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Introduction to the Central Limit Theorem

I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a non-technical treatment, and simply illustrates the important implications of the central limit theorem.) For those using R, here is the R code to find the probability for the example in this video: Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000: 1-pnorm(66000,62000,32000/sqrt(100)) [1] 0.1056498 Or, standardizing: 1-pnorm((66000-62000)/(32000/sqrt(100))) [1] 0.1056498 1-pnorm(1.25) [1] 0.1056498