This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Weighted geometric mean" – news · newspapers · books · scholar · JSTOR (February 2022) (Learn how and when to remove this template message)

In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean.

Given a sample ${\displaystyle x=(x_{1},x_{2}\dots ,x_{n})}$ and weights ${\displaystyle w=(w_{1},w_{2},\dots ,w_{n})}$, it is calculated as:

${\displaystyle {\bar {x))=\left(\prod _{i=1}^{n}x_{i}^{w_{i))\right)^{1/\sum _{i=1}^{n}w_{i))=\quad \exp \left({\frac {\sum _{i=1}^{n}w_{i}\ln x_{i)){\sum _{i=1}^{n}w_{i}\quad ))\right)}$

The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean.