If in a series of observations a statistical weight (w i) is assigned to each value, a weighted mean x ̄ w can be calculated by the formula: \[\overline{x}_{w}=\frac{\sum w_{i}\ x_{i}}{\sum w_{i}}\]
Source:
PAC, 1994, 66, 595. 'Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)' on page 599 (https://doi.org/10.1351/pac199466030595)