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

Solution :

In the 2n observations, half of them equals a and remaining half equal -a. Then, the mean of total 2n observations is equal to 0.

\(\therefore\)   SD = \(\sqrt{\sum(x – \bar{x})^2\over N}\)

\(\implies\)  4 = \(\sum{x^2}\over 2n\)

\(\implies\)  4 = \(2na^2\over 2n\)

\(\implies\)  \(a^2\) = 4

\(\therefore\)   a = 2

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