Where the statistical wear is

Ivars Peterson, in his blog, The Mathematical Tourist, explains how a detective take a mathematical approach to some everyday questions:

Marks on objects can provide intriguing statistical glimpses of usage patterns. The darkened leaves of a well-thumbed book may point to favorite passages; the distinctive hollows of oft-traversed steps suggest the characteristic tread of countless feet….



I happened to notice a particularly striking example of such “statistical wear” on the door to the men’s restroom, just down the hall from my office. Entry to the restroom was by a swinging door, which opened inward with a push. Countless hands pushing on the door had worn away the brown stain in one particular area, reflecting where men had preferred to place a hand. The result was a roughly circular spot—a two-dimensional statistical distribution—with the most wear in the middle and progressively less wear away from the center….

What pattern would you expect to see on a nearly identical swinging door to the women’s restroom? The pattern is similar, but it is lower and a little closer to the door’s edge, reflecting a lower average height and a greater preference for pushing with less force. As a result, the pattern has a significantly greater overlap with the door’s brass plate.