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 May 5th, 2018, 02:01 AM #1 Senior Member   Joined: Nov 2011 Posts: 248 Thanks: 3 Statistics Theorems Which is the statistics theorem that is the most important in statistics?
 May 5th, 2018, 05:06 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 I would say that it is the "Central Limit Theorem". It says that the average of a large number of independent trials, from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$. A variant say that the sum of n trials from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle n\mu$ and standard deviation $\displaystyle \sqrt{n}\sigma$. That is the reason the normal distribution is so important. We can, for example, think of, say, the probability that each person in a large population will contract a given disease as following the same, unknown, probability distribution so we can, with confidence, use the normal distribution for the entire population.
May 5th, 2018, 09:39 AM   #3
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 Originally Posted by Country Boy I would say that it is the "Central Limit Theorem". It says that the average of a large number of independent trials, from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$. A variant say that the sum of n trials from any probability distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$ will follow, approximately, the Normal Distribution with mean $\displaystyle n\mu$ and standard deviation $\displaystyle \sqrt{n}\sigma$. That is the reason the normal distribution is so important. We can, for example, think of, say, the probability that each person in a large population will contract a given disease as following the same, unknown, probability distribution so we can, with confidence, use the normal distribution for the entire population.

That is the most important theorem from frequentist statistics. It plays absolutely no role in Bayesian statistics.

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