Mathematics
The Berry-Esseen Theorem: Quantifying the Accuracy of Normal Approximation
Quick fact
The Berry-Esseen theorem guarantees that the maximum error in using the normal distribution to approximate the cumulative distribution function of a standardized sample mean is at most a constant times the third absolute moment divided by the square root of the sample size—about 0.4 to 0.5 times that ratio for independent samples.
Why this is interesting
You know that averages of random samples become bell-shaped as the sample grows—but how good is that approximation for a finite sample? The Berry-Esseen theorem provides the answer.