Can someone explain Benford’s Law to me. I get that certain numbers show up more often in large data sets, but why?
In: Mathematics
Benford’s law says that the first digit of a number picked from a large range of numbers tends to be a 1. Think of it like this
between 1 and 20, 11 of the 20 numbers start with a 1, more than half. between 1 and 99, 11 of the 99 numbers start with a 1. This repeats for 0-200 and 0-999 etc always holding the max of “just over half” and the min of “about 11%” so if you average that for all ranges, you get that about 30% of numbers in an unknown range start with 1.
it seems like this should apply to all digits equally, but take 9. between 1 and 89, 1 number starts with 9, basically 1/89%. going up to 99 brings us back to 11/99, but now 11 is the max and “almost 0” is the min, so again average it over all ranges, and you get more like 4% of lead numbers
You can then apply this to some fraud cases. If the numbers span multiple orders of magnitude AND should be roughly random, AND there are a lot of them, you should expect them to match Benford’s law pretty well. If they dont, one of the 3 requirements is probably false. if you know the first and last are true, you can say “these probably arent actually random”
Latest Answers