Weighted mean allows introducing encoded preference to the measure

It can be helpful if we know and want to encode some additional information in the measure, so the mean is more representative.

Some examples of where we’d use a weighted mean:

1. In a time series data we could introduce bias towards the more recent data since it’s usually more indicative of future behavior.
2. We could weight votes from locals in some local-centric survey over tourists and passersby since their vote might be more relevant
3. Having multiple data sources, knowing the data quality of each of them, we could weight up the sources we know are much better quality.
4. Class imbalance scenarios
5. Reducing the influence of outliers, also described in Avoiding outlier magnitudes makes the measure robust.