What is a continuous random variable?

A continuous random variable is characterized by its ability to take on an infinite number of values within a specified range. This means that between any two values, no matter how close they are, there can always be another value. For instance, the height of individuals can be measured in infinitely precise units, allowing for values such as 5.8 feet, 5.83 feet, 5.835 feet, and so forth. Because of this trait, continuous random variables are often associated with measurements and can represent quantities on a continuous scale.

In contrast, the other options describe types of variables that do not meet the criteria for being continuous. A variable that can only take on a finite number of values is discrete, which is fundamentally different from a continuous variable. Additionally, a variable that cannot be measured does not fit the definition of a random variable at all, as random variables are associated with outcomes and measurements. Finally, the option describing a variable that only takes values on whole numbers refers to discrete variables, which once again highlights the distinction from continuous random variables.