I'm writing a mapping application that I am writing in python and I need to get the lat/lon centroid of N points. Say I have two locations
a.lat = 101
a.lon = 230
b.lat = 146
b.lon = 200
Getting the center of two points is fairly easy using a euclidean formula. I would like to be able to do it for more then two points.
Fundamentally I'm looking to do something like http://a.placebetween.us/ where one can enter multiple addresses and find a the spot that is equidistant for everyone.
Have a look at the pdf document linked below. It explains how to apply the plane figure algorithm that Bill the Lizard mentions, but on the surface of a sphere.
poster thumbnail and some details http://img51.imageshack.us/img51/4093/centroidspostersummary.jpg
Source: http://www.jennessent.com/arcgis/shapes_poster.htm
There is also a 25 MB full-size PDF available for download.
Credit goes to mixdev for finding the link to the original source, and of course to Jenness Enterprises for making the information available. Note: I am in no way affiliated with the author of this material.
Adding to Andrew Rollings' answer.
You will also need to make sure that if you have points on either side of the 0/360 longitude line that you are measuring in the "right direction"
Is the center of (0,359) and (0, 1) at (0,0) or (0,180)?
If you are averaging angles and have to deal with them crossing the 0/360 then it is safer to sum the sin and cos of each value and then Average = atan2(sum of sines,sum of cosines)
(be careful of the argument order in your atan2 function)
The math is pretty simple if the points form a plane figure. There's no guarantee, however, that a set of latitudes and longitudes are that simple, so it may first be necessary to find the convex hull of the points.
EDIT: As eJames points out, you have to make corrections for the surface of a sphere. My fault for assuming (without thinking) that this was understood. +1 to him.
The below PDF has a bit more detail than the poster from Jenness Enterprises. It also handles conversion in both directions and for a spheroid (such as the Earth) rather than a perfect sphere.
Converting between 3-D Cartesian and ellipsoidal latitude, longitude and height coordinates
Separately average the latitudes and longitudes.
