year 8 maths

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9H
Interquartile range
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9H Interquartile range
EXTENSION
Sometimes it is useful to know a number that describes the amount of spread in a dataset. Two commonly
used measures of spread are range and interquartile range.
Let’s start: Golfing
Three golfers record their scores over five games. In golf, lower scores are better.
Alfred: 82, 87, 80, 112, 79
Brenton: 90, 89, 91, 92, 89
Charlie: 72, 103, 94, 83, 80
• Which golfer do you think is best? Explain.
• Which golfer is most consistent? Explain.
• Alfred’s range of values (112 − 79 = 33) is larger than Charlie’s (103 − 72 = 31) . Discuss whether
this means that Charlie is a more consistent golfer than Alfred.
■ The range and interquartile range are summary statistics known as ‘measures of spread’.
■ Around the world, there are several different methods used for finding the quartiles and the
interquartile range (IQR). This is one of those methods:
• Sort the data into ascending order.
• If the number of values is odd, the median will be one of those values. The values below
and above the median form two groups of equal size.
• If the number of values is even, it is easier to form two groups of equal size.
• Split the data into two equal-size groups.
• The median of the lower half is called the lower quartile .
• The median of the upper half is called the upper quartile .
• IQR = upper quartile − lower quartile
Key ideas
lower half
}
For example: 1 5 7 9 10 11
Lower quartile
= (7 + 9) ÷ 2
= 8
■ Outliers affect the range but not the IQR.
⎹
IQR = 19.5 − 8
= 11.5
upper half
}
13 17 19 20 23 28
Upper quartile
= (19 + 20) ÷ 2
= 19.5
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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