gewichtetes

Gewichtetes is a German adjective meaning “weighted” and is used to describe quantities, methods, or procedures that incorporate weights assigned to individual data points or components. The term is common in statistics, mathematics, data analysis, and related fields.

In usage, gewichtetes appears in phrases such as gewichtetes Mittel (weighted mean), gewichtete Summe (weighted sum), or gewichtete Regression (weighted regression). The core idea is that each component contributes to the result in proportion to its weight, rather than equally. Weights reflect importance, frequency, reliability, or other criteria that distinguish data points.

A typical example is the weighted mean of values x_i with weights w_i, defined as sum(w_i x_i) / sum(w_i). Weights are usually nonnegative and sum(w_i) > 0. Weighted sums and averages extend to various computations, including variance, regression, and sampling where some observations count more than others.

In practice, gewichtetes is used across disciplines such as econometrics, data science, and graph theory, where weights may represent probabilities, costs, or distances. In computer science and machine learning, weighted quantities appear in loss functions, feature weighting, and algorithms that operate on weighted graphs or datasets.

Grammatically, gewichtetes is one possible attributive form depending on gender, number, and case of the noun it modifies, with the root Gewicht- (weight) providing the semantic basis for the concept of weighting. The commonly encountered phrases often favor gesundheitliche, context-appropriate endings like gewichtetes Mittel or gewichtete Regression.