We've probably only been scratching the surface of what can be done to improve this. A recent small trial found that hyperlinking explanations to statistical and methodological terms in journal articles could improve physicians' understanding. (That's something we've started doing at PubMed Health. Although it's early days yet for us with coverage, they're getting clicked on quite a bit.)
Statistical literacy needs a combination of literacy, mathematical, and critical skills (PDF). In communication, numbers will always be tangled up with words (and sometimes words are better, as I discuss here).
Journalists are key to helping turn this problem around. They probably aren't getting the training they need, according to this study from 2010 - but that might be improving...slowly. Thankfully, Frank Swain from the Royal Statistical Society reports encouragingly on journalists' desire to learn more about statistics in the era of data journalism.
Want to learn more about basic statistics in health studies? Trials show that reading this book, Know Your Chances, could help.
And if you're wondering about how your own mathematics competency is faring since you left school, here's an online test. Mind you, it would help a lot if we had a clearer way of communicating numbers. The confusion over what means mean is a good case in point, covered here at Statistically Funny.
This post was updated on 30 January 2016: the original shorter post was written when Evelyn Lamb and I were co-moderating a session at Science Online.