What's with all these earthquakes?

The Earth is trembling. A magnitude 5.9 earthquake hit Virginia on August 23 at 17:51 UTC. Twelve hours earlier, a magnitude 5.3 quake shook southern Colorado (I slept through it; it was 360 km away). On August 20, a magnitude 7.0 hit off the coast of eastern Australia, and another magnitude 7.0 earthquake took place in northern Peru on August 24 at 17:46 UTC, just a few hours ago as I write this. What gives? Are we seeing a swarm of related events? Is the Earth shaking itself apart? It's easy enough to think so. But our brains are wired in a way that makes them easily fooled (proof). What we need to do is not panic -- always a good start -- and think this through. Happily, we have an exceptionally good tool for this sort of problem: science. Well, science and a tiny touch of math.

Get me some stats, stat!