### Something I didn't know: Benford's Law

James Fallows has a good discussion of something I didn't know about: Benford's Law:

It turns out that if you list the population of cities, the length of rivers, the area of states or counties, the sales figures for stores, the items on your credit card statement, the figures you find in an issue of the(Wikipedia entry)Atlantic, the voting results from local precincts, etc, nearly one third of all the numbers will start with 1, and nearly half will start with either 1 or 2. (To be specific, 30% will start with 1, and 18% with 2.) Not even one twentieth of the numbers will begin with 9.

This doesn't apply to numbers that are chosen to fit a specific range -- sales prices, for instance, which might be $49.99 or $99.95 -- nor numbers specifically designed to be random in their origin, like winning lottery or Powerball figures or computer-generated random sums. But it applies to so many other sets of data that it turns out to be a useful test for whether reported data is legitimate or faked.

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