Mathematics - Statistics Question with Solution | TestHub

$Y\left(\overline{x}\right)=a\overline{x}+b=\frac{a\left(1+2+3+\dots .+17\right)}{17}+b=17$

$\frac{a\left(17\times 18\right)}{17\times 2}+b=17$

$9a+b=17$

$\sigma \left(X^2\right)=\frac{{\displaystyle \sum }{x}^2}{n}-{\left(\frac{{\displaystyle \sum }x}{n}\right)}^2$

$=\frac{1^2+2^2+\dots +{17}^2}{17}-{\left(\frac{1+2+...+17}{17}\right)}^2$

$=\frac{17·18·35}{6·17}-{\left(\frac{17·18}{2·17}\right)}^2$

$=105-81=24$

$\therefore \sigma \left(Y^2\right)=a^2\sigma \left(X^2\right)=a^2·24=216$

$\Rightarrow a^2=\frac{216}{24}=9$

$a=3$

$\therefore b=17-27$

$\therefore b=17-27$

$b=-10$

$\therefore a+b=-7$