You're looking to solve the centroid problem.  Your locations describe a 
polygon and you want the centroid of that.

A few Google searches on calculating centroids should lead you the right way.

--- On Mon, 1/18/10, Jim Tolbert <[email protected]> wrote:

> From: Jim Tolbert <[email protected]>
> Subject: [Xastir] Off Topic: Method to deterrmine location of N minimum 
> points from a dataset
> To: "XASTIR" <[email protected]>
> Date: Monday, January 18, 2010, 8:05 PM
> Sorry for the off topic, but I am not
> sure where to start and I figured some of you folks probably
> know..  Any suggestions on what I should search on?
> 
> I want a method to calculate the locations of N points from
> a dataset of locations that has a minimum cumulative
> distance.  That, what are the locations of a given
> number of Basepoints so that the distance from the dataset
> to one of he basepoints is
> minimized.   Specifically, if I have a set of
> all the locations in a service area and I want to know where
> to place service providers in the dataset, were should I put
> them if I have two service providers, where should I put
> them if I have three providers, etc.
> 
> I am sure I did this as a home work problem long ago in a
> computer programming class, but I can't seem to come up with
> a simple means of doing it.   I am betting
> the method is detailed out there somewhere, but I can't find
> the correct search parameters.
> 
> Please send any suggestions to me at
> 
> jim at RiverRidge-WI dot net
> 
> Thanks all................ jt
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