In Part III we made a distinction between a sample and a population, noting that a population is every member of a system that we could analyze and that a sample is the discrete subset of a population that we actually analyze. We collect and analyze samples with the hope that we can use their properties to deduce something about the populationâ€™s properties. We accomplish this by using suitable mathematical models.

Investigation 18. So, what does it mean to build a model? Consider the histograms in Figure 4. What property of the population are we attempting to model? What do your responses imply about the modelâ€™s general mathematical form? What does it mean to test a model and how might we accomplish this?

There are a variety of ways in which we might model our data, three of which we consider in this section: the binomial distribution, the Poisson distribution, and the normal distribution.