The average can vary from a given sample set over time and be used as a comparison. For a statement like "IQs are going up/down" you could probably get away wit

The average can vary from a given sample set over time and be used as a comparison. For a statement like "IQs are going up/down" you could probably get away with simply monitoring the average over time. If you start digging around to see that you're fairly comparing the groups then you'll almost always be able to split hairs. Most statistics outside of a theoretical context are flawed if you poke them hard enough.