TITLE:
Asymptotic Properties of the Size-Weighted Mean
AUTHORS:
Eugene P. Canjels
KEYWORDS:
Size-Weighted Mean, Weighted Mean, Asymptotic Distribution, Hypothesis Testing
JOURNAL NAME:
Open Journal of Statistics,
Vol.16 No.1,
February
24,
2026
ABSTRACT: 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.