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Question

Find the mean deviation about the median for the following data: 13,17,16,14,11,13,10,16,11,18,12,17.

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Solution

Given data: 13,17,16,14,11,13,10,16,11,18,12,17.

Arranging in increasing order 10,11,11,12,13,13,14,16,16,17,17,18.

Total number of terms is 12 which is odd.
Median=((122)thobservation+((122)+1)thobservation)2

=6thobservation+7thobservation2

M=(13+14)2=272=13.5


Mean deviation about median = |xiM|n

M.D.(M)
=(|1013.5|+|1113.5|+|1113.5|+|1213.5|+|1313.5|+|1313.5|+|1413.5|+|1613.5|+|1613.5|+|1713.5|+||1713.5|+|1813.5|)12

=(|13.5|+|2.5|+|2.5|+|1.5|+|0.5|+|0.5|+|0.5|+|2.5|+|2.5|+|3.5|+|3.5|+|4.5|)12

=3.5+2.5+2.5+1.5+0.5+0.5+0.5+2.5+2.5+3.5+3.5+4.512

M.D.(M)=(28)12

M.D.(M)=2.33


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