weighted mean

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:

$x ̄ w = ∑ w i x i ∑ w i$

Comment:

Unless the weights can be assigned objectively, the use of the weighted mean is not normally recommended.

Source:

PAC, 1994, 66, 595 (Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)) on page 599