It is the flaw of averages that causes businessmen, engineers, generals and others to underestimate risk in the face of uncertainty.How true is that statement. As a practitioner of Operations Research in the business world I often am not just providing solutions for my employer but also playing referee. I'm not sure how many times I have had to tell a manager or associate to recheck their assumptions before they bring their analysis up the chain of command. One of my previous bosses had a great phrase that he would tell me, "Does it pass the smell test?" In other words can you step back and say with certainty that your assumptions are right on the mark.
Sam Savage has a great point about flawed analysis based on assumptions alone. The crucial emphasis should be on the assumptions themselves. All good analysis should make sure that the assumptions are correct and reflect the real world implications. The article cites the recent problems with the home mortgage crisis. A lot of assumptions in the risk models that gave AAA ratings to mortgage-backed securities were not taking into account future market cycles and risk.
So should averages be used in analysis? By all means, no pun intended. Statistical inferences and generalities require average value of numerical populations. Averages do have their place in analysis when comparing samples. Yet so do standard deviations, variance, correlation, and so on. There is more to risk modeling than just the simple average.