Mathematics - Statistics Question with Solution | TestHub

Mean of $a,b,8,5,10$ is 6 $$\begin{array}{rl}& \Rightarrow \frac{a+b+8+5+10}{5}=6\\ & \Rightarrow a+b=7\end{array}$$ Given that Variance is $6.8$ $$\begin{array}{rl}& \therefore \text{ Variance }=\frac{\sum {\left({\mathrm{X}}_{\mathrm{i}}-\mathrm{A}\right)}^2}{\mathrm{n}}\\ & =\frac{(\mathrm{a}-6{)}^2+(\mathrm{b}-6{)}^2+4+1+16}{5}=6.8\end{array}$$ $$\begin{array}{rl}& \Rightarrow a^2+b^2=25\\ & a^2+(7-a{)}^2=25\\ & \Rightarrow a^2-7a+12=0\\ & \therefore a=4,3\text{ and }b=3,4\end{array}$$