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# Re: [Phys-L] Fwd: Benford

The discovery of this "law" goes back to 1881, when the American astronomer Simon Newcomb noticed that . . logarithm tables . . that started with 1 . . were much more worn than the other pages.

from the wikipedia article

On Oct 29, 2012, at 12:41 PM, brian whatcott wrote:

Oldie but oldie! Used for detecting tax return irregularities: people dream up way to many 5's too few ones.
[From an ECN on line piece....]

Brian W

Dr. Benford discovered, in a huge assortment of number sequences --
random samples from a day's stock quotations, a tournament's tennis
scores, the numbers on the front page of The New York Times, the
populations of towns, electricity bills in the Solomon Islands, the
molecular weights of compounds the half-lives of radioactive atoms and
much more -- [something unexpected.]

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.

A strange feature of these probabilities is that they are "scale
invariant" and "base invariant."

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