Centers of the United States
The College Mathematics Journal
Just where is the geographic center of the United States? And where is the population center? In this article we describe how to find these and other geographic features of the U.S. The approach we take is appropriate for a first-year calculus course, and indeed it was in a student research project in such a course that this material originated. The problems that we consider are to find, for the contiguous forty-eight states (sorry, Alaskans and Hawaiians—you will have to adapt this method accordingly for your situation), the area and perimeter, the geographic center and median, and the population center and median. The tools we need are a map of the U.S., a sheet of graph paper, some data from the U.S. Census Bureau, and a computer algebra system (CAS).
Richeson, David. "Centers of the United States." The College Mathematics Journal 36, no. 5 (2005): 366-373. https://www.tandfonline.com/doi/abs/10.1080/07468342.2005.11922151