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Discrete vs. Continuous Data

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Hi. This tutorial covers discrete and continuous data. We're going to focus in on quantitative data today, otherwise known as numerical data. And we're going to look at the difference between discrete data and continuous data.

One way to think about discrete is I think of it just as a straight line of just dots, whereas continuous, I think of it as a line. These analogies will make sense when we look at the definitions. So let's start with discrete data.

So discrete data is data that has distinguishable spaces between possible values. So an example of this is shoe size. So let's take a look at, if we think about shoe size, shoe size, if we just think about a couple, we might have 7, 7 and 1/2, 8, 8 and 1/2, 9. So there are distinguishable spaces between possible values.

So what I mean by that is that you can have 8. You can have 8.5. You can have 9. But is there a common shoe size of 9.25 or 9.6? No. So since that value is not possible in the shoe size example, we call this discrete data. So there is a space where 9.25 is.

OK, if we think now about us a second example here-- change in pocket. So change in pocket, we might have $0.25. We might have $0.33, $0.34, $0.35. But can we have 34 and 1/2 cents, $0.345? In that case, no. So since that value is not possible in our data set, we call that discrete data.

OK, number of books in a backpack-- 1, 2, 3. Can you have 3.5 books in your backpack? No. So there is a distinguishable space at 3.5. So again, if we think about discrete data, I think of it as just dots, where you have spaces between each value.

Now, let's contrast that now with continuous data. So continuous data is data that can be measured as finely as is practical, so there are no spaces between values. So some examples of this are true height, true weight, 40 meter dash time, and really, many other measurable quantities. So again, it's data that can be measured as finely as is practical.

So if we're thinking about the true height of someone, so somebody might be 6' 3". That would be a value associated with true height. But if we wanted to measure that person more accurately, if we had a way of measuring somebody very, very accurately, they might end up being 6' 3.7513". That's a possible height value. It's hard to measure that finely, but if we needed to, we could. So because there are no possible heights within reason that we're not able to measure to, the true height of somebody is considered a continuous variable.

Same thing with true weight. You might have some somebody that weighs 152.439 pounds. If we wanted to get more accurately, if we had a better and better scale, we could measure that person more accurately. So true weight here is considered a continuous. It would be continuous data or a continuous variable.

40 meter dash time-- so if somebody is going to run a 40 meter dash time, they might run it and 4.3785 seconds. That's a continuous variable because we can measure it as finely as practical. Eventually, our measuring tool will be no longer able us to get any more accurate. But if we were if we weren't defined by our measuring device, all possible values of a 40 meter dash time could be taken by that variable.

So that's continuous data. So when I think of continuous data, again, I think of just a straight line. So there's no gaps within the variable, unlike discrete data.

Let's take a look at a couple of different variables here and decide if they would be considered discrete variables or continuous variables. So I have six of them laid out here. I'm going to use D for Discrete and C for Continuous as we label each of these.

OK, so let's start with number 1, number of rabbits observed in a field study. So is it discrete? Are there gaps between possible data values, or is it continuous? Can we measure it as finely as possible so that there aren't any gaps between possible data values.

So for number 1, I would say the number of rabbits would be discrete. We can't have 3.5 rabbits observed in a field study, so there are possible data values. You can really only have positive integer values for number of rabbits. So that one's discrete.

Number 2-- size of a car's gas tank. OK, so are there gaps between possible values, or can we measure it as finely as practical? And for size of a car's gas tank, we can measure that as accurately as our measuring device allows us to. So we'd figure out the volume of this thing, and that would be a continuous variable.

All right, number 3-- number of text messages sent today. I would say that one, it would certainly be discrete. We can't send 50.35 text messages in a day. So there are gaps between possible data values.

Number 4-- number of donuts eaten this week. OK, I would definitely not say that I ate 2.98473 donuts this week. So again, that one would be discrete. You could say, oh, I've eaten 3 and 1/2 donuts a week, but you're not really going to get any more specific than that.

All right, number 5-- level of lead in water. If we took a sample of water, and somehow we were able to measure the amount of lead in that, again, based on our measuring device here, we would probably be able to estimate that pretty accurately, where any value would be possible. So I would consider number 5 to be a continuous variable.

And number 6, number of goals scored in a soccer match-- I would say, again, this one is discrete. Can't score 7 and 1/2 goals in a soccer match, so that would also be discrete there.

All right, so as you study numerical variables, I think it's important to determine whether or not they are discrete or continuous. So that has been your tutorial on discrete versus continuous data. Thanks for watching.