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# If the SD of X is $\sigma_X$ then SD of $\large\frac{aX-b}{c}$ ( where a,b,c are constants ) is:

(A) $\large\frac{a-b}{c}$$\sigma_X \quad(B) \large\frac{a}{c}$$\sigma_X ^2$$\quad (C) \large\frac { \left | a \right |} { \left | c \right |}$$ \sigma_X$ $\quad$ (D) $\large\frac { \left |\; a^2\;\right |} { \left | c^2 \right |}$$\sigma_X ^2 Can you answer this question? ## 1 Answer 0 votes Given X, X, \sigma_X ^2 =$$ \large\frac{1}{N}$$\Sigma ( X - \overline X )^2 Let Y = \large\frac{aX-b}{c}$$\Rightarrow \overline Y = \large\frac{a\overline X-b}{c}$
$\Rightarrow Y - \overline Y = \large\frac{aX-b}{c} $$- \large\frac{a\overline X-b}{c}$$ = \large\frac{a}{c} $$(X - \overline X) \Rightarrow \sigma_Y ^2 =$$ \large\frac{1}{N}$$\Sigma ( Y - \overline Y )^2 \Rightarrow \sigma_Y ^2 = \large\frac{1}{N} \large \frac{a^2}{c^2}$$ (X - \overline X)^2$$= \large\frac{a^2}{c^2}$$\sigma_X ^2$
$\Rightarrow \sigma_Y = \large\frac { \left | a \right |} { \left | c \right |}$$\sigma_X$

edited Mar 27, 2014