# central limit theorem

Six Sigma – iSixSigma Forums Old Forums General central limit theorem

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• #39910

A.S.
Participant

request help from experts to explain central limit theorem please

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#122575

Ron
Member

The central limit theorem guarantees that if we sample from a non normally distributed population we will get approximately the same results as we would if the population were normally distributed, provided that we take a large sample.

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#122579

Mikel
Member

Is that a money back guarantee?
How large a sample?

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#122586

Robert Butler
Participant

The post below should be of some help.
https://www.isixsigma.com/forum/showmessage.asp?messageID=70982
While I said it in the post I’ll repeat it again since it is the one aspect of the concept that seems to be most often lost in translation – the central limit theorem does NOT apply to individual samples from a distribtuion.  it applies to MEANS OF GROUPS OF SAMPLES from a distribution.  In other words – if you take 30 or a 100 or 1000 samples from a non-normal distribution the distribution of those INDIVIDUAL SAMPLES will STILL be non-normal.  If you take those 1000 samples and lump them into groups where each group is comprised of roughly  2-100 INDIVIDUAL SAMPLES each and take the means of those groups the distribution of the GROUP MEANS will approach normality.
The real hook is the issue of the number of samples in each group needed to give the distribution of the group means a normal shape.  For a uniform distribution 2-3 samples per group will suffice but for things like an exponential distribution the number of samples per group can easily approach and even exceed 100.

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