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# If SD of $X$ is $\sigma$ then SD of $\large\frac{aX+b}{c}$ ( where $a,b,c$ are constants ) is

$\begin {array} {1 1} (A)\;\large\frac{a}{c} \sigma & \quad (B)\;|\large\frac{a}{c}| \sigma \\ (C)\;|\large\frac{c}{a}| \sigma & \quad (D)\;\large\frac{c}{a} \sigma \end {array}$

Let $Y = \large\frac{aX+b}{c}$
$\Rightarrow \overline Y = \large\frac{a\overline X +b}{c}$
$\Rightarrow Y-\overline Y = \large\frac{a}{c} ( X - \overline X)$
$\large\frac{1}{N} $$\Sigma ( Y - \overline Y )^2 = \large\frac{a^2}{c^2} \large\frac{1}{N}$$ \Sigma ( X - \overline X )^2$
$\sigma_y^2=\large\frac{a^2}{c^2} \sigma^2$
$\sigma_y= |\large\frac{a}{c} | \sigma$
Ans : (B)