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Reasoning about variation

The Challenge of Developing Statistical Literacy, Reasoning, and Thinking
Reading, C. & Shaughnessy, J. M.
Ben-Zvi, D. & Garfield, J.
Kluwer Academic Publishers, Dordrecht, The Netherlands

"Variation is the reason why people have had to develop sophisticated statistical methods to filter out any messages in data from the surrounding noise" (Wild &amp; Pfannkuch, 1999, p. 236). Both variation, as a concept, and reasoning, as a process, are central to the study of statistics and as such warrant attention from both researchers and educators. This discussion of some recent research attempts to highlight the importance of reasoning about variation. Evolving models of cognitive development in statistical reasoning have been discussed earlier in this book (Chapter 5). The focus in this chapter is on some specific aspects of reasoning about variation.<br>After discussing the nature of variation and its role in the study of statistics, we will introduce some relevant aspects of statistics education. The purpose of the chapter is twofold: first, a review of recent literature concerned, directly or indirectly, with variation; and second, the details of one recent study that investigates reasoning about variation in a sampling situation for students aged 9 to 18. In conclusion, implications from this research for both curriculum development and teaching practice are outlined.