The average that one reading decides
Three readings of one screen: 341 ms, 526 ms, and one that was nonsense. The mean said forty seconds; the middle value would not have moved. Which average a report uses is a decision, not a detail.
A report on our own dashboard lists every screen in the product by how long it takes to open, slowest first. This morning it put one screen at the top with an average of forty seconds, which would be a serious fault if it were true.
The three readings behind that average were 341 milliseconds, 526 milliseconds, and one absurd one. Sorted, the middle value is 526 milliseconds. The mean is 40,289. Same three numbers, same screen, same morning — two answers that would send you to completely different places.
Why this matters for a kitchen
Most hospitality reporting is mean-based, because the mean is the average everybody learned at school and the one a spreadsheet gives you by default. That is fine for takings, where one enormous order really did happen and really should pull the figure up.
It is a poor choice for anything that measures time, because times have a long tail on one side and a hard floor on the other. A ticket cannot take less than no time, but it can take an hour if a printer jammed and nobody noticed until the guest asked. That single hour, in a service of eighty tickets, adds most of a minute to your "average prep time" — and a minute on that number is the difference between a kitchen that looks fine and one that looks like it needs another pair of hands.
So a chef looks at the report, does not recognise the kitchen it describes, and stops looking at the report. That is the real cost. Not the wrong number: the lost habit.
What to ask of a report
Three questions, none of which need any maths.
How many readings is this built from? An average of three is not an average, it is three numbers with a line drawn through them.
What is the worst one? If the worst is wildly far from the average, the average is being pulled by it and you want to go and look at that one incident rather than at the summary.
Would the middle value say the same thing? If the mean and the middle value disagree strongly, the mean is describing an outlier and the middle value is describing your normal day. Usually you want both on the page, side by side, and you want to know which one you are reading.
We have not changed which average our own board shows yet, and we are not going to do it quietly. Changing what a number means under somebody who has been reading it daily for a month is its own kind of dishonesty. But the question is on the table, which is where it should be.