year 8 maths

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570 Chapter 9 Data collection, representation and analysis
Example 12
Finding the IQR
Find the interquartile range of the following sets of data.
a 1, 15, 8, 2, 13, 10, 4, 14
b 2, 7, 11, 8, 3, 8, 10, 4, 9, 6, 8
SOLUTION
a Sorted: 1 2 4 8 10 13 14 15
1 2 4 8 10 13 14 15
Median = 2 + 4
13 + 14
Median =
2
2
= 3 = 13.5
IQR = 13.5 − 3
= 10.5
b Sorted: 2 3 4 6 7 8 8 8 9 10 11
2 3 4 6 7 8 8 9 10 11
Lower quartile Upper quartile
IQR = 9 − 4
= 5
EXPLANATION
Values must be sorted from lowest to highest.
Lower quartile = median of the lower half .
Upper quartile = median of the upper half .
IQR = upper quartile − lower quartile
Sort the data and ignore the middle value
(so there are two equal halves remaining).
Lower quartile = median of the lower half .
Upper quartile = median of the upper half .
IQR = upper quartile − lower quartile
Exercise 9H
EXTENSION
UNDERSTANDING AND FLUENCY
1–6, 7–9(½) 6, 7–9(½)
7–9(½)
1 Consider the set of numbers 1, 3, 2, 8, 5, 6 .
a State the largest number.
b State the smallest number.
c Hence, state the range by finding the difference of these two values.
2 Consider the set of numbers 1, 2, 4, 5, 5, 6, 7, 9, 9, 10 .
a State the median of 1, 2, 4, 5, 5 .
b State the median of 6, 7, 9, 9, 10 .
c Hence, state the interquartile range by finding the difference of these two values.
3 Consider the set of numbers 1, 5, 6, 8, 10, 12, 14 .
a State the median of the lower half ( 1, 5, 6 ).
b State the median of the upper half ( 10, 12, 14 ).
c Hence, state the interquartile range.
4 Complete these sentences.
a The median of the lower half is called the ______ ______.
b The difference between the highest and ______ values is the range.
c In order to calculate the IQR, you should first ______ the numbers from lowest to highest.
d The upper quartile is the ______ of the upper half of the sorted data.
e When calculating the IQR , you remove the middle term if the number of values is ______.
f The range and IQR are examples of a measure of ______.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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