# Benford’s law

I recently read about Benford’s law on an economists blog. Apparently, many natural data sets, entries begin with the number 1 about 1/3 of the time, which is quite disproportionate. I’ve twisted my brain into a pretzel just thinking about this law and what it means about how we define numerical quantities. According to the law:

“Besides the number 1 consistently appearing about 1/3 of the time, number 2 appears with a frequency of 17.6%, number 3 at 12.5%, on down to number 9 at 4.6%. In mathematical terms, this logarithmic law is written as F(d) = log[1 + (1/d)], where F is the frequency and d is the digit in question.”

The practical implications of Benford’s law is that it can be used to identify falsified data and fraud. It’s an interesting rule that also illustrates that not everything is distributed according to the normal or exponential distributions. Benford’s law was used on an episode of NUMB3RS to solve a series of burglaries. I’ll have to write more on NUMB3RS later, which I am addicted to, since it uses many OR mathodologies.