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Central Limit Theorem and Sampling Distributions (302784)

Keywords: central limit theorem, sampling, normal distribution

The topic for my poster will be a demonstration of the central limit theorem through sampling distributions selected randomly from a large data set. My poster will demonstrate the distribution of values created by repeated sampling from the same population. I will use a data set (#08443) from the High School and Beyond data (1984), available to member institutions from the ICPSR website. The data set I will use for the demonstration has 1,720 variables and 14,825 cases. The data set is part of the U.S. Department of Education, National Center for Education Statistics data base. I will show several random sampling distributions of different sizes to illustrate the central limit theorem. My students often have problems with the concept of a random sample having a sampling distribution approximately normal, even when the population from which it was drawn is non-normal. Properties of the sampling distributions will be shown statistically and graphically.