 did you do? Okay, I hit the right error, control shift down. And I look at all my data, it adds up to 100%. Right. Also remember that in order to get this at the 100%, that we represented our data on the left, which represents test scores, not in the format of decimals or percentages in this case, but as whole numbers. So if you have the information of test scores in the format of percentages or decimals, sometimes it might be easier to multiply at times of 100, representing the data as basically whole numbers so that when you get your percentages over here, then it'll basically add up to the 100%. So now we can ask questions such as, or this calculation, for example, means that what would be the likelihood, for example, that we would get a 64% we're at the 2.2% likelihood. That's not the question of what's the likelihood that I get 64 or under. That would be one of the cumulative types of questions. So then we can of course ask questions. What's the likelihood that I get 64% or above, for example, and we'll do some of those calculations in a little bit here. But for now, let's continue plotting out our graph. Now you could just take these percentages and plot the graph out this way. So I can select my item up top. I'm going to hit control shift down. And then I'm going to say control backspace taking me back to the top so I can insert another histogram so I can go into or let's let's do a actual chart this time. So I can say this is going to be charts. And this is going to be a bar chart, not a histogram. So the bar chart. And of course, you get this nice smooth bell curve looking thing because of course we did this with our our actual formulas and functions. So this is going to be the P of X. I'll leave I'll leave that there and it's graphing now the percent the percent likelihoods. But we need to fix that bottom bit. So I'm going to select the data up top. I'm going to go into the select data and on the I'm going to edit this side and we want to pick up our numbers, which are starting at 34 not one. That's why it's that's why it's messed up here. So we're going to put our cursor on 34 control shift down and then I'm going to say okay now you got to be kind of careful making sure it picks it up over here because sometimes Excel gets a little little finicky over here. So if this just has one number then something got messed up when you did that you have to do it again. But I'm going to say okay. And so now if I scroll up top so now we've got this nice bell curve in that middle point is around you know the 75 at that middle point nice and smooth. Okay. And so then we can also add an area type of bell curve. I'm going to pull this to the side. We will get back to it soon because we could then think I would like to compare is there a way to compare my data to the actual data the actual data versus the bell curve. So we'll think about that and a little bit. But first note that you can also plot this with an area. So I'm going to select this item again control shift down and then I'm going to hit control backspace. And this time we're going to go into the insert tab and we're going to go to the charts and graphs. And if you select I believe this one then down here you've got your areas down below. So we'll pick this is the area. And so I'll pick that one. And so now you've got a graph that gives you that the area graph. And this is the one that we can we can work with because oftentimes when you're thinking about the bell curve you're trying to get the area under the curve that's going to be part of our calculations because that's going to give us our probability. So let's once again I got to fix this bottom bit. So I'm going to go up top and go to the select data. I'm going to go to the edit over here and select this one again and then pick our X's holding control shift down. Usually like you could hit the control backspace. But again sometimes that messes it up. So I just like to go OK and then OK and see if it picks it up and be awfully careful with Excel when we do that part. Because again Excel gets a little wonky sometimes right there. So there we there we have it. So we'll get a little bit more fancy on this one and say can we can we plot questions like if it's over a certain amount or under a certain amount. And can we get the Z score on there. So we'll do that in future presentations. But for now let's put this at the bottom of our stack of charts cool charts that we've been making. So notice that if you just want to see the shape of it the bar chart works well. The area chart is going to give us that area. However which is what we're usually thinking in when we're thinking of the of the normal distribution. Now we could compare this to our actual data. So let's do our actual and then let's put our frequency frequency. That's totally not spelled right. Is it. There's no way I'll spell check it. Oh they say it is. I don't know I'll take their word for it. I still have my doubt font group. Let's go black white rapid center it. I'll make it a little bit larger and now I'm going to do a frequency of our actual data to see how many times out of the thousand test scores we have that we get to each of these X's. So this is going to count our actual data in accordance with these X's. So I'm going to say this equals the frequency tab. And then I mean this is an array formula. So fancy array formula. I'm going to pick my data over here control shift down all of the data control backspace up to the top. Then I need to pick my X arrays. So I'm going to say comma and then put my cursor on the X arrays control shift down control backspace taking me back up. So this is saying all right Excel I would like you to find all of this data and see and put it into the groups are buckets with these numbers being in essence the top part of the bucket right. So it's going to take everything below 34 up to and including 34 and then everything from 34 or above 34 up to and including 35 and so on. Hopefully I got the cutoffs right there. So if I scroll down there it is not picked up this last bit down there which I don't want to hang out that far. So I'm going to change this to three and so there we have it. And so then if I put my totals down here I can say alt enter. This should add up to 100 percent. Let's percentify at home tab number percentify and then alt enter for the sum function. This should add up to a thousand because that's how many we told Excel to count. That's how many sample test scores that we had in our data set. Now if I want to compare this I can't compare this to the P of X directly. I could make a histogram from this right. I could make a histogram and I'll come up to a similar kind of histogram. But what I'd like to do is say well how can I get the percentages. So I can either I can either make this into percentages or I can make the percentages into a frequency by multiplying the percentages times a thousand. Now normally it'd be easier to say percent of total to make to make our data into a percent. So I'm going to say black white center. So I'm going to take every number divided by the total. This equals this number divided by control shift down. I just want that thousand. So enter double clicking on it. I'm going to make this second number absolute at four so that that bottom number doesn't move down as I copy the formula down. I'm going to make it a percent before copying it down. Home tab number group percentifying it couple decimals fill handle double clicking it copying it down. So now I have a set of data similar to this set of data. So this is my actual percent of the total. And this would be my predicted you know percents of whatever total I'd be using. And so then I can I can take my difference and I can say okay what's the difference between my actual data and this is the perfect bell curve minus my actual percent data percentifying this home tab number percentify add some decimals and then copy it on down. So now we can see our differences here. So when we're thinking about our data then I'll stop it here. We'll continue on with this next time. But the general idea is we can take our actual data set in real life and practice. You can actually build your data set but you would need the mean and the standard deviation to do so in practice. You might not know those numbers of course and you would take your data and then calculate those numbers to mean the standard deviation. If the median is similar to the mean it's likely it might follow a normal distribution. So you might then plot a normal distribution in this format being then able to create our graphs. And then we can also look at our actual data and compare it to the normal distribution at each point which could also give us an indication as to how close the actual data mirrors a normal distribution. We'll continue on with our graphs in a future presentation.