Sammanvägt

Sammanvägt is a term used in statistics, data analysis, and everyday Swedish to describe a value formed by combining multiple components with assigned weights. It corresponds to what in English is called a weighted or aggregated measure, and is commonly seen as sammanvägt medelvärde or sammanvägd index.

Definition and calculation: A sammanvägd statistic gives each component a influence proportional to its weight. The standard example is the weighted mean: weighted mean = sum(w_i * x_i) / sum(w_i). If the weights sum to 1, this reduces to the sum of w_i times x_i. Weights can be normalized or left as original values, depending on the context.

Weight choices and data handling: Weights should reflect relative importance, frequency, or reliability of components. If the components operate on different scales, standardization or normalization may be required before applying weights to avoid scale bias. Mis-specified weights can bias the resulting value, so the method and justification for weighting are important.

Applications: The concept is used in education to compute sammanvägda betyg (overall grades) based on subject credits, in survey research to produce population-representative estimates through sampling weights, and in finance or performance measurement to build composite scores or indices from multiple indicators.

Example: Suppose three components have values 80, 70, and 90 with weights 0.5, 0.3, and 0.2. The weighted mean is (0.5*80 + 0.3*70 + 0.2*90) / (0.5+0.3+0.2) = 79. Sammanvägt results emphasize more important components according to their weights.

Etymology and related terms: The word combines samman- (together) and vägt (weighted). Related concepts include viktat medelvärde and olika sammanvägda index.