Weighted average

A weighted average combines a set of values into a single summary number while letting some values count for more than others, based on a weight assigned to each one. This differs from a simple average, where every value contributes equally regardless of its importance or reliability.

It is calculated as the sum of each value multiplied by its weight, divided by the sum of the weights: weighted average = sum(value * weight) / sum(weight). A student's grade point average weighted by course credit hours, a portfolio return weighted by dollars invested in each holding, and a survey result weighted to correct for who was over- or under-sampled are all weighted averages; the last case is the basis of survey weighting.

Weighted averages matter whenever treating every observation as equally important would misrepresent the whole: averaging a conversion rate across stores with very different traffic volumes, without weighting by traffic, lets a tiny store's rate count as much as a flagship store's. An exponential moving average is itself a weighted average, with weights that decay for older observations. The main pitfall is failing to disclose that a reported average is weighted, or choosing weights that quietly favor a particular outcome, since the choice of weights can shift the result as much as the underlying data does.