Benford distribution

Strange things about numbers: The Benford’s law.


Last time i could have the chance to talk with Bleue Deep from the Förexdevel team she told me about a strange and quite funny thing about digits in the real world. She told me: “This Benford’s law is an archetype. A funny and very strange one.”

So, what’s strange with it ?

In few words, in many and many and many real world data the digit 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently. Here is the distribution:

Benford distribution

Benford distribution

It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws, which are very common in nature.

In other words the 1 is really the leading one, the 2 really the second leading one, etc…

It became a law, the Benford’s law simply because there is even an equation that describes this funny phenomenon in many, many, many, natural real-world data.

Benford’s law totally discredits the equiprobability philosophical concept.

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