Numbers and Monday's Afternoon Game Show Question

Monday afternoon I asked a question that caused a lot of controversy, most of it because I didn't really phrase the question very well.   Here it is:

"Take a bank, any bank and look at all the accounts that have money in them.  Look at the balances on those accounts.  Half of those balances have something in common.  What?"

The usual answers are what you'd expect - negative, overdrawn etc.   The answer is - If you look at the balance of money in each account, over half of those numbers begin with 1, 2 or 3.  Over 30% of them will begin with 1.  It's called Benford's Law, discovered by a bored mathematician back in the 1930's.   Here's the long explanation -'s_law

The simple version - Take any list of real world numbers - heights of buildings, electric bill amounts, population numbers/death rates - and they are much more likely to begin with low digits )1,2 and 3) than larger digits (7.8 and 9).  Here's the graph...

Remember that's real world numbers, not made up numbers.  If you want to know how it's used, think of accountants looking for false information on things like tax returns or business records.  If they take all the numbers from a business and start to find more numbers that don't begin with 1 or 2, that can be used as evidence that someone is stealing or embezzling.  I'm fascinated by numbers and have continued to look this up and will talk about it more on Tuesday.