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Abstract Details

Activity Number: 173
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
Abstract:

We review recent interpretations of the mean, the mean deviation (MD) and the standard deviation (SD) of a set of numbers, or of a discrete random variable. For each quantity, we begin with the (empirical) cumulative distribution function (CDF) or a suitable transformation of it, and then find the location of a vertical line that renders equal the (finite) areas of two regions bounded by the line itself, the (transformed) CDF and the horizontal line y=0 or y=1. Here, we extend the above interpretations 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.


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