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 $k x_{1}, k x_{2}, k x_{3}, k x_{4}, k x_{5}$
$SD =\sqrt{\frac{k^{2} \Sigma x_{i}^{2}}{5}-\left(\frac{k \Sigma x_{i}}{5}\right)^{2}}$
$=\sqrt{\frac{k^{2} \Sigma x_{i}^{2}}{5}-k^{2}\left(\frac{\Sigma x_{i}}{5}\right)^{2}}$
$=k \sqrt{\left(\frac{\Sigma x_{i}^{2}}{5}\right)-\left(\frac{\Sigma x_{i}}{5}\right)^{2}}=ks$