Find the mean deviation about the median for the data 13,17,16,14,11,13,10,16,11,18,12,17.
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Solution
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Arranging the data in ascending order 10,11,11,12,13,13,14,16,16,17,17,18 Here the numbers of observations n=12 (even) M=(122)thobservation+(122+1)thobservation2 M=6thobservation+7thobservation2 M=13+142=272=13.5 The deviations of the respective observation from the median, i.e.xi−M are
The absolute values of the deviations ∣xi−M∣ are 3.5,2.5,2.5,1.5,0.5,0.5,0.5,2.5,2.5,3.5,3.5,4.5 The required mean deviation about the median is M.D.(M)=∑12i=1|x1−M|12