Why does Benford’s Law work? This law says numbers in a data set are more likely to start with low digits (1, 2) than high digits (8, 9), but there are exactly as many numbers in existence beginning with each digit.

Question

Why does Benford’s Law work? This law says numbers in a data set are more likely to start with low digits (1, 2) than high digits (8, 9), but there are exactly as many numbers in existence beginning with each digit.

In: Mathematics

Answer 1

When you say “there are exactly as many numbers in existence” you’re looking at the wrong thing. Sure, if you weight all numbers equally, then each digit 0-9 is used about the same number of times.

But as you said, Benford’s law is about *data*, not numbers. Each number is not treated the same, but rather each data point is.

And data points are more likely to have low digits than high digits (it’s rare that a certain measurement is scaled exactly to a multiple of 10 to make all digits 1-9 evenly likely).