I have a (one dimensional) set(I will name it S), and I would like to create a new set(I will name it R) with exactly n points (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.

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.