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 if you gather up a bunch of random numbers that appear “in the wild” and you tally up the first digits of each of these numbers then you will tend to find lots of 1’s and not many 9’s (and in fact you expect more ‘s than 2’s, more 2’s than 3’s, etc). This tends to happen when you have a range of numbers which is spread out over multiple orders of magnitude. The reason is that when numbers are spread out over many orders of magnitude, it tends to be roughly uniform when measured on a “log scale”. This just means that the number of data points between x and 2x will be about the same for different values of x. In other words, there should be about as many values between 100 and 200 as there are between 200 and 400 and between 400 and 800. If you just look at first digits, this means that you should expect the same number of 1’s as you have 2’s and 3’s combined or even as many as you have 4’s, 5’s, 6’s, and 7’s combined.
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