Mathematics - Statistics Question with Solution | TestHub

Finding the ${\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}} \& {\mathrm{f}}_{\mathrm{i}}{{\mathrm{x}}_{\mathrm{i}}}^2$ we get, 

Now, from above table we get, $\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}=176$

Now, finding  $\overline{\mathrm{x}}=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{176}{22}=8$

Now, finding variance, we get,

${\mathrm{\sigma }}^2=\frac{1}{\mathrm{N}}\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}{}^2-(\overline{\mathrm{x}}{)}^2$

$\Rightarrow {\mathrm{\sigma }}^2=\frac{1}{22}\times 2048-(8{)}^2$

$\Rightarrow {\mathrm{\sigma }}^2= 93.090964$

$\Rightarrow {\mathrm{\sigma }}^2= 29.0909$

$\Rightarrow \left[{\mathrm{\sigma }}^2\right]= \left[29.0909\right]=29$