The shop had to choose between two couriers, and both had sent a year of delivery times. Both had a median of two days. On that number there was nothing to choose between them.
The owner's daughter drew a box for each. The box covers the middle half of the deliveries, and for both couriers it ran from one day to three. Still identical.
The difference was in the whisker on the right. For the first courier it reached four days. For the second it reached fourteen.
A quarter of every courier's deliveries lie in that upper whisker, however long it is. For the first company that quarter is spread between three and four days — a slight delay. For the second it is spread between three and fourteen, which means some customers wait a fortnight.
She checked one more thing before recommending it: both companies had sent about the same number of deliveries, so the two pictures were built on comparable evidence.
The shop chose the first courier, and the owner explained why to his staff in one sentence: the two companies are equally good on a typical day, and only one of them is safe on a bad one.
His daughter added a second reason. Nobody complains about a typical delivery. The reputation of a shop is built almost entirely out of its worst quarter.