Types of Data, Chapter 1 (Section 1.2)

Objectives

1. Understand the structure of a typical data set 2. Distinguish between qualitative and quantitative variables 3. Distinguish between ordinal and nominal variables 4. Distinguish between discrete and continuous variables

Continuous Variables

Continuous variables are quantitative variables that can take on any value in some interval. The possible values of a continuous variable are not restricted to any list. Continuous variables can, in principle, take on any value within some interval. For example, height is a continuous variable because someone's height can be 68, or 68.1, or 68.1452389 inches. The possible values for height are not restricted to a list.

Qualitative Variables

Qualitative variables classify individuals into categories. Qualitative variables, also called categorical variables, classify individuals into categories. For example, college major and gender are qualitative variables. *Another way to distinguish qualitative from quantitative variables: Quantitative variables are counts or measurements, whereas qualitative variables are descriptions.*

Quantitative Variables

Quantitative variables tell how much or how many of something there is. Quantitative variables are numerical and tell how much or how many of something there is. Height and score on an exam are examples of quantitative variables. *Another way to distinguish qualitative from quantitative variables: Quantitative variables are counts or measurements, whereas qualitative variables are descriptions.*

Discrete Variables

Discrete variables are quantitative variables whose possible values can be listed. The list may be infinite — for example, the list of all whole numbers. Discrete variables are those whose possible values can be listed. Often, discrete variables result from counting something, so the possible values of the variable are 0, 1, 2, and so forth

Nominal Variables

Nominal variables are qualitative variables whose categories have no natural ordering. A nominal variable is one whose categories have no natural ordering. Gender is an example of a nominal variable.

Ordinal Variables

Ordinal variables are qualitative variables whose categories have a natural ordering. An ordinal variable is one whose categories have a natural ordering. The letter grade received in a class, such as A, B, C, D, or F, is an ordinal variable.

Data Sets

Table 1.1 illustrates some basic features that are found in most data sets. Information is collected on individuals. In this example, the individuals are students. In many cases, individuals are people; in other cases, they can be animals, plants, or things. The characteristics of the individuals about which we collect information are called variables. In this example, the variables are major, exam score, and grade. Finally, the values of the variables that we obtain are the data. So, for example, the data for individual #1 are Major = Psychology, Exam score = 92, and Grade = A.