Question

Let $x_1,x_2,.....x_n$ be $n$ observations with mean $m$ and standard deviation $s$. Then the standard deviation of the observations $a{x}_1,a{x}_2,.....a{x}_n$, is

• A. $a+s$
• B. $s/a$
• C. $\left|a\right|s$
• D. $as$

Answer 1

The correct option is C $\left|a\right|s$

$S.D\left(ax\right)=\sqrt{E[ax-a\overline{x}{]}^2}=\sqrt{E\left[a\right(x-\overline{x}{)}^2]}=\sqrt{a^2.E\left[\right(x-\overline{x}{)}^2]}=|a|.\sqrt{E\left[\right(x-\overline{x}{)}^2]}=|a|.S.D\left(x\right)=|a|s$