Benford´s law

Browsing through the web thanks to my good and favorite program Stumble Upon(http://www.stumbleupon.com/) I found a very interesting webpage explaining the Benford´s law.

Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way(wikipedia.com).

It is in this wepage http://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/ in which I found a video that explained it and showed some examples proving the law.

Thanks to a friend of mine which happened to had some free time at work, he tried to prove it filling an excel list with the population in our state(Jalisco, MEX). It is quite impressing, check the graph.

(courtesy of my friend Guillermo Vidales)

This law explains that if you take out the first digit of any number in a list, the probability of number one appearing in the list would be the following:

1= 30.10%
2= 17.60%
3= 12.50%
4= 9.70%
5= 7.90%
6= 6.70%
7= 5.80%
8= 5.10%
9= 4.60%

For example. If you got in a list the number 1,223 2,343 6,343 3,34333 , you first have to take out the first digit and it would give you this: 1 , 2 , 6 , 3 Now that you took out all the first digits, count how many 1´s ,2´s and so on, are in the list and divide them by the size of your list. The result will amaze you because it follows the Benford´s law.

IMPORTANT: It will only follow the Benford´s law if and only if the list numbers behave in a natural way. For example, the population in any given city, country, state etc.. or the sizes of the states in any given country, stock market etc.. All numbers which are not previously assigned.

In the video they show that this law helped a company detect a fraud by just analizing the data of the money that was taken out of the company.

if you want the excel list to check it out and test it yourself, just email me.