Why menu benchmarks use the median, not the average

The two words

The average adds every price and divides by how many there were. The median lines every price up in order and takes the one in the middle: half the items cost less, half cost more.

On symmetrical data they land close together. Menu prices are not symmetrical.

What one expensive dish does

A section of a menu might run from thirty dirhams to two hundred, with most lines clustered near the lower end. Add a single showpiece at nine hundred and the average jumps. The median does not move at all, because the item in the middle is still the item in the middle.

Premium menus carry those showpieces deliberately. They are a positioning device, not a typical line, and a statistic that lets one of them drag the headline figure upwards is reporting the device rather than the market.

The middle half is the other half of the answer

A median on its own tells you where the centre is and nothing about the shape. Two markets can share a median of ninety dirhams: one running from eighty to a hundred, the other from forty to three hundred. Pricing into those two is a completely different exercise.

So a median should always be published with the middle half of the market beside it: the band containing the central half of all prices, with a quarter cheaper below and a quarter dearer above. Statisticians call those boundaries the first and third quartiles. In plain text it is simply the middle half.

Reading a distribution in practice

Suppose a category has a median of ninety-seven dirhams and a middle half running from sixty-nine to a hundred and forty. That tells you three useful things at once. The centre of the market is just under a hundred. A quarter of the market prices below seventy, which is where the value end sits. And a quarter prices above a hundred and forty, which is where you would be if you went high.

Now add that the range reaches nine hundred. The average of that set would sit somewhere above the median, in a place where almost nothing is actually priced, and it would be the number quoted in the meeting.

When an average is the right choice

Averages are not wrong, they are wrong here. If you are calculating what you will actually take at the till, you need the average, weighted by how many of each dish you sell, because revenue adds up rather than lining up in order.

The distinction is clean: the average answers questions about totals, the median answers questions about position. A benchmark is a question about position.

Why this is not a technicality

The choice of statistic decides whether a benchmark can be argued with. An average can be moved by one line on one menu, which means a competitor adding a showpiece changes your benchmark without changing the market. A median resists that, and a median published with its spread lets the reader see the showpiece rather than absorbing it invisibly.