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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
Abstract #322697
Title: Visualizing Mean, Mean Deviation and Standard Deviation of a Continuous Random Variable
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

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.

Authors who are presenting talks have a * after their name.

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