I started doing a bit of a thought experiment – according to the Census Bureau, the US land area is 3,531,905.43 square miles and with a 2010 population of 308,745,538 there are 87.4 persons per square mile. There were 46,792,300 people living in the 50 most populous cities in the United States in 2010, or a little more than 15% of the population (15.15%).

Those 15% of the population live in just over 11,000 square miles (11,006 to be more or less exact) or 0.312% of the US land mass, for a population density of 4251.5 per square mile. Clearly, because these are the 50 largest cities, they do not represent “average.” So, I decided to remove those 46,792,300 people in their 11,006 square miles from the US population density to see how that changes things for those of us who do not live in the largest 50 cities.

If you do not live in one of the 50 largest cities, on average you live in a population density of 74.4 persons per square mile.

So then I increased the scope to the largest 100 cities. That covers 19.4% of the US population – 59,847,102 – and .488% of the land mass who live in a population density of 3470.75 per square mile.

I then brought the list to the top 275 most populous cities in the US, places with names such as Temecula, California (population just over 100,000) and a little place called Green Bay, Wisconsin (104,000). 27% of the US population lives in .76% of the landmass with a population density of 3127 per square mile. The other 73% of us living in 99.24% of the rest of the country live 64 to a square mile. But it’s much more complicated than that.

According to the National League of Cities, there were 19,492 municipal governments in the US in 2007. In 2007, 257 of them reached over 100,000, currently there are 275 so these numbers are somewhat out of date, but still point to the idea that the “Average” American does not live 87.4 per square mile. The question is though, how much of that landmass is actually inhabited at all.

In “Fooled by Randomness,” Nassim Taleb talks about this idea – that we’re easily fooled by statistics and that there are plenty of examples where 90% of a given population can be above average. His example: A village of 10 people – 9 of whom earn a salary of $30,000 and one desperately poor chap who earns $1000 yearly for an average yearly salary of $27,100.

There are 50 states and when their individual population densities are compared, 27 have an average population density greater than average. Consider this for a moment: New York State has the 7^{th} highest population density in the country – 412.3 persons per square mile. But the “average” New Yorker does not live in even that great a population density. Remove NYC’s 42% of the state’s population – remembering that because it’s the largest city in the country, by definition it is not average – and its 303 square miles, and what you’ve got a density of 239.26 per square mile.

And here’s something else to consider, the 23 states with lower than “average” population densities account for only 19.1% of the country’s population, meaning the 27 states with higher population densities are where 80.9% of the population live.

In 2003, the Census Bureau classified 94.6% of the country as rural open space. So, if we multiply the 3,531,905.43 square miles by the remaining 5.4% we come up with 1,907,228.93 square miles and a population density of 161.88. If we go back to the beginning of this post by subtracting the populations and landmasses of the 275 largest cities in the US, the average population density decreases to 119.34.

Now after having done this analysis over a few hours, I came across the Thoreau Institute’s website detailing much of my own exploration – http://ti.org/vaupdate36.html with an XLS download no less. Their agenda is different than mine – theirs is to explore the environment, mine was to explore numbers – but their data was helpful in that pursuit.

The real US population density would seem to be about twice what the official numbers show. But I’ve wiped out 94.6% where people “don’t live” from the landmass calculation, how come it only affected the population density by 100%? Because where people do live, we live in clusters, in areas where the land is largely developed. If you remove from consideration areas where few people live the actual density in which we live isn’t affected. If no one lived in those areas, the real density wouldn’t have changed, so clearly some people are living there. By removing cities with populations over 100,000 from the mix, the density number rises by about 36%.

The numbers are skewed and the “average” does not tell the true story of how close together we live.