This paper is from Session 6E: Modeling distributions to connect chance processes, data production, and data distributions

which comes under Topic 6: Innovation and reform in teaching probability within statistics

Visual representations of empirical probability distributions when using the granular density metaphor

Presenter

• J Todd Lee (Elon University, United States)

Co-author

• Hollylynne Stohl Lee (North Carolina State University, United States)

Abstract

This paper is an expository on searching for intuitive visualizations of empirical probability distributions. The visualizations use the granular density metaphor for probability density functions (Lee & Lee, 2009) to provide a way for students to build from equiprobable intuitions of probability to standard discrete and continuous distributions. The visualizations dynamically link the sampling process with the formation of an empirical distribution, while remaining true to the granular density metaphor for both the empirical and theoretical density functions. We present and discuss several examples along with conceptual and mathematical ideas that support use of these visualizations.