2009.
In 2009, Ivan’s total income was $12,000. In 2019, Ivan’s total income was $24,000.
c. Show that Ivan earned the same amount of money from gardening in 2009 and 2019.
d. Show that Ivan earned six times as much money from washing windows in 2019 as in 2009.
e. How much more money did Ivan earn from painting houses in 2019 than in 2009?
🔎 Reasoning Tip
Use the fractions you found in part a.
👀 Show answer
2a.
- 2009: Gardening sector = 180° → $\tfrac{180}{360} = \tfrac{1}{2}$ (half).
- 2019: Gardening sector = 90° → $\tfrac{90}{360} = \tfrac{1}{4}$.
2b.
- Gardening: Halved.
- Painting houses: Stayed the same (135° in both years).
- Washing windows: Tripled (45° → 135°).
2c. 2009 gardening = $\tfrac{1}{2} \times 12{,}000 = 6{,}000$. 2019 gardening = $\tfrac{1}{4} \times 24{,}000 = 6{,}000$. ✅ Same amount in both years.
2d. 2009 washing = $\tfrac{1}{8} \times 12{,}000 = 1{,}500$. 2019 washing = $\tfrac{3}{8} \times 24{,}000 = 9{,}000$. $9{,}000 \div 1{,}500 = 6$. ✅ Six times as much.
2e. 2009 painting = $\tfrac{3}{8} \times 12{,}000 = 4{,}500$. 2019 painting = $\tfrac{3}{8} \times 24{,}000 = 9{,}000$. Increase = $9{,}000 - 4{,}500 = 4{,}500$. ✅ Ivan earned $4,500 more$ from painting houses in 2019.
3. The pie charts show the results of a survey about the types of chocolate preferred by men and by women. 480 men took part in the survey. 600 women took part in the survey.
a. How many men chose plain chocolate?
b. How many women chose plain chocolate?
c. Hassan thinks that more men than women like milk chocolate. Is Hassan correct? Show how you worked out your answer.
d. The ‘Caramel’ sector is the same size for men and for women. Without doing any calculations, explain how you know that more women than men chose ‘Caramel’.
👀 Show answer
3a. Plain (men) = $90^\circ$ out of $360^\circ$ = $\tfrac{1}{4}$. Number = $\tfrac{1}{4} \times 480 = 120$ men.
3b. Plain (women) = $81^\circ$ out of $360^\circ$ = $\tfrac{81}{360} = 0.225$. Number = $0.225 \times 600 = 135$ women.
3c. Milk (men) = $135^\circ$ out of $360^\circ$ = $\tfrac{135}{360} = 0.375$. Number = $0.375 \times 480 = 180$ men. Milk (women) = $120^\circ$ out of $360^\circ$ = $\tfrac{120}{360} = \tfrac{1}{3}$. Number = $\tfrac{1}{3} \times 600 = 200$ women. ✅ Hassan is incorrect — more women (200) than men (180) chose milk chocolate.
3d. The Caramel sector is the same angle for both men and women, but since more women (600) than men (480) took part, the actual number of women choosing Caramel must be larger.
4. The pie charts show the favourite sports of the students in two schools. There are 1600 students in Castlehill School. There are 1100 students in Riverside School.
Which school had the larger number of students who chose tennis as their favourite sport? Show your working.
👀 Show answer
Castlehill School: Tennis = 10% of 1600 = $0.10 \times 1600 = 160$ students.
Riverside School: Tennis = 14% of 1100 = $0.14 \times 1100 = 154$ students.
Final Answer: ✅ Castlehill School had the larger number of students choosing tennis (160 vs 154).
🧠 Think like a Mathematician
Task: Compare the proportions of cars sold by two garages and work out Ekta’s totals given that Kabir sells 600 cars in 2019.
Pie charts:
- Kabir’s garage: Kia 90°, Ford 120°, Seat 120°, Nissan 30°.
- Ekta’s garage: Kia 45°, Ford 40°, Seat 155°, Nissan 120°.
Kabir’s totals (600 cars):
- Kia: (90/360) × 600 = 150
- Ford: (120/360) × 600 = 200
- Seat: (120/360) × 600 = 200
- Nissan: (30/360) × 600 = 50
Questions:
👀 show answer
- a i) Ekta’s Kia share = 45°/360° = 1/8. If she sells the same Kia number as Kabir (150), then total = 150 ÷ (1/8) = 1200 cars.
