The village clinic was sent two new thermometers and asked to test them before the old ones were thrown away. The nurse did it properly: she put both into water held at exactly thirty-seven degrees, took ten readings from each, and wrote them down.
The first thermometer read thirty-seven every time except twice, when it read thirty-six point nine and thirty-seven point one. The second read thirty-four, then forty, then thirty-six, then thirty-nine, and so on.
She worked out the average of each set. Both came to thirty-seven. On that number alone the two instruments were identical.
The doctor looked at the two columns and did not need a calculation. The first thermometer is reliable: whatever it says, the true temperature is within a tenth of a degree. The second is useless: it reads thirty-four for a patient who is at thirty-seven, and forty for the next one.
Averaging hides exactly the thing a clinic needs to know. A thermometer is not used ten times on ten patients and then averaged. It is used once, on one patient, and the decision is made from that single reading.
She kept the ten readings anyway, in the back of the ledger, because a supplier who disputes a return will ask to see the numbers rather than the conclusion.
She sent the second one back with a note that said its average was perfect and that this was not the relevant question.