The Practical Scope of the Central Limit Theorem
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The Central Limit Theorem (CLT) is at the heart of a great deal of applied problem-solving in statistics and data science, but the theorem is silent on an important implementation issue: how much data do you need for the CLT to give accurate answers to practical questions? Here we examine several approaches to addressing this issue – along the way reviewing the history of this problem over the last 290 years – and we illustrate the calculations with case-studies from finite-population sampling and gambling. A variety of surprises emerge.
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