calculate the latitude and longitude of the center point of that set

[ColinJDenman]

(09-25-2018 05:18 PM)ijabbott Wrote:  It's not always possible unless the points all lie on the same side of a great circle.

Presumbaly the general case is that there are two points, one antipodal to the other.
One case might be preferred in your condition above, though the degenerate case of all points on that great circle would make both points valid? In the case of a random distribution of coordinates, I would guess there might be no simple preferred solution. Perhaps least mean squares summation of the coordinates from the solutions might distinguish one as preferable.

Note that I am not a geographer