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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  
Senior Member Joined: Oct 2009 Posts: 733 Thanks: 247  Quote:
That is the most important theorem from frequentist statistics. It plays absolutely no role in Bayesian statistics.  

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