Every decade, the Census determines the center of the U.S. population. It explains it like this:
The center is determined as the place where an imaginary, flat, weightless and rigid map of the United States would balance perfectly if all residents were of identical weight. In 2000, Edgar Springs, Mo., was announced as the new U.S. population center.
For the 2010 Census, the center moved in a more southernly direction and ended up in Texas County, Mo., about 2.9 miles from Plato. The Census has put out this wonderful interactive graphic that lets you see how the center has shifted south and west since 1790: