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Central Limit Theorem

**Central Limit Theorem (CLT) -** states that for multiple samples taken from a population (with known mean and variance), if the sample size is large, then the distribution of the sample mean, or sum, will converge to a normal distribution even though the random variable x (individual data points within a sample) may be non-normal. This proves to be a key concept in probability theory as it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. It usually gives the below conditions

1. Sample means always follow normal distribution irrespective of distribution of individual data in population

2. Mean of sample means tends to population mean as the number of samples tend to infinity

3. Variance of sample means is 'n' times less than the variance of population, where 'n' is size of sample

E.g. Consider the roll of 2 dice. If this is done multiple times and the average or the sum of the rolls is plotted, then this plot will converge to a normal distribution

Applause for the respondents - Neeru Chaudhary, Manoj Kumar Alagesan, Vastupal Vashisth

Review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

Q. 155

Explain the practical application of Central Limit Theorem while collecting and analyzing data. Provide a few practical examples to support your responses.Please remember, your answer will not be visible immediately on responding. It will be made visible at about 5 PM IST on 30th April 2019, Tuesday to all 53000+ members. It is okay to research various online sources to learn and formulate your answer but when you submit your answer, make sure that it does not have content that is copied from elsewhere. Plagiarized answers will not be approved. (and therefore will not be displayed)

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