Convert frequencies to pie-chart angles and back
Use the whole-circle total of 360° · Calculate a sector from its frequency share · Avoid comparing counts from angles without group totals
Section E10.3 · Extended · Statistical charts and distributions
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Ratios
- Angle measurement
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Use the whole-circle total of 360°
- Calculate a sector from its frequency share
- Avoid comparing counts from angles without group totals
A sector represents a share of one whole
In the illustrative 20-journey table, walking has 8, bus 6, cycling 4 and car 2. Sector angle=frequency/total×360°, giving 144°,108°,72°,36°. The angles sum to 360°. Frequencies sum to 20; the circle does not independently encode that total.
Recover counts when the total is known
A 72° sector represents 72/360=1/5 of its chart total. In a 50-person chart this is 10 people; in a 100-person chart it is 20. Equal angles across charts mean equal shares, not necessarily equal counts. Pie charts require non-overlapping categories that together cover the stated whole.
Sources for this lesson
Pause and explain
Do equal 72° sectors in charts of 50 and 100 people represent equal counts?
Worked example
Calculate the walking sector angle for 8 of 20 journeys.
Show the worked solution
- Walking share=8/20=0.4.
- Angle=0.4×360°.
Answer 144°.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For the illustrated 20 journeys, calculate the bus and car sector angles.
Give me a hint
Multiply each frequency share by 360°.
Compare my reasoning
- Bus: 6/20×360°=108°.
- Car: 2/20×360°=36°.
Bus 108°; car 36°.
Look for these in your work
- Use the same whole
- Check the sector units
A pie chart describes 60 students. A category has angle 90°. Find its frequency.
Give me a hint
Use 90/360 of the total.
Compare my reasoning
- The share is 1/4.
- Frequency=60/4=15.
15 students.
Look for these in your work
- Convert angle to a fraction
- Apply the stated total
Chart A has 50 people and a 72° blue sector; chart B has 100 people and a 54° blue sector. Which has more blue observations?
Give me a hint
Compute both counts before comparing.
Compare my reasoning
- A: 50×72/360=10.
- B: 100×54/360=15.
B has more, 15 versus 10, despite its smaller angle.
Look for these in your work
- Account for different totals
- Compare counts rather than angles alone
Common mistakes
- Use the chart’s total for a count conversion.
- Equal sector angles in unequal totals need not represent equal counts.
What can you explain now?
Do equal 72° sectors in charts of 50 and 100 people represent equal counts?
Compare with the explanation
No; they represent 10 and 20 people.
The same share is applied to different group totals.
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Make it stick
Do equal 72° sectors in charts of 50 and 100 people represent equal counts?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.