Question:
Let $x_{i}(1 \leq i \leq 10)$ be ten observations of a random variable $X$.
If $\sum_{i=1}^{10}\left(x_{i}-p\right)=3 \quad$ and $\quad \sum_{i=1}^{10}\left(x_{i}-p\right)^{2}=9 \quad$ where
$0 \neq p \in \mathbf{R}$, then the standard deviation of these observations is :
Correct Option: , 3
Solution:
S.D. $=\sqrt{\frac{\sum_{i=1}^{10}\left(x_{i}-p\right)^{2}}{10}-\left(\frac{\sum_{i=1}^{10}\left(x_{i}-p\right)}{10}\right)^{2}}$
$=\sqrt{\frac{9}{10}-\left(\frac{3}{10}\right)^{2}}=\frac{9}{10}$
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