A data consists of $\mathrm{n}$ observations:
$\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots \ldots, \mathrm{x}_{\mathrm{n}}$. If $\sum_{\mathrm{i}=1}^{\mathrm{n}}\left(\mathrm{x}_{\mathrm{i}}+1\right)^{2}=9 \mathrm{n} \quad$ and
$\sum_{i=1}^{n}\left(x_{i}-1\right)^{2}=5 n$, then the standard deviation of
this data is :
Correct Option: , 2
$\sum\left(x_{i}+1\right)^{2}=9 n$ ..............(1)
$\sum\left(x_{i}-1\right)^{2}=5 n$ ................(2)
$(1)+(2) \Rightarrow \sum\left(x_{1}^{2}+1\right)=7 n$
$\Rightarrow \frac{\sum x_{i}^{2}}{n}=6$
$(1)-(2) \Rightarrow 4 \Sigma x_{i}=4 n$
$\Rightarrow \Sigma x_{\mathrm{i}}=\mathrm{n}$
$\Rightarrow \frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}=1$
$\Rightarrow$ variance $=6-1=5$
$\Rightarrow$ Standard diviation $=\sqrt{5}$
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