For stats geeks only.

The chart below shows the distribution of Texas population by density. The x-axis depicts densities in 100 ppsm increments. (E.g., 0-100 ppsm, 100-200 ppsm, etc.) The y-axis shows the number of people living at each density.

The area under the curve represents the total population. Roughly half the area lies to the right of the red line at 2100 ppsm.

(To correct for the arbitrariness of the increments, I smoothed the curve by averaging the value associated with each density with its immediate neighbors. Also, I cut off the curve at 10,800 ppsm because the distribution became too sporadic to the right of that point.)

What's kinda sorta interesting if you squint at it just right is that the distribution appears to fit a power-law distribution; i.e., it's proportional to x^{k} for some constant k. Power law distributions characterize lots of random phenomena, including earthquake magnitudes, the net worth of individuals, the frequency of words in a text, the popularity of websites, the number of species per genus, and, most pertinently, the distribution of cities by population. (See the Wikipedia link above.) Given the distribution of city populations, I suppose the distribution of population density should have been no surprise (big cities are generally denser than small ones), but it was -- I would have guessed that more people live at a density of, say, 2,000 to 2,500 ppsm than live at a density of 500 to 1,000 ppsm.