Atul Dev
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Atul Dev's post in Central Limit Theorem, Law of Large Numbers was marked as the answerReaCentral Limit Theorem (CLT) gives us three conditions:
1) Mean of sample means tends to population mean as the number of samples tend to infinity.
2) Sample means always follow normal distribution irrespective of distribution of individual data in population.
3) Variance of sample means is 'n' times less than the variance of population, where 'n' is size of sample.
Law of Large Numbers (LLN) states that as the sample size grows, its mean gets closer to the average of the whole population.
Here it can be noted that CLT talks about 'Mean of Sample Means approaching Population Mean' whereas LLN talks about 'Mean of Large Sample approaching Population Mean'. So there is a difference in both the approaches. Practically, in Statistical Quality Control (SQC), it is sometimes convenient to deal with grouped samples, and for this purpose, CLT provides us a powerful tool to draw inferences about the population.
CLT makes 'non-normal' data 'normal' only if we are dealing with sample averages. In case we have to deal with the population data directly, which is not normally distributed, then CLT will not help us.
Read why this answer was selected as the best - https://www.benchmarksixsigma.com/forum/topic/34877-central-limit-theorem-law-of-large-numbers/?do=findComment&comment=43909