How can we describe a variable that may assume any numerical value?

A variable that may assume any numerical value is best described as a continuous random variable. Continuous random variables can take on an infinite number of values within a given range. This characteristic allows them to represent measurements like height, weight, temperature, or time that can vary smoothly rather than in distinct steps.

In contrast, a discrete variable can only take on specific, separate values, such as the number of students in a classroom, where only whole numbers are possible. A bounded variable might imply some limitations on the range of values it can take, but this does not necessarily describe the nature of numerical values that a variable can assume. A fixed variable would suggest that its value does not change over time or under different conditions, which is contrary to the concept of variability inherent in continuous random variables. Thus, a continuous random variable appropriately captures the essence of a variable that can take on any numerical value.