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Benford’s Law

Learn how random numbers aren’t so random.

What would you say if someone said they could tell that you were lying about any numbers—like the price of a candy bar—just by looking at one digit? Bill, taxes, and prices all seem to follow this same pattern known as Benford’s Law. So what is it and how can someone tell if you made up the numbers just by looking at one digit?kid learning

Benford’s Law states that the numbers 1–9 show are most likely to show up as the first digit of a number in this order: 1, then 2, then 3, then 4, and so on in that order until 9. Because of this anomaly, you can theoretically look at a list of numbers and figure out if they are made up. Too many numbers starting with 8 or 9 and it starts to look fishy.

The coolest thing is that Benford’s Law is actually used every day!

Supposedly, the Internal Revenue Service, the people who collect taxes for the federal government, use Benford’s Law to find people cheating on their taxes. But don’t think that just because you know about it, you can cheat on your taxes. The IRS has a lot of tools in their pocket to find the people that are cheating on their taxes.

In fact, Benford’s Law has been used as evidence in courts. These cases are usually about fraud or other financial crimes. It’s never the key piece of evidence, but it can be used to prove that numbers were made up by showing the patterns are not natural.

Besides fraud and tax evasion, Benford’s law is sometimes used to catch other criminals. Money gained from crime needs to be laundered—which means made to look like it didn’t come from a crime. Researching the flow of money and the amounts moved around can often help arrest bad guys.

Benford’s Law is also used to check scientific research. If the data recorded doesn’t follow the Law, it’s double-checked to make sure that it’s right.

One place you can find a lot of numbers that don’t follow Benford’s Law is the phonebook. (If you can find a phonebook.) Part of the reason is that all the numbers in the phonebook are the same length. And because they’re from similar areas, the first three digits are going to be the same. So the area code is going to be the same for large blocks of numbers.

Benford’s Law works because numbers are a natural thing. Nature is often repetitive. Look at the leaves on a maple tree. They all look the same. Fractals are repeating number sequences that are often found in nature. If you looked at a fake maple tree, all the leaves would be too perfect. And that is similar to how Benford’s Law is used to find fraudulent patterns.

Now that you know a little something about it, try to see if you can find Benford’s Law in your day-to-day life. Check the bill from the grocery store. Are there more ones and twos than eights and nines (besides the cents)? And remember, always be honest when it comes to numbers; they never lie.


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