Part IV. Ways to Model Data

Investigation 18: Building and Testing Models

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 population’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 model’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.