Informally, determining the centroid is often described as finding the point upon which the shape (cut from a uniform plane) would balance.
[2] One example of a refined approach using an azimuthal equidistant projection, also potentially incorporating an iterative process, was described by Peter A. Rogerson in 2015.
[3][4] The abstract says "the new method minimizes the sum of squared great circle distances from all points in the region to the center".
These include: As noted in a United States Geological Survey document, "There is no generally accepted definition of geographic center, and no completely satisfactory method for determining it.
"[1] In general, there is room for debate around various details such as whether or not to include islands and similarly, large bodies of water, how best to handle the curvature of the Earth (a more significant factor with larger regions) and closely related to that issue, which map projection to use.