Diversity, Variability, and the Probable Error: Building Intuition

• Activity Number: 699
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Robert Jernigan*+
• Companies: American University
• Keywords: variability ; diversity ; probable error ; intro course ; eda

Abstract

Diversity, Variability, and the Probable Error: Building Intuition Robert W. Jernigan, American University, Washington, DC 20016 Students new to statistical concepts often struggle with the notion of measuring variability. Our standard measures, variance and standard deviation, can seem unduly cumbersome to the uninitiated. Full understanding of the why and and how of these measures often needs more mathematical background than many students possess. We illustrate how the concepts of diversity and quantitative variability are confusing. So much so that, in our textbooks even our most basic measures of variability, must be accepted before intuition about the measures can be developed. This seems backwards. As an introductory measure of variability, I propose reviving an old measure called the probable error (one half of the inter-quartile range). Examples are given to motivate this measure, building on students' more intuitive ideas about variability. Relationships with outlier bounds and 68-95-99.7-type rules of thumb are also illustrated and discussed. Some historical perspective is given including why probable error, at best only an introductory measure of variability, is very much misnamed.