Measure of nearness of a point to others

So I was trying to figure this out.

Lets say I have a given set of points, in co-ordinates format (x,y).

Now I want to find the co-ordinate pair within this set which would be the closest to all the other points.

In the sense that lets say the point I want is (x1, y1).

If I want to convert all other points into this one using a +-1 changes (increments or decrements) in either the x or y co-ordinates (or both at once), then how would I find the point that would minimize the number of these changes required?

Is there some measure for this?

Thanks