Q. If the standard deviation of a variable $x$ is $\sigma$, then the standard deviation of another variable $\ \frac{ax + b}{c}$ is
A) $\frac{\sigma a + b}{c}$
B) $\frac{\sigma a}{c}$
C) $\sigma$
D) None of these
Explanation
(b)
Standard deviation does not depend on origin but it depends on scale, so,
$\frac{ax + b}{c} = \frac{ax}{c} + \frac{b}{c}$
$\Rightarrow \$Standard deviation of $\frac{ax + b}{c}is\frac{a\sigma}{c}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.