Imagine you’re trying to figure out which ice cream flavor is the most popular by looking at the number of likes each flavor gets on social media. Every number from 1 to 9 has an equal chance to be the first number, like every slice of a pizza being the same size. But there’s this quirky rule called Benford’s Law that says smaller numbers, like 1, 2, and 3, show up as the first number more often than bigger ones, like 7, 8, or 9. It’s like finding out that the pizza slices aren’t all the same size after all, and that the pepperoni slices (which represent the smaller numbers) are getting bigger and bigger every day!
Here’s a fun test: what if we looked at the number of stars people gave to movies on a movie review site? I would like to know if Benford’s Law works there, too. Maybe the first number of the star ratings (like five stars for a super cool movie or 1 star for a boring one) follows this unusual but exciting rule (Minding the Data, 2020).
However, there are places where Benford’s Law might decide to take a nap and not show up (Carlton Collins, 2017). For instance, if we counted how many times each number from 1 to 10 appeared in a classroom’s math test scores, Benford’s Law probably wouldn’t hold. That’s because test scores have a set range (nobody gets a 15 out of 10 on a test!), and Benford’s Law likes it when numbers can stretch out and cover more ground, like how a cat stretches from one end of the couch to the other.
So, while Benford’s Law might help us spot patterns in places full of numbers, like the tallies of movie stars or the first digits of significant random counts, it breaks down in scenarios where numbers are confined to a small playground, like our classroom test scores. It’s a fascinating glimpse into the hidden rhythms of numbers in our world, showing us there’s more to digits than meets the eye—or the first digit, to be exact!
References
Carlton Collins, J. (2017). Using Excel and Benford’s law to detect fraud. Journal of Accountancy.
Minding the Data. (2020). Benford’s law in real life | finding real world examples. YouTube.