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

Question

Dr. Abubacker · Accepted Answer

(c)
Let $a,a,\ldots n\$times and $–a, - a,\ldots..,n$ times, ie, mean=0
And SD=$\sqrt{\frac{n(a - 0)^{2} + n( - a - 0)^{2}}{2n} = 2}\ \ \ \ \ \ \ \ \ \ (given)$
$\Rightarrow 4 = \frac{2na^{2}}{2n}$
$\Rightarrow a^{2} = 4$
$\Rightarrow |a| = 2$

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

Explanation

Reviewed by Dr. Abubacker

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