Animating Statistics: A New Kind of Applet for Exploring Probability Distributions

Abstract

In this article, I introduce a novel applet (“module”) for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive application based on Wolfram Research's novel computable document format (CDF) technology. It features over thirty common discrete and continuous distributions and can be used to illustrate concepts such as random samples, population and sample means and medians, histograms, kernel density estimators, boxplots, and cumulative distribution, survival, and hazard functions all while dynamically linking samples and estimators to adjustable distribution parameters in real-time. Additionally, the module includes real-world datasets to aid in communicating the concept of fitting a distribution to data. It is hoped that the module will be helpful to instructors at both the high school and college levels for the conceptual understanding of distributions. A simplified version geared specifically toward out-of-class student learning in the introductory course is also made available for students' use. Both are accessible from http://www.baylor.edu/statistics/disttool.

• Probability distributions
• Wolfram CDF technology
• Interactive learning environments
• Monte-Carlo simulation