 by looking at the data results. So then we'd have to run some statistical analysis on it. So then I would like to tell Excel to count the number of heads, simply count the number of heads. Now, conceptually that we would just take our data set and we'd say this is how many times it came out heads. If you did this and you actually flipped the coin, then you would have to tally out how many times it counts as head. But Excel will do that for us with our random generated tools here so we can play with this stuff a lot more quickly and understand it more conceptually and understand Excel formulas. So this is equals count if. So it's taking this data. We can take either one, but if we take the numerical data, we're gonna say count if there's a one. And if we take the data that's the text data, we can say count if you see a heads, count if you see heads, then pull that. And we came out to 52. And then you can do the same thing for the tails. So I'm gonna say Excel, take this data and count if, if it was this column, you see a two, or count if over here you see a tails. And then if I sum those two up, notice I didn't do exactly 100 flips and I'm kind of happy that I didn't. Oftentimes in statistics people use 100 because if I had 100 and there was 52 heads out of 100, well, that's 52%. But it's useful to do that added step of saying, well, what if it wasn't 100 flips, then you would have to do the math to think about how much it was out of. Meaning if it wasn't out of 152 wouldn't be 52%. If you came out with 52. So if I sum those up, it came out to just 99 flips. So we flipped it 99 times, came out heads 52 times, came out tails 47 times. All right, well, then we can say if I take that 52 divided by 99, that's how I'm gonna get the percent. So I can pull out the trustee calculator, 52 over 99 is gonna give us, if I move the decimal two places over 52.53 about, it's rounding, right? If I multiply times 100 times 100, the percent 52.53 about. And then if I look at the other one, tails is gonna be 47 over 99. If I move the decimal two places over 47.47 about, and that will give us the total percent of 100%. So we don't have to flip it exactly 100 times in order to get a percent, right? Which is often what you see an example problem. So if I do that with a formula, it would just be the 52 over the 99. And this would be the 47 over the 99. This is a common calculation to see, right? You've got the sum and then the total. And then I wanna see, I want to see then the percent of each item compared to the total. So this is like a running percent, which is quite common calculation, very useful to be able to visualize and excel or mathematically, because it's very common and useful. All right, I'm going down here. Now we go down. And so now we could do this many more times in Excel. So now I'm gonna use the same random between function here. And I could test it out and say, let's say we're gonna do a few different tests and we're gonna flip it anytime between two times and 15 times. Now, just like you would expect, if I flip it just two times, then you're not gonna get a result that's gonna be representative. In this case, I got two tails. And that might not, obviously if I got two tails, that's gonna be misleading. So I don't have a big enough sample to really tell me anything about the data, right? The more times I flip it intuitively, you would expect that we're likely to get closer to the 50-50, right? But still three times is still, you might get three tails if you flipped it three times, right? This is a test where we flipped it four times. So I'm just using the random generator tool and just in each cell flipping it two times. This one we flipped it three times. In test three, we flipped it four times. At a test four, we flipped it five times and so on and so forth. So you can see as we go through the results, as we flip it more times, you would expect that we would get a result closer to what we know the actual result is in the actual population, just knowing it intuitively or theoretically or logically if it was a fair coin, using our conceptual knowledge would be 50-50, right? The entire pop, if we flipped it infinite amount of times. All right, so then, so if I, so this is another random generator tool and this will keep on populating random generations and so you can test it randomly and I can copy this entire test which will keep randomly generating every time I click on something in this table and I can then paste it down here one, two, three. In other words, pasting the value only and then I can run my statistical testing on it. So in this case, we had the test of two, we came out with two heads and zero tails. So if I was to do my percentage, two out of two is 100% for the heads, zero out of two is zero for the tails so and there's our 100% so that adds up to 100%. So this is kind of misleading, we only flipped it two times and we came out with a result that obviously isn't gonna give us too much information about the entire population if we were to flip it infinite amount of times. So this would not be sufficient to overturn the null assumption that it's fair coin because we don't have enough of a sample to really get an information. In this case, we have three so it happened to come out one heads and two tails for three so one divided by three is 33% about and two divided by three is 67% and in this case, we flipped it four times, it happened to come out two heads, two tails which are four and 50, 50 and this one, it came out five times, we flipped it five times, two heads, three tails and so on and so forth. Now in Excel to get these results, what we did is we used count if again, I said count if these two cells have a one in it and so two of them had a one in it and on the second one, I said count if