In many situations we are faced with two numbers 0 ˂ a ≤ b as values of some variable and we are forced to produce a compromise value which in some way is intermediate between a and b. Such a compromise value can be termed an average or a mean of a and b and we would expect it to lie between a and b, with equality if and only if a = b. There are many different kinds of mean in elementary mathematics (see, for example, “Connected means” in the June 1988 Gazette). Perhaps the following three are the best known and the most important.