Average Speed Bumps: Four Perspectives on Averaging Speeds

highway, where each car travels at a constant speed. Assume that the distribution of the speeds is the same throughout the length of the highway. You adjust your speed so that during a given time unit you overtake the same number of cars as the number of cars that overtake you. Does this mean that your speed is the median of the speeds of the cars on the highway? Surprisingly, the answer is no! (Clevenson, Schilling, Watkins, & Watkins, 2001). Imagine further a radar device at the side of the highway, measuring and recording the speeds of all the cars that pass this point within a fixed time interval. Again, contrary to lay expectations, the arithmetic mean of these recordings would generally not reproduce the arithmetic mean of the speeds of all the cars on the highway (Stein & Dattero, 1985). The above examples illustrate that identifying the correct average may have its difficulties (the correct answers for both cases will be detailed later). Average speed, in general, is not all that self-evident a concept. The apparently simple question “what is the average speed of the cars that drive on the highway?” is equivocal. As students of introductory statistics know, the term average may be interpreted in various ways and hence may assume several different forms. One needs to know in what sense the average is supposed to represent a set of observations. Four Faces of the Average Speed