Pie Charts
Understand Pie Charts for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Pie charts show each category as a sector whose angle is proportional to its frequency.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
Topic overview
A pie chart represents data as sectors of a circle, where the angle of each sector is proportional to the frequency it represents.
The angle for each category is calculated as \(\frac{\text{frequency}}{\text{total frequency}} \times 360\). The angles must sum to 360 degrees, and checking this catches arithmetic errors before they cost marks.
Pie charts show proportions clearly but have limitations. The actual frequencies cannot be read from the chart unless the total is given, and comparing two pie charts is misleading unless their totals are equal or their sizes reflect those totals. Working backwards from an angle to a frequency requires the total to be known.
Revision notes
Calculating the angles
Angle \(= \frac{\text{frequency}}{\text{total frequency}} \times 360\).
Calculate each category separately. The angles must add to 360 degrees, which provides a check. Round sensibly and adjust the largest sector if rounding causes the total to differ.
Working backwards
To find a frequency from an angle: frequency \(= \frac{\text{angle}}{360} \times \text{total frequency}\).
This requires the total to be known. Without it, only the proportion can be found, not the actual frequency.
Limitations
Frequencies cannot be read directly unless the total is given.
Comparing two pie charts is misleading unless the totals are equal, because equal angles represent different frequencies when the totals differ. Many small sectors make a pie chart hard to read.
Key points
- Angle = (frequency ÷ total) × 360.
- Angles must sum to 360 degrees.
- Pie charts show proportions clearly.
- Frequencies need the total to be found.
- Comparing pie charts needs equal totals.
- Many small sectors make reading difficult.
Worked examples
Example 1
A category has a frequency of 12 out of a total of 60. Work out the angle of its sector. [2 marks]
Working
Example 2
A sector has an angle of 90° and the total frequency is 200. Work out the frequency it represents. [2 marks]
Working
Example 3
Explain why comparing two pie charts can be misleading. [2 marks]
Working
Common mistakes
Forgetting to multiply by 360.
The fraction must be converted into an angle.
Not checking the angles sum to 360.
This catches arithmetic errors before they cost marks.
Reading a frequency directly from a sector.
The total is needed to convert an angle into a frequency.
Comparing pie charts with different totals.
Equal angles represent different frequencies unless the totals match.
Exam tips
- Show the fraction before multiplying by 360.
- Check your angles add to 360 degrees.
- State that the total is needed to find frequencies.
- Name unequal totals as the comparison problem.
Key terms
- Pie chart
- A circular diagram divided into proportional sectors.
- Sector
- One slice of a pie chart.
- Angle
- The size of a sector, proportional to its frequency.
- Proportion
- The fraction of the total that a category represents.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.