Learning about Benford's Law

Originally, Benford's Law was observed by the astronomer Simon Newcomb in 1881. He was referencing the logarithm tables, which were tomes listing the values for logarithms of different numbers. He noticed that the pages of the books were more worn out and discolored at the beginning than they were at the end. In fact, the pages that deal with numbers that begin with 1 were significantly more worn out than pages that begin with 9. As the initial digits climbed, the pages were less and less worn.

This phenomenon was noticed again in 1938 by the physicist Frank Benford. He tested this against data in a number of domains, and the principle now bears his name.

In practical terms, this means that about one-third of the numbers in the sequence begin with the digit 1, a little more than 15 percent begin with 2, about 12 percent begin with 3, and the rest until the digit 9 are all below 10 percent. Five percent of the numbers begin with 9. The following is a graphical representation...