Thinking back over my recent blog on moving west, I realize I have missed an opportunity to make a point that tends to be missed when folks talk about statistics. I have just sat through a number of repeated meetings about education and school improvement in which people tried to compare complex distributions of students and subjects by comparing them with a single number. That single number was almost always an average of some kind, although the distinction between mean and median tends to be lost in the drive to have "a number" to use to compare distributions. It seems that people who would question anything you say will suddenly fall silent at statements like, "15 is more than 12, thus God exists." In the nation of the mathematically insecure, the person who quotes numbers has great power. Even if the numbers are purely "Potemkin" numbers created on the spur of the moment... "I have here in my hand a list of 205—a list of names that were made known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping policy in the State Department".
We are a people in love with, and easily duped by statements of quantity. Averages are our favorite pieces of mis-information. But the center, the average location of population, for the 300,000,000 plus US citizens is in an empty field with the nearest residence over 100 yards away (my estimate, not an exact measure). The center of mass of the US population is near a city with a population of about 65 people in an area with a population density of about ten persons per square mile.
It is in some ways very typical of the wide planes areas to the west, which with exceptions in a few big cities have population densities from 0-10 persons per square mile. Only a few miles to the north-east, south-east or north-west the population density rises to over 1000 per square mile in St. Louis, Memphis, and Kansas City.
About 1/3 of the total population of the United States lives in one of ten urban centers, and almost one in ten live in one of the two population centers of New York/Newark in the East and Los Angeles/Long Beach in the west. Both are a long way in both physical and metaphorical distance from the quiet little field south-west of Plato, Missouri.
The US population that is nestled mostly in areas of high density is centered in a grassy field beside a tiny stream near a small quiet village in a very sparsely populated rural area.
Centers are generally a weak measure to describe the great variability of a population in any measure. It's not that averages are bad... it's just that...well, averages ARE bad.