A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Common examples are variables that must be integers, non-negative integers, positive integers, or only the integers 0 and 1. Continuous Variable. If the possible outcomes of a random variable can be listed out using a finite (or countably infinite) set of single numbers (for example, {0, […] In statistics, numerical random variables represent counts and measurements. The number of permitted values is either finite or countably infinite. Continuous Variable Definition. Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. They come in two different flavors: discrete and continuous, depending on the type of outcomes that are possible: Discrete random variables. Some examples will clarify the difference between discrete and continuous variables. If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.. In contrast, a discrete variable over a particular range of real values is one for which, for any value in the range that the variable is permitted to take on, there is a positive minimum distance to the nearest other permissible value.