In a series of 2n observations, half of them | vedclass

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Question

(c) Let $a, a, ........n$ times and $-a, -a, -a, -a, ........n$ times i.e., mean = $0$ and $S.D.$ $ = \sqrt {\frac{{n{{(a - 0)}^2} + n{{( - a - 0)}^2}

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(c) Let $a, a, ........n$ times and $-a, -a, -a, -a, ........n$ times i.e., mean = $0$ and $S.D.$ $ = \sqrt {\frac{{n{{(a - 0)}^2} + n{{( - a - 0)}^2}}}{{2n}}} $

$2 = \sqrt {\frac{{n{a^2} + n{a^2}}}{{2n}}} = \sqrt {{a^2}} = \pm a$.

Hence $|a|\; = 2$.

$x_i$	$0$	$1$	$5$	$6$	$10$	$12$	$17$
$f_i$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals

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