In any discrete series (when all values are n | vedclass

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(D) For any frequency distribution,the relationship between Mean Deviation $(M.D.)$ about the mean and Standard Deviation $(S.D.)$ is given by the ine

Vedclass · Accepted Answer

$M.D. \le S.D.$

Vedclass · Answer

(D) For any frequency distribution,the relationship between Mean Deviation $(M.D.)$ about the mean and Standard Deviation $(S.D.)$ is given by the inequality $M.D. \le S.D.$This is because the variance of the absolute deviations from the mean is always non-negative.Specifically,for a set of values,the $S.D.$ is defined as $\sqrt{\frac{1}{N}\sum f_i(x_i - \bar{x})^2}$ and the $M.D.$ about mean is $\frac{1}{N}\sum f_i|x_i - \bar{x}|$.By the properties of dispersion,the root mean square deviation is always greater than or equal to the mean absolute deviation,hence $M.D. \le S.D.$

$x$	$4$	$5$	$6$	$7$	$8$
$f$	$6$	$7$	$10$	$8$	$3$

Class	$1 - 10$	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$
$f_i$	$5$	$7$	$8$	$6$	$4$

Class	$0-6$	$6-12$	$12-18$	$18-24$	$24-30$
Frequency	$a$	$b$	$12$	$9$	$5$

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

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