44 CHAPTER 3 Graphics and Summary StatisticsFigure 3.6. Defi nitions for the sample median: even and odd cases (taken from the
Cartoon Guide to Statistics with permission).
This is a lot smaller than the average of 12, when the number 38
is included. We shall next look at the median, and for this example, see
how the median is affected by the outlier.
The following cartoon (Fig. 3.6 ) defi nes median and illustrates how
it is affected by the outlier in the TV viewing example.
In this case, with the value 38 included, the median is 7 (compared
with 12 for the mean), and by taking the outlier out of the data set, the
median drops only to 6 (compared with 5.5 for the mean). So the
removal of the outlier has a big effect on the mean, dropping it by 6.5
hours, but not so large for the median, dropping it by only 1 hour. In
statistics, we say that the median is “ robust ” with respect to outliers,
and the mean is not robust. Note that when 38 is removed, the data has
a distribution that is far less skewed to the right. When the data are