Question

if the variance of 1,2,3,4......
..,10 is 99/12 , then S.D. of 3,6,9,12 ......,30 is​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Variance of 1,2,3,.........10 is} \;\mathsf{\dfrac{99}{12}}$

$\underline{\textsf{To find:}}$

$\textsf{Variance of 3,6,9,.........30}$

$\underline{\textsf{Solution:}}$

$\textsf{We know that,}$

$\textsf{If each data is multiplied by a constant k, the new variance is}$

$\mathsf{k^2}\;\textsf{times the old variance}$

$\textsf{Then,}$

$\textsf{Variance of 3,6,9,........30 is}$

$\mathsf{=3^2{\times}\dfrac{99}{12}}$

$\mathsf{=9{\times}\dfrac{99}{12}}$

$\textsf{Using}$

$\boxed{\textsf{Standard deviation}\mathsf{=\sqrt{\textsf{variance}}}}$

$\therefore\textsf{Standard deviation of 3,6,9,........30}$

$\mathsf{=\sqrt{9{\times}\dfrac{99}{12}}}$

$\mathsf{=\sqrt{3{\times}\dfrac{99}{4}}}$

$\mathsf{=\dfrac{3}{2}\sqrt{3{\times}11}}$

$\mathsf{=\dfrac{3}{2}\sqrt{33}}$

$\underline{\textsf{Answer:}}$

$\textsf{New variance is }$

$\mathsf{\dfrac{3}{2}\sqrt{33}}$