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Question

Find the mean deviation about mean and median for the following data.
CI15610111516202125
f295410

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Solution

CI fcf
x xf|x¯¯¯x|
f|x¯¯¯x| |xM| f|xM|
0.55.5 2 2 3 6 11.83 23.66 11.5 23
0.510.5 9 11 8 72 6.83 61.47 6.5 58.5
10.515.5 5 16 13 65 1.83 9.15 1.5 7.5
15.520.5 4 20 18 72 3.17 12.68 3.5 14
20.525.5 10 30 23 230 8.17 81.7 8.5 85
f=30 xf=445 f|x¯¯¯x|=188.66
f|xM|=
188
Mean(¯¯¯x)=xff=44530=14.83
Mean deviation about mean =f|x¯¯¯x|f=188.6630=6.29

Here, N=f=30
N2=302=15
Median class =10.515.5
L=10.5,f=5,cf=11 and h=15.510.5=5
Median(M)=L+N2cff×h
=10.5+15115×5
=10.5+4
Median(M)=14.5
Mean deviation about median =f|xM|f=18830=6.27

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