I have a list of states, major cities in each state, their populations, and lat/long coordinates for each. Using this, I need to calculate the latitude and longitude that corresponds to the center of a state, weighted by where the population lives.
For example, if a state has two cities, A (population 100) and B (population 200), I want the coordinates of the point that lies 2/3rds of the way between A and B.
I'm using the SAS dataset that comes installed called maps.uscity. It also has some variables called "Projected Logitude/Latitude from Radians", which I think might allow me just to take a simple average of the numbers, but I'm not sure how to get them back into unprojected coordinates.
More generally, if anyone can suggest of a straightforward approach to calculate this it would be much appreciated.
The Census Bureau has actually done these calculations, and posted the results here: http://www.census.gov/geo/www/cenpop/statecenters.txt
Details on the calculation are in this pdf: http://www.census.gov/geo/www/cenpop/calculate2k.pdf