Population Weighted Density

Residential density is notoriously difficult to calculate in a meaningful way. The obvious calculation is # people divided by land area, but this would distort the data if large unoccupied lands were included as land area in the calculation along with highly dense centers of population. Urban areas should be recognized as different from rural or suburban locations, but how do you delineate the boundary between them?

Although a wealth of demographic data is gathered by census tracts, tracts come in irregular shapes and sizes. The formula below is one way researchers standardize quantities to be able to compare different sized tracts.

In 2012, the US Census Bureau used Population Weighted Density to more accurately describe density. As the description implies, areas with high concentrations of people are weighted more heavily than sparsely populated locations. The equation looks like this:

I wanted to understand how to "weight" a quantity and started to plug in numbers to see how to actually apply this formula.

As an example: 2 census tracts, each with 100 sq ft. Tract A has 2 people. Tract B has 100 people. The traditional measure of density would weigh both parcels equally and calculate density as: total pop÷total area: 102÷200 sq ft=0.51

Population Weighted Density: [(2÷100x2)+(100÷100x100)+(if there was a Tract C, etc)]÷102=0.98

The weighted density more accurately reflects the perceived density (PD in the equation above) since it gives more weight to areas with higher population. If the density were based solely on the larger tract, density would be 100/100=1.0. In our example, weighted density is 0.98.

Data downloaded from the US Census Bureau shows Honolulu ranks as the #4 most dense metropolitan statistical area (MSA) in the country. (Why aren't we included in more studies about major metropolitan areas?)

Most of the above information comes from this article by CityLab.