Explanation

(c)
Given, $\sum_{}^{}{x_{i}^{2} = 400}\ and\ \sum_{}^{}{x_{i}^{\ } = 80,}since\ \sigma^{2} \geq 0$
$\Rightarrow \frac{\sum_{}^{}x_{i}^{2}}{n} - \left( \frac{\sum_{}^{}x_{i}^{\ }}{n} \right)^{2} \geq 0$
$\Rightarrow \frac{400}{n} - \frac{6400}{n^{2}} \geq 0$
$\Rightarrow \ \ n \geq 16$
$\therefore n\ = 18$