So, what we're transitioning to then is how do I look at probability distributions for numerical data? To answer this question, we actually need to break up numerical data even further into distinct groups. In this case, there are actually two types of numerical data: discrete numerical data and continuous numerical data. So, what are discrete numerical variables? They're the variables whose outcomes are only counted numbers. So, literally, when you look at a numerical variable, the only numbers that make sense are the counting numbers: zero, 1, 2, 3, 4. Only these counting numbers make sense. So, what are some examples of this? Let's say asking a person, "How many dogs do you own?" You would say one, you would say four, you would say zero. You would not say two and a half. Please do not cut your dog in half. Alright, let's say we were looking at the number of books you've read this year. You could say five, you could say 30, but you can't say 20.3. You're not going to cut your book in half. Even the idea of rolling a dice, that is a discrete numerical variable because the dice faces are 1, 2, 3, 4, 5, and 6. You don't go to the casino, roll a dice, and they say, "Okay, you got 3.4." No, no, no. You only use counting numbers. So then, how do we deal with those numerical variables that have decimals? Where they are called continuous numerical variables. Continuous numerical variables cannot be listed because they occur over a range. Some examples of this would be distance. How far does it take to drive from here to LA? Well, that distance will be a range of numbers based on where your home is. For some people, it's one mile away, for other people, it's 25.8 miles away, for other people, it's 106 miles away. The idea is that with distance, we aren't teleporting from point A to B and suddenly moving from zero to 30 miles. We are continuously moving over that distance. Similarly, time. Time is considered a continuous numerical variable because for all of you guys who have watched "The Flash" or if you're watching "Back to the Future," you know that it's silly to think we can jump through time. No, we all know time happens continuously. Volume is an example of a continuous numerical variable because you are continuously pouring liquid into your cup when you're calculating the volume. Alright, I'm going to give you guys a few minutes to work on example two and identify in each one of them is the numerical variable discrete or is it continuous. Feel free to just write the letter "D" next to the examples that are discrete and the letter "C" next to the ones that are continuous. I'll give you a moment to work on. Is the weight of a newborn kitten discrete or continuous? Definitely continuous. Weight is definitely one of those examples of a continuous numerical variable. Is the number of kittens in a litter discrete or continuous? This one's definitely discrete because you're looking at the number of kittens. Alright, when you're looking at the number of kittens, a half a kitten does not make sense. If you saw half a kitten, I think all of us would be concerned. So, for me, a lot of ways I like to keep track of discrete versus continuous is I will ask the question, "Does one half make sense?" Does the idea of one half make sense? Alright, because like we saw with weight, can a kitten weigh a half a pound? Absolutely. So when your answer to "one-half" makes sense, yeah, it can be continuous versus if the answer is no, like can you have one half of a kitten? Heck no, please don't cut a kitten in half. That's when you know your variable is discrete. So, I always use that kind of half question to help be my guide if it's continuous or discrete. Let's keep going. Height of people in the course, continuous or discrete? It's going to be continuous. Perfect, because height is an ever-changing number. Number of iPhones in the classroom, yeah, definitely discrete again. Please don't cut your iPhone ever in half, please. That would be just terrible for the iPhone. Let's keep going. The amount of sodium in your bloodstream, the amount of concentration, yeah, for all of you science majors in the room, concentration is always going to be a continuous value. Oh, I like F. Number of inches of rainfall in a single day, yeah, this one's kind of tricky, right? Like we started seeing the words "number of," and we started thinking, "Okay, okay, guys, then that means discrete." But notice when I highlighted "number of," I also emphasized what we are measuring. See, kittens and iPhones need to be whole items, but notice in this particular problem, we're looking at inches of rainfall. Inches is a measurement of distance - how high was their rain above the ground? And so, that one is actually continuous. Last one, guys. The total of your last grocery bill, discrete or continuous? It's going to be continuous. Generally, money is going to be continuous. I mean, just think about it. With money, we have cents, and that is not a whole number. Now, the only instance where money might be discrete is if you are counting in pennies, alright? Because if you're counting in pennies, then the idea of a decimal translates into a whole number. So for instance, if you're looking at 0.51, well then that's 51. So, that would be one of the rare situations where you're looking at this discreetly. But honestly, how often are you counting in pennies? Not very often. When you're going to Starbucks and you're buying your coffee and they say it's $4.57, they are not saying it's 457 pennies. We don't generally count in pennies. And so, for the most part, when we are looking at money, it's going to be considered a continuous variable.