For a sum of n independent random variables from the same distribution with mean μ and standard deviation σ, the resulting sum has mean = n·μ and standard deviation = √n·σ.

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Unidentified Speaker — But what is the Central Limit Theorem? [zeJD6dqJ5lo]

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the mean for the sum on the bottom will be mu times the size of the sum, and the standard deviation will be sigma times the square root of that size

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But what is the Central Limit Theorem?3Blue1Brown
Created: 8/10/2026, 3:51:19 PM

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