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© Boardworks Ltd 20111 of 7
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© Boardworks Ltd 20112 of 7
Calculating averages
© Boardworks Ltd 20113 of 7
Comparing hurdles scores
Here are the top eleven 50 m goat racingtimes in seconds for 2007 and 2008.
2007 2008
12.1 12.3
14.0 13.7
15.3 15.5
15.4 15.5
15.4 15.6
15.6 15.9
15.7 16.0
15.7 16.1
16.1 16.1
16.7 17.1
17.0 22.9
The interquartile range is a better measure of spreadwhen the data contains an outlier.
2007 2008
Mean
Range
Why might this comparison be unfair?Which year was better and why?
15.4 16.14.9 10.6
Work out the mean and range.
© Boardworks Ltd 20114 of 7
Finding the interquartile range
The interquartile range (IQR) is therange of the middle half of the data.
The lower quartile is thedata value that is one quarter
of the way along the list(when written in order of size).
The upper quartile isthe data value that is
three quarters of the wayalong the ordered list.
interquartile range = upper quartile – lower quartile
When there are outliers in the data, it is more appropriate to calculate the interquartile range.
© Boardworks Ltd 20115 of 7
Locating the upper and lower quartiles
16.1 – 15.3 =16.1 – 15.5 =
interquartile range for 2007:interquartile range for 2008: 0.6
0.8
2007 2008
Median
Range
IQ Range
2007 200812.1 12.314.0 13.715.3 15.515.4 15.515.4 15.615.6 15.915.7 16.015.7 16.116.1 16.116.7 17.117.0 22.9
4.9
0.8
10.6
0.6
Compare the 2007 and 2008 goat racingresults by finding the median and lowerand upper quartiles then compare theinterquartile ranges with the ranges.
15.6 15.9
© Boardworks Ltd 20116 of 7
The location of quartiles
When there are n values in an ordered data set:
lower quartile =n + 1
4th value
median =n + 1
2th value
upper quartile =3 (n + 1)
4th value
interquartile range = upper quartile – lower quartile
© Boardworks Ltd 20117 of 7
Finding the interquartile range