Benford's Law

Date: 08/06/98 at 18:19:53
From: Elisabeth Edwards
Subject: Benford's Law

What is Benford's law? I heard about this law in the newspaper and am 
curious about it.

Date: 08/13/98 at 13:50:23
From: Doctor Benway
Subject: Re: Benford's Law

Hi Elisabeth,

I found the following information about Benford's Law at this website: 

   http://mathworld.wolfram.com/BenfordsLaw.html   

   Benford's Law

  "Also called the First Digit Law, First Digit Phenomenon, or Leading   
   Digit Phenomenon. In listings, tables of statistics, etc., the 
   Digit 1 tends to occur with Probability approximately 30%, much 
   greater than the expected 10%. This can be observed, for instance, 
   by examining tables of Logarithms and noting that the first pages 
   are much more worn and smudged than later pages. The table below, 
   taken from Benford (1938), shows the distribution of first digits 
   taken from several disparate sources. Of the 54 million real 
   constants in Plouffe's Inverse Symbolic Calculator database, 30% 
   begin with the Digit 1."

In other words when you have tables of numbers, the digit "1" occurs 
more often than any of the other numbers do. The Web site also shows a 
few examples of where this happens. If you're interested in learning 
more about this, I suggest checking out the site.

For more information, see Kevin Brown's MathPages (under Probability 
and Statistics):

   Benford's Law
   http://www.mathpages.com/home/kmath302/kmath302.htm   

and Peter Wolfenden's page:

   The Significant Digit Phenomenon, AKA Benford's Law
   http://www.wolfendens.com/digit.html   

- Doctor Benway, The Math Forum
Check out our web site! http://mathforum.org/dr.math/