Ask HN: best way to become a "Numerati"?

Not sure if "Numerati" is the best word. I already have a maths degree, but did little with statistics so far. I am capable of reading a book on statistics, but it is not the same as getting some practical experience.

I guess I could just start with randomly selected data sets, but somehow that doesn't seem to be enough motivation (like stock market data: seems unlikely to discover something new, with all the Quants already working on it). So I guess what I mean is, among other things: how to find worthwhile statistical problems for starting out? I am not into sports, so betting is kind of out. Also missed the elections, since I am not from the US. I look forward to the book by the 53something website guy, though.