Let $x_1,x_2,x_3\_\_\_\_\_\_x_n$ be $n$ observation such that $\Sigma {\left(x_i\right)}^2=400$ and $\Sigma x_i=40$ then a possible value of $n$ among the following is 

$x_1{x}_2{x}_3\mathrm{.........}{x}_n$

$\Sigma x_i^2=400$

$x_1^2+x_2^2+\mathrm{......}+x_n^2=400$

$\Sigma x_i=40\Rightarrow x_1+x_2+x_3+x_n=40$

A M of $m^{th}$ power $>m+n$ power of A. M.

$\frac{x_1^m+x_2^m+\mathrm{......}+x_n^m}{n}>{\left(\frac{x_1+x_2+\mathrm{....}+x_n}{n}\right)}^m$

$\Rightarrow Putm=2$

$\Rightarrow \frac{x_1^2+x_2^2+\mathrm{......}+x_n^2}{n}\text{≥}{\left(\frac{x_1+x_2+\mathrm{......}+x_n}{2}\right)}^2\Rightarrow \frac{400}{n}\text{≥}{\left(\frac{40}{n}\right)}^2\Rightarrow \frac{400}{n}\text{≥}\frac{1600}{n^2}$

$\Rightarrow 400n\ge 1600\Rightarrow n\ge 4$