## 17 July 2008

### Population densities vary over nine orders of magnitude

The United States has an area of 3,794,066 square miles, and a population, as of the 2000 census, of 281,421,906. This gives a population density of 74.2 people per square mile.

But what is the average population density that Americans live at? It's not 74.2 per square mile. Only about 11 percent of Americans live in census block groups (the smallest resolution the census goes down to; there are about 200,000 of these, corresponding to about 1,500 people each) lower than this density. That's not too surprising; that average includes lots of empty space.

But the median American, it turns out, lives in a block group with a density of 2,521.6 per square mile. At least, when I asked the web site I was using for the distribution of block groups by population density that's what it said; the front page says this number is 2,059.23. I suspect the smaller number is actually the median population density of block groups, not of individuals; the block groups tend to have lower populations in less dense areas, which explains the difference. This number was surprisingly high to me, and seems to illustrate how concentrated population is.

In case you're wondering, the most densely populated block group is one in New York County, New York -- 3,240 people in 0.0097 square miles, for about 330,000 per square mile. The least dense is in the North Slope Borough of Alaska -- 3 people in 3,246 square miles, or one per 1,082 square miles. The Manhattan block group I mention here is 360 million times more dense than the Alaska one; population densities vary over a huge range.

Here's a table; in the first row is a percentile n, in the second row the population density such that n% of Americans live in a block group with that density (in people per square mile) or less. (Generating such a table at fakeisthenewreal.com is slow, which is why I'm providing it here.)
 Percentile 5 10 20 30 40 50 Density 29.3 64.9 226.9 677.5 1499.8 2521.6 Percentile 60 70 80 90 95 Density 3737.2 5257.1 7529 13261.9 24219.5
I hesitate to interpret this. But I must admit that I'm curious if demographers have some way of predicting the general shape of this data. It's clear in the US that more people live at "intermediate" densities than at very high or low ones -- but that's not exactly a meaningful statement.

(Facts from fake is the new real, crunching Census Bureau data.)

By the way, Wikipedia has an article entitled list of U. S. states by area. This includes an almost entirely useless map which colors the larger states darker. I can see which states are larger without the colors, because they're larger, which is kind of the point of a map. The area the state takes up on my screen should be proportional to its actual area.

Anonymous said...

The colored maps are land area and water area, not total area, so the maps would have to be distorted (or more distorted) to have land or water area proportional to screen pixels. Those would be interesting maps to see, and probably more intuitive than the colors, but also a lot harder to create.

Anonymous said...

Computer software has made it amazingly simple to create horrendous maps.

Something like the role Excel (or was it Lotus 1-2-3?) played in introducing the American public to the tools necessary to create poorly designed bar charts...

Jonathan

JimB said...

Just being picky, but...

If there had been a single block group anywhere with zero people living in it, wouldn't that result in density varying over an infinite number of orders of magnitude?

I'm not sure "nine" is really meaningful here. If a few people moved into that least-dense block group, you'd lose an order of magnitude.

Michael Lugo said...

Jim,

you're right, although I suspect that block groups by definition don't have zero population. The Census is about counting people; why would they be counting in places where there are no people?

The lower bound is a bit suspect, though.

Anonymous said...

why would they be counting in places where there are no people?

That sounds suspiciously like applied mathematician talk. The elegant solution is clearly to count people everywhere so as to avoid special cases.

Anonymous said...

Population density is a far more critical topic than you may imagine. Want to have some more fun with mathematics? Consider what population density does to per capita consumption. Then consider what happens when falling per capita consumption collides with rising productivity (per capita output).

I've done this and more in "Five Short Blasts: A New Economic Theory Exposes The Fatal Flaw in Globalization and Its Consequences for America." If interested in learning more about this important new economic theory, I invite you to visit either of my web sites at http://OpenWindowPublishingCo.com or http://petemurphy.wordpress.com. There you can read the preface, join in the blog discussion and, of course, purchase the book if you like.

Please forgive the somewhat spammish nature of this reply, but I don't know how else to open up a discussion of this critical dimension of population density without drawing attention to the book that explains the theory.

Pete Murphy
Author, "Five Short Blasts"

Paul Soldera said...

