keno
09-02-2006, 01:31 PM
http://www.rexswain.com/benford.html
Here's an excerpt. If you're intrigued, click on the link and learn something you'd never guess.
"Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from 1 through 9. All nine numbers would be regarded as equally probable.
But, as 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 -- this is not so.
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."
It's raining, I just had a lithotripsy yesterday and the anesthetic continues to rule, so give me a break. Better yet, don't give me a break. This is great stuff. Not as spectacular to some as the possibility that Lance is spending time in a Hilton, but fascinating, nevertheless.
keno
Here's an excerpt. If you're intrigued, click on the link and learn something you'd never guess.
"Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from 1 through 9. All nine numbers would be regarded as equally probable.
But, as 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 -- this is not so.
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."
It's raining, I just had a lithotripsy yesterday and the anesthetic continues to rule, so give me a break. Better yet, don't give me a break. This is great stuff. Not as spectacular to some as the possibility that Lance is spending time in a Hilton, but fascinating, nevertheless.
keno