Question

Let $a,b,c,d,e$ be the obserations with mean $m$ and standard deviation $\sigma$. The standard deviation of the observations $a+k,b+k,c+k,d+k,e+k$, is

• A. $\sigma$
• B. $k\sigma$
• C. $k+\sigma$
• D. $\sigma /k$

Answer 1

The correct option is A $\sigma$

We know $Var(ax+b)=a^2.Var\left(x\right)$
or $S.D(ax+b)=|a|.S.D\left(x\right)$
Here, $a=1,b=k$
$\therefore S.D(x+k)=S.D(a+k,b+k,c+k,d+k,e+k)=1.S.D(a,b,c,d,e)=\sigma$