Topic A, B, C, & D: Foundations
- [Voiceover] What I have here is a list of ages of the students in a class. And what I wanna explore in this video is different ways of representing this data, and then see if we can answer questions about the data. The first way we can think about it is as a frequency table. Frequency table. Frequency table. What we're gonna do is, we're gonna look at each ... for each age, for each possible age that we've measured here, see how many students in the class are of that age. So we could say, the age is one column, and then the number, the number of students of that age ... Or we could even say, the frequency. Frequency. When people say, "How frequent do you do something?" They're saying, "How often does it happen? "How often do you do that thing?" Frequency. Or we could also say ... Actually, I'll just write "number." I'm always a fan of the simpler. Number at age, which we could also consider the frequency at that age. Frequency of students. All right. So what's the lowest age that we have here? Well, the lowest age is five. So I'll start with five. And how many students in the class are age five? How frequent is the number five? Let's see, there is one, two. Let me keep scanning. Looks like there's only two fives. So I could write a two here. There are two fives. And now let's go to six. How many sixes are there? Let's see, there is one six. There's only one six-year-old in the class. All right. Seven-year-olds. See, there's one, two, three, four seven-year-olds. Four seven-year-olds. Now, what about eight-year-olds? Eight-year-olds, I'm gonna use a color that I have not used yet. Eight-year-olds, we have no eight-year-olds. Zero eight-year-olds. And then we have nine-year-olds. Let's see. Nine-year-olds, we have one, two, three, four nine-year-olds. Four nine-year-olds. 10-year-olds? What do we have? We have one 10-year-old, right over there. And then 11-year-olds. 11-year-olds, there are no 11-year-olds. And then, let me scroll up a little bit. And then finally, 12-year-olds. 12-year-olds, there are one, two 12-year-olds. So what we have just constructed is a frequency table. It's a frequency table. You can see, you can see for each age, how many students are at that age? So it's giving you the same information as we have up here. You could take this table and construct what we have up here. You would just write down two fives, one six, four sevens, no eights, four nines, one 10, no 11s, and two 12s, and then you would just have this list of numbers. Now, a way to visually look at a frequency table is a dot plot. So let me draw a dot plot right over here. A dot plot. And a dot plot, we essentially just take the same information, and even think about it the same way. But we just show it visually. In a dot plot, what we would have ... In a dot plot, what we would have ... Actually, let me just not draw an even arrow there. We have the different age groups, so five, six, seven, eight, nine, 10, 11, and 12, and we have a dot to represent, or we use a dot for each student at that age. So there's two five-year-olds, so I'll do two dots. One, and two. There's one six-year-old, so that's gonna be one dot, right over here. There's four seven-year-olds, so one, two, three, four dots. There's no eight-year-olds. There's four nine-year-olds, so one, two, three, and four. There's one 10-year-old. So let's put a dot, one dot, right over there for that one 10-year-old. There's no 11-year-olds. I'm not gonna put any dots there. And then there's two 12-year-olds. So one 12-year-old, and another 12-year-old. So there you go, we have a frequency table, dot plot, list of numbers. These are all showing the same data, just in different ways. Once you have it represented in any of these ways, we can start to ask questions about it. So we could say, "What is the most frequent age?" Well, the most frequent age, when you look at it visually, or the easiest thing might be just to look at the dot plot because you see visually, the most frequent age are the two highest stacks. There's actually seven and nine are tied for the most frequent age. You'd have also seen it here, where seven and nine are tied at four. And if you just had this data, you would actually, you'd have to count all of them to kind of come up with this again and say, "Okay, there's four sevens, four nines. "That's the largest number." So this is, if you're looking for, what's the most frequent age? When you just visually inspect here, probably pops out at you the fastest. But there's other questions we can ask ourselves. We can ask ourselves, "What is the range? "What is the range of ages in the classroom?" And this is once again where maybe the dot plot jumps out at you the most, because the range is just the maximum age ... or, the maximum data point minus the minimum data point. So what's the maximum age here? Well, the maximum age here, we see it from the dot plot, is 12. And the minimum age here, you see, is five. So there's a range of seven. The difference between the maximum and the minimum is seven. But you could have also done that over here. You could say, "The maximum age here is 12. "Minimum age here is five. "And so let's subtract ..." You find the difference between 12 and five, which is seven. Here, you'd have done ... You still could have done it. You'd say, "Okay, what's the lowest? "Let's see, five. Are there any fours here? "Nope, there's no fours. "So five's the minimum age. "And what's the largest? "Is it seven? No. "Is it nine? Nine, maybe 10. "Oh, 12. 12. "Are there any 13s? No. "12 is the maximum." So you say, "12 minus five is seven" to get the range. But then we could ask ourselves other questions. We could say, "How many ... "How many older ... "older than nine?" is a question we could ask ourselves. And then, if we were to look at the dot plot, we'd say, "Okay, this is nine." And we'd care about how many are older than nine. So that would be this one, two and three. Or you could look over here. How many are older than nine? Well, it's the one person who's 10 and then the two who are 12. So there are three. And over here, if you said, "How many are older than nine?" Well, then you'd just have to go through the list and say, "Okay, no, no, no, no, no, no, no, "okay, here, one, two, three." And then not that person right over there. So hopefully you ... This is just an appreciation for yet another two ways of looking at data, frequency tables and dot plots.