 be the easiest way to do it based on this table. But you can also say that if I use the absolute numbers over here, the spades are from 1 to 13. So you could try to tell Excel that you want to sum this column if the numbers between 1 and 13. I believe when we did it, we did it based on this column here. But in any case, Excel can add that up for you. It'll add it up, and then we can take the percent. So we can say, OK, well, I've got 1, 2, 3, 3 out of 5,000 draws. Well, let me do that again. 1, 2, 3, 3 out of 5,000. And that comes out to 2, 4.66. And this one is 1, 3, 3, 4 out of 5,000. That comes out to 26.68%. The percentages out of all of them, of course, add up to 100, because that's going to give us our check number. And we would expect that it would be about 25%, which is 13 over 52 cards in the deck, 13 of every suit over 52. So you can see this one is off, but they're somewhere in the range that we would expect. So the results seem to verify that this is a fair deck that has actually 52 cards in it. We can also do the same thing and say, well, what if we were to count each card, but there's four cards of each suit? So anyway, in the cases of aces, I can say, well, there's four aces out of 13. I'm sorry, four aces out of 52. So we would expect that we would draw an ace if we did this infinite amount of times, the whole population of the cards, about 7.6. So we can tell Excel, try to count the number of aces. So we've got another sum if formula, meaning I want you to sum the range. So we're going to tell Excel, sum up this range of the results if the result has an ace in it. Now notice when I look for an ace, it's easier to look at this column, because this is the card number that's going to show me the one ace here, another one. So we can tell Excel, sum up this column if the criteria, this column, has a one in it. Otherwise, it gets a little bit more confusing. We could also say, sum up this column if this column has either a one or the next ace is down here, or a 27, or a 40. So it would be easier to use these two columns. Sum up this result if this column has a one in it. So we do that here. We're going to sum it up. Sum criteria, criteria range if it's equal to a one. And if we do that, then these are the results we get. And this first one, for example, is 363 over divided by the total, 5,000. 5,000 gives us 7.26. This one's 7.46. And again, they look somewhat within a range that seems reasonable if we compare that to what we expect to happen. If we did this infinite amount of times, it would be 4 over 52, or 7.69%. And then again, we can look at the differences. And some are under. Some are over. That's kind of what we would expect. So based on this kind of statistical drawing, it looks somewhat like a fair deck. Now we could make histograms of this. What we did here is try to make a histogram of the entire data set. So we just did a histogram, and then I adjusted the histogram to try to give me each number. But the problem with the histogram, if you're trying to do that, is that it needs a range. So this is going from 1 to 2, 2 to 3, 3 to 4, and so on. But you could see that it gives you just how many times we drew, in essence, each number is basically what I'm looking for. And you can see it's kind of somewhat even, because you would expect if you did an infinite amount of times. For example, if there was each number, 1 over 52, is that percent-wise, 1.92% times 5,000. We did this 5,000 times. You would expect them to be hovering around 96. That's kind of what you would expect to be the case. And so there we have it. Now you could also make that with a bar chart. So in this case, I used a bar chart to look at the results. So now I've got 1 through 52, so I did the same thing. But this time, I assigned this to the x-axis and the results to the y-axis. And now this one's notice the bar chart's a little bit nicer, because now I can just have one number represented down here instead of the bucket ranges, even though you can kind of get a similar chart with both of them. And then I added the numbers. It's a little crowded in, but you get the idea. And then this is going to be a histogram of the percent results. So just to get an idea of that, we've got the percent results. Now remember, the percents, you would expect to be around 1 over 52. You would expect them to be hovering around 1.92. And that's kind of what we have here. So it's a little bit over here. But 1.92 is kind of what we would expect. It's kind of like the middle point of a histogram like that. And that's kind of what you see here. So here's the bucket 1.54 to 1.72. There were seven results in that bucket range and so on and so forth. OK, so the next thing we can say, well, what if I wanted to skew the data? How could I represent that in Excel if it wasn't a fair deck? Like there's a card missing or something. Well, we can do the same kind of random generation 1 to 52. And there's multiple ways that you can then take that randomly generated number set and then skew it in whatever way you want if you wanted to practice using a data set that wasn't exactly fair, depending on what you're doing. But for us, let's just say that we took our data. This represents an even 1 over 52, as if you drew one card 5,000 times out of a 52 fair deck. And then we're going to go into it using in Excel the find function and replace. So now we're going to replace everything that was a 29 with a 1. So we're going to remove all the 29s, which I think is like a 3 or something of some diamonds or something. And then we're going to replace it with a 1, which is an ace of spades. So now someone has stacked the deck with the ace of spades and removed the 3 of diamonds or something like that. So let's see what that would look like.