Mathematics - Statistics Question with Solution | TestHub

Total students $=20$

$\Rightarrow { \left(x+1\right)}^2+\left(2x-5\right)+\left(x^2-3x\right)+x=20$

$\Rightarrow x^2+2x+1+2x-5+x^2-3x+x=20$

$\Rightarrow 2x^2+2x-24=0 \Rightarrow x^2+x-12=0$

$\Rightarrow x=-4, 3 \left(\because x>0\right)$

$\therefore x=3$

Average $=\frac{{\left(x+1\right)}^2\times 2+\left(2x-5\right)3+5\left(x^2-3x\right)+7\times x}{20}$

$=\frac{32+3+0+21}{20}=2.8$

Hence, required mean is $2.8$