Asymptotic Properties of the Size-Weighted Mean

Applied researchers often compute weighted means where the weights reflect the relative size of each observation. Despite their common use, the statistical properties of these size-weighted means appear to be poorly understood, as the existing statistical literature and most software applications typically address three other types of weights—survey, precision, and frequency weights. In this paper, I demonstrate that the size-weighted mean is asymptotically normal, derive an estimator for its variance, and discuss several practical considerations relevant to its application.