Question

If the S.D. of a set of observations is 8 and if each observation is divided by −2, the S.D. of the new set of observations will be
(a) −4
(b) −8
(c) 8
(d) 4

Answer 1

(d) 4

If a set of observations, with SD $\sigma$, are multiplied with a non-zero real number a, then SD of the new observations will be $\left|\mathit{a}\right|\sigma .$
Dividing the set of observations by − 2 is same as multiplying the observations by $\frac{1}{-2}$.

$$\begin{gathered} \mathrm{New}\mathrm{S}.\mathrm{D}.=\left|-\frac{1}{2}\right|\times 8 \\ =\frac{8}{2} \\ =4 \end{gathered}$$