Difference Between Discrete vs Continuous Variables

Difference Between Discrete vs Continuous Variables

You step into a statistics class, and the first question you are asked to answer is, what is the difference between discrete and continuous variable? For you to be able to answer this question satisfactorily, you must first get to understand the innate characteristic of each of these two variable types. For a start, one must be able to describe what a variable is before you even think of discerning the difference between the existing types of variables. A variable is any data item whose value keeps on changing but can be measured.

A discrete variable can be described as simply a statistical data item whose value is constant and can be determined accurately to a degree of certainty. On the other hand, the continuous variable is the exact opposite because it has a value that keeps changing but what makes it difficult to measure is the fact that it can take an infinite number of values. Having defined the two terms in simplified manners, you are now ready to look into detail what sets apart the two types of variables.

Key Difference Between Discrete And Continuous Variables

When looking at the difference between discrete and continuous variable, it is also good to appreciate that there are some similarities between these two data items which makes it difficult for some people to differentiate them. Understanding the differences is as equally important as learning the similarities between them.

The simplest similarity that a discrete variable shares with a continuous variable is that both are variables meaning they have a changing value. Besides that, they are also statistical terminologies used for comparative analysis.

So what are the key differences that will stand out when looking at discrete vs continuous variable? There a number of differences and depending on different literature, these variables can be grouped into different categories to make it easy for the reader to understand. Some literary works will simply split them into individual differences. For the purpose of this article, we have gone with the former technique and just classified them as the key difference between discrete and continuous random variables. These differences are as highlighted below:

  1. Unlike a discrete quantitative variable which applies for both class limits and non-overlapping classification, a continuous variable only applies without including the upper-class limits, and this is especially true for mutually exclusive classification.
  2. A discrete variable has a complete range of values. What this means is that the values within a range to which can be assigned a discrete variable are known and exact. To the contrary, those values that a continuous random variable can take within a specified range are not exact nor complete.
  3. A continuous variable is uncountable while a discrete variable has countable values.
  4. The data set for a discrete variable is finite meaning it has an end value while a continuous variable can take up an infinite value which implies that it can have endless values.
  5. The values of continuous variables must always belong to a range or a continuum while the values of a discrete variable are independent and can exist on their own without being related to a range of other values.
  6. If you were to plot a graphical representation of a continuous variable, you would end up with connected points forming a line or polygon whereas a discrete variable can be represented graphically using isolated points.

In other literature, you will come upon another difference which states that a continuous variable is random, but we have opted to omit that from the list of key differences above because the term random is what actually defines a continuous variable and hence it would be a repetition including it above.

To better understand the differences between a continuous vs discrete variable, one should come up with as many discrete variable examples as there are continuous variable examples.

Main Differences Between Discrete vs Continuous Variables

Basis of ComparisonDiscrete Variable Continuous Variable
Meaning A variable with a limited number of values which are isolated Is characterized by variables with unlimited number of ranging values
Values Countable Measurable
Range of specified number Complete or whole Incomplete
Represented by Lone points on a graph Linked points
Classification Do not overlap Overlapping
Assumes Separate or distinct value A value between a range

Definition of Discrete Variable

In our introduction, we briefly defined a discrete variable in simple terms. At this point, you already know what differentiates a discrete variable from a continuous one. You should be able to easily point out whether the amount of rainfall in a forest is a continuous or discrete variable. You should also be able to tell what differences exist between the amount of water in the oceans and the amount of water in a glass because between these two; one is a continuous variable while the other one is a discrete variable.

In defining a discrete variable, the most obvious characteristic of it should clearly be brought forth. On that note, we can define discrete variable in two stages; the first one is to mention that it is a statistical variable and then we can add that it takes a finite amount of time to count its value. One may ask, what is a statistical variable?

Well, a statistical variable is one that takes values within boundary limits in no apparent inherent order. A simple example of discrete variable can be given of the total amount of money in your bank account. There is no doubt that you can count with ease all the money you have saved in your bank account.

Variables can also be categorized into separable families, and in that case, a discrete variable is one such variable which is why it is also referred to as a categorical variable. Another distinguishing feature of a discrete variable is that it is a whole value meaning that there can’t be another value between any two categories of its value.  

Discrete variable example:

Some of the examples of discrete variables may include the number of train derailments in Europe, the number of students in a class, the total animals in a zoo or the number of bridges in a country. With these examples, you should be able to tell what is a discrete variable. There are many more discrete variable examples, all you have to do is look around you for items that you can count with ease.

Definition of Continuous Variable

The definition of a continuous variable takes into account two major points; that it is a random variable and can take on any value within a continuum. Therefore, when tasked to define what is a continuous variable always note that it has to be characterized by randomness. From our previous discussion, we already know that such a continuous quantitative variable uncountable and its values can be infinite.

If you were given a statistical item and asked to categorize it as either discrete or continuous variable, you should be able to tell if it is continuous by simply taking into account the maximum value it can take. If it can take on an endless value, then it is an example of continuous variable.

There are many examples of continuous variables but just to give you a perspective, a few of them have been listed below.

Continuous variable example:

  • The temperature of an object
  • The speed of a moving object
  • Amount of snow
  • Particles of sand

Remember that to exhaustively define continuous variable, you have to think of these continuous variables examples to get the correct perspective of what this statistical term means. This will also help in comparing the discrete vs continuous stats.

Conclusion of the Main Difference Between Discrete vs Continuous Variables

By now you already know what entails to a statistical variable and how to differentiate continuous vs discrete variables. Whenever you are asked to discern discrete and continuous variables, think about their most distinguishing features.

More so the discrete vs continuous examples highlight these features quite well. For the discrete variable, we know that to be its ability to be countable while for the continuous variable we know it to take on infinite values. These features form the basis for the underlying principles of the statistics of continuous and discrete variables.