Data analysis plays an important role in people's lives. Citizens need to be able to conduct critical analyses of statistical information in the work place, in their personal lives, and when portrayed by the media. However, becoming a conscientious consumer of statistics is a gradual process. The experiences that students have with data in the middle grades can potentially lay the foundation for developing statistical reasoning. Statistical thinking requires students to engage in both mathematical and nonmathematical thinking. This article contains innovative tasks that have been used to help students construct a robust, "mathematical" understanding of the mean as a mathematical point of balance and to describe students' responses to such tasks as they constructed this understanding. (Contains 6 figures.)