Enter values together with their weights to compute a weighted mean with automatic weight normalisation, for weighted scores and indicators.
权重和不必等于 1，会自动归一化。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Weighted mean | xbar_w = sum w_i · x_i / sum w_i | ISO 3534-1:2006, Statistics - Vocabulary and symbols |
| Weight normalization | w_i' = w_i / sum w_i, so the normalized weights sum to 1 | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |
| Special case | With equal weights it reduces to the arithmetic mean | ISO 3534-1:2006, Statistics - Vocabulary and symbols |
| Variance of a weighted sum | For independent terms, Var( sum w_i X_i ) = sum w_i^2 · Var(X_i) | Cramer H., Mathematical Methods of Statistics (1946) |