Visualization of the central limit theorem

The Central Limit Theorem is a key topic of Hong Kong Advanced Supplementary Level Mathematics and Statistics syllabus. The theorem says that the sample mean will follow a normal distribution when the sample size n is large enough, regardless of the original distribution of the sample. One of the obstacles encountered by students in learning this theorem is that they cannot visualize how distributions of sample mean approximate normal when n gradually increases. In order to help the learning and teaching of the Central Limit Theorem, an interactive system was developed using the Chinese version of Excel. This system simulates a very simple but time-consuming experiment for finding the value of π. At one stage, users can input the number of trials and then obtain the mean value of all estimated π in a few seconds. When the number of trials in increased, one will observe that the estimated mean value approaches the actual value of π. At another stage, the user can input the number of experiments and the number of trials of each experiment. If these numbers are large enough, the graphical output would display a normal distribution curve. This paper will describe details concerning the development and outstanding features of such an interactive system. Copyright © 1998 Hong Kong Institute of Education.