Statistics
Grade 3-5Pie Charts
A pie chart shares out the full 360° of a circle in proportion to each category's frequency, so every calculation involving a pie chart comes back to comparing a part of the data to the whole. This lesson covers calculating a sector angle, finding a frequency from a given angle, finding the total from just one sector, and comparing pie charts that represent different sample sizes.
What you need to know
- The whole circle is 360 degrees and represents the total frequency.
- The angle for a category is its frequency over the total frequency, times 360.
- To read a pie chart, do the reverse: angle over 360, times the total.
- Pie charts show proportions, not actual frequencies, unless the total is given.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Calculating a sector angle
Divide the frequency for a category by the total frequency, then multiply by 360° to find its angle.
40 students were asked their favourite colour, and 10 chose Red. The angle for Red is 10/40 × 360 = 90°.
Finding a frequency from a given angle
Divide the sector's angle by 360°, then multiply by the total frequency to find how many items or people that sector represents.
A pie chart shows the favourite fruit of 72 students, and the Apple sector has an angle of 60°. The number who chose Apple is 60/360 × 72 = 12.
Finding the total from just one sector
If one sector's angle and frequency are both known, find how many people or items one degree represents, then multiply by 360° to find the total.
The Orange sector has an angle of 72° and represents 8 students. One degree represents 8 ÷ 72 students, so the total is 8 ÷ 72 × 360 = 40 students.
Comparing pie charts with different totals
Two sectors with the same angle in different pie charts do not represent the same frequency unless the totals are also the same, since the angle only shows a proportion of that chart's own total. Convert each angle back to an actual frequency using its own total before comparing.
School A has 200 students, and School B has 320 students. Both have a "Cycling" sector with an angle of 45°. School A: 45/360 × 200 = 25 students. School B: 45/360 × 320 = 40 students. School B has more, by 15 students, even though the angles are equal.
Worked examples
Three exam-style questions, fully solved
40 students were asked their favourite colour. 10 chose Red. Calculate the angle for Red on a pie chart.
Easy- 1.Divide the frequency by the total: 10 ÷ 40
- 2.Multiply by 360°: (10/40) × 360
Answer: 90°
In a pie chart showing favourite fruit, the Orange sector has an angle of 72° and represents 8 students. Find the total number of students surveyed.
Medium- 1.Find how many students one degree represents: 8 ÷ 72
- 2.Multiply by 360° to find the total: (8 ÷ 72) × 360
Answer: 40 students
In School A (200 students), the "Cycling" sector of the pie chart has an angle of 45°. In School B (320 students), the "Cycling" sector also has an angle of 45°. Which school has more students who cycle, and by how many?
Hard- 1.Find the number of cyclists in School A: (45/360) × 200 = 25
- 2.Find the number of cyclists in School B: (45/360) × 320 = 40
- 3.Compare and find the difference: 40 − 25
Answer: School B has more, by 15 students
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
In a pie chart representing 60 people, 20 chose pizza. What angle represents pizza?
In a pie chart, the sector for "walking" has an angle of 90°. What fraction of the total chose walking?
A pie chart represents 40 students. One sector has an angle of 72°. How many students does it represent?
In a pie chart of 90 people, one group contains 30 people. What angle represents this group?
A pie chart shows three categories with angles 150°, 120° and x. Work out x.
A pie chart represents 200 people. How many degrees represent one person?
Avoid these
The mistakes students make most often
Comparing sector angles directly between two pie charts with different totals, without converting each angle back to an actual frequency first.
Forgetting to multiply by 360° when finding an angle, or forgetting to divide by 360° when working from an angle back to a frequency.
Using the wrong total in a calculation, such as using one category's frequency instead of the overall total frequency.
When finding the total from a known angle and frequency, setting up the division the wrong way round.
Rounding an angle or frequency too early in a multi-step problem, which compounds into a larger error by the final answer.
FAQ
Questions students and parents ask
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