 Statistics and Excel. Bell Curve. Test score example part number three. Get ready, taking a deep breath, holding it in for 10 seconds, looking forward to a smooth, soothing Excel. Here we are in Excel. If you don't have access to this workbook, that's okay because we basically built this from a blank worksheet. However, we started in a prior presentation, so you might want to go back there if you want to start with a blank worksheet. But if you do have access to this workbook, there's three tabs down below. Example, practice blank. Example, in essence, answer key, practice tab, having pre-format of cells, so you can get to the heart of the practice problem. Blank tab is where we started with a blank worksheet and are continuing at this point in time. Quick recap of what we have done thus far. We've been creating our bell curve or normal distribution, and we're not stopping building the bell curve yet. Why? Because I didn't hear no bell. I didn't hear no bell. We don't stop building the bell curve until we hear a bell for crying. Okay, we probably won't hear a bell like even at the end. But in any case, we started our normal distribution thought process practice problem with a common scenario to both students and instructors. That being, of course, grades, we actually constructed our randomly generated grades, which is a great tool to use and excel when practicing found under the data tab up top analysis. If you don't have the analysis group, we showed how to create the analysis group. Once we did that, we are imagining that we are in essence the instructor that has access to all the data for past grades. We took that data and then did our standard calculations with it, giving us the mean, the standard deviation, the median. We noticed that the median is similar to the mean, which is one indication that this data set might mirror somewhat or the bell curve might mirror this data and be a good representation of the data. We then wanted to plot our data using a smooth bell curve. So we said, what's the lowest X and the highest X that are going to be plotted on our curve that would be reasonable? We said, if we can capture almost all of the data or the huge substantial part of the data, if we go out for standard deviations, that's where we got to the 34 to the 115. On the X, remembering that in practice, of course, you would think it'd be very, you can't go really below zero in terms of test scores or above 100 typically in most cases. But when you think about a bell curve, theoretically, the ends go on indefinitely. And also remember that we represented our test scores in terms of whole numbers as opposed to percentages. We then calculated our norm dot dist for each of these areas so that we can then create our graph, which was the blue part of the graph over here by going to the insert tab, going to the charts. And we inserted an area graph, which is this one. And then we said, OK, that's great. But what we would also like to do is to be able to say what would be the likelihood, for example, that we've got 80 or below on a test score. We get anything from zero up to an 80%. We can do that with a calculation as we did here, which is the norm dot dist calculation. However, instead of saying, I'm going to have it the non cumulative, we made it cumulative. So this has given us the data or the likelihood of us getting from zero up to 80%, which would be the area of the curve. If you were to think of the drawing drawing the curve, the orange area up to the curve up to this point. Now remember that if you actually look at your data over here, you might say, OK, if I find the 80 on this side, the likelihood that I get an 80, this is whole numbers, but representing an 80%. And then it would be 3.48. You might say I could just add these up. But that's not exactly the answer. Remember 70.99 because it's the area under the curve, which means that there's basically calculus related to it. So it's going to be possibly I could give you an approximation, but it's not going to give you the exact answer possibly. Then we can also represent this in terms of the Z score, which we calculate by saying the number that we want 80 minus the mean, the middle point 74.92 divided by the standard deviation representing the spread. And this gives us a number that is in relation to how far away from the center point we are at. And then I can use that also to create the same calculation here, but instead of using X using the C score to get to this 69.26%. So now when we look at our graph over here, we actually graphed this orange area with this fancy calculation, which is highly useful because the graphs are really useful to be able to look at when you're trying to understand what is happening. And for those of us that are not good at drawing graphs by hand, it's very useful, although somewhat tedious at first to figure out how we can basically graph this and draw the line right here. So the way we did this is we did a logical test and we just said, hey, I want to use my if logical test and say that if this number is less than or equal to the point we're looking at, in this case, the 80 that we found over here, making that absolute, then I want you to give me this number. And if not, I want you to give me just blank double quotes, just nothing. And so that's why it graphs this stuff down to that point where it's 80, and then there's nothing after that point. So when I add that second graph on top of this one, you can see now the orange part of the graph is just kind of overlaying the blue parts basically on top of it. And you get that nice distinction. So now let's do a little bit more with this distinction because that could be a useful tool. Now, the other question that we might have is saying, okay, well, what if, if I'm looking at an operator of less than. So we're now we're going to say less than. And I'm going to make this blue now because this is going to be represented by the blue part of the graph, font group bucket. Let's make this like a blue. It's not the exact same color blue, but a blue. And then I'm going to say, well, if this is rep, if the orange is representing the amount up to the 80, then the blue is going to be the inverse, right? So that's going to be P of X is going to be greater than the 80. So I can say, okay. And of course, I can do this by just saying this is going to be equal to one minus what I got here, right? And so if that's 6926, then this is going to be home tab number group percentify adding some decimals, the 30.74. And if I add those two up, I'm holding control to get the 100. They add up to, of course, the 100%. Now, if I was to do a formula for.