Statistics JEE

Algebra Level 3

The $S.D(standard\quad deviation)$ of the variate $x$ is $\sigma$ .Find the $S.D$ of the variable $\frac{ax+b}{c}$

\sigma b

\frac{\sigma b}{c}

\sigma a

\frac{\sigma a}{c}

\sigma

1 solution

Tanishq Varshney
Feb 14, 2015

Let $y=\frac{ax+b}{c}$

$y=Ax+B$ where $A=\frac{a}{c}$ , $B=\frac{b}{c}$

$\bar{y}=A\bar{x}+B$

$y-\bar{y}=Ax+B-(A\bar{x}+B$

$(y-\bar{y})^{2}=A^{2}(x-\bar{x})^{2}$

$\sum(y-\bar{y})^{2}=A^{2}\sum(x-\bar{x})^{2}$

$n\sigma^{2}_{y}=A^{2}(n\sigma^{2}_{x})$

$\sigma_{y}=|A|\sigma_{x}$

Taking positive value of $A$

Required S.D = $\sigma\frac{a}{c}$

do upvote