How random are random digits?
Day 73 / 365
If you look at the newspaper and collect every number that appears in it, and look at the first digits of those numbers, you would expect them to be uniformly distributed. So on an average, we should have 1/10th of the numbers starting with 1, 1/10th starting with 2 and so on. That’s what our intuition would tell us, and as is the case a lot of times, our intuition will be wrong.
If you actually did this exercise, you will find that there would be a lot of numbers starting with lower digits like 1, and a lot less starting with higher digits like 8,9. In fact, about half of all the numbers will have 1 or 2 as their first digit!
This law is named after the physicist Frank Benford. He surveyed empirical data from 20 different domains including surface areas of rivers, populations of different cities, molecular weights, physical constants. And he concluded that the frequency of numbers starting with a digit decreases as the digit increases, as shown in the image below.
So besides being an amusing fact, is there any practical use of this law? Indeed there is!
Applications in Fraud Detection
Benford’s law has been used to detect fraud in a lot of cases. The point being that naturally occurring numbers would not be as uniform as we think they are, instead they are expected to follow the above law. So if we have manufactured data, and it does not follow the above law, that can be used as evidence to prove that the data is fraudulent.
This story is part of my 365 Day Project for 2019. Read about it here
Yesterday’s blog — What’s so great about sliced bread?