Alice--i was driving on a highway recently for one hour at a constant and very special speed.

Bob--what was so special about it?

Alice--the number of cars i passed was the same as the number of cars that passed me!

Bob--your speed must have been the mean of the speeds of the cars on the road.

Alice--or was it the median?

Bob--these two are often confused. maybe it's neither? we'll have to think about this.

Was Alice's speed the mean, median, or neither?

Note: Assume that any car on the road drives at a constant nonzero speed of s miles per hour, where s is a positive integer. And suppose that for each s, the cars driving at speed s are spaced uniformly, with d(s) cars per mile, d(s) being an integer. And because each mile looks the same as any other by the uniformity hypothesis, we can take mean and median to refer to the set of cars in a fixed one-mile segment, the half-open interval [M, M+1), at some instant.

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