Why 30.1% of numbers start with 1
Since there are nine possible digits, you would expect that one-ninth (11.11%) of the numbers would have 1 in the leading digit position. However, this is not what you will find– about 30.1% of the numbers will start with 1. It gets even stranger from here.
(via hn)
Why do I post this? Well, I love math. I love problems like this. After reading through the whole explanation, this is what I got out of it:
It’s a little misleading to say 30.1% of numbers start with 1. Actually, a wide enough distribution covering several orders of magnitude will follow Benford’s Law. What does this mean?
This seems to have been key in catching Bernie Madoff’s scheme.
The point is that a randomly generated set will not follow Benford’s Law. By faking the tax returns, a set of normally distributed numbers was generated. You would expect that a huge distribution such as tax returns would follow Benford’s Law. As such, it must have triggered an in depth review into Madoff.
