Reasoning about Variability in Comparing Distributions

Variability stands in the heart of statistics theory and practice Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners’ reasoning about variation in a comparing distributions situation during their extended encounters with an Exploratory Data Analysis (EDA) curriculum in a technological environment. The current case study is offered as a contribution to understanding the process of constructing meanings and appreciation for variability within a distribution and between distributions and the mechanisms involved therein. It concentrates on the detailed views (and tools to support them) of variability in comparing groups using various statistical representations. Learning statistics in conceived as cognitive development and socialization processes into the culture ans values of „doing statistics“ (enculturation). In the light of the analysis, a description of what it may mean to begin reasoning about variability in comparing distributions of equal size is proposed, and implications are drawn. First published November 2004 at Statistics Education Research Journal: Archives