Benford’s Law – Proof By Arm Waving

Benford’s Law – Proof By Arm Waving

Benford’s Law is a pretty amazing discovery.  It states that for real data, like statistical tables, numerical listing ( like addresses, populations, lengths of rivers, etc… ) and other groups of numbers, that we are not to expect a uniform distribution of leading digits.  For example, one would think that for a list of all river lengths, in any unit of measurement, that there would be relatively equal number of them that start with the number 1, 2, 3 and so forth, with each number having 1/9th the possibility of being the leading digit. However it is proven that the distribution looks more like this:

1 = 30.1%
2 = 17.6%
3  12.5%
4 = 9.6%
5 = 7.9%
6 = 6.6%
7 = 5.8%
8 = 5.1%
9 = 4.5%

I thought a good idea would be to see if this law holds true, for the file sizes found on my hard drive.  There is a good listing of number, found in the real world, and at first glance, I would think that there is an equal likelihood that all the numbers are represented equally as the leading digit.

You can download and run my program below, you’ll need the .net Framework to run it.  Find that here, if you don’t already have it.

Benford program

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