They are considering what features to use to tell what is typical of the two groups so they can be compared. Students support their ideas with information in the data itself. They are developing ways to think about data that will lead to deep understanding of more formal statistics. The rich mathematical discussions in my class are an outgrowth of my participation in professional development that focused on inquiry-based teaching and the big ideas we should be teaching. But since high-stakes testing arrived, professional development meetings often focus on how to improve test scores, not on how to improve learning.
Testing involves sampling student knowledge.
It is fragmented and only examines learning outcomes. It seldom looks at how well a student understands complex ideas. A typical test item might give students a set of data and ask for the median. Students would not be asked to select the appropriate statistic to address a question and justify their choice. Yet knowing how to find the median, without knowing when to use it, is useless, except on tests.