For 20 observations of variable $x$, if $\sum\left(x_{\mathrm{i}}-2\right)=20$ and…
For 20 observations of variable $x$, if $\sum\left(x_{\mathrm{i}}-2\right)=20$ and $\sum\left(x_{\mathrm{i}}-2\right)^2=100$, then the standard deviation of variable $x$ is
$2$
$3$
$4$
$9$
Solution
Note that standard derivation is independent of change of origin.
$\therefore \quad$ S.D. of $x_{\mathrm{i}}=$ S.D. of $\left(x_{\mathrm{i}}-2\right)$
$\begin{aligned}
\therefore \quad \text { S.D. of }\left(x_{\mathrm{i}}-2\right) & =\sqrt{\frac{1}{\mathrm{n}} \sum_{\mathrm{i}}^{20}\left(x_{\mathrm{i}}-2\right)^2-\left[\frac{\sum\left(x_{\mathrm{i}}-2\right)}{\mathrm{n}}\right]^2} \\
& =\sqrt{\frac{100}{20}-(1)^2} \\
& =2 \\
\Rightarrow \text { Required S.D } & =2
\end{aligned}$