Testing Benford's Law

Imagine a large dataset, for example a list of every country's population. Chances are, the probablity of leading digit being 1 more than it being 2. And 2 as a leading digit would occur more often than 3, and so on. This odd phenomenon is Benford's Law.

Benford's Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. It tends to be most accurate when values are distributed across multiple orders of magnitude.This law is use to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions.

The assumptions regarding the data to be examined by Benford’s Law are:
      Numeric data
      Randomly generated numbers:
            – Not restricted by maximums or minimums
            – Not assigned numbers
      Large sets of data magnitude of orders (e.g., numbers migrate up
      through 10, 100, 1,000, 10,000, etc.)

See the Wikipedia article or this Numberphile video for a more thorough discussion