- a ii) Ekta’s Ford share = 40°/360° = 1/9. If she sells the same Ford number as Kabir (200), then total = 200 ÷ (1/9) = 1800 cars.
- a iii) Ekta’s Nissan share = 120°/360° = 1/3. If she sells the same Nissan number as Kabir (50), then total = 50 ÷ (1/3) = 150 cars.
- b) Method: Work out the fraction of the pie chart for each car make. Then use: $\text{Total cars} = \dfrac{\text{Number of cars of that make}}{\text{fraction of circle for that make}}$.
- c) The best method is the fraction-of-circle method. It works with any pie chart and avoids needing to redraw diagrams.
❓ EXERCISES
6. The pie charts show the proportions of different sizes of T-shirts sold in a shop on two days. On Monday, the shop sold 144 T-shirts. On Tuesday, the shop sold the same number of small T-shirts as on Monday.
a. How many small T-shirts did the shop sell on Tuesday?
b. How many T-shirts did the shop sell altogether on Tuesday?
👀 Show answer
Step 1: Monday small T-shirts
Monday small = $80^\circ$ out of $360^\circ$ = $\tfrac{80}{360} = \tfrac{2}{9}$. $\tfrac{2}{9} \times 144 = 32$ small T-shirts.
Step 2: Tuesday small T-shirts
Tuesday small = $40^\circ$ out of $360^\circ$ = $\tfrac{1}{9}$ of total. If this equals 32, then total = $32 \times 9 = 288$.
Final Answer:
- a. 32 small T-shirts
- b. 288 T-shirts in total
7. The pie charts show the proportions of types of rice sold by two shops in May.
a. Copy and complete this table to show the amounts of rice sold by Shop A.
| Type of rice | Degrees in pie chart | Kilograms sold |
|---|---|---|
| Black | 30° | 6 kg |
| Brown | 120° | ? kg |
| Red | 60° | ? kg |
| White | 150° | ? kg |
| Total | 360° | ? kg |
🔎 Reasoning Tip
Use the fact that 6 kg of rice is represented by 30° in the pie chart.
b. In May, Shop B sold the same number of kilograms of red rice as Shop A. Copy and complete this table showing the amounts of rice sold by Shop B.
| Type of rice | Degrees in pie chart | Kilograms sold |
|---|---|---|
| Black | 20° | ? kg |
| Brown | 180° | ? kg |
| Red | 30° | ? kg |
| White | 130° | ? kg |
| Total | 360° | ? kg |
🔎 Reasoning Tip
Use the fact that the number of kilograms of red rice sold is the same in both tables.
c. Sofia says: “In Shop A, 60° of the pie chart represents red rice. In Shop B, 30° of the pie chart represents red rice. This means that, without doing any calculations, I can say that the total amount of rice sold in Shop A is double the total amount of rice sold in Shop B.” Explain why Sofia is incorrect.
👀 Show answer
| Type of rice | Degrees in pie chart | Kilograms sold |
|---|---|---|
| Black | 30° | 6 kg |
| Brown | 120° | 24 kg |
| Red | 60° | 12 kg |
| White | 150° | 30 kg |
| Total | 360° | 72 kg |
| Type of rice | Degrees in pie chart | Kilograms sold |
|---|---|---|
| Black | 20° | 4 kg |
| Brown | 180° | 36 kg |
| Red | 30° | 6 kg |
| White | 130° | 26 kg |
| Total | 360° | 72 kg |
Sofia is incorrect because the pie charts show proportions, not actual quantities. Shop A’s 60° represents 12 kg of red rice, and Shop B’s 30° represents 6 kg of red rice. The actual total sold in both shops is the same (72 kg each). Therefore, the size of the angle does not directly show the total — only the fraction of the whole.
⚠️ Be careful!
- Proportion ≠ count: a larger sector means a larger share, not necessarily a larger number. You need the totals for each chart.
- Always use totals: number in a category = $(\text{sector angle}/360^\circ)\times \text{total}$ or $(\%\!/100)\times \text{total}$.
- Equal sectors can hide unequal counts: same angle in two charts gives different counts if the totals differ.
- Match categories & legends: confirm colors/labels are consistent across the charts before comparing.
- Don’t compare by arc length: compare by central angle or stated percentage, not how long the edge looks.
- Quick checks:$1\%=3.6^\circ$, $25\%=90^\circ$, $50\%=180^\circ$. Angles in each chart must sum to $360^\circ$.
- Show your working: write the fraction/percentage first, then multiply by the chart’s total to avoid mistakes.