Mathematics - Statistics Question with Solution | TestHub

Given ${\displaystyle \sum _{i=1}^9{x}_i}-45=9$

$\Rightarrow \sum _{i=1}^9{x}_i=54$

Also $\sum _{i=1}^9\left(x_i^2-10x_i+25\right)=45$

$\Rightarrow \sum _{i=1}^9{x}_i^2-10\times 54+25\times 9=45$

$\Rightarrow \sum x_i^2=45+540-225$

$=360$
$\therefore {\sigma }^2=\frac{{\displaystyle \sum x_i^2}}{N}-{\left(\frac{{\displaystyle \sum x_i}}{N}\right)}^2$

$=\frac{360}{9}-{\left(\frac{54}{9}\right)}^2$

So, variance $=40-36=4$

$\therefore SD=2$