Turn a frequency into an angle
30 people out of 120 surveyed chose tea. What angle represents them on a pie chart?
Find the fraction of the total first, then scale it up to 360°.
Year 8
Draw and interpret pie charts
Convert frequency data into pie chart angles accurately, justify when a pie chart is or is not the right choice, and compare categories visually.
Lesson overview
Statistics and data
A pie chart splits a full turn (360°) between categories in proportion to their frequency. To find the angle for a category, divide its frequency by the total frequency, then multiply by 360°. A pie chart is best for showing how a whole splits into parts -- it isn't suitable for showing change over time or for data with too many categories to compare easily.
Every category's angle must add up to 360°
A survey of 120 people found: Tea 30, Coffee 60, Juice 20, Water 10.
| Drink | Tea | Coffee | Juice | Water |
|---|---|---|---|---|
| Frequency | 30 | 60 | 20 | 10 |
| Angle | 90° | 180° | 60° | 30° |
Check your angles by adding them -- they must total exactly 360°.
Is a pie chart the right choice?
A pie chart works well for parts of a whole, but not for every data set.
Favourite subject in a class survey
Parts of one whole group
Temperature each month of the year
Better as a line graph -- shows change over time
Ask: does this data show parts of a whole, or change over time?
Worked example
40 students picked a favourite sport: Football 20, Swimming 10, Tennis 6, Athletics 4. Draw the pie chart.
| Sport | Football | Swimming | Tennis | Athletics |
|---|---|---|---|---|
| Frequency | 20 | 10 | 6 | 4 |
- Find the total: 20 + 10 + 6 + 4 = 40 students.
- Divide each frequency by 40, then multiply by 360°.
- Football: × 360° = 180°. Swimming: × 360° = 90°.
- Tennis: × 360° = 54°. Athletics: × 360° = 36°.
- Check the angles add to 360°, then draw each sector.
Try it
Work out the angle for each category before answering, and check your angles sum to 360°.
Question 1
A survey of 60 people found 15 prefer cats. What angle represents them on a pie chart?
Question 2
A pie chart has sectors of 120°, 100° and 90°. What is the missing sector's angle?
Question 3
Which data set is best shown as a pie chart?
Question 4
In a pie chart, category A has an angle of 144°. What fraction of the data does A represent?
Question 5
80 people were asked their favourite season. Winter got a 45° sector. How many people chose winter?
Common mistakes
Watch for these when working through the lesson.
- Using the frequency itself as the angle, instead of scaling it to 360°.
- Forgetting to find the total frequency before dividing.
- Choosing a pie chart for data that changes over time, when a line graph fits better.
Related topics
These ideas fit closely with this lesson.
- Scatter graphs, line of best fit and correlation.
- Choose the most appropriate graph for a data set.
- Calculate mode, median, mean and range from small data sets.