> mean versus medians, confidence levels or margins of error

It's basic when you are attending an undergraduate course but most people can understand mean (as a dictionary might generically define it) and have a general feeling for margin of error (again, not in the mathematical way.)

Statistics has been the most difficult course in my CS course. For some reason when I start counting events to get a probability I find several perfectly plausible ways to count them, get five different probabilities and none of them is the correct answer.

And about being "trivial to manipulate [numbers] to generate the headline you want" a politician once told me that you can show the same numbers in any way you want, as in to demonstrate a thesis or its opposite.