Discrete vs Continuous Variable – Difference Between Discrete and Continuous Variables

The difference between discrete and continuous variables is that the former relates to a specific and often simplistic number, the value of which has been obtained purely through counting, whereas the latter is a progressive, changing number that is instead measured over time and is often complex.

It’s certainly a daunting thought to consider that you could step into a statistics class and the first question you may be asked to answer is, what is the difference between discrete and continuous variables? If you’ve never heard the terms before, this is sure to lead to immediate confusion.

Luckily for you, we’re going to provide you with plenty of examples to help you differentiate them as well as a continuous and discrete data definition to make their areas of differentiation as clear as possible. We’ve left no stone unturned in the pursuit of providing you with total clarity before you head back into the classroom or office.

Definition of Discrete – What Does Discrete Mean?

The exact definition of discrete variable is: “A discrete variable relates to any number that can be obtained purely through counting and has a very precise and specific end value.”

The mention of the word “counting” in the description above is the enormous deciding factor when it comes to determining what kind of variable you’re looking at.

You don’t count when you’re analyzing continuous metrics because they’re infinite and don’t have a start or end point. It’s impossible to summarize their quantity until you stop measuring them. In other words, they’re a number that you can’t definitively count, as strange as that might seem.

On balance, discrete data values do have a start and end point. There’s always a minimum and maximum whereas there’s no such thing with continuous metrics. They can quite literally go on forever.

This is a major difference between discrete and continuous data because when the variable values are finite and have a predetermined value, they cannot possibly be categorized as continuous. They have a precise end value and a precise start value. The word “counting” in and of itself implies that there is a set value in the first place.

For you to fully understand what separates discrete vs continuous satisfactorily, you must first get to understand the innate characteristics of the discrete vs continuous variables from a numeric perspective so that regardless of whether you’re asked to describe discrete or continuous, you’ll know exactly where you stand.

For a start, one must describe what a variable is before you even think of discerning the difference between discrete and continuous. A variable is any data item whose value keeps on changing but can be measured. It can also be described as something that isn’t confined to a fixed pattern and may change.

A major variation between a discrete vs continuous variable can be found in the nature of the data being measured with each.

Technically speaking, though the number being counted with a discrete variable can be different depending on the quantity of whatever it is that you’re counting, a discrete variable isn’t variable at all.

This is because the number being counted is specific. The variable aspect here is merely the quantity being counted from instance to instance. As we previously mentioned, it has a finite (definite and conclusive) value. This is what sets it apart from a continuous metric which is completely open-ended.

When comparing a discrete vs continuous variable, it’s vital to remember that the continuous variable is the exact opposite of discrete because it has a value that keeps changing. What makes it difficult to measure is the fact that it can take on an infinite number of values at any given moment. Its value isn’t fixed, whereas a discrete value is.

One is dynamic (continuous), whereas the other is static (still and unchanging.)

Definition of Continuous – What Does Continuous Mean?

The definition of continuous variable is: “A discrete variable relates to any number or metric that progressively changes and can take on any value.”

It’s this infinite or unlimited number of values capacity that gives us the underpinning variation between discrete vs continuous statistical data. You’ll know whether you’re dealing with a value that is discrete or continuous by whether or not it has a definitive “end” point.

An example that can help us to separate discrete vs continuous variables would be a tally chart based on gathered data. The final values presented in each section of the tally chart would define discrete variable parameters because they would be based on very specific numbers and counting and have conclusive final values.

We could also observe discrete parameters in action when counting a stack of plates. Because there is a ‘first’ plate and a ‘last’ plate, this means that the numerical information being gathered can’t be continuous because it doesn’t change. The size of the plate stack would always remain constant regardless of how many plates were in it.

On balance, we would see the difference between discrete and continuous variables easily when observing a standard bank account. This is because the values being presented in a bank account constantly change and therefore cannot be categorized as discrete data.

Another great example is an Excel spreadsheet, or any live spreadsheet collecting numerical data. When you’re using a system like this, you’re constantly updating the sheet with information that can completely vary in nature. This makes it undeniably continuous in nature.

Interestingly, a spreadsheet can also revolve around discrete variable principles, too. This occurs when you’re entering set numbers into the different sections that then combine together to form a whole. The reason why a spreadsheet would be classified as discrete under these circumstances is because all of the data being gathered falls within one overriding set quantity.

If you’re entering live numerical information onto a spreadsheet, then the moment that you click the save button, this would also technically convert the spreadsheet from being a continuous form of data to being a discrete form of data.

This is because the numerical values contained on the sheet are no longer changing and have now been given a specific start and end point. They’ve gone from being ‘open’ numbers to being ‘closed’ and therefore confined.

All of these forms of value collection serve as excellent discrete vs continuous examples that we can draw on in the real world to help us set discrete and continuous variables apart from one another.

Having defined discrete vs continuous in simplified manners along with their separate definitions and some useful practical examples, you are now ready to look into greater detail at what sets discrete vs continuous data apart by reviewing the difference between discrete and continuous in our quick reference table.

What Is Main the Difference Between Continuous and Discrete Variables?

Below we’ve laid out some super easy to understand examples of discrete vs continuous data that serve to conclusively separate discrete and continuous variables apart from one another.

Basis of Comparison	Discrete 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
Real world examples	The number of pebbles in a jar, the number of shoes in a wardrobe, the number of people in a room	A bank account, a live spreadsheet, the number of people coming in and out of a building in real time, an ECG monitor

To make things even easier for you, we’ve also created an FAQ that explores the most commonly asked questions about discrete and continuous variable types so that you can easily cast a quick glance over it any time you need to refresh yourself on the difference between continuous vs discrete variable types.

Discrete and Continuous Variable Difference – FAQ

Below are outlined the most common queries about discrete and continuous variables by people just like you who are trying to gain a better understanding of them:

What’s the difference between discrete and continuous counting?

Discrete counting means that the value of the data you’re collecting has a definitive end point and final value number. Continuous counting means that there is no definite end point or value and the counting could go on forever.

What do the words “continuous” and “discrete” mean when you’re comparing continuous vs discrete variable data?

Continuous means “forming an unbroken whole” whereas discrete means “individually separate and distinct.” This reflects both the potentially never ending and respectively conclusive natures of the data gathered using discrete vs continuous variables.

How do you know if something is a continuous vs discrete variable?

It’s relatively easy to discern the variables between discrete vs continuous data because one type (discrete) focuses on the act of counting a set quantity of something, whereas the other (continuous) revolves around measuring a nonspecific and changing value.

What are some discrete vs continuous examples that can help me to understand them better?

Some examples of discrete values would be the value of a stack of coins, the number of biscuits in a tin, or the number of stones in a jar. These values are all discrete because they are made out of a set number that doesn’t alter.

Some great continuous examples would be a bank account, a live spreadsheet containing numerical data, and an ECG monitor. What makes these examples continuous is the fact that the numerical data being measured has no set value and can change from one second to the next.

So What Is Discrete and Continuous Variable? – Conclusion

By now, you finally know what a statistical variable entails and how to differentiate continuous vs discrete variables from one another effectively. Whenever you are asked to summarize discrete and continuous variables, think about their most distinguishing features.

Just remember that the discrete vs continuous examples highlight their key summary features quite well. For the discrete variable, we know that its specific and conclusive nature distinguishes it while for the continuous variable we know that it can take on infinite values. These features form the basis for the underlying principles of the statistics of continuous and discrete variables.