The most important aspect of the Central Limit Theorem is that no stipulation is made concerning the population from which one is sampling. From a pedagogical point of view, a student needs to draw a random sample from a population with a known distribution and then to compare the sample mean with the population mean to see "how close", he or she comes. Any student who does this will know the difference between the two. Students will also be led to understand the difference between the population mean and the mean of the sample means. It is not enough for a teacher to talk about these ideas - concrete experience with sampling is necessary for success. It is hoped that these experiments go some way towards enabling students to observe the central limit phenomenon operating, as well as providing empirical evidence of the truth of the theorem.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education