The role of descriptive statistics

Descriptive statistics plays a subsidiary role in the stochastics curriculum, it is used to introduce notions in probability theory by analogy to corresponding notions in descriptive statistics and to motivate problems in inferential statistics. New ideas are to be developed and discussed in this paper which might enrich teaching descriptive statistics and change its status, namely exploratory data analysis, "open mathematics", and the idea of visualization. Descriptive statistics can and should be taught as interesting subject of its own right. Furthermore the new ideas have consequences on the view on statistics as a whole.