Reading Pie Charts Teach GCSE Maths Crops Grown in the UK, 2003 7% 5% oilseed rape 10% barley 24% other crops 8% wheat 42% horticulture 7% sugar beet 4% 5% peas & beans Crops Grown in the UK, 2003 Reading Pie Charts

Reading Pie Charts © Christine Crisp "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" © Christine Crisp

Pie charts are used to display qualitative data. red blue black white green other If we had the colours of a collection of cars, the size of each slice could represent the number of cars of a given colour. If we had the names of TV “soaps”, the size of a slice could show how many of a group of viewers liked that one best. EastEnders Corrie Emmerdale Casualty

e.g.1 The chart shows the hours of overtime worked by 3 employees, Alpha, Beta and Gamma. Overtime (hours) If Alpha worked 18 hours and Beta worked 4 hours can you decide with your partner how many hours Gamma worked? Alpha Beta Gamma 14 18 4 Ans: 14 hours. Alpha’s 18 hours is shown by half the circle, so Beta and Gamma’s hours together also come to 18.

The size of the slices of pie are not usually as obvious as in the overtime example. We use angles to give the size. Alpha worked 18 hours, shown by 180. Overtime (hours) Alpha Beta Gamma What size of angle represents 1 hour? 14 hours 180 Ans: 10 ( = 180 ÷ 18 ) 140 How many hours are shown by 40 ? 18 hours 40 Ans: 4 hours 4 hours How many degrees is the angle in the final slice? Ans: 360 – 180 – 40 = 140

The total frequency is given by the total angle, 360 The size of the slices of pie are not usually as obvious as in the overtime example. We use angles to give the size. Alpha worked 18 hours, shown by 180. Overtime (hours) Alpha Beta Gamma 14 hours The total frequency is given by the total angle, 360 180 140 18 hours 40 4 hours

360 = 360 3 = If we know the total frequency, the angle showing a frequency of 1 360 total frequency = e.g. if the total frequency = 20, the angle showing a frequency of 1 = 360 ÷ 20 = 18 If we do not know the total frequency, we can use the frequency and angle of any slice. 3 The angle showing a frequency of 1 = frequency of the slice angle of any slice e.g. if the frequency of a slice = 3 and angle = 90 , the angle showing a frequency of 1 = 90 ÷ 3 = 30

e.g.2 For the following pie chart, find (a) the angle that represents a frequency of 1 (b) the frequencies represented by each slice. 20 total frequency = 60 120 90 150 25 15 (a) Total frequency = 60, so a frequency of 60 is shown by 360 a frequency of 1 is shown by 360 ÷ 60 = 6 (b) frequency shown by 120 = 120 ÷ 6 = 20 frequency shown by 90 = 90 ÷ 6 = 15 frequency shown by 150 = 150 ÷ 6 = 25

140 60 e.g.3 For the following pie chart, find (a) the angle that represents a frequency of 1 (b) the frequencies of the slices not given. 140 frequency, 7 60 Solution: (a) Frequency of 7 is shown by 140

140 60 140 ÷ 7 = 20 e.g.3 For the following pie chart, find (a) the angle that represents a frequency of 1 (b) the frequencies of the slices not given. frequency, 7 140 60 Solution: (a) Frequency of 7 is shown by 140 so, a frequency of 1 is shown by 140 ÷ 7 = 20

e.g.3 For the following pie chart, find (a) the angle that represents a frequency of 1 (b) the frequencies of the slices not given. 140 frequency, 7 60 Solution: 3 (a) Frequency of 7 is shown by 140 so, a frequency of 1 is shown by 140 ÷ 7 = 20 (b) Frequency shown by smallest slice = 60 ÷ 20 = 3

e.g.3 For the following pie chart, find (a) the angle that represents a frequency of 1 (b) the frequencies of the slices not given. 8 frequency, 7 140 160 60 Solution: 3 (a) Frequency of 7 is shown by 140 so, a frequency of 1 is shown by 140 ÷ 7 = 20 (b) Frequency shown by smallest slice = 60 ÷ 20 = 3 3rd angle = 360 – 140– 60 = 160 Frequency shown by 3rd slice = 160 ÷ 20 = 8

50% 72 Pie charts are often used to show percentages. e.g. The pie chart shows the proportions of a garden given up to lawn, flowers, vegetables and other things including paths. (a) What percentage of the garden is given over to vegetables? flowers other vegetables lawn 72 50% (b) If the total area is 200 m2, what area is used for flowers? Solution: (a) Vegetables make up 25% of the garden.

360 ÷ 72 = 5, so 1/5th of the garden is flowers. (b) If the total area is 200 m2, what area is used for flowers? flowers other vegetables lawn 72 50% Solution: There are 2 equally good ways of doing this part: Method 1: Total area = 200 m2, so 200 m2 is shown by 360 1 m2 is shown by 360 ÷ 200 = 1·8 Area for flowers = 72 ÷ 1·8 = 40 m2 Method 2: 360 ÷ 72 = 5, so 1/5th of the garden is flowers. Area for flowers = 200 ÷ 5 = 40 m2

SUMMARY A slice of pie represents a frequency. We use angles to measure frequencies. To find an unknown angle or an unknown frequency, we can use the angle given by a frequency of 1. We can find the angle used to show a frequency of 1, either by dividing 360 by the total frequency, or dividing any angle by the frequency it represents. Pie charts can be used to show percentages.

Exercise 1. The colours of a sample of 18 cars are shown in the pie chart. Colours of Cars (a) How many cars were blue? other (b) What size angle shows a frequency of 1? white 60 180 (c) How many cars were white? What fraction is this of the total? 100 blue red

(c) Number of white cars = 60 ÷ 20 = 3 Exercise Total frequency = 18 Solution: Colours of Cars (a) Number of blue cars = 9 ( half the cars ) other (b) Angle showing a frequency of 1 360 ÷ 18 = 20 white 60 180 (c) Number of white cars = 60 ÷ 20 = 3 100 blue red As a fraction, this is 1 3 6 1 = 18 6

Exercise 2. The pie chart shows the percentages of certain crops grown in a region. Crops (a) What percentage is given to oilseed rape? other (b) How large is the angle used to show “other” crops? oilseed rape barley Solution: 108 (a) Oilseed rape is 25%. 144 (b) The angle used for “other” crops wheat = 360 – 90 – 144 – 108 = 18