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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 $| a | =$

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$2$

$\frac{\sqrt{2}}{n}$

$\sqrt{2}$

$\frac{1}{n}$

answer is A.

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Detailed Solution

Mean $\bar{x} = 0 S . D = \sqrt{\frac{\sum x^{2}}{n} - {(\bar{x})}^{2}} = \sqrt{\frac{2 n a^{2}}{2 n} - o^{2}}$
$2 = \sqrt{a^{2}} \Rightarrow | a | = 2$

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