If SD of $X$ is s, then SD of the variable${\rm{\mu }} = \frac{{aX + b}}{c}$, where $a,\;b,\;c$ are constants, is

$\left| {\frac{a}{c}} \right|{\rm{\sigma }}$

$\left| {\frac{c}{a}} \right|{\rm{\sigma }}$

$\left| {\frac{b}{c}} \right|{\rm{\sigma }}$

$\left| {\frac{{{c^2}}}{{{a^2}}}} \right|{\rm{\sigma }}$

JEE MATHEMATICS MCQ: STATISTICS

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Application +4 | -1

If SD of

X

is s, then SD of the variable

\mathrm{\mu } = \frac{{aX + b}}{c}

, where

a,\;b,\;c

are constants, is

View answer and explanation

Correct option: B

\left| {\frac{a}{c}} \right|\mathrm{\sigma }

Option B (

\left| {\frac{a}{c}} \right|\mathrm{\sigma }

) is correct because the standard deviation scales linearly with the coefficient of X and inversely with the divisor.

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{x_1},{x_2}, \ldots ,{x_n}

\bar X,

{x_i} + 2\;i;i = 1,\;2, \ldots ,n

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