Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and suggests how they can be used explicitly by teachers and students to support work on statistical investigations. It goes on to describe some of the ways in which students at school level can interact with different statistical representations using technology, and illustrates the interactions using common examples of statistical diagrams, graphs and tables. The descriptions of these interactions are based on a theory of representational versatility that espouses the importance of engaging with statistical representations in a conceptual as well as a procedural manner. Some implications for the teaching and learning of statistics are also considered. (Contains 3 tables and 4 figures.)