Q. If the variance of 1, 2, 3, 4, 5, ..., 10 is $\frac{99}{12}$, then the standard derivation of 3, 6, 9, 12, ..., 30 is
A) $\frac{297}{4}$
B) $\frac{3}{2}\sqrt{33}$
C) $\frac{3}{2}\sqrt{99}$
D) $\sqrt{\frac{99}{12}}$
Explanation
(b)
Given, $\sigma_{10}^{2} = \frac{99}{12} = \frac{33}{4}$
$\Rightarrow \ \ \sigma_{10} = \frac{\sqrt{33}}{2}$
SD of required series $= 3\sigma_{10} = \frac{3\sqrt{33}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.