Mathematics - Statistics Question with Solution | TestHub

Mean, $\overline{x}=\frac{a+b+68+44+48+60}{6}=55$

$\Rightarrow a+b+220=330$

$\Rightarrow a+b=110 ...\left(i\right)$

Variance, ${\sigma }^2=\frac{{\displaystyle \sum _{}^{}}{\left(x_i-\overline{x}\right)}^2}{n}$

$\Rightarrow {\sigma }^2=\frac{{\displaystyle {\left(a-55\right)}^2+{\left(b-55\right)}^2+{13}^2+{11}^2+7^2+5^2}}{6}=194$

$\Rightarrow {\left(a-55\right)}^2+{\left(b-55\right)}^2+364=1164$

$\Rightarrow {\left(110-b-55\right)}^2+{\left(b-55\right)}^2=800$

$\Rightarrow 2{\left(55-b\right)}^2=800$

$\Rightarrow \left(55-b\right)=20$

$\Rightarrow b=35$

$\Rightarrow a=75$

$\Rightarrow a+3b=75+105=180$