Weighted mean

Suppose $w_1, \ldots, w_n$ be positive numbers whose sum is not zero, the "weights". Then the weighted mean of $a_1,a_2,\ldots,a_n$ is defined to be $$\frac{w_1 a_1 + w_2 a_2 + \ldots + w_n a_n}{w_1\!+\!w_2\!+\!\ldots+\!w_n}.$$

If all the weights are equal to each other, the weighted mean equals the mean.