If we take a random page from any book or a paper or whatever you like, and select all the numbers from it, almost 30% of all numbers will begin with 1, 17% begin with 2 , 11% begin with 3, and the percentage goes down with the number till it reach 9. this is called the benford’s law
Benford's law - Wikipedia
Benford's law, also called the Newcomb-Benford law, the law of anomalous numbers, or the first-digit law, is an…
It is said that if the first digits of the numbers you selected does not comply with this law, then the numbers were not random.
This phenomenon was first observed by Simon Newcomb and later formulated by Frank Benford. This phenomenon can be used for almost everything, where all the 9 numbers have equal probability of appearing as the first digit(eg: length of river, height of a tower.. etc.).
The most common use of this phenomenon is in the accounting and taxes. where they use it to asses fraud or irregularities in the books.
This is how it works, let’s take the general ledger and take the first digit of all the revenue and expenditure and consider benford’s law, if it does not comply with the benford’s law, then there is a chance of irregularities in the books, and better review it again, this is also used by the tax legislators but with a more complex equation.
The benford’s law is being used in a lot of areas including the elections which is held a lot of disagreements from the experts. they say there are lot of factors other than fraud that would lead to the change in the curve. but still other possibilities of the uses of the phenomenon are being explored.
This will completely change the way we asses randomness, so whatever data we consider there is a high chance that the fist digit obey the benford’s law. this is happening because the as we go to the bigger numbers we will have to pass the smaller first digits, that means the further we go the more chance are given for the 1s and 2s.
Mathematically the benford’s law is based on the logarithm with base-10, which shows that the probability that the leading digit of a number will be n can be calculated as log(1+1/n). there are more complex and advanced studies and explanations based on the same law, but this is the general idea. The graph that represent the benford’s law is shown below
Even though the benford’s law is widely criticized, it is still a very useful tool to analyze data. it is not a find any fraud kind of tool it is just to analyze data and give us a red flag so that we can review it again. this is one of greatest discoveries , to which the uses are still largely to be discovered.