gewichteter

Gewichteter is a German adjective meaning “weighted” and is used across academic and practical contexts to indicate that a quantity has been adjusted by weights assigned to individual components. In mathematics, statistics and data analysis, gewichteter describes measures that give different importance to different observations or elements.

The most common application is the gewichteter Mittelwert (weighted mean) or gewichteter Durchschnitt (weighted average). If x_i denotes observations and w_i the corresponding weights, the weighted mean is often written as sum_i w_i x_i divided by sum_i w_i. If all weights are equal, the weighted mean reduces to the ordinary arithmetic mean. Weights reflect frequency, relevance, reliability or sample size, and can be positive in standard uses. In some modeling contexts, negative weights may be used but require careful interpretation and justification.

Besides the weighted mean, the term appears with other weighted quantities, such as gewichtete Summe (weighted sum) or gewichtete Preise (weighted prices). In practice, weighted calculations are common in survey sampling, meta-analysis, finance, signal processing and data fusion, where different data points contribute to the result according to their assigned weights.

In grammar, gewichteter functions as an attributive adjective in phrases like der gewichtete Durchschnitt or ein gewichteter Durchschnitt. The form shows typical German declension: der gewichtete Durchschnitt, einen gewichteten Durchschnitt, die gewichteten Durchschnitte, etc.

Overall, gewichteter denotes an adjusted value that integrates varying importance or contribution across its components.