1 Exploring Students ’ Understanding of Statistical Variation

(Do not circulate without a written consent from the first author) This study investigated students ’ understanding of the concept of the standard deviation. In particular, students ’ understanding of the factors that affect, and how they affect, the size of the standard deviation were investigated. Thirteen students enrolled in an introductory statistics course participated in the study. Students engaged in two activities during a one-hour interview. In the first activity, they arranged a number of bars on a number line to produce the largest and smallest standard deviation. The second activity asked students to judge the relative sizes of the standard deviation of two distributions. Initial analysis identified rules/strategies that students used to construct their arrangements and make comparisons. A discussion of these distinctive rules and the conceptions they represent is presented