This question already has an answer here:
As stated by Wikipedia (here):
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time.
I find this fascinating and confusing. Benford's original contribution came after the first statement of the phenomenon, and in it he used a data sample with over 20 thousand entries. It has since been tested on data samples that number in the hundreds of thousands.
Statistically, it seems sound. But why should it be true? What is the intuition behind this phenomenon?
Most importantly, is there a proof?