How to Measure Anything: Finding the Value of "Intangibles" in Business, Second Edition

Chapter 9. Sampling Reality: How Observing Some Things Tells Us about All Things

It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible.

—Aristotle (384 B.C.-322 B.C.)

If you want 100% certainty about the percentage of defective bricks from a kiln, you have to test all of them. Since testing the failure load of a brick requires compressing it in a press and measuring the force under which it cracks apart, this would require the destruction of every brick you make. If you want to have most of the bricks left over to use or sell, you only get to test a few bricks to learn something about all of them.

The group you want to learn about is the population, in this case, the bricks produced. A test of every single item in a group you want to learn about (e.g., testing every brick produced) is a census. Obviously, a census is impractical for bricks, since you would have no bricks left when the census is complete, but it is practical in other situations. A monthly inventory is usually a census, and the balance sheet is a census of every asset and liability. The U.S. Census tries to count every human being in the country, although in reality it falls a bit short of this.

But lots of things are more like bricks than like accounting transactions. There are a number of reasons it is impractical to test, track, weigh, or even count every item in a population. But we ...