The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

CHAPTER 10

I Come to Bury SIGMA, Not to Praise it

We have seen that representing an uncertain number by a single point provides no indication of risk or uncertainty. So, long ago, even before the Steam Era, mathematicians came up with a yardstick for measuring the degree of uncertainty that has become the gold standard. Unfortunately, it is a Red Word: SIGMA (the Greek letter σ), also known as the STANDARD DEVIATION. People also often refer to the square of SIGMA, which is known as the VARIANCE or σ². One Red Word is confusing enough, let alone three of them and a Greek letter that all mean pretty much the same thing. Basically, they all measure how wide the distribution of an uncertain number is. This is usually obvious from looking at the shape (see Figure 10.1). The wider the distribution is, the greater is the possible variation and the higher the value of SIGMA and the VARIANCE.

Figure 10.1 Distributions with the same average but different degrees of variation.

I have asked thousands graduate students and managers over the years to indicate by a show of hands whether they could write the formula for SIGMA. Although virtually all have heard the term, only a small fraction can actually define it. What kind of gold standard is that?

You may have heard of SIX SIGMA, a set of practices for improving the quality of manufactured goods or services, originally developed by Motorola. ...