Chebyshev's Sum Inequality/Discrete

Theorem
Let $a_1, a_2, \ldots, a_n$ be real numbers such that:
 * $a_1 \ge a_2 \ge \cdots \ge a_n$

Let $b_1, b_2, \ldots, b_n$ be real numbers such that:
 * $b_1 \ge b_2 \ge \cdots \ge b_n$

Then:
 * $\ds \dfrac 1 n \sum_{k \mathop = 1}^n a_k b_k \ge \paren {\dfrac 1 n \sum_{k \mathop = 1}^n a_k} \paren {\dfrac 1 n \sum_{k \mathop = 1}^n b_k}$