Mathematics - Statistics Question with Solution | TestHub

$5+3+7+a+b=25\Rightarrow a+b=10$
S.D.$=\sqrt{\frac{5^2+3^2+7^2+a^2+b^2}{5}-5^2}=2$
$=\frac{a^2+b^2+83}{5}-25=4\Rightarrow a^2+b^2=62$
$\Rightarrow (a+b{)}^2-2ab=62\Rightarrow ab=19$
so equation whose roots are a and b is$x^2-10x+19=0$