A demonstration of Benford's Law

Benford's Law says that, no matter what the measuring system, no matter what is being measured, the result is much more likely to start with 1 than with any other digit. One man put it to the test.

Actually, many men put it to the test. And many women. Benford's Law has been around a long time. Populations of cities are more likely to start with the number one than with any other. The digit '1' will appear at the beginning of one third of the results. Change that population population measurement to families instead of individuals, and Benford's law still applies. Change it to the number of pets and it still applies. Change it to the radius of a circle around a city and it still applies; whether that radius is measured in inches, centimeters, or miles.


Chad Orzel, author of How to Teach Physics to Your Dog, had heard of Benford's Law. He'd also heard accusations that Amazon had doctored its sales rankings. Benford's Law has been used to detect voter, claims, and financial fraud in the past, since people who committed the fraud were likely to try to make their numbers as random as possible; thereby failing the Benford test. Intrigued, he tracked his hour-to-hour sales rankings and incorporated the 6,818 values into a chart:

The result is within 5% of expected numbers. Orzel seems not over-awed by the result, but he's pleased that his chart-making has allowed him to put off some work.

Anyone who wishes to hear more from Chad Orzel can buy his book or look up his writings at Uncertainty Principles.


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