Weighted MeanΒΆ
Global Algorithm - One-Dimensional Algorithm
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