Classifying discrete and continuous variables

0:00- [Instructor] We're told that a baker weighs every sourdough loaf she bakes and records the mass rounded to the nearest gram. Is the mass of a loaf a discrete variable or a continuous variable? Pause this video and see which of these choices you agree with. Okay, so let's work on this together now.

0:17So just remind ourselves, a discrete variable is one that it can take on an infinite number of values, but you can essentially count them. So if it was zero, one, two, three, four, five, obviously you could keep counting forever, but those would be discrete. It is countable.

0:33Maybe I'll write it here. You can count it. Now, a continuous variable is something where you can't really count it. Not only could it take on zero, one, two, three, it could take on every value in between zero and one, every value in between one and two, so on and so forth.

0:48It's not easy to count or you can't count it. Now, this one is interesting because first, they tell us how the baker measured it. Well, when you look at the measured weight, it's going to be rounded to the nearest gram. So this right over here is going to be countable.

1:06The loaf of breads can only be zero, one, two, three, four, five, six, seven, all the way up to whatever. I guess you could have some very big bread. This is countable, but they're not asking us is the measured mass, or maybe I should say the recorded mass of a loaf a discrete variable or a continuous variable?

1:24They're saying the mass of the loaf itself. Well, the mass of the loaf itself, we're not talking about rounding it or how it was recorded, that thing can take on any value between two whole numbers. It's very unlikely in fact that it's going to be exactly a whole number.

1:42So I would say this is closer to being continuous. You might be able to make some argument that you could count the number of atoms in it or something like that, but let's not go that extreme. For all purposes, this is essentially a continuous variable. It could be five point, I don't know how much bread might weigh.

2:02Maybe it's a couple hundred grams. It could be 100.2 grams. It could be 100.291 grams. It could be 100.2912389 grams, so on and so forth. So I would consider this to be continuous. So let's see, choice A, continuous, because the true mass of a loaf is almost never exactly a whole number of grams.

2:20Yeah, that's pretty good. Well, I mean, well, no, that's not true because if the true mass was, you know, 1.5, 2.5, 3.5, that still is countable. So I actually wouldn't go with that. Continuous because between any two possible masses, every mass in between is also possible.

2:41Yeah, that's right. That's essentially the argument we just made. Between one and two, it could also be 1.3942. Between three and four, it could be pretty close to pi number of grams. It can be these very long decimals, which is very hard to count, assuming we're not going to the extreme of counting atoms.

2:58So definitely, I like that choice. Let's do another example here. So let me erase that, erase that and give ourselves another question. So here we're told a motion-triggered camera at a desert waterhole records how many times a single bighorn sheep visits during one night.

3:23There's no limit on how many visits the camera can record. Is the number of visits a discrete variable or a continuous variable? So again, pause this video and try to think that through. Well, the sheep's either going to make zero, one, two, three, four, five, six.

3:37It can make an arbitrary number. At some point there I guess probably is some limit to how many... There's a finite amount of time, but it could be any arbitrary number. But as we said before, this is definitely countable. So this is definitely going to be a discrete variable.

3:55So let's see. I'll rule out continuous, continuous, discrete because the possible values can be listed even though the list never ends. That's right. Let's see, discrete because sheep cannot visit a waterhole more than a few times in one night. No, that's not why we're saying it's discrete.

4:08Even if it were possible that the, which it isn't, but even if it were possible for the sheep to visit a billion times or an infinite number of times, well, I won't say infinite, an arbitrary high number of times, we would still say it's discrete 'cause it's all about being discrete is that you can actually count the possible outcomes.