Benford's Law

According to Wikipedia:

Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. Graphically:

To test this I used a dataset containing country populations of all countries. The distribution of first digits is:

1    72
2    36
5    32
3    30
4    16
7    14
8    13
6    13
9    12

Plotting this data gives:

It is very close to the theoretical graph bove. Benford's law is admissible in US courts and has been used to show that financial data submitted by the Greek government to the EU was probably false.

How does it work? Think about what happens when you double numbers:

start with: 1,2,3,4,5,6,7,8,9
then double: 2,4,6,8,10,12,14,16,18
then again: 4,8,12,16,20,24,28,32,36
and son on, If you count up the first digits: 1:8, 2:5, 3:3, 4:2, 5:1 ..... ones are more common than twos etc. The same conclusion is reached if you just write down the numbers 1,2,3,4,....and continue until you are too bored to go on, then count the number of ones, two, threes....

The code used to generate the above graphic is in my code blog.