The Grapes of Math: Benford’s Law


A presenter at AMATYC recommended a dozen, or two books about math written for general audiences. I am reading through them looking for things that might interest Quantitative Reasoning students. Already in Chapter 2 of Grapes of Math I have found Benfords Law. Benford’s Law states that, typically, in a long set of data the first digit is one 30% of the time and the frequency of first digits decreases until it is under 5% for a leading digit of 9. Benford speculated that the probability a leading digit is x is log(x+1)-log(x).

Benford’s Law is used in forensic accounting. A Wesley Rhodes had his fraud exposed partially on the basis of Benford’s Law. That would make a good story to motivate it. It is also another example of the use of logarithms in the appropriate section of our current Math 131 book.

Another interesting story indicates that the presidential election in 2009 was manipulated because one candidate’s vote totals followed Benford’s Law and another candidate’s did not.

The same chapter has a nice discussion of scaling in biology of land vertebrates and metabolism- including an image of a log-log graph that linearizes the underlying power functions.

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