Weighted arithmetic mean

Description

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. Therefore data elements with a high weight contribute more to the weighted mean than do elements with a low weight. The weights cannot be negative. Some may be zero, but not all of them (since division by zero is not allowed). The weighted arithmetic mean (or weighted average) is used if one wants to combine average values from samples of the same population with different sample sizes.

Related formulas

Variables

WAMWeighted arithmetic mean (dimensionless)
wiThe sizes of the different sample (dimensionless)
xiSeries of values (dimensionless)