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Question

Find the mean deviation about median for the following data.
CI8121317182223272832333738424347
f1482071110246

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Solution

CI fi cf Midvalue
xi
|xiM| fi|xiM|
7.512.5 14 14 1018.21 254.94
12.517.58 22 1513.21 105.68
17.522.520 42 208.21 164.2
22.527.5 7 49 253.21 22.47
27.532.5 11 60 301.79 19.69
32.537.5 10 70 35 6.79 67.9
37.542.5 24 94 4011.79 282.96
42.547.5 6 100 45 16.79 100.74
fi=100 fi|xiM|=3243.11
Here, N=100, N2=1002=50
Median class =22.527.5
L=22.5,cf=42,f=7 and h=27.522.5=5
Median(M)=L+N2cff×h
=22.5+50427×5
=22.5+5.71
=28.21
Mean deviation about the median =fi|xiM|fi
=3243.11100
=32.43

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