The possible dangers and anomalies arising from the casual interpretation of “mean values” or “averages” are well known. The “velocity problem” is often cited as an example (see e.g. [1,2]). A typical version of this problem is as follows: A cyclist goes from A to B at 20 mph and returns from B back to A at 10 mph. What is the average speed? The casual answer is 15 mph, the arithmetic mean of the two speeds; this is wrong. The correct answer, obtained by dividing the total distance travelled by the total time taken, is obtained as 13.3 mph, and this latter figure is readily shown to be the harmonic mean of the two speeds. Langley goes on to say that “the harmonic mean is often appropriate when the data consists of ratios (miles per hour, . . .)”; this is true but not specifically informative. Reichmann comments that “the arithmetic mean cannot properly be used to average rates of speed” and “the harmonic mean is always the right one to use to average rates . .-.”; these generalisations are incorrect.