Mathematics - Statistics Question with Solution | TestHub

$\begin{array}{rl}& \because \text{ mean }=9\\ & \therefore 53+\mathrm{a}+\mathrm{b}=72\\ & \Rightarrow \mathrm{a}+\mathrm{b}=19\\ & \because {\sigma }^2=\frac{37}{4}\text{ and }(\overline{\mathrm{X}}{)}^2+{\sigma }^2=\frac{\sum {\mathrm{x}}_1^2}{\mathrm{N}}\\ & \Rightarrow 81+\frac{37}{4}=\frac{529+{\mathrm{a}}^2+{\mathrm{b}}^2}{8}\\ & \Rightarrow 648+74=529+{\mathrm{a}}^2+{\mathrm{b}}^2\\ & \Rightarrow {\mathrm{a}}^2+{\mathrm{b}}^2=193\\ & \because \mathrm{a}+\mathrm{b}=19\Rightarrow {\mathrm{a}}^2+{\mathrm{b}}^2+2\mathrm{ab}=361\\ & \Rightarrow 2\mathrm{ab}=168\\ & \Rightarrow \mathrm{ab}=84\\ & \therefore \mathrm{a}+\mathrm{b}+\mathrm{ab}=103\end{array}$