On Population-Weighted Density

Population-weighted density is the mean of the densities of subareas of a larger area weighted by the populations of those subareas. It is an alternative to the conventional density measure, total population divided by total area. This paper shows that population-weighted density is equal to conventional density plus the variance in density across the subareas divided by the conventional density. This density alternative is very dependent on the size and configuration of the subareas, an issue that has not been adequately addressed by most users. Urban sprawl is associated with lower densities, and the choice of the appropriate density measure is dependent upon the negative consequences of sprawl being considered. Comparison of conventional and population-weighted densities show the latter to be more highly skewed and to sometimes rank urban area densities very differently. Population-weighted density is more strongly related to the size of the urban area, especially size in earlier years, demonstrating the effect of the timing of urban growth on density.