I have a set _S_ of real numbers, and I would like to create a new set _R_ with exactly n real numbers (not necessarily from the set) that represent it best.

What I mean by best?

Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.

> To be specific, how do I minimize the [Hausdoff distance](http://en.wikipedia.org/wiki/Hausdorff_distance) between _S_ and _R_?

I hope I've been clear enough in what i want. 
I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there. 

Thank you in advance.

(**Edited** in light of the comments below.)