What “Benford’s law” is, and if it’s actually valid for numbers in real life

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What “Benford’s law” is, and if it’s actually valid for numbers in real life

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Benford’s law gives a distribution of the first digit in a random number picked from a random number range. Around 30% of these will be 1. The concept around this is that if you are analyzing some document looking for signs that the numbers were made up then you would expect the distribution to be more aligned with what people perceive as random or have a true random distribution rather then follow Benford’s law. And this concept is valid and used all over the place to find forged numbers.

However the specific Benford’s law is very conditional. It assumes a random number within a random range. And this holds true for a lot of different datasets. Especially very large datasets. However if the number range is not random then it no longer applies. For example dates do not follow Benford’s law. And for example prices for single items are not randomly selected but tend to start with 9 more often. This can throw off the distribution in various accounting books unless you account for this. You might also see that a maximum transfer limit or approval limit for funds have a significant impact on the distribution of numbers as well, even in legitimate cases. So if a set of numbers does not fit Benford’s law that does not mean they are faked, it just means you should look into why this is.