1. 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

2. 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

3. 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

4. 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.

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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.

14. 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

15. 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.

16. 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

17. (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

18. 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