1: Introduction to Discrete Data

Overview Section

This lesson serves as an introduction to discrete data and many of the popular distributions used to describe it. Usually, we associate discrete data with qualitative characteristics, but as we'll see, ordered or even numerically meaningful categories can also be considered discrete. Numerical summaries and visual displays can likewise be constructed to reflect these properties.

Among the many distributions used for describing discrete data, we focus here mainly on the binomial distribution, which applies to data with exactly two outcomes, and introduce other discrete distributions in relation to the binomial. If the binomial doesn't apply for a particular reason, what might a suitable alternative be?

Finally, we introduce the likelihood function and show how it can be used to estimate a population parameter. Discrete data lends itself particularly well to this concept because the likelihood can be interpreted as the probability of observing our data for a given value of the parameter. The intuitive estimate for the parameter is then the value that maximizes this probability.

Upon completion of this lesson, you should be able to:

  Objective 1.1

Recognize different types of discrete data, such as nominal and ordinal, and what type of visual display is appropriate for each.

  Objective 1.2

Construct and interpret relevant characteristics in visual displays for discrete data, such as frequency tables and mosaic plots.

  Objective 1.3

Distinguish among various types of discrete distributions and determine how they can be applied to sample data, depending on how the data was collected.

  Objective 1.4

Interpret a likelihood function and use it to provide an estimate of a population parameter.