I'm not sure what median Center of population means. Mean would be the geographic center accounting for location. Is the median just the 50th percentile in latitude and longitude?
https://www2.census.gov/geo/maps/DC2020/PopCenter/CenterPop_...
It’s the point the that minimizes the distance to all the input points in Euclidean space.
For something like population, where there are few gaps in data points, you would expect them to be basically the same because there is probably someone within a few miles of the mean.
This means that an extra person in Hawaii impact the "median center of population" more than an extra person in San Francisco because the mean is part of the calculation, opposed to just a stack ranking. Is this correct?