Benford's Law: Why So Many Numbers Start With One
Around thirty per cent of numbers in real datasets begin with 1, and only five per cent with 9. People inventing figures don't reproduce that — which is how the pattern became an auditing tool.
Topic
Probability Theory
The Central Limit Theorem: Why Bell Curves Are Everywhere
One die is flat. Ten dice added together make a bell curve. The shape is a property of adding independent things — which tells you exactly when to expect it and when not to.
The Law of Large Numbers: Small Samples Are Wild
Seven heads in ten flips is unremarkable; seventy thousand in a hundred thousand would be extraordinary. The same probability, different room for chance — with consequences most people miss.
Simpson's Paradox: True in Every Group, False Overall
A treatment beats its rival for small stones, beats it for large stones, and loses when you combine the patients. Nothing was miscalculated — which is what makes it worth understanding.
The Base Rate Fallacy: Start With How Common It Is
The quiet, bookish stranger sounds like a librarian. There are a hundred times more salespeople — so the shy ones alone outnumber every librarian in the country.
Bayes' Theorem: The 99% Accurate Test That Is Wrong 91% of the Time
A rare disease, a 99% accurate test, a positive result — and roughly a 9% chance you're ill. The gap comes from one number most people leave out entirely.
Black Swan Events: The Model Was Never the Problem
Every observed swan was white until Australia. No amount of confirming evidence establishes a universal rule — and the most confident moment is often the one just before the record breaks.
Power Laws: When the Average Describes Nobody
The world's tallest person barely moves a room's average height. The world's wealthiest moves it by a factor of millions. Almost all statistical intuition is built for the first case.
Regression to the Mean: The Jinx That Is Just Arithmetic
Praise a great performance and the next is worse; criticise a bad one and the next improves. A flight instructor learned this lesson over years of observation — and it was never about motivation.