General Central Limit Theorem (CLT) Activity

This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet (http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/) by extending the applet functionality and providing the capability of sampling from any SOCR Distribution. Goals of this activity: provide intuitive notion of sampling from any process with a well-defined distribution; motivate and facilitate learning of the central limit theorem; empirically validate that sample-averages of random observations (most processes) follow approximately normal distribution; empirically demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal; illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process); show that the variation of the sample average rapidly decreases as the sample size increases.