# Benford’s Law

This is an article about the discovery of new sets of data that seem to obey Benford’s Law–a curious mathematical characteristic of the numbers we collect from the world that is really more conjecture than law.

http://www.newscientist.com/article/mg20827824.700-curious-mathematical-law-is-rife-in-nature.html

It seems that in scores of data sets collected from natural phenomena, the numbers we see tend to start with the digit 1 far more often than, say, with the digit 6.  Indeed, statistical analysis shows that when you look at population numbers, death rates, street addresses, lengths of rivers, stock prices, and more recently, depths of earthquakes and brightness of gamma rays, the observed numbers start with the digit 1 about 30% of the time.  The occurences of other digits as the leading digit fall as you go up the scale.

Apart from being a natural curiosity, Benford’s Law has proven to have some very useful applications.  Scientists can use Benford’s Law to help predict phenomena and look for trends in data, as the rule gives number-crunchers an idea of what they might be looking at from the start.

Additionally, Benford’s Law has been successfully used to identify all kinds of numerical fraud–tax fraud, voter fraud–because when people are faking numbers, they tend to evenly distribute leading digits.  Benford’s Law tells the data-police that if approximately 1/9 of the numbers they are looking start with 1, then something fishy is going on.

Keep that in mind next April.

Categories: ApplicationStatistics

#### patrick honner

Math teacher in Brooklyn, New York