In any discrete series, the relationship between mean deviation from mean (M.D) and standard deviation (S.D) is

M.D = S.D

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M.D > S.D

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M.D < S.D

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$M . D \leq S . D$

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Solution

The correct option is D
$M . D \leq S . D$

$S . D = \sqrt{\frac{1}{N} \sum f_{i} (x_{i} - ¯ x)^{2}} a n d M . D = \frac{1}{N} \sum f_{i} | x_{i} - ¯ x | l e t | x_{i} - ¯ x | = y_{i}$

$S . D^{2} - M . D^{2} = \frac{1}{N} \sum f_{i} y_{i}^{2} - {(\frac{1}{N} \sum f_{i} y_{i})}_{i}^{2} = σ^{2} (y) \geq 0 ∴ S . D \geq M . D$

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In any discrete series, the relationship between mean deviation from mean (M.D) and standard deviation (S.D) is

The correct option is D M.D≤S.D S.D=√1N∑fi(xi−¯x)2andM.D=1N∑fi|xi−¯x|let|xi−¯x|=yi S.D2−M.D2=1N∑fiy2i−(1N∑fiyi)2=σ2(y)≥0∴S.D≥M.D