Ever wanted to know what the historical center for population in a state based on decennial census data? Check out the 2010 Guide to State and Local Census Geography includes a quick summary of 2010 Census data based on geography. Check out these reports at: http://www.census.gov/geo/www/guidestloc/guide_main.html
Below is a quick example of some of the data available for Connecticut
CONNECTICUT CENTERS OF POPULATION
http://www.census.gov/geo/www/2010census/centerpop2010/historical/historical_cenpop_09.html
| Year | North Latitude | West Longitude | 
|---|---|---|
| 20106 | 41° 29′ 49″ | 72° 52′ 13″ | 
| 20006 | 41° 29′ 41″ | 72° 52′ 28″ | 
| 19905 | 41° 29′ 49″ | 72° 52′ 10″ | 
| 19804 | 41° 29′ 26″ | 72° 52′ 34″ | 
| 19703 | 41° 29′ 17″ | 72° 52′ 38″ | 
| 19603 | 41° 32′ 11″ | 72° 53′ 00″ | 
| 19503 | 41° 30′ 33″ | 72° 52′ 57″ | 
| 19402 | 41° 32′ 12″ | 72° 53′ 29″ | 
| 19302 | 41° 32′ 11″ | 72° 53′ 22″ | 
| 19201 | 41° 30′ 08″ | 72° 51′ 47″ | 
| 19101 | 41° 30′ 54″ | 72° 50′ 20″ | 
| 19001 | 41° 31′ 23″ | 72° 49′ 06″ | 
| 18901 | 41° 31′ 41″ | 72° 48′ 00″ | 
| 18801 | 41° 32′ 49″ | 72° 46′ 21″ | 
 1  Source:   U.S. Department of Commerce, Bureau of the Census, Fourteenth Census of  the United States, 1923
2 Source: U.S. Census Bureau, recomputation for historical county level data which relied upon aggregate county level population data with an estimated county centroid resulting in a possible error of up to one mile.
3 Source: U.S. Department of Commerce, Bureau of the Census, Centers of Population for States and Counties, 1974
4 Source: U.S. Census Bureau, Geography Division, recomputation from archived national block group/enumeration area data resulting in a possible error of up to 1,000 feet.
5 Source: U.S. Census Bureau, Geography Division, recomputation from archived national block group data resulting in a possible error of up to 1,000 feet.
6 Source: U.S. Census Bureau, computation from national block-level data
			2 Source: U.S. Census Bureau, recomputation for historical county level data which relied upon aggregate county level population data with an estimated county centroid resulting in a possible error of up to one mile.
3 Source: U.S. Department of Commerce, Bureau of the Census, Centers of Population for States and Counties, 1974
4 Source: U.S. Census Bureau, Geography Division, recomputation from archived national block group/enumeration area data resulting in a possible error of up to 1,000 feet.
5 Source: U.S. Census Bureau, Geography Division, recomputation from archived national block group data resulting in a possible error of up to 1,000 feet.
6 Source: U.S. Census Bureau, computation from national block-level data
