Question-13 If the variance of 1,2,3,4,5, \ldots, 10 is \frac{99}{12}, then the standard deviation of 3,6,9,12, \ldots, 30 is
A)
\frac{297}{4}B)
\frac{3}{2} \sqrt{33}C)
\frac{3}{2} \sqrt{99}D)
\sqrt{\frac{99}{12}}Answer: B)
Explanation
Given,
\sigma_{10}^{2}=\frac{99}{12}=\frac{33}{4} \Rightarrow \sigma_{10}=\frac{\sqrt{33}}{2}Standard Deviation of required series
=3 \sigma_{10}=\frac{3 \sqrt{33}}{2}Since, if we rm.’ltiply each observation with any factor (i.e., 3 here) the standard deviation also gets multiplied by that factor