Answer:

When a variable can take any value in an interval it is said to be continuous.

For example, the height of an adult person is a continuous variable (usually in the interval from 150cm to 200 cm). Length, temperature and time are further examples of continuous variables. In applied statistics, a variable is a measurable factor, characteristic, or attribute of an individual or a system.

In other words, something that might be expected to vary over time or between individuals. Random variables are an idealization of this in mathematical statistics, where they are defined as measurable functions from a probability space to a measurable space.