Continuous Variable

In Mathematics, a variable can be classified into two types, namely: discrete or continuous. If a variable can take on two or more distinct real values so that it can also take all real values between them (even values that are randomly close together). In this case, the variable is continuous in the given interval. If a variable will take a non-infinitesimal break on each side of it, and it does not contain any values, then it is discrete around that value. In some instances, a variable will hold discrete values in some areas of the number line and continuous in others areas..

Continuous Variable Definition

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. 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. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

Types of Continuous Variables

There are two types of continuous variables namely interval and ratio variables.

  • Instant variable
  • Ratio variable

Instant variable

A variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer?

Ratio variable

Ratio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses.

Difference between Discrete and Continuous Variable

Below are the main differences between discrete and continuous variables.

Discrete Variable

Continuous Variable

It is a variable whose value is obtained by counting.

It is a variable whose value is obtained by measuring.


Number of planets around the Sun

Number of students in a class


Number of stars in the space

Height or weight of the students in a particular class

Range of specified numbers is complete.

Range of specified numbers is incomplete, i.e. infinite.

It assumes a distinct or a separate value.

It assumes any value between two values.

Continuous Variable Example

Continuous variables would take forever to count. In fact, we would get to forever and never finish counting them. For example, take an age. We can’t count “age”. Because it would literally take forever. For example, it could be 37 years, 9 months, 6 days, 5 hours, 4 seconds, 5 milliseconds, 6 nanoseconds, 77 picoseconds…and so on.

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