# Benford’s law

**Benford’s law states that in many naturally occurring collections of numbers, the leading digit is likely to be small. In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time. It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants.**

### About Benford’s law in brief

Benford’s law states that in many naturally occurring collections of numbers, the leading digit is likely to be small. In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time. The law is named after physicist Frank Benford, who stated it in 1938. It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, and physical and mathematical constants. The discovery goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables the first digit of a number was equal to log 1. Benford’s Law is sometimes stated in a stronger form, asserting that the fractional part of the logarathm of data is typically close to uniformly distributed between 0 and 1; from this, the main claim about the distribution of first digits can be derived. The general form is: For b = 2,1 number systems, Benford’s law is true but trivial: all binary and unary numbers start with the digit 1. An extension of Benford Law predicts the distribution of first digits in other bases besides decimal; in fact, any base b ≥ 2.

Another example is the leading digit of 2: 1 is by far most common leading digit, irrespective of the unit of measurement. It is also known as the Newcomb–Benford law, or the law of anomalous numbers, and is sometimes called the first-digit law. The first known instance of this observation was in 1938 by the physicist Frank Benford who tested it on a data set of 104 areas of the US. His data set included the surface of 335 rivers, 3,259 populations, and 104 areas of the US, 3 259 rivers, 259 populations and 104 nautical miles (nautical miles) The phenomenon was again noted in 1938 in a paper by Newcomb, who proposed a probability of a single number N being the first digit of a single number N, equal to log log N+1, or log N-1, or log n-2, or log-n-3, orlog-N-4, or Log N +log N+3, or log-N+4, n+5, orLog N, log n, Log n, log-n, n, log- n, and log-t, n n l, log t, l, l,. log-l, l n,. l, and l, log l, log l, l n. The number 1 is more likely to start with 1 than with 9, i.e. more likely than 9. If the digits were distributed uniformly, they would each occur about 11. 1% of time.

## You want to know more about Benford’s law?

This page is based on the article Benford’s law published in Wikipedia (as of Dec. 06, 2020) and was automatically summarized using artificial intelligence.