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> or less, I bet the actual equation is more complicated

https://en.wikipedia.org/wiki/Central_limit_theorem

I’m a bit tired otherwise I’d write something more rigorous. There are different ways the central limit theorem is expressed and proved here—there are more powerful ways to state it that require more complicated proofs, and there are simpler versions that are simple to prove.

A simple version will suffice here. Treat the resistors as iid variables with finite variance σ². When you average them, the variance of the average is σ²/n. More or less… this means that if your resistors are ±10%, and you have 16 of them, you get something with (fuzzy math) ±10%/√16 = ±2.5%.

There’s a lot of unstated assumptions in what I just wrote. But you’ll see the “grows proportional to √n” a lot in stats.




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