In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Let $x_{i} / f_{i}; i = 1, 2, \dots, n$ be a frequency

distribution. Then,

$= \sqrt{\frac{1}{N} \sum_{i = 1}^{n} f_{i} {(x_{i} - \bar{X})}^{2}}$ and $M.D. = \frac{1}{N} \sum_{i = 1}^{n} f_{i} |x_{i} - \bar{X}|$

let $|x_{i} - \bar{X}| = z_{i}; i = 1, 2, \dots, n .$ Then,

${(S.D.)}^{2} - (M.D.)^{2} = \frac{1}{N} \sum_{i = 1}^{n} f_{i} z_{i}^{2} - {(\frac{1}{N} \sum_{i = 1}^{n} f_{i} z_{i})}^{2} = σ_{z}^{2} \geq 0$

$\Rightarrow S.D. > M.D.$

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