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
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