Median center of United States population
The median center of U.S. population is determined by the United States Census Bureau from the results of each census. The Bureau defines it to be:

As of the 2020 U.S. census, this places roughly 165.7 million Americans living on each side of a longitude line passing through a location in Gibson County, Indiana, and the same number living on each side of a latitude line through the same point. During the 20th century the median center of U.S. population moved roughly  southwest, from a location in Randolph County, Indiana to a location in Daviess County, Indiana. The majority of this southwest shift happened in the second half of the century, as the center shifted within a narrow circular band between 1900 and 1950 – all within roughly  of the 1900 starting point in Randolph County. See also 
 Mean center of the United States population
 Center of population
 Geographic center of the United States
 Geographic center of the contiguous United States

References 

Demographic history of the United States
Center of population