Statistics: Pie Charts and the Mean
Statistics: Pie Charts and the Mean covers reading and interpreting a pie chart, including working out what a sector represents using fractions, percentages or angles, and calculating the mean (the everyday 'average') of a set of numbers by adding all the values together and dividing by how many there are.
Before you start
Make sure you're comfortable with these topics first:
Method
- Before reading any value from a pie chart, check what the whole circle represents (the total number of items, people or amount).
- To find how many items a sector represents when it is labelled as a fraction, find that fraction of the total amount using division and multiplication.
- To find how many items a sector represents when it is labelled as a percentage, find that percentage of the total amount.
- To find how many items a sector represents when only its angle is given, remember that the full circle is 360 degrees, so divide the sector's angle by 360 and multiply by the total amount.
- To calculate a mean, add together every value in the set first, being careful not to miss any, then divide this total by the number of values.
- If a mean and all but one value are known, find the missing value by multiplying the mean by the number of values to find the total, then subtracting the known values from this total.
- Check that a calculated mean makes sense: it should sit somewhere between the smallest and largest value in the set.
Worked example
A pie chart shows how 180 pupils travel to school. The sector for 'car' has an angle of 70 degrees. Work out how many pupils travel to school by car.
- Recall that the whole pie chart, representing all 180 pupils, is equal to 360 degrees.
- Write the car sector as a fraction of the whole circle: 70/360.
- Simplify this fraction if possible: dividing both parts by 10 gives 7/36.
- Find 7/36 of 180 pupils: first divide 180 by 36, which gives 5.
- Multiply this by 7 to find the number of pupils who travel by car: 5 x 7 = 35.
Practice questions
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Q1A pie chart shows the favourite pets of 60 pupils. The sector for 'dog' represents 1/3 of the pupils. How many pupils chose dog as their favourite pet?Show answer
Answer: 20 pupils
Q2A pie chart shows how a family spends its monthly budget of 2,400 pounds. The 'housing' sector represents 45% of the budget. How much is spent on housing?Show answer
Answer: 1,080 pounds
Q3A pie chart is divided into sectors for 200 people, one of which has an angle of 90 degrees. How many people does this sector represent?Show answer
Answer: 50 people
Q4Five rowers recorded these times, in seconds, for a race: 48, 52, 45, 55, 50. Calculate the mean time.Show answer
Answer: 50 seconds
Q5The mean of four numbers is 18. Three of the numbers are 15, 24 and 26. Find the fourth number.Show answer
Answer: 7
Q6A pie chart shows how 45 pupils voted for a new library book. The sector for 'adventure' has an angle of 120 degrees. How many pupils voted for adventure?Show answer
Answer: 15 pupils
Q7Six matches in a football tournament had these attendances: 305, 320, 410, 285, 330 and 300. Calculate the mean attendance.Show answer
Answer: 325
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A pie chart shows how 300 people voted in a survey about their favourite season. The sector for 'summer' represents 2/5 of the people. How many people chose summer?
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The mean number of books read by a group of 6 pupils in a term is 9. Five of the pupils read 7, 11, 8, 6 and 12 books. Work out how many books the sixth pupil read.
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A pie chart shows how a market stall's weekly income of 840 pounds is split between three products: vegetables, fruit and flowers. The angle for vegetables is 150 degrees and the angle for fruit is 126 degrees. Work out how much income comes from flowers.
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Free printable worksheet
Want more practice on paper? Download the statistics: pie charts and the mean worksheet pack - 6 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.
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