Benford’s Law Is Puzzling But True

Benford’s Law Is Puzzling But True

If you take any group of numbers that’s large and spread-out enough — from the populations of every city in the world to the numbers on the front page of the newspaper — what’s the chance that any of those numbers starts with 1? If there was an even chance for any digit from 1 to 9 to be the first one, you’d expect every number to have an 11% chance of starting with 1. But that’s not actually what happens. In a big group of numbers, each one has a whopping 30% chance of starting with 1, a slightly lower chance of starting with 2, and a lower chance still of starting with 3, and so on until 9, which has the lowest chance of starting any given number.

This is known as Benford’s Law, named for physicist Frank Benford who in 1938, actually rediscovered the phenomenon first found by mathematician Simon Newcomb in 1881. When using a book of logarithmic tables, Newcomb noticed that the beginning pages (those containing numbers starting with 1) were more worn than the others. Today, this law is used to sniff out false data in everything from elections to business accounting.

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