In a set of 2n observations, half of them are equal to 'a' and the remaining half are equa…

Question

In a set of $2n$ observations, half of them are equal to 'a' and the remaining half are equal to '--a'. If the standard deviation of all the observations is 2; then the value of $|a|$ is:

Accepted Answer

Mean $=0$ (equal numbers of $+a,-a$).

$$\sigma^2 = \frac{2n\cdot a^2}{2n} = a^2 \implies \sigma = |a|$$

Given $\sigma=2$: $|a|=2$

Solutions · 1