From the 2010.census.gov page: 
Historically, the center of population has followed a trail that
reflects the sweep of the nation's brush stroke across America's
population canvas. The sweep reflects the settling of the frontier,
waves of immigration and the migration west and south. Since 1790, the
location has moved in a westerly, then a more southerly pattern. In 2000,
the new center of population was more than 1,000 miles from the first
center in 1790, which was near Chestertown, Md.
The mean center of population 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.

Year	Center of Population	Location
1790	Kent County, Maryland	23 miles east of Baltimore
1800	Howard County, Maryland		18 miles west of Baltimore
1810	Loudoun County, Virginia	40 miles northwest by west of Washington, D.C.
1820	Hardy County, West Virginia	16 miles east of Moorefield
1830	Grant County, West Virginia	19 miles west-southwest of Moorefield
1840	Upshur County, West Virginia	16 miles south of Clarksburg
1850	Wirt County, West Virginia	23 miles southeast of Parkersburg
1860	Pike County, Ohio	20 miles south by east of Chillcothe
1870	Highland County, Ohio	48 miles east by north of Cincinnati
1880	Boone County, Kentucky	8 miles west by south of Cincinnati
1890	Decatur County, Indiana		20 miles east of Columbus
1900	Bartholomew County, Indiana	6 miles southeast of Columbus
1910	Monroe County, Indiana	In the city of Bloomington
1920	Owen County, Indiana	8 miles south-southeast of Spencer
1930	Greene County, Indiana	3 miles northeast of Linton
1940	Sullivan County, Indiana	2 miles southeast by east of Carlisle
1950	Clay County, Illinois	3 miles northeast of Louisville
1960	Clinton County, Illinois	6.5 miles northwest of Centralia
1970	St. Clair County, Illinois	5 miles east-southeast of Mascoutah
1980	Jefferson County, Missouri	1/4 mile west of DeSoto'
1990	Crawford County, Missouri	9.7 miles southeast of Steelville'
2000	Phelps County, Missouri		2.8 miles east of Edgar Springs
2010	Texas County, Missouri	2.9 miles from Plato