Copie de 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.
-- 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