 Statistics and Excel. Coin flip statistics example. Got data? Let's get stuck into it with statistics and Excel or one note in this case, but we'll talk about Excel too. You're not required to, but if you have access to one note, we're in the icon left hand side, one note presentation, 1315 coin flip statistics example in Excel tab. We're also uploading transcripts to one note so you could use the immersive reader tool, possibly change the language if you so choose and then either read the transcript or listen to the transcript and multiple different languages tying it out to the video presentations using the timestamps. One note desktop version here, data on the left hand side, remembering the two major categories of statistical problems, one being where we have all the data all the information for the entire population and are applying our statistical tools to organize that information so we can get meaning from it and two a situation where we don't have all the data all the information for the entire population and are often reliant on samples of that data and then we apply similar statistical tools not so much so that we can fully understand the example the sample itself, but so that we can infer the results of that sample to the entire population. Now here we're thinking more of the second of those buckets where we don't know the entire population. However, oftentimes it's useful to think about situations where we do know the entire population and we can get basically the answers and then we can also take a sample from that population and use our sampling techniques to see if when we infer the results of the sample to the entire population they are applicable and so in a prior presentation we did that with heights. We had an entire population of heights. We took samples of those heights to see how representative these samples were to the entire population. Now we'll do a similar kind of thing with coin flips which is a little bit easier sometimes because you have like the 50-50 the two results on the coin flips as opposed to the heights data where you have the range of the heights but also it's a little bit more mathematical and theoretical because when we think about coin flips the entire population you can think of as a conceptual type of thing which would be an infinite amount of flips. So in other words when we're thinking about coin flips if we had a coin and we kind of assumed that if it was a fair coin that would be our general assumption the fair coin would mean that anytime I flip it you're going to get an even chance of it coming up heads or tails. So that's going to be like the null hypothesis and then how would we test whether or not that is indeed the case. Well we would have to flip it a bunch of times and then test whether or not what we think would be happening is indeed what is happening and if we come up with evidence that that is not the case something else is happening then the question is what kind of statistical evidence would we need to override the general null assumption that it would be 50-50. Now when we think about this from a statistical sampling concept you would think about well what's the entire population here that we're thinking about well it's a conceptual idea that if you flipped the coin an infinite amount of times then you would come out to 50-50 but obviously in the real world you will never be able to flip the coin an infinite amount of times. So any amount of times that you flip the coin in theory you can think of as a similar kind of concept as when we took a sample of the entire population of heights. So any amount of flips is going to be some finite example of the amount of flips of the conceptual concept of flipping it an infinite amount of times and if it was a completely fair coin we know the outcome of an infinite number of times just conceptually would be 50-50 if it was a fair coin. So that's kind of the idea. So then two things like like always we would like to do here we would like to say we want to know this conceptually for statistical and we also want to think about how we can we test this out in Excel so we'll give an idea of how we can use Excel tools to kind of test this out. Now obviously if you were to generate this in Excel you can use something like the random generator again last time we used a random generator to just give us a random decimal number of multiple decimals out. This time however we're going to use the random between so if I want to simulate a coin flip I can basically say look what I want to do is I'm just going to assign a one to heads two to tails and now that I have a numerical assignment to my outcomes I can use a random generator random between the bottom being one the top being two and then Excel will give us this random generation which basically simulates anything that's random between two numbers right so now we've got our random generator that we can play with and simulate something of this nature. So now as I look at my random generation I can use this formula and I can copy it down to as many cells that I want. Now however many cells I copy it down to if I copy it down to a hundred cells that would be like simulating a hundred flips of the coin and a hundred flips of the coin is kind of like from a sampling idea or concept a hundred flips out of an infinite amount of flips a sample of a hundred out of a sample out of the actual population which is a conceptual idea of infinity right so then so then if we if we take a look at our I can then basically organize my data so once I have my random coin flips I can then I can then say this random generator is going to keep on generating random results so I'm going to copy this random generated field and paste it static so now it's pasted without the actual formula but just as hard-coded ones and twos I can also use excel if I want to then give me the results in terms of words I can use a formula in excel to say if there's a one tell me it's a heads right so we'll do that in excel if you want to if you want to see those formulas to do that but but conceptually I can just say well one is a head and two is a tails I sorted it by heads and then tails here so we can sort them heads on top tails on the bottom I can get an idea from doing that just saying it looks kind of close to 50 50 maybe right but I can't really tell just