What characterizes a discrete variable?

A discrete variable is characterized by consisting of separate, indivisible categories. This means that discrete variables take on specific, distinct values and cannot be subdivided meaningfully within the context of the data. For example, the number of students in a classroom is a discrete variable because you can have 25 students or 26 students, but not a fraction of a student.

In contrast, a continuous variable can take any value within a given range, which would not align with the definition of discrete variables. While discrete variables can be numerical, they are not limited strictly to numerical measurements; they can also encompass categories such as different types of fruits or colors. Furthermore, the notion that discrete variables can be both qualitative and quantitative is true, but it does not capture the essence of what distinguishes discrete variables from continuous ones. Therefore, the defining feature of discrete variables is their nature of consisting of distinct, separate categories.