Pie Charts
A pie chart is a circular diagram divided into sectors, where the angle of each sector is proportional to the frequency of the category it represents, so the whole circle of 360 degrees shows how a total is split between categories. Pie charts are drawn and interpreted throughout the Processing and Representing Data strand of GCSE Statistics, usually alongside frequency tables.
Before you start
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Method
- Find the total frequency by adding up all the category frequencies.
- Work out the angle for one item by dividing 360 by the total frequency.
- Multiply the angle for one item by each category's frequency to get that category's sector angle.
- Check that all the sector angles add up to 360 degrees before drawing.
- Draw each sector with a protractor, labelling or colour-coding it, and add a key if needed.
- To read a pie chart, divide the given sector angle by 360, then multiply by the total frequency.
Worked example
A survey of 90 students asks their favourite subject. 40 chose Maths, 25 chose Science, and the rest chose Art. Find the sector angles for Maths, Science and Art.
- Total students = 90.
- Angle for one student = 360 / 90 = 4 degrees.
- Maths angle = 40 x 4 = 160 degrees.
- Science angle = 25 x 4 = 100 degrees.
- Art students = 90 - 40 - 25 = 25, so Art angle = 25 x 4 = 100 degrees.
- Check: 160 + 100 + 100 = 360 degrees, so the angles are correct. Final answer: Art's sector angle = 100 degrees.
Practice questions
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Q1A pie chart represents 60 people. What angle represents 1 person?Show answer
Answer: 6 degrees (360 / 60)
Q2In a pie chart representing 120 people, 30 people chose 'Yes'. What angle represents 'Yes'?Show answer
Answer: 90 degrees (30/120 x 360)
Q3A sector has an angle of 72 degrees in a pie chart representing 50 people in total. How many people does this sector represent?Show answer
Answer: 10 people (72/360 x 50)
Q4A pie chart shows four categories with angles 90, 120, 60 and x degrees. Find x.Show answer
Answer: 90 degrees (360 - 90 - 120 - 60)
Q5A pie chart represents 200 people. One sector has an angle of 45 degrees. How many people does it represent?Show answer
Answer: 25 people (45/360 x 200)
Q6Chart A represents 80 votes and has a 'Green Party' sector of 45 degrees. Chart B represents 150 votes and has a 'Green Party' sector of 30 degrees. Which chart represents more actual Green Party votes?Show answer
Answer: Chart B (12.5 votes compared with 10 votes)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A pie chart shows how 45 people travel to work. The sector for 'Car' has an angle of 160 degrees. Work out the number of people who travel by car.
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90 students were asked their favourite sport: football, tennis or swimming. 45 chose football and 20 chose tennis. (a) Work out how many chose swimming. (b) Work out the angle that should be drawn for swimming on a pie chart.
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A pie chart compares the favourite drinks of 150 people. Tea has a sector of 108 degrees and Coffee has a sector of 96 degrees. The remaining people chose Juice. (a) Work out the number of people who chose Tea. (b) Work out the number of people who chose Juice.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the pie charts worksheet pack - 19 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 17 of GCSE Statistics Foundation Workbook 1 and chapter 21 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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