My favorite data is data that is both counter intuitive and tests the efficacy of commonly held beliefs. Emily Oster's (writing for 538) presents such data in her investigation of vitamin efficacy. Short version of this article: Data that associates vitamins with health gains is based on crap observational research. More recent and better research throws lots of shade on vitamin usage.
Specific highlights that could make for good class discussion:
-This article explains the flaws in observational research as well as an example of how to do good observational research well (via The Physician's Health Study, with large samples of demographically similar individuals as described in the portion of the article featuring the Vitamin E study). This point provides an example of why controlled, double-blind lab research is the king of all the research.
-This is an accessible example as most of your students took their Flintstones.
-The article also demonstrates The Third Variable Problem. As illustrated in the graph above, taking vitamins also correlates with higher levels of education and lower levels of obesity. Hence, pure observational research that touts the benefits of vitamins fails to address the health benefits associated with education and good general health.