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,[3] 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. --'s_law Check out the wikipedia page's_law Also the mathematica page: This video: And this paper on why its not easy to derive: 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