Central limit theorum is easily one of the most fundamental and profound concepts in statistics and perhaps in mathematics as a whole. In probability theory, the central limit theorum (CLT) states conditions under which the mean of a suffiently large number of independent random large variables (each with finite means and variance) will be normally distributed, approximately. Huh? If you are having trouble understanding central limit theorum and need help trying to solve it, check out this tutorial. Things will seem a lot clearer once you follow along with this step by step video providing an introduction to central limit theorum and the sampling distribution of the mean.
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