Question

If the standard deviation of a variable X is σ, then the S.D. of the variable $\frac{aX+b}{c}$, where a, b, c are constants,is __________________.

Answer 1

Let standard deviation of X be σ.
Then standard deviation of $\left(\frac{aX+b}{c}\right)$
$$\begin{gathered} =\mathrm{S}.\mathrm{D}\left(\frac{a}{c}\left(X\right)+\left(\frac{b}{c}\right)\right) \\ =\left|\frac{a}{c}\right|\mathrm{S}.\mathrm{D}\left(X\right)+\mathrm{S}.\mathrm{D}\left(\frac{b}{c}\right) \\ =\left|\frac{a}{c}\right|\sigma +0 \\ \mathrm{i}.\mathrm{e}\mathrm{standard}\mathrm{deviation}\mathrm{of}\frac{aX+b}{c}=\left|\frac{a}{c}\right|\sigma . \end{gathered}$$