Ursula Gather and
P. Laurie Davies
No 2004,20, Papers from Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE)
The first example involves the real data given in Table 1 which are the results of an interlaboratory test. The boxplots are shown in Fig. 1 where the dotted line denotes the mean of the observations and the solid line the median. We note that only the results of the Laboratories 1 and 3 lie below the mean whereas all the remaining laboratories return larger values. In the case of the median, 7 of the readings coincide with the median, 24 readings are smaller and 24 are larger. A glance at Fig. 1 suggests that in the absence of further information the Laboratories 1 and 3 should be treated as outliers. This is the course which we recommend although the issues involved require careful thought. For the moment we note simply that the median is a robust statistic whereas the mean is not.
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