A people's center of the United States JUN 16 2014
The center of the population of the United States has been moving steadily west and south since 1790. This video shows the progression until 2010:
You can step through the animation yourself on the US Census Bureau site. It's interesting to see how even the changes are...there was one big jump from 1850 to 1860 and a slow down in westward migration from 1890 to 1940, but other than that, it shifted west about 40-50 miles each decade.