Benford’s Law or First Digit Law

http://www.surveymonkey.com/sr.aspx?sm=EepAhQxVG6EO9tyceHlnAmeYm7y_2fg4HOmy8lQZ6U33I_3d
Notice that the distribution of first digits for “cash in wallet” is nearly identical to “first digit of street address.” One might expect that the distribution would be uniform — meaning that a street address beginning with 5 is just as likely as one beginning with 9. But it is not. In fact the proportion seems to follow a regular pattern.

Both of these statistics follow Benford’s Law, which you can learn about here: http://en.wikipedia.org/wiki/Benford’s_law

Our results match Benford’s Law very well. But not all first digit samples do match it. Which ones do? What about stock prices? 🙂

Prof. Tucker Balch
Georgia Institute of Technology”

 

“The discovery of Benford’s law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables (used at that time to perform calculations) the earlier pages (which contained numbers that started with 1) were much more worn than the other pages.[3] Newcomb’s published result is the first known instance of this observation and includes a distribution on the second digit, as well. Newcomb proposed a law that the probability of a single number N being the first digit of a number was equal to log(N + 1) − log(N).

The phenomenon was again noted in 1938 by the physicist Frank Benford,[2] who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 physical constants, 1800 molecular weights, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of Reader’s Digest, the street addresses of the first 342 persons listed in American Men of Science and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford (making it an example of Stigler’s Law).

Leading digit meters feet In Benford’s law
Count % Count %
1 26 43.3% 18 30.0% 30.1%
2 7 11.7% 8 13.3% 17.6%
3 9 15.0% 8 13.3% 12.5%
4 6 10.0% 6 10.0% 9.7%
5 4 6.7% 10 16.7% 7.9%
6 1 1.7% 5 8.3% 6.7%
7 2 3.3% 2 3.3% 5.8%
8 5 8.3% 1 1.7% 5.1%
9 0 0.0% 2 3.3% 4.6%”
http://en.wikipedia.org/wiki/Benford’s_law#Mathematical_statement
http://en.wikipedia.org/wiki/Benford’s_law#Explanations

Additional Sources of Info

Following Benford’s Law, or Looking Out for No. 1, By Malcolm W. Browne
(From The New York Times, Tuesday, August 4, 1998)
http://www.rexswain.com/benford.html

Benford’s Law
http://mathworld.wolfram.com/BenfordsLaw.html

The First-digit Law (Benford’s Law)
“According to Wikipedia, this law was used to discover fraud in the 2009 Iranian elections…”
http://powerofproofs.wordpress.com/2011/01/07/the-first-digit-law-benfords-law/
“Similarly, the macroeconomic data the Greek government reported to the European Union before entering the Euro Zone was shown to be probably fraudulent using Benford’s law, albeit years after the country joined.”
http://en.wikipedia.org/wiki/Benford’s_law#Macroeconomic_data

Benford’s law, or the First-digit law
http://statistic-on-air.blogspot.nl/2011/08/benfords-law-or-first-digit-law.html