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Question

Calculate the mean deviation from the median of the following data.

Class1020203030404050506060707080Frequency 4 6 10 20 10 6 4

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Solution

Calculation of mean deviation from median,

ClassMid~value(x_{i})Frequency(fi)Cumulative frequency|di|=|xi45|fi|di|1020154430120203025610201203040351020101004050452040005060551050101006070656562012070807546030120fi=60fi|di|=680

Here, fi=N=60. So, N2=602=30

The cumulative frequency just greater than 30 is 40 and the corresponding class is 40-50.

So, 40-50 is the median class.

l=40, cf=20, h=10 and f=20

Now, median =1+N2cff×h=40+302020×10=40+5=45

Mean deviation from median =fi|di|fi=68060=1133

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