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  4. Let xi(1 ≤ i ≤ 10) be ten observations of a random variable X. If displaystyle∑i=110(xi-p)=3 and displaystyle∑i=110(xi-p)2=9 where 0 ≠ p ∈ R, then the standard deviation of these observations is :

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Q. Let $x_{i}(1 \leq i \leq 10)$ be ten observations of a random variable X. If $\displaystyle\sum_{i=1}^{10}\left(x_{i}-p\right)=3$ and $\displaystyle\sum_{i=1}^{10}\left(x_{i}-p\right)^{2}=9$ where $0 \neq p \in R$, then the standard deviation of these observations is :

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Solution:

Variance $=\frac{\Sigma\left( x _{ i }- p \right)^{2}}{ n }-\left(\frac{\Sigma\left( x _{ i }- p \right)}{ n }\right)^{2}$
$=\frac{9}{10}-\left(\frac{3}{10}\right)^{2}=\frac{81}{100}$
$S.D. = \frac {9}{10}$