Question

In a series of 20 observations , 10 observations are 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 value of k.

Answer 1

Here, n = 20 , $\overline{x}=0$

$\therefore \sum (x_i-\overline{x}{)}^2=\sum (x_i{)}^2=20k^2$

var (x) $=\frac{1}{n}\{\sum (x_i-\overline{x}{)}^2\}=\frac{20k^2}{20}=k^2$

S.D. (x) = $\sqrt{k^2}=2$

$\therefore k=\pm 2$