# Weighted Mean¶

Weighted Mean of a data set is similar to the mean, but the values in the data set are weighted differently. The basic formula is stated as follows:

$\mu_{\text{weighted}} = \frac{\sum_{i=1}^{N} w_i \cdot Y_i}{\sum_{i=1}^{N} w_i} \, \text{,}$

where $$Y_i$$ is the $$i$$th value in the data set, $$N$$ is the length of the data vector and $$\mu_{\text{weighted}}$$ is the weighted mean value.

Input Parameters

Parameter Type Constraint Description Remarks
$$Y$$ $$Y \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input data vector of length $$N$$
$$W$$ $$W \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input weighting vector of length $$N$$ If $$\sum w_i = 1$$ , the algorithm simplifies to $$\mu_{\text{weighted}} = \sum w_i \cdot Y_i$$ .

Output Parameters

Parameter Type Constraint Description Remarks
$$\mu_{\text{weighted}}$$ $$\mu_{\text{weighted}} \in \mathbb R$$   Weighted mean value of data $$Y$$ The result is sensitive to improper values such as ‘nan’, ‘inf’, ‘null’, etc.

Single Steps using the Algorithm