Question 23
Let $x_1 \le x_2 \le \dots \le x_{2n-1}$ be real numbers and $A$ be their arithmetic mean. Show that
$$
2 \sum_{i=1}^{2n-1} (x_i - A)^2 \ge \sum_{i=1}^{2n-1} (x_i - x_n)^2.
$$
$$
2 \sum_{i=1}^{2n-1} (x_i - A)^2 \ge \sum_{i=1}^{2n-1} (x_i - x_n)^2.
$$