Explanation For Benfords Law
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Explanation For Benfords Law

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What is benfords law.

Explanation transition words. One out of nine digits. The law states that in many naturally occurring collections of numbers the leading significant digit is likely to be small. Benfords law also called the newcombbenford law the law of anomalous numbers or the first digit law is an observation about the frequency distribution of leading digits in many real life sets of numerical data.

Intuitively one might expect that the leading digits of these numbers would be uniformly distributed so that each of the digits from 1 to 9 is equally likely to appear. Benfords law states that in listings tables of statistics etc the digit 1 tends to occur with probability much greater than the expected 111 ie one digit out of 9. For example most numbers in a set about 30 will have a leading digit of 1 when the expected probability is 111 ie.

Comments on benfords law. Benfords law holds true for a data set that grows exponentially eg doubles then doubles again in the same time span but also appears to hold true for many cases in which an exponential growth pattern is not obvious eg constant growth each month in the number of accounting transactions for a particular cycle. Benfords law is an observation about the leading digits of the numbers found in real world data sets.

Benfords law also known as the law of first digits or the phenomenon of significant digits is the finding that the first digits or numerals to be exact of the numbers found in series of records of the most varied sources do not display a uniform distribution but rather are arranged in such a way that the digit 1 is the most frequent followed by 2 3 and so in a successively decreasing manner down to 9. The probability was defined by benford in the law of anomalous numbers proceedings of the american philosophical society vol. Benfords law also called the first digit law states that the leading digits in a collection of data set are probably going to be small.

4 march 31 1938 pp. History and etymology for benfords law after frank benford 1948 american physicist note.

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