Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a historical study helped to distinguish different aspects and levels of understanding of concepts and helped us as instructional designers to look through the eyes of students. In this paper, we focus on an historical phenomenology of mean and median, and give examples of how hypotheses stemming from the historical phenomenology led to the design of instructional activities used for teaching experiments in grades 7 and 8 (12-14-years old).