massweighted

Massweighted, typically written as mass-weighted or mass weighted, describes a quantity that is calculated by giving each component a weight proportional to its mass. This approach is used when the mass of each part is believed to reflect its contribution to the overall property being measured. The standard formula for a mass-weighted average of a variable x across components i is x_massweighted = (sum_i m_i x_i) / (sum_i m_i), where m_i is the mass of component i. If all masses are nonnegative and the total mass is nonzero, the mass-weighted average is well defined.

Mass weighting contrasts with simple (unweighted) averages and with other weighting schemes such as number weighting. It is particularly appropriate when the property of interest scales with mass or when larger components should have a proportionally larger influence on the result. In continuous distributions, the discrete sum is replaced by an integral using the mass distribution as the weighting function.

Common applications include isotopic chemistry, where atomic weights are mass-weighted averages of isotopic masses according to natural abundances, and astrophysics or planetary science, where mass-weighted means emphasize more massive stars, planets, or components in a system. Mass weighting is also used in material science and spectroscopy to reflect how different masses contribute to observed signals.

Limitations arise when mass is not the relevant factor for weighting; in such cases alternative weighting schemes (e.g., by volume, concentration, or probability) may be more appropriate.