Probability and Statistics > Basic Statistics > Discrete vs continuous variables

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In an introductory stats class, one of the first things you’ll learn is the difference between discrete vs continuous variables. In a nutshell, discrete variables are like points plotted on a chart and a continuous variable can be plotted as a line. Before you start, you might want to read these two articles, which define each type of variable and give you lots of examples of each variable type:

Definition of a discrete variable.

Definition of a continuous variable.

## Discrete vs Continuous variables: A Brief Overview.

**Discrete variables **are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You could also count the amount of money in *everyone’s* bank account. It might take you a long time to count that last item, but the point is — it’s still countable.

**Continuous Variables** would (literally) take forever to count. In fact, you would get to “forever” and never finish counting them. For example, take age. You can’t count “age”.** Why not?** Because it would literally take forever. For example, you could be:

25 years, 10 months, 2 days, 5 hours, 4 seconds, 4 milliseconds, 8 nanoseconds, 99 picosends…and so on. You *could* turn age into a discrete variable and then you could count it. For example:

- A person’s age in years.
- A baby’s age in months.

Take a look at this article on orders of magnitude of time and you’ll see why time or age just isn’t countable. Try counting your age in Planctoseconds (good luck…see you at the end of time!).

## Discrete vs Continuous variables: Steps

Step 1: Figure out how long it would take you to sit down and **count out** the possible values of your variable. For example, if your variable is “Temperature in Arizona,” how long would it take you to write every possible temperature? It would take you literally forever:

50°, 50.1°, 50.11°, 50.111°, 50.1111°, …

If you start counting now and never, ever, ever finish (i.e. the numbers go on and on until infinity), you have what’s called a **continuous variable.**

If your variable is “Number of Planets around a star,” then you can count all of the numbers out (there can’t be an infinite number of planets). That is a **discrete variable**.

Step 2: Think about “hidden” numbers that you haven’t considered. For example: is time a discrete or continuous variable? You might think it’s continuous (after all, time goes on forever, right?) but if we’re thinking about numbers on a wristwatch (or a stop watch), those numbers are **limited** by the numbers or number of decimal places that a manufacturer has decided to put into the watch. It’s unlikely that you’ll be given an ambiguous question like this in your elementary stats class but it’s worth thinking about!

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The link for “How to classify a variable as discrete or continuous” from the STA2023 FAQ goes to “How to Classify a Variable as Quantitative or Qualitative in Statistics.”

Thanks–the link is fixed :)

The article was helpful, especially in explaining the time question. There was a similar question in Chapter 1 homework, smth with 11 flashlights (sorry, I don’t remember word for word ) that involved time and I wasn’t sure if the correct answer was discrete or continuous.

Great, glad it helped!

Stephanie

This article was very helpful. I never thought to think of continuous pertaining to infinity, but that is probably why it is called continuous. I also like the time example. As first I thought it was continuous because I thought well time goes on forever, but there are only so many hours in a day.

When working in our books these variables threw me off a bit because sometimes they seemed to be both to me not one or other. This article is helpful in deciphering between the two.

I think this article was helpful. I especially like the examples given and pointers on how to think about a problem. The concept still gets a little confusing, but I think with more practice I’ll get the hang of it.

I like the simplified way this article explains the difference between discrete and continuous. Yes, sometimes the contributing factors can be ambiguous, but at least your time examples give me a clearer way to correctly determine the answer. In other words, it’s easy to assume that statistics is a field that is all black and white. But this article proves otherwise. Thanks!

This is the way to go to understand statistics. I like the way it is simplified and it explains everything you need to know on a level that you can understand. I like the examples that it gives and it breaks the information down. Because sometimes you get stuck and don’t know how to work a problem and this helps you out.

Good article, I agree with the time example you would think on and on forever when in fact it does not go on it is limited.

When I was looking at this in the book, I was confused sometimes because (by prefernce) I thought it could be either. This explanation is a lot better formated, now to get to work with examples!

I’m glad these examples are helping you :)

And what about geometrical distribution?!! It is discrete, but it takes infinite number of values… :-) I think simplification is not always a good way to understanding.

Wow this was amazing. I am just learning statistics and thios made it so much easier for me. Thank You

wow…this really helpd me!

An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A person’s age is an example of a _________numerical variable.

Why is this not discrete? My book tells me the answer is continuous.

An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. How long a person has been a licensed driver is an example of a ________ numerical variable.

Same for this one. My book tell me this is continuous.

These both have to do with time. 1, I thought time was a discrete variable and 2 you could count the years someone has had their license or their age.

Thanks it helped me understand the difference between the two.

Waooo I like these examples.it made me understood the concept very well.thank you for the good job.

I have been really helped!!

Wow this was really helpful to because i was stuck When i pick my book read it was confussing but thanks this explaination

Dear Professor,

TX for putting this book on stats together.

You cut through all the stuff for me.

I will be taking stats in the summer and have been preparing since mid November to little avail.

We think alike, both wanting to get from point A to point B the quickest and easiest route possible. Too bad textbooks do not have the same idea as what you put in your book.

Please accept my gratitude.

YOU have dispelled my fear.

By the way, what is your take on the course offered at statistics.com?

Respectfully,

Gregory

Thanks, Gregory. I wish you success with your summer class.

I have no knowledge about the course at statistics.com. My only comment is that at $599 is does seem expensive.

Regards,

Stephanie

nice explanation

Thanks for the explanation ….

If it is in a decimal form, will it be clasified directly as a discrete variable?

No, because decimals can be continuous, e.g. from 0.0 to 1.0 you can have 1.2, 1.9. 2.8999999, 8.501234 and a zillion things in between.

I have a question, would you classify “all the stars”, or “all of the sand” as discrete or continuous? I believe they would be discrete, because you can not have a half of a star, it is either 1 or 0, but it would take forever to actually count them. I appreciate your feedback. Thank you so much for this site, it has been a great help.

Jen

You do have to have whole, countable objects (like you said), but in order for an item to be discrete, it also has to be countable. As the universe is infinite, then there are infinite numbers of stars, “number of stars” is infinite, so it’s continuous. As for all of the sand…I *think* there’s sand elsewhere in the universe, so it too would be infinite and continuous.

That makes a lot more sense, thank you.

Hi!

I recently had to complete an antimicrobial practical where I tested the effect of antibiotic (positive control), mouth wash (no inhibition) and a disinfectant (there was an inhibition) on e.coli bacteria. Now that I have the results I can measure the diameter of inhibition on the bacteria.

I can’t understand which data is continuous and which one is categorical.

I have to carry out a test in R studio by the way.

I’d love your input. Thank you.

Excellent work as always!