What is “Density”?


If population density is population over area, defining the area is an important start. But is this really the best way to define density? This simplistic density measure is known as average density. It determines the number of people per square mile in an area, but says nothing about how they are distributed across that area. Looking at the map in part 1, it is clear that the population density in LA is not concentrated in a single place, but instead distributed widely across the UA, with pockets of higher density areas. The map below shows population density by quintile by Census tract for the New York CSA, CBSA, UA and CDP, and those areas’ respective boundaries. The map paints a very different picture of density than the map of Los Angeles.

Zooming in once again, it becomes clear that the density for New York’s UA is concentrated in one place: downtown New York City. This concentration of density corresponds with the more common conceptualization of density. Thus while the average density of Los Angeles’s UA may be higher, the densest parts of New York’s UA are more dense than those in LA.



Defining Density


It turns out that people have had qualms with average density for a while and noted that it is a crude metric for measuring population density. Indeed, if one wanted to construct a dense city they should hardly look to Los Angeles for guidance.

A while ago some like-minded people began working on alternative population density metrics to more accurately capture density as it is commonly conceived: a concentration of population at an urban core. In 2001 Gary Barnes of the University of Minnesota came up with a population-weighted methodology, followed by work in 2008 by Jordan Rappafort of the Kansas City Fed. By 2012, the year of the problematic press release, even Census had begun publishing population-weighted density figures. According to Census, population-weighted density “can be thought of as the average of every inhabitant’s census tract density.”

So how do these differing definitions affect population density statistics? Dramatically. The table below shows that LA only has higher population density with the average density measure–and even then, only at the UA and CBSA levels. These values for population density are slightly different from the Census report from 2012 as this uses the 2016 vintage of American Community Survey (ACS) data; however, they are similar enough that the results are comparable. The density values are defined as such:

Average Density: \(\frac{\sum{P_i}}{\sum{A_i}}\) where \(P_i\) and \(A_i\) are the population and area of the \(_i\) Census tract respectively.

Population-Weighted Density: \(\frac{\sum{P_i}\sum{d_i}}{\sum{P_i}}\) where \(P_i\) and \(d_i\) are the population and density of the \(_i\) Census tract respectively.

Area (sq mi) Population Average Density Pop-weight Density
LA - CDP 470 3,906,722 8,310 17,549
NYC - CDP 301 8,461,961 28,069 63,459
LA - UA 1,703 12,315,281 7,228 13,101
NYC - UA 3,429 18,410,210 5,367 34,148
LA - CBSA 4,848 13,189,366 2,720 12,440
NYC - CBSA 8,294 20,031,443 2,415 31,537
LA - CSA 33,955 18,463,122 543 10,215
NYC - CSA 13,854 23,568,545 1,701 27,399

Summary statistics

To understand more clearly how these different distributions of density led to the results they did, it helps to see the distributions themselves. Below, one can see a frequency distribution showing the density for all the census tracts in the respective urban areas. The subsequent summary statistics show that the densest census tract in New York is double than of the densest in Los Angeles.

Los Angeles New York
1st Qu. 6718 4757
3rd Qu. 16630 45760
Max. 100200 248200
Mean 13140 30300
Median 10420 17280
Min. 0 0