I wonder if you looked at any given 'western' country the general shape of the distribution would be similar - given that the underlying economic forces that shift people internally are likely to be the same. I am sure someone has done this. As for census block definitions, if I recall correctly, census tracts are the smallest break and they are kept consistent over time to make for apples-to-apples comparisons of census data. I guess you could get one that has no population due to out-migration, but something tells me the stats guys wouldn't like this, and they'd re-draw the boundaries.

Michael Lugo said...

Paul,

you may be right. But at the same time, most European countries don't have quite the same spaces where nobody lives that the US has. Also, the distribution of population density turns out to be surprisingly complicated, which I may post about later, although I'm probably just rediscovering things demographers already know.

Paul Soldera said...

I wonder if this - http://www.fakeisthenewreal.org/by_density/?classing=quantile&units=sqmi&div=50 - is a bit misleading as it pertains to why we choose to live where we do. It looks like a huge range, but qualitatively, is it really that large? Feels very Schelling-like - http://en.wikipedia.org/wiki/Thomas_Schelling

humble biped said...

@jimb - Good point about the arbitrary spread of the data. There are only half a dozen block groups with population densities in the thousandths of a person per sq. mi. range, most with populations in the single digits. I would guess that it would actually be a big deal to quadruple the population of these area, since they're generally mountainous and inaccessible.

I believe that there are a few empty block groups. They were ignored when I crunched the data.

@paul soldera - Census tracts do change over time, albeit not radically. I'm not sure I understand you reference to Schelling. I can assure you that there is a vast qualitative difference between the settlement patterns in the mountains to Alaska, Sun Belt suburbs, and the high-rise apartment districts of major cities.

Paul Soldera said...

@humble piped - the curve gave the impression that people in the highest density areas are making different decisions 'about density' than people in the middle or at the bottom. I don't think they necessarily are. They make decisions about jobs, sun, family, the beach, comfort and contentment (among others). The curve is the outcome of these individual decisions - but trying to infer back from the curve is dangerous. The Schelling ref. was a simply that individual decisions on a micro level can have unintended macro consequences. This looked like a possible case. It may not be. I'm just thinking out loud.

humble biped said...

Your point about individual decisions is apt. I would individual decisions are shaped by governmental policy and by ecological conditions. Most people live, and most density variations occurs, within metropolitan areas, where policy and planning at a small scale can have big impacts.

I hope that the curve isn't making any claims. It's comforting but unsurprising that the data produce a logarithmic distribution. The page is meant to provide the data, not make any judgments A page over at Radical Cartography makes a good stab at interpreting the data.

Matt V said...

here's a link to a google satellite view of the densest block in the US.

Matt V said...

forgot to mention - it's the curved set of apartment buildings in the photo above that constitutes the densest census block.

Matt V said...
Anonymous said...

The Wikipedia map is colored for a reason--Alaska and Hawaii are included on the map as insets at different scales. Because of this, you cannot simply look at the map and determine which states are largest (Alaska appears smaller than Texas!).

Anonymous said...

Plotting the areal density (people/square mile) in the presence of a large number of skyscrapers - like in NYC - heavily misrepresents the data. Traditionally, areal density has been plotted as a substitute for space/person because most buildings were a few stories tall. A better model of population density would be to figure out the volume/person - how much "personal space" an individual has. NYC will have substantial personal space, whereas slums in third-world countries will not.

humble biped said...
This comment has been removed by the author.
humble biped said...

No sensible person would ever use population density to draw conclusions about the amount of space available to each person.

Anonymous said...

Late, but Matt V's dense block is on a ridge. The big building at the right (east) end is at the top of the hill. I don't know if they are 8 or 10 or 12 story buildings, but that's it, just apartment buildings, narrow alley behind, probably 10-14 units per floor, and in that neighborhood under fairly high pressure - I'll guess 2.5 - 3 people per room.

Because there are so many people, there is no need to extend across a street, to incorporate a park, etc, etc, so this block is made up entirely of dense, stacked dwelling space. Doubling the size of the block would incorporate a street, lowering the density...

Unknown said...

Your statement that the BG is the smallest geography used by the CB is incorrect. It *is* the smallest geography at which SF Long Form (sample) data is released. However, population data is released at the BLOCK level, which can be significantly smaller than the block group to which it belongs. Try densities at the block level.

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