 Statistics and Excel, Deck of Cards, Statistics and Excel. Got data? Let's get stuck into it with Statistics and Excel. Or actually OneNote here, but we'll still talk about Excel. You're not required to, but if you have access to OneNote, we're in the icon left-hand side, OneNote Presentation 1325, Deck of Cards, Statistics and Excel tab. We're also uploading transcripts to OneNote so that you could use the Immersive Reader Tool, changing the language if you so choose, and then being able to either read the transcript or listen to this transcript in multiple different languages using the timestamps to tie into the video presentations. OneNote desktop version here, remembering the two major categories of statistical problems we are working with. Number one, where we have all the data of the population, we then using our statistical tools to organize that data in such a way that we can extract meaning from it. Number two, where we don't have all the data of the entire population, but maybe we can get a sample of the population applying statistical tools to that sample in a similar way as we would apply statistical tools to the entire population, not because we're interested in the sample itself, but hoping that we can take the information from the sample and it will tell us something about the entire population. Now in prior presentations, we looked at examples such as heights where we took an entire population and then took a sample from that population so that we can test out whether or not the sample does give us information that we can possibly apply to the entire population. We thought about a more theoretical situation of a coin flip where the entire population is basically infinity, infinite number of coin flips, and the sample then would be however many times we flip a coin in order to test that out. Now we want to take a look at a deck of cards because when we look at a coin flip, for example, you still have only those two options, 50-50, the deck of cards adds a little bit more complexity because now we have 52 cards in a deck, so we want to be thinking about the statistical implications, how we might organize the data, as well as how we might use our tools of Excel to help us out with our analysis when we're working with something like a deck of cards. When we think about a deck of cards, we have numbers of the cards and we have the suits of the cards that we're going to have to be dealing with. Now with the numbers of the cards, it goes from ace or one, two, three, four, five, six, up to ten, and then it doesn't keep on going up to thirteen, but it kind of does because you've got the jack, queen and king. So we could assign a number to all the cards. We can say, well, they're basically numbered from one to thirteen, and notice if you play different games, you might say, well, some games say that all the face cards count for ten or something like that. Those are particular games, but if we just simply assign a number to the cards, we can do that and say, well, there's one to thirteen. That can be a useful tool for working in Excel or even for memorization of certain things. And then we have the suits. I'm not putting the suits in any kind of order of importance. The suits might have different implications for different games that are being played, but the suits, we have the four suits, spades, hearts, diamonds and clubs. So if we take each of the cards then, such as an ace, we could have four aces, the ace of spades, ace of hearts, ace of diamonds, ace of clubs. Therefore, we have four aces of different suits. We have four twos of different suits. We have four threes of different suits, and so on and so forth, and we've got the four jacks of different suits for queens and for kings. So if we add all this up, we can put this into a table to try to analyze this, right? We could say, okay, well, if I number the cards one to thirteen, and then each of those cards have four of each of them, that's going to give us four of each card or fifty-two. So you can add these up both ways nicely in a table, right? So now you've got one, two, three, four. I can sum up this column to get to fifty-two, or I can say how many of each suit are in a deck, how many spades, how many hearts, how many diamonds, how many clubs, thirteen of each, thirteen plus thirteen plus thirteen plus thirteen is going to be fifty-two. So that's nice. That's useful for us to kind of organize this in our minds and on the page. But now I still have this kind of issue if I want to set up some kind of statistical problem, because I don't have one numerical value for each card, right? I have to say two things in order to name one card. I've got to say, well, this is an ace of spades or an ace of hearts or an ace of diamonds. I don't have one number that can stand for the card. So that's going to be kind of an issue for us that we'll take a look at in a second. Now, if I just run some standard statistical kind of analysis, I can say, well, one card out of fifty-two. What if I had a deck of fifty-two cards? It was an even deck of fifty-two cards, and I draw one card out of fifty-two. Well, then the chances of it being any one of those numbers, if it was chances of it being an ace of hearts or whatever, is one out of fifty-two, right? Or one point nine-two if I move the decimal about over. And I can say, okay, well, what are the odds of any suit? I think that's how you spell suit, right? Or is that like a business suit? I don't know. Thirteen out of fifty-two, because there's thirteen of each suit. Thirteen of each suit out of fifty-two. So the odds of pulling a hearts or the odds of clubs or whatever, twenty-five percent, right? Because it's thirteen over fifty-two. And then I can say, okay, well, what are the odds of one number of any suit? Meaning, what are the odds that I choose an ace or a jack? Well, there's four jacks in the deck of fifty-two. So I can then say, well, then four over fifty-two is going to be about seven point nine-six or so on and so forth. Standard statistical analysis we can get just from that table. Now, the next thing we might do if we're trying to analyze this more, is I could say, well, why don't I assign a number to each of the cards that's a unique number? Now, obviously there's many different ways that you can do this, but the concept would be if I assign a number to it, then I can have just one cell representing any card. So for example, here we had, if I regroup my table over here vertically, I can just say, okay, I need two columns the way I had it before, right? I need the ace to thirteen, which represents the king of spades. And then it starts over, ace of hearts to thirteen, which is the king of hearts, ace of diamonds to thirteen, the king of diamonds and so on. But what I'd like to do is assign one number to it. So I'm going to make this other column and just assign one through fifty-two. So now I've got one number assigned to each card. And if I can do that, and again, there's no like uniform numbering system. I could have put the clubs on top or the hearts on top or whatever. But once I have a numbering system with one number, then I can use my Excel tools a little bit easier and it might...