Language and the telling of data stories have fundamental roles in advancing the GAISE agenda of shifting the emphasis in statistics education from the operation of sets of procedures towards conceptual understanding and communication. In this paper we discuss some of the major issues surrounding story telling in statistics, challenge current practices, open debates about what constitutes good verbalization of structure in graphical and numerical summaries, and attempt to clarify what underlying concepts should be brought to students' attention, and how. Narrowing in on the particular problem of comparing groups, we propose that instead of simply reading and interpreting coded information from graphs, students should engage in understanding and verbalizing the rich conceptual repertoire underpinning comparisons using plots. These essential data-dialogues include paying attention to language, invoking descriptive and inferential thoughts, and determining informally whether claims can be made about the underlying populations from the sample data. A detailed teacher guide on comparative reasoning is presented and discussed. (Contains 4 figures.)