This dissertation focused on the notion of distribution as a conceptual link between data and chance. The goal of this study was to characterize a conceptual corridor that contains possible conceptual trajectories taken by students based on their conceptions of probability and reasoning about distributions. A small-group teaching experiment was conducted with six fourth graders to investigate students' development of probability concepts and reasoning about distributions in various chance events over the course of seven weeks. The two major findings are as follows: First, students' qualitative reasoning about distributions involved the conceptions of groups and chunks, middle clump, spreadout-ness, density, symmetry and skewness in shapes, and "easy to get/ hard to get" outcomes. Second, students' quantitative reasoning arose from these quanlitative descriptions of distributions when they focused on different group patterns and compared them to each other.