Question

Standard deviation for n observations $x_1,x_2\dots x_n$ is '5' then the standard deviation of n observations $5x_1,5x_2,\dots 5x_n$ will be ___

Answer 1

We have seen that if we multiply the data with any constant k, variance of data will be multiple of $k^2$ of the old variance.
Given the standard deviation of $x_1,x_2\dots x_n$ is 5
So variance will be = 25
now, if we multiply each term with '5' the variance (new) will be equal to $(5{)}^2$ (old variance)
$\Rightarrow 25\times 25=625$
So, standard deviation will be $\sqrt{625}=25$