The term Continuous Variable describes the group of variables whose values are obtained by measuring something. For example, consider the case of temperature, there can be no single value of temperature. Mainly this is because of the ever-changing values of temperature. The value of temperature does not remain the same even during the course of one single day, let alone a week, a month, or a year. So we categorize the case of temperature into Continuous Variables. Now we will compare Continuous Variable with Discrete Variable to help us better understand this topic.

Continuous Variable vs. Discrete Variable-

We saw earlier that a Continuous Variable can be described as a group of variables that have values that can be counted or put next to a number.

Now for the sake of establishing a difference, we will look at The Discrete Variable.

A Discrete Variable can be a described variable that has a finite number of possible values. 

Put in simple terms, this means that a Discrete Variable will have only a particular number of values. That number can either be finite or countably infinite.

A Countably Infinite value means that we don’t know what the value is right now, but we will know what value is when we get to it.

An example of a Discrete Variable may be the amount of currency in a person’s bank account at one instance in time.

Now we will look at the two types of Continuous Variables.

Types of Continuous Variable-

There are two types of Continuous Variables:-

1. Instant Variable: – An Instant Variable can be described as the difference between each class of continuous variables. For example, the difference between 40°C and 30°C on a temperature scale will always be the same as the difference between 30°C and 20°C, but there will still be infinite values between 30°C and 40°C and there will still be infinite values between 20°C and 30°C.
2. Ratio Variable: – The Ratio Variables are basically the intervals between the sets of values of Continuous Variables. Like, if we consider the range, between 30°C and 40°C, there will be basically infinite values between the range. For example: – 31.5°C. It exists between 30°C and 40°C.

Now we shall discuss the concept of random variables which will help us better understand Continuous variables.

Random Variable-

A random Variable is the mathematical representation of an entity that is influenced by the event of a Random Activity.

Now we see Discrete Random Variable and Continuous Random Variable.

Discrete Random Variable: – The Discrete Random Variable is a variable, the values pertaining to which can be counted. What this basically means is that the values which the Discrete Random Variable can have can be counted. The Discrete Random Variable cannot take on values that cannot be counted. The Discrete Random Variable may also take on values that are countably infinite. Countably Infinite values are the values whose values we don’t know yet but we will when we come close to them. If we talk about The Probability Distribution of a Discrete Variable, it may be the list of probabilities associated with each of those finite countable values that The Discrete Random Variable can take on. If we have to represent The Discrete Random Variable using the Number System, it may be represented by the set of Natural Numbers (N).

Continuous Random Variable: – The Continuous Random Variable is a variable whose set of values i.e. the values which the variable represents, cannot be counted. For example, temperature. The Temperature may have multiple values even during the course of a day, let alone a greater unit of time. If we have to represent The Continuous Random Variable using The Number System, it may be represented as the set of real numbers. The Probability Distribution of a Continuous Random Variable is a set of values that we cannot physically count.

Different Types of Continuous Random Variables-

There are three types of Continuous Random Variables: – The Uniform Continuous Random Variable, The Normal Continuous Random Variable, and the Exponential  Random Variable.

Uniform Continuous Random Variable: – In a Uniform Continuous Random Variable, each value that is represented on the graph has equal probability. 

Normal Continuous Random Variable: – In a Normal Continuous Random Variable the graph is drawn on the basis of a classic “Bell Curve”.

Exponential Continuous Random Variable: – The Exponential Continuous Random Variable is represented by the figure below.

Examples of Continuous Variables-

1. We already discussed one example of Continuous Variables which is temperature.
2. Another example is the weighing scale. The weight of a person cannot belong to a finite set of values. It can be any number of values.
3. The third example is the speed of a vehicle. This can be an infinite set of values.
4. Another Example is the height of a person.
5. One more example may be described as the colour of a tie.

Conclusion

In this article, we started with a brief introduction to the Continuous Variable. In the Introduction, we started with the comparison of Continuous Variable and Discrete Variable. Then we discussed the types of Continuous Variables and Random Variables. There are two types of Continuous variables that are instant variables and ratio variables. Talking random variables, there are three types of random variables- discrete random variables and continuous random variables. We have even discussed the three types of continuous random variables- uniform continuous random variable, normal continuous random variable, and exponential continuous random variable. There are a few examples also to understand them in a better way.