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Sunday, January 29, 2006

 

Benford’s Law

`Dr. Benford derived a formula to explain this. If absolute certainty is defined as 1 and absolute impossibility as 0, then the probability of any number “d” from 1 through 9 being the first digit is log to the base 10 of (1 + 1/d). This formula predicts the frequencies of numbers found in many categories of statistics. [..]

Given a string of at least four numbers sampled from one or more of these sets of data, the chance that the first digit will be 1 is not one in nine, as many people would imagine; according to Benford’s Law, it is 30.1 percent, or nearly one in three. The chance that the first number in the string will be 2 is only 17.6 percent, and the probabilities that successive numbers will be the first digit decline smoothly up to 9, which has only a 4.6 percent chance.’




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