Pie Charts - Showing Parts of a Whole
A pie chart is a circular chart divided into slices. Each slice represents a category, and the size of the slice is proportional to that category's share of the total. Pie charts are ideal for showing how a whole is divided into parts.
How Pie Charts Work
A full circle = 360 degrees = 100% of the data. Each category's angle is calculated as:
Angle = (Frequency ÷ Total) × 360
Worked Examples
40 students were asked their favourite subject. Maths 10, English 8, Science 14, Art 8. Calculate the angle for each slice.
| Subject | Frequency | Calculation | Angle |
|---|---|---|---|
| Maths | 10 | 10/40 × 360 | 90° |
| English | 8 | 8/40 × 360 | 72° |
| Science | 14 | 14/40 × 360 | 126° |
| Art | 8 | 8/40 × 360 | 72° |
| Total | 40 | 360° |
A pie chart has a slice of 90 degrees out of 360. The total is 200 people. How many people does that slice represent?
90/360 = 1/4. 1/4 × 200 = 50 people.
Reading a pie chart: A chart shows transport methods. The Bus slice covers 135 degrees out of 360. There are 80 people total. How many travel by bus?
135/360 × 80 = 3/8 × 80 = 30 people.
Advantages and Limitations
| Advantages | Limitations |
|---|---|
| Shows proportions clearly at a glance | Hard to compare slices of similar size |
| Good for part-to-whole relationships | Exact values are not easy to read |
| Visually appealing | Not suitable for data with many small categories |
Key Takeaways
- Angle = (Frequency ÷ Total) × 360. All angles must sum to 360°.
- Pie charts show proportions, not exact values – always include a key or label.
- To find a frequency from an angle: Frequency = (Angle ÷ 360) × Total.
Practice Questions
- 60 people were surveyed about pets. Dogs 24, Cats 18, Fish 12, Other 6. Calculate the angle for each sector.
- A pie chart slice has an angle of 72 degrees. The total is 50. How many does it represent?
- A pie chart shows budget: rent 150 degrees, food 90 degrees, transport 60 degrees, savings 60 degrees. What fraction of the budget goes on food?
- A pie chart has four sectors: A = 120 degrees, B = 90 degrees, C = 80 degrees, D = ?. Find angle D and the fraction of the total it represents.
- A total of 180 students were surveyed. One sector = 40 degrees. How many students does this sector represent?