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  4. If ∑(xi-8)=9, ∑(xi-8)2=45, i=1,2, ldots . .18 then standard deviation of x1, x2 ldots . x18 is

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Q. If $\sum\left(x_{i}-8\right)=9, \sum\left(x_{i}-8\right)^{2}=45, i=1,2, \ldots . .18$ then standard deviation of $x_{1}, x_{2} \ldots . x_{18}$ is

Solution:

$V(x-8)=\frac{45}{18}-\left(\frac{9}{18}\right)^{2}=\frac{5}{2}-\frac{1}{4}$
$V(x-8)=\frac{9}{4} $
$\Rightarrow \sqrt{V(x-8)}=\frac{3}{2}$