Weighted mean

A weighted mean lets some values count for more than others, which is what you need when categories differ in importance or in sample size. The formula is $\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$, read as weighted x-bar, where $w_i$ is the weight attached to the value $x_i$. If tests count 70 percent of a grade and homework counts 30 percent, a student with a 90 test average and an 80 homework average earns $0.7(90) + 0.3(80) = 63 + 24 = 87$, where the weights already total 1 so the denominator is 1 and drops out. The ordinary mean is just the special case in which every weight is equal.