year 8 maths

9G
Mean, median, mode and range
565
for categorical data. It can also be used for numerical data, but it may not be an accurate
measure of centre. For example, in the dataset below the mode is 10 and it is also the largest
data value.
1 2 3 10 10
Key ideas
■ Some summary statistics are called measures of spread.
• The range is a measure of spread.
• The range of a dataset is given by the formula:
Range = maximum data value − minimum data value
For example, in the dataset below the range is 7 − 1 = 6
5 7 2 5 1
maximum
minimum
• In the future you will encounter some other measures of spread, such as interquartile range
and standard deviation.
Example 11
Finding the range, mean, median and mode
Consider the ages (in years) of seven people who are surveyed in a shop:
15, 31, 12, 47, 21, 65, 12
a Find the range of values. b Find the mean of this set of data.
c Find the median of this set of data. d Find the mode of this set of data.
e If another person is surveyed who is 29 years old, what will be the new median?
SOLUTION
a range = 65 − 12
= 53
b mean = 203 ÷ 7
= 29
EXPLANATION
Highest number = 65, lowest number = 12
The range is the difference.
Sum of values = 15 + 31 + 12 + 47 + 21 + 65 + 12 = 203
Number of values = 7
c values: 12, 12, 15, 21 , 31, 47, 65
median = 21
Place the numbers in ascending order and see that the
middle value is 21 .
d mode = 12 The most common value is 12 .
e values: 12, 12, 15, 21 , 29 , 31, 47, 65
new median = (21 + 29) ÷ 2
= 25
Place the numbers in ascending order.
Now there are two middle values ( 21 and 29 ), so the
21 + 29
median is = 50 2 2 = 25 .
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.