For my purposes, I can assume a homogeneous distribution of points within the polygon. What I want to find is the average distance from points within a polygon to a specified point. I don't know where to start and have found similar info online but nothing exact.
Ideally, I would like to do this for an entire Thiessen polygon layer. I have many polygons and a layer with one point in each polygon, and within each of those I would like to find the average distance to the point.
If you are confused by my question, here's an example:
Within a country, what is the average distance one must travel to reach the Capitol? It can be assumed that people are evenly distributed throughout the country.