Box and Whisker Plots WHY? HOW?
Box and Whisker Plots WHY? HOW?
Box and Whisker Plots WHY? HOW?
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EXAMPLEFor Set F1. Order the data from smallest to highest (34 obs)150 156 156 157 158 160 163 164 164 165 165 166167 168 168 170 170 170 170 172 172 172 173 173173 173 174 174 174 175 177 177 177 1802. Median = 170 + 170 2= 170cmUpper quartile = 173 cmRange 180 – 150 = 30Lower Quartile = 164 cmIQR = 9 cm<strong>Box</strong>plot of F emale150160170180Fem aleUse the figures given to check on the outlier shown i.e. using the IQR rule we can seethat the lower quartile minus 1.5 times the IQR is equal to 150.5 cm.Now construct a <strong>Box</strong> <strong>and</strong> <strong>Whisker</strong> Plot for the set M <strong>and</strong> compare with set F. Whatare you conclusions? ****Note that there are no outliers. Check yourself that the lower <strong>and</strong> upper limits foroutliers are 159.5cm <strong>and</strong> 195.5cm respectively.You may wish to record your class heights <strong>and</strong> compare these with the year 11 UKstudents.Additional thoughtsWhat do you think would happen to the median of the UK year 11 boys if the tallest boywas actually 213cm? Do you think it would change? Obviously this height would beconsidered an outlier using the IQR rule. This should tell you something about themedian, <strong>and</strong> whether it is affected by outliers. What about the mean? Does thischange?Which would be the ‘better’ measure of centre? See if you can find out when youshould use the mean instead of the median, <strong>and</strong> when the 2 values will be the same.**** For Set MMedian = 177 cmUpper quartile = 182 cmRange 193 – 165 = 28Lower Quartile = 173 cmIQR = 9 cm
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