# Benford's Law

It turns out that many [there are plenty of exceptions] naturally occurring numerical data sets obey Benford's Law. For base 10, Benford's Law says that the leading significant digit d of a data item occurs with probability P(d)=log(1 + 1/d) So the number 1 occurs approximate 30% of the time as the leading significant digit and the number 9 occurs less than 5% 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, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude. -- https://en.wikipedia.org/wiki/Benford's_law Check out the wikipedia page https://en.wikipedia.org/wiki/Benford's_law Also the mathematica page: http://mathworld.wolfram.com/BenfordsLaw.html This video: https://youtu.be/XXjlR2OK1kM And this paper on why its not easy to derive: http://tinyurl.com/p7v3xnw There is a lot more on the internet about this if you want to follow it up . . . NOTE: this example was derived from this one http://ggbtu.be/m350891