Distributions and Outliers

The one idea: A single average hides the shape of your data. Before you report any summary number, look at the whole distribution — because business data is usually lopsided, so the mean often describes no real customer, and the outliers you'd be tempted to delete are frequently the actual story.

⚠️ The trap: "Average revenue per customer is $340, so that's roughly what a typical customer spends." That feels right and it's wrong. Business data is long-tailed, so the mean gets dragged into the empty space between a crowd of small values and a few whales — report the median when you mean "typical," and keep the mean only for questions about totals (mean × count = total).

"Average revenue per customer is $340." It's a clean sentence, it fits on a slide, and it may describe no actual customer. If ten customers spend $50 and one spends $3,240, the average is $340 — a number sitting in empty space between a crowd at $50 and a whale at $3,240. Anyone who plans around "the $340 customer" is planning around a ghost.

The mean is not wrong; it's just one number trying to summarize a whole distribution — the full shape of how values spread. Before you report any summary statistic, you owe the data one look at its shape. This single habit — look at the distribution first — separates analysts whose numbers survive scrutiny from analysts who get ambushed by their own averages.

Why shape comes before summary

Two datasets can share a mean and describe completely different worlds:

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