Step-by-step Solution:

We are given the inequality: \[ \frac{\sum x_{i}^{2}}{n} \geq \left(\frac{\sum x_{i}}{n}\right)^{2} \] Substituting the given values: \[ \sum x_{i}^{2} = 400, \quad \sum x_{i} = 80 \] \[ \frac{400}{n} \geq \left(\frac{80}{n}\right)^{2} \] \[ \Rightarrow \frac{400}{n} \geq \frac{6400}{n^{2}} \] Multiplying both sides by \( n^2 \) (since \( n > 0 \)): \[ 400n \geq 6400 \] \[ \Rightarrow n \geq \frac{6400}{400} \] \[ \Rightarrow n \geq 16 \] Since \( n \) must be a given option greater than or equal to 16, the possible value of \( n \) is: \[ \boxed{20} \]