We show that for any convex object Q in the plane, the average distance between the Fermat-Weber center of Q and the points in Q is at least 4(Q)/25, and at most 2(Q)/(3 3), wher...
The Fermat-Weber center of a planar body Q is a point in the plane from which the average distance to the points in Q is minimal. We first show that for any convex body Q in the ...