According to the U.S. census, the mean center of the population shifted west every decade since 1790. They show the change in a simple animation.
The mean center of population, traditionally referred to as simply the center of population, is provided for the 2010 Census and each census since 1790. In 2010, the mean center of population was located at 37°31'03" North latitude, 92°10'23" West longitude in Texas County, Missouri, 2.7 miles northeast of Plato, Missouri.
The inclination might be to read this as people moving west, which is partially true, but don't forget immigration increasing the populations too.