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Question

Find the mean deviation about the median for the data
xi579101215
fi862226

Solution
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xi fiCumulative frequency|xiM||xi7| fi|xiM|
5 8 8 216
7 6 14 0 0
9 2 16 2 4
10 2 18 3 6
12 220 5 10
15 6 26 8 48
Total 26 84
Here, N=26 (even)
So, Median M=(N/2)thobservation+(N/2+1)thobservation2
M=13thobservation+14thobservation2
M=7+72=7 (Here, 13 and 14 both lies in the cumulative frequency 14, so corresponding observation for both is 7)

Mean deviation about median =fi|xiM|fi
=8426
=3.23

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