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Average enough independent measurements and the spread of the answers takes a bell shape.

Mathematics Facts, sourced to Wolfram MathWorld.

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What it means

This is why the bell curve is everywhere, and it is a stronger claim than it looks. The underlying quantity can be lopsided, lumpy or bounded on one side. Average enough independent draws of it and the averages still pile up into the same curve, described by nothing but a center and a width. It is the reason a poll of a thousand people can carry a stated margin of error at all.

The claim comes from Wolfram MathWorld.

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