In a series of 2n observations,half of the ob | vedclass

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(A) The total number of observations is $2n$.There are $n$ observations equal to $a$ and $n$ observations equal to $-a$.The mean $\bar{x} = \frac{n(a)

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$2$

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(A) The total number of observations is $2n$.There are $n$ observations equal to $a$ and $n$ observations equal to $-a$.The mean $\bar{x} = \frac{n(a) + n(-a)}{2n} = \frac{0}{2n} = 0$.The standard deviation $\sigma$ is given by $\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{2n}}$.Since $\bar{x} = 0$,$\sigma = \sqrt{\frac{\sum x_i^2}{2n}}$.Here,$\sum x_i^2 = n(a^2) + n(-a)^2 = 2na^2$.Substituting the values,$2 = \sqrt{\frac{2na^2}{2n}} = \sqrt{a^2} = |a|$.Therefore,$|a| = 2$.

In a series of $2n$ observations,half of the observations are equal to $a$ and the remaining are equal to $-a$. If the standard deviation of the observations is $2$,then what is the value of $|a|$?

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