Weighted Average
Weighted Average is a statistical technique used to compute an average while taking into account the relative importance of each value, represented by a weight. Unlike the simple arithmetic mean, where all observations are equally important, the weighted average assigns a coefficient to each data point that reflects its relevance, frequency, or reliability.
In artificial intelligence and data science, weighted averages are widely used. For instance, in evaluating multi-class classification models, metrics like “weighted precision” or “weighted F1-score” adjust for class imbalance: rare classes contribute less to the overall metric, preventing skewed evaluations. In recommendation systems, weighted averages of ratings can reflect both the user’s score and the credibility or trustworthiness of the rater.
The method also plays a key role in finance (portfolio returns weighted by asset risk or market capitalization), economics (consumer price indices), and industry (quality scores weighted by production volumes).
Weighted averages serve as a way to respect contextual importance. In machine learning, this often means avoiding misleading interpretations: if one class represents only 1% of the data but carries critical significance (e.g., fraudulent transactions), analysts can assign it higher weight in evaluation metrics to ensure it isn’t drowned out by majority classes.
Mathematically, a weighted average is calculated as the sum of each value multiplied by its weight, divided by the sum of the weights. This flexibility makes it adaptable: weights can reflect probabilities, frequencies, financial exposures, or even expert judgment.
One challenge lies in choosing the right weights. Poorly selected weights can distort insights as much as ignoring them altogether. In practice, determining weights may come from empirical data (frequency counts), domain expertise, or optimization goals (e.g., maximizing fairness or minimizing risk).
References :
- Wikipedia – Weighted arithmetic mean: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean
- Towards Data Science – Weighted Averages in Machine Learning: https://towardsdatascience.com/weighted-averages-in-machine-learning-9f6fcd7153f6
