Mathematics - Statistics Question with Solution | TestHub

For $a,b,c$

mean $=\frac{a+b+c}{3}\left(=\overline{x}\right)$

$b=a+c$

$\Rightarrow \overline{x}=\frac{2b}{3}$   $...\left(1\right)$

$\mathrm{S}.\mathrm{D}.\left(a+2,b+2,c+2\right)=\mathrm{S}.\mathrm{D}.\left(a,b,c\right)=d$

$\Rightarrow d^2=\frac{a^2+b^2+c^2}{3}-{\left(\overline{x}\right)}^2$

$\Rightarrow d^2=\frac{a^2+b^2+c^2}{3}-\frac{4b^2}{9}$

$\Rightarrow 9d^2=3\left(a^2+b^2+c^2\right)-4b^2$

$\Rightarrow b^2=3\left(a^2+c^2\right)-9d^2$