Describing Distributions

In the past, when I taught describing distributions of quantitative data I would give notes and examples on the different shapes (skewed, symmetric, unimodal, etc).  This year the students were (supposed) to have read about these ideas the night before. When they came to class I handed out these data on AP scores for all exams from 2012, and asked them to find 3 datasets -- one that was skewed right, one skewed left, and one symmetric.  They were much more engaged and talkative, and we were able to have conversations like "what would it mean for exam scores to be right skewed?,"  which we wouldn't have had in the past. We still did some notes right at the end of class, but overall engagement was much higher.

4 big ideas of AP Statistics

Grant Wiggins recently challenged Algebra teachers to "identify four big ideas that could ground the course and make it more intellectually worthy." While I don't teach algebra, it got me thinking about AP Statistics and if I could condense the course to 4 big ideas.  Here's what I came up with:

1. Summarizing data graphically and numerically allows one to decide if a helpful model applies, as well as demonstrate what "typical" and "unusual" data are.

2. Gathering data is the most important part of the statistical process. Garbage in, garbage out.

3. To be able to make any sort of decision about a population based on a sample relies on a solid understanding of randomness, whose descriptive language is probability.

4.  Any inferential decision/prediction must be accompanied by a probability statement. 


What are your 4 big ideas?