When the average describes nobody.

Almost every quantity in a business has a floor of zero and no ceiling. Order values, invoice payment delays, time on site, salaries, donation sizes: all of them pile up near the bottom and trail off to the right.

In that shape the mean sits well above what a typical observation looks like, because it is dragged by the tail. It is not wrong, but it answers a question about the total rather than a question about a typical case, and those get conflated constantly.

Compute both. If the mean is much higher than the median, you have a long tail worth looking at directly, because a small number of records is carrying a large share of the total.

In a customer base that usually means two distinct populations sharing one table: retail and wholesale, self-serve and enterprise. The right response is not to pick a statistic, it is to split the population and describe each.

A mean and median that agree closely tells you the opposite, and is worth knowing too: it means the average is safe to quote and one large customer is not steering your reporting.

When you need the total. Average order value multiplied by order count is revenue; median order value multiplied by order count is nothing at all. If the figure will be multiplied by something, you want the mean.

When the distribution is genuinely symmetric, which does happen with measurements and rarely with money.

And when comparing like with like over time, where the same bias applies to both periods and mostly cancels — though a single unusually large order in one period will still move it, which is exactly the case where somebody reports growth that did not happen.