If the standard deviation of a variable `X \ is \ sigma` , then standard deviation of variable `(a X+b)/c` is

Options

A. (a) `asigma`
B. (b) `a/csigma`
C. (c) `|a/c|sigma`
D. (d) `(asigma+b)/c`

Answer

(c) `|a/c|sigma`

Explanation

Correct option is option 3


If the Standard Deviation of variable `X` is

`sigma(X)=sqrt(frac{sum_(i=1)^N (X_i-barX)^2}{N}`


For `(a X+b)`

Mean, `frac{(aX_1+b)+(aX_2+b)+...+(aX_N+b)}{N}`

`=afrac{(X_1+X_2+...+X_N)}{N}+b`

`=abarX+b`


`sigma(aX+b)=sqrt(frac{sum_(i=1)^N (x_i-barx)^2}{N}`

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