The present study investigates the processes of how German middle school students (age 14) interpret, contrast and evaluate different (informal) statistical measures in order to summarise and compare frequency distributions. To trace the developing insights into the properties of these measures, this paper uses the 'emergent modelling' perspective: measures are understood as models, which can either be used to make sense of a given situation or to reason about the statistical measures themselves, e.g. in terms of when they can be applied adequately. The emergent modelling approach is used (1) as a theoretical framework for describing students' conceptual development, and (2) as a design heuristic for developing a teaching-learning arrangement aiming at developing insights about (frequency) distributions and statistical measures. In the qualitative analysis of a design experiment, two students' emerging contextual and statistical knowledge is identified, revealing the intertwined nature of both types of knowledge. Overall, this paper illustrates the important role the emergent modelling perspective can play for designing as well as describing students' learning pathways in statistics education.