Visualizing the median as the minimum-deviation location

The calculus proofs of this property of the median presented in mathematica l statistics texts are not very instructive. A noncalculus proof has been p ublished, but is still somewhat lengthy and likely to deter some nonmathema tical readers. To make the proof more memorable, teachers can make the mini mization task more real by using a concrete criterion such as total distanc e traveled, rather than simply an abstract sum of absolute deviations. We s uggest a short, simple, heuristic graphical approach, which we illustrate u sing a Java applet. We pose, and give proofs for, a related optimization pr oblem.