 for more content, study advice and exam questions. Enroll in statistics by MJ, link in the description below. Hi everyone, it's MJ and welcome back to the course on statistics. Now this is the ninth chapter and I know we've really looked at exploratory data analysis, general probability, random variables, probability distributions, joint probability distributions, generating functions, compound distributions and even the central limit theorem. So this might be chapter nine, but in a weird and wonderful way, I'm almost of the opinion that this should have been chapter one. This is the very start of statistics and I'm gonna explain why in this video because if we had to look at statistics and when you ask ourselves, what is the aim of the subject? What is the point? What is the purpose? Why do we do it? We would see that stats is focused with one very simple task and that is to take data and turn that data into information, okay? That is all statistics is about. How it does that, we can actually break it into two components. The one component is calculating of things known as statistics and that's where the subject gets its name and the other part is with something known as inference. Now inference is something we're gonna deal with later on in the course. So I'm gonna be spending the rest of the video talking about statistics but you need these things in order to do inferences which you need in order to do information. So to explain the big picture, I'm going to be giving an example, okay? And the example is as follows. Let's say you have a university with a whole bunch of students and you need to ask yourself as let's say you're head of the student representation board or something like that, so you need to ask should we have a big party, okay? This is the decision we need to know but in order to come up with this decision we need information. We wanna know do people actually wanna have a party? What type of party do they want? When should the party be? But to get this information we don't have the time or the resources to ask everyone. So what do we do in this situation? We need the information but it's going to be quite expensive to obtain all of this information. Fortunately, and this is where statistics comes in, what we can do is we can ask a few students. So instead of trying to ask everyone we can just ask a few of them. And let's say we ask five of them and we see that four say yes and one says no. So we get this very interesting results that 80% said yes. And what we can then do is say well maybe what does that, or what information can that tell us about everyone? And then we now have our information so we can know what our decision needs to be and we can now have an event that is going to affect the university students. So that is the story. What I wanna do now is just explain to you what all the jargon is. Remember we've been doing all of these other weird and wonderful things, they're very high level concepts and I found a lot of students struggle with the jargon. So what we're gonna be doing now is just labeling each of these things in this party so that we understand what it is. All the university students can be thought of as the population. So we have our population over here. We then do something known as a survey, okay? And once we've asked a few students, this will be our sample. Okay, so we have our population is everyone but the five people are the sample. Now this is where it gets interesting, okay? Before we ask the student whether they wanna go to the party or not whether they think the party's a good idea. So before we ask him the question, the student can either be yes or no. And because it can be either one of these things, it's known as a random variable. Think of the student almost as a coin before you toss it. Once the student has answered and they've partaken in the sample, so after the student answers or after we flip the coin, what we have is an observation. And this would be in the situation, I mean, if we have to use our notation, we use the capital X to denote the random variable and we will use the lowercase X to denote observation. In this case, the observation can either be yes or the observation can be no. Then what we can do, and this is where stats becomes very mathematical, is we need to do calculations in order to determine our statistics. And 80% yes, as you all know, that is a statistic. But what exactly is a statistic? If we had to define this in a more technical terms, we can say that a statistic is a function of our random sample. So if we donate our random sample by X underscore, then a statistic is anything of a function of this random sample. What we're using here is a very famous statistic known as X bar. And the rest of the next video is gonna be dedicated to this X bar. Because we know that X bar is equal to a sum of the observations divided by the total number of observations, which in our case was equal to one plus one plus zero plus one plus one, where one denotes a yes to the party and we asked five people, four said it, and if you do the math, we get 0.8. And I mean, there it looks like the math is quite easy, but as you guys know from all the earlier videos, the mathematics does get a little bit more complicated than that. And that's why, like I say, this should be the first video. This should be chapter one, because when you start delving into the maths, it does get intimidating. People are like, oh, stats isn't for me, but once you see the bigger picture, you'll start understanding why this is so cool. Where things do get a little bit confusing is that yes, the students are random variables, but the statistic itself, X bar, is also a random variable. And because it is a random variable, we're gonna see that it has its own probability distribution. And that was actually the whole point of that central limit theorem was discussing what the distribution is of the statistic. Now this statistic is a very special one, as it is also an estimator. And it is an estimator for the population's mean, which we donate by that symbol called mu. Now the reason why we're interested in estimators, and this is something that we will discuss in later courses, is because then we can start asking questions like what is the probability that more than 50% of the university students actually want to come to the party? The problem with this is we need to know what the variance is of the sample, and like I said, we'll get to that a little bit later. But this does into something known as hypothesis testing. And once we have hypothesis testing, we can use that to create information. And once we have that information, we can then make our decision on whether to have a party or not. There's no point throwing a massive party and people don't actually want to go to it. So you can actually save a lot of money and make the right decision when you understand statistics. So what we're gonna be doing for the rest of the videos in this chapter is just looking at some of the mathematical properties of X bar and also something known as S, which is going to be our random samples variance. But we'll discuss that in separate videos. What I wanted to do is just give you a little bit of an overview to show you where we're going with all of this maths. Because like I said, with all the previous stuff, it can sometimes get a little bit confusing, it can get a little bit crazy. But once you understand the big picture, you can see, okay, this is what we're doing, this is why we're doing it, and hopefully it will make a lot more sense. So I'll see you guys in the next video where we will be discussing more about the sample mean. See you then, cheers. For more content, study advice, and exam questions, enroll in Statistics by MJ, link in the description below.