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Discrete vs Continuous variables: How to Tell the Difference

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Watch the video, or read the article below:

discrete vs continuous variables

Time is a continuous variable.


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 variables on a scatter plot.

Discrete variables on a scatter plot.



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!

graph

This graph of -4/5x+3 has continuous variables — it could go on forever…

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!

Check out our Youtube channel for more stats tips and help!

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Discrete vs Continuous variables: How to Tell the Difference was last modified: March 22nd, 2018 by Stephanie

15 thoughts on “Discrete vs Continuous variables: How to Tell the Difference

  1. magdalene

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

  2. Tobi

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

  3. Gregory

    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

  4. Andale

    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

  5. Andale

    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.

  6. Jen

    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

  7. Andale

    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.

  8. Polina

    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.