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Standard Deviation about Mean for Continuous Frequency Distributions

In a series o...

Question

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

\frac{1}{n}

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\sqrt{2}

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2

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

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Solution

The correct option is B $\sqrt{2}$
Total number of observations $= 2 n$
Half are equal to $a$ and half are equal to $- a$
Therefore, mean $¯ x = 0$

Standard deviation:
$\sum \frac{{| x_{i} - ¯ x |}_{i}^{2}}{2 n} = \frac{2 n a^{2}}{2 n} = a^{2} = S . D = 2$

$\Rightarrow | a | = \sqrt{2}$

Hence, option B.

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In a series of 2n observations, half of them equal a and remaining half equal −a. If the S.D. of the observations is 2, then |a| equals

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