The Practical Scope of the Central Limit Theorem

David Draper; Erdong Guo

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arXiv · 2111.12267

The Practical Scope of the Central Limit Theorem

David Draper·Erdong Guo

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Abstract

The \textit{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: \textit{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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David Draper, Erdong Guo. 2021-11-24. The Practical Scope of the Central Limit Theorem. https://arxiv.org/abs/2111.12267

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