The Choice of Average

Definition

"Average" is not one number but a loose label for three distinct calculations — the mean (sum divided by count), the median (the middle value), and the mode (the most frequent value) — that coincide only sometimes and can diverge sharply when data contains outliers or comes from mixed populations. Because all three are technically "an average," whoever reports a statistic can select whichever one best supports the story they want to tell, without technically lying.

In the Book

Levitin's central illustration is a room of nine people where eight have a net worth near $100,000 and one is $500,000 in debt: the mean collapses to $33,222 — a number that badly misrepresents the room — while the median ($100,000) and mode ($101,000) describe it accurately, because the mean is uniquely sensitive to outliers. He then walks through a start-up's payroll, showing how the same underlying finances can be reported five different ways — emphasizing "average employee salary," "profit per employee," or bundling owners' bonuses into the salary average — each version legally true but engineered to produce a different impression for employees versus investors. He also flags the "mixed population" trap with the deliberately absurd statistic that "on average, humans have one testicle": true only because slightly more women than men exist in the world, a mean that describes no one.

Why It Matters

Recognizing that "average" hides a choice — not a single fact — lets you ask which measure was used and why, and to reconstruct the underlying distribution rather than accepting a single summary number at face value. This applies anywhere a single figure is used to represent a population with real variation: salaries, test scores, home prices, response times, customer satisfaction. The same dataset can be made to look egalitarian, alarming, or reassuring purely through the choice of which average to headline, so the concept turns "what's the average?" into "which average, and what does it hide?"