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 your data spans multiple orders of magnitude (some are 1 digit, some are 2, some are 3, etc.) then the data tends to follow Benford’s Law. It happens because every time something adds an extra digit, there are 10 times more possible numbers. Heights of buildings is a good example – if you had 5 buildings whose heights differed by 50 feet each, and the shortest one was 900 feet, they’d be 900, 950, 1000, 1050, and 1100. You have a lot more possibilities for those values to start with 1 than other digits.