Question

The S.D. of a variate x is $\sigma$. The S.D. of the variate $\frac{ax+b}{c}$ where a, b, c are constants, is

• A. $\left(\frac{a}{c}\right)\sigma$
• B. $\left|\frac{a}{c}\right|\sigma$
• C. $\left(\frac{a^2}{c^2}\right)\sigma$
• D. None of these

Answer 1

The correct option is B $\left|\frac{a}{c}\right|\sigma$

$\sigma =\sqrt{\frac{{|x_i-\overline{x}|}^2}{n}}$
Now ${\overline{x}}_{new}=\frac{a\overline{x}+b}{c}$
${\sigma }_{new}=\sqrt{\frac{{|\frac{a{x}_i+b}{c}-\frac{a\overline{x}+b}{c}|}^2}{n}}=\left|\frac{a}{c}\right|\sigma$