Sunday, January 27, 2013

Random isn't always random

Random Patterns

Have you ever looked at what is supposed to be a random set of numbers and think some numbers appear more so than others.

It turns out that in a given list of numbers representing anything from electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers bout 30% of the numbers will begin with the digit 1. And less will begin with 2, even less with 3, and so on, until only one number in twenty will begin with a 9. The bigger the data set, and the more orders of magnitude it spans, the more strongly this pattern emerges.

The mathematical formula describing this digit distribution is called Benford's law, and its explanation, only discovered in 1998, has to do with logarithms and power laws. Simply put, it says that the values of measurements are more likely to start with the digit 1 than with 9 because there are typically more small things than there are big things.

Benford's law has been used in fraud cases to prove that a data set that doesn't conform to the law must be fraudulent. After all, when forging numbers, most people naturally assume that they should give all digits equal play to make the data seem random.

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