Visualizing Mean, Mean Deviation and Standard Deviation of a Continuous Random Variable

• Activity Number: 173 - Novel Approaches to Pedogogy
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Mamunur Rashid* and Jyotirmoy Sarkar
• Companies: Mathematics Dept. at DePauw University and Indiana University-Purdue University Indianapolis
• Keywords: Cumulative Distribution Function ; Euclidean Method ; Mean Squared Deviation ; Solid of Revolution

Abstract

We review recent interpretations of the mean, the mean deviation (MD) and the standard deviation (SD) of a set of numbers. For each quantity, the process begins with the empirical cumulative distribution function (ECDF) or a suitable transformation of it, and then finds the location of a vertical line that renders equal the areas of two regions bounded by the line itself, the (transformed) ECDF and the horizontal line y=0 or y=1. Here, the above interpretations are extended to a continuous random variable. These interpretations help users of statistics refine their intuition, and anticipate the numerical values of the mean, the MD and the SD even before evaluating them using the Calculus.