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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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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

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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$

 

answered Jan 27, 2014 by thanvigandhi_1
edited Mar 27, 2014 by rvidyagovindarajan_1
 

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