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Question

In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is :

A
M.D.=S.D.
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B
M.D.S.D.
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C
M.D.
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D
M.D.S.D.
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Solution

The correct option is D M.D.S.D.
Let xifi;i=1,2,...,n
be the frequency distribution
Then, S.D.=1Nni=1fi(xi¯¯¯¯¯X)2
and M.D.=1Nni=1fixi¯¯¯¯¯X
Let xi¯¯¯¯¯X=2i;i=1,2,...,n
Then (S.D.)2(M.D.)2=1Nni=1fizi2[1Nni=1fizi]2
=σz20S.D.M.D.

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