Question

Let $x_1,x_2,x_3,x_4$ and $x_5$ be the observations with mean $m$ and standard deviation $s$. The standard deviation of the observations $k{x}_1,k{x}_2,k{x}_3,k{x}_4$ and $k{x}_5$ is

• A. $k+s$
• B. $s/k$
• C. $ks$
• D. $s$

Answer 1

Answer: (C)

Here, $m=\frac{\Sigma x_i}{5},s=\sqrt{\frac{\Sigma x_i^2}{5}-{\left(\frac{\Sigma x_i}{5}\right)}^2}$
For observations $k{x}_1,k{x}_2,k{x}_3,k{x}_4,k{x}_5$
$SD=\sqrt{\frac{k^2\Sigma x_i^2}{5}-{\left(\frac{k\Sigma x_i}{5}\right)}^2}$
$=\sqrt{\frac{k^2\Sigma x_i^2}{5}-k^2{\left(\frac{\Sigma x_i}{5}\right)}^2}$
$=k\sqrt{\left(\frac{\Sigma x_i^2}{5}\right)-{\left(\frac{\Sigma x_i}{5}\right)}^2}=ks$