Question

If the SD of a set of observation is $8$ and each observation is divided by $-2$, then the SD of the new set of observations will be.

• A. $-4$
• B. $-8$
• C. $8$
• D. $4$

Answer 1

Answer: (D)

$4$

We know that, if X and Y are two variables such that $Y=\frac{X}{a},a\ne 0$
Then, ${\sigma }_Y=\frac{1}{|a|}{\sigma }_X$, where ${\sigma }_Y$ is the SD of new observations, ${\sigma }_X$ is the SD for old observations and $a$ is the factor from which each observation is being divided by
$\therefore$ SD of the new observations $=\frac{8}{|-2|}=4$.