Eli5: Why Benford’s law works ?

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Pretty much the title.
I understand this is a law but can there be a reason why this happens?
For background: for almost all real life data like population, GDP and other real word stats, probability of it having 1 is like almost 30% which keeps decreasing with 9 to be least probable.
But why this happens, is this just a fascinating pattern in randomness?

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7 Answers

Anonymous 0 Comments

Say you are looking at the average household salary of a population. If most of the range is between 40k and 200k then 100k out of 160k of the salaries start with a 1. Thats basically what causes Benfords law, when you cross an order of magnitude half your values will start with a 1 until you get up to the 2s.

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