In a series of 20 observations, 10 observation each equal to `k` and each of the remaining half is equal to `-k`. If the standard deviation of the observations is 2, then write the value of `k`.

Answer

`k=pm 2`

Explanation

Here, `n=20, \bar{x}=0`
$$
\begin{aligned}
&\therefore \sum\left(x_{i}-\bar{x}\right)^{2}=\sum\left(x_{i}\right)^{2}=20 k^{2} \\
&\left.\operatorname{var}(x)=\frac{1}{n} \sum\left(x_{i}-\bar{x}\right)^{2}\right\}=\frac{20 k^{2}}{20}=k^{2} \\
&\text { S.D. }(x)=\sqrt{k^{2}}=2 \\
&\therefore k=\pm 2
\end{aligned}
...