Imagine spending an entire day cataloguing every available number which has some sort of real world representation (meaning that they can’t just be random, made-up numbers – they actually have to have some sort of meaning). This means street addresses, phone numbers, social security numbers, heights of various trees, lengths of rivers, numbers of gumballs in a jar, populations of various towns and cities, mathematical constants etc… the possible source of numbers is practically limitless. Now, take all of these numbers and sort them by their leading digit (that is, the number that comes first).
Benford’s law states that the number 1 occurs more frequently than any other number – making up nearly a third of all leading digits! Number 2 is far behind in second place, occurring only 17.6% of the time, then number 3 with 12.5% and so on, all the way to number 9, occurring only 4.6% of the time. The same holds true for many other areas that have almost nothing in common: the Dow Jones index history, size of files stored on a PC, the length of the world’s rivers, the numbers in newspapers’ front page headlines, and many more.
The law is called Benford’s law after its (second) founder, Frank Benford, who discovered it in 1935 as a physicist at General Electric.
The “first digit law” emerges in groups as disparate as populations, death rates, physical and chemical constants, baseball statistics, the half-lives of radioactive isotopes, answers in a physics book, prime numbers, and Fibonacci numbers. In other words, just about any group of data obtained by using measurements satisfies the law.
This pattern continues to hold true even if the units of measurement are changed (feet changed to yards, yards changed to kilometers, pounds changed to ounces, etc…) or even if the bases are changed entirely.
Benford’s law has been used as a method for spotting fraudulent accounting data by looking at the first significant digit of each data entry and comparing the actual frequency of occurrence with the predicted frequency. Most white collar criminals are unaware of Benford’s law and will use each digit about 10% of the time for the first significant digit in a number.
Benford’s law has been invoked as evidence of fraud in the 2009 Iranian elections.
Visit http://en.wikipedia.org/wiki/Benford’s_law to know more about Benford’s Law.
