 Statistics and Excel, Population Variance and Standard Deviation. Get ready, take it a deep breath, holding it in for 10 seconds and 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 starting in a prior presentation, so you could start back there. However, if you want to start here with simply a blank worksheet, you can do that as well. 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-formatted cells so you can get right to the heart of the practice problem. Blank tab is where we started with just a blank worksheet so we can practice formatting cells within Excel as we work through the practice problem. So last time what we did is to try to think about this concept of the standard deviation which gives us an idea of the disbursement, the spread of the data around that middle point which we are defining as the mean. We thought about the intuitive way that we might come about this if we didn't know firsthand or first off about the standard deviation calculation by starting with an average deviation where we basically took our data points, we've had a very simple data set, and we took our data points and we compared it to the mean, the middle point, the average, and then we basically took the absolute value of those items and divided by the count to get a number to give us an idea of where things are populated around that middle point. So we basically took like the mean, the average of the distances from each data point to the middle. Now let's make a quick little histogram here just so we can see our data. So I'm going to select our data set and go to the insert tab and then insert tab, chart. Let's add a histogram that we've seen in prior presentations, pretty boring histogram like that. Let's add a couple buckets here. I'm going to put some buckets down below and we'll go into our buckets on the left. Let's make like eight buckets just to make it. So there we have kind of an idea of our data set, right? Like if I was to picture this data set, what we have is that middle point, the average, the mean is in the middle, which doesn't have any, which is here, and then the data are around that. We wanted to include some negative and positive numbers just to show that you might have negative and positive numbers on the mean around that midpoint. So then we have two on the negative side and two on the positive side. So that's kind of a pictorial representation of the data. And we're trying to say, well, the middle kind of point in this small little data set is the middle of zero, right? We're trying to think about what's the distance from basically that middle point with the small data set. Okay, so now we're going to do a similar kind of thing, but now we're going to use the actual calculations that are typically used. And that's going to be the standard deviation and we'll calculate the variance, which is kind of a component of the standard deviation. Now, be aware that there's different calculations for if you're dealing with the entire population versus the sample. Imagine an entire population firsthand. So remember the two buckets we talked about of kind of statistical problems. One, you have all the data. That's what we're imagining here. So we're dealing with the entire population and two, where you have just simply a sample of the data and the calculations will be a little bit different. So right now we're going to look at, they'll be very similar, but a little bit different. Right now we're going to be dealing with a population, the entire population. The variance of the population. So population. I'm going to do black and white on the header, home tab, fonts group, drop down on the bucket, making it black and white. And then let's add another formula. So I'm going to draw out the formula again by going to the insert tab, symbols and equation. So now we've got our equation item. I'm going to go to the tools now and then ink. I'm going to write in the equation with our little ink thing here. So let's see if we can write this thing in and see if it'll populate properly. So here we go. So I'm going to say this is going to be a sigma. So usually shown as a sigma squared. So it's not seeing my sigma thing. There it is. Sigma squared. And then so here we have it. I'm going to say that that's equal to that's what we usually use to represent the variance. So the symbol oftentimes will be sigma squared. Okay, so then we're going to do our sum sign looking like this. And so then on top, I'm going to put an N up here, which it doesn't see yet. But then when I go down here and I put the I equals one, then it sees that it still doesn't see my N up top. So, okay, let's see if I erase the N. Erase the N. The N is too ugly. It doesn't want to see it N up top. Let's erase this. I think I put a J there. Let's make this an I. Make sure it's an I. So I equals one. Okay, I'm going to keep on going even though it still doesn't see my N. And I'm going to say that this is going to be a brackets. I'm going to say X. So it thinks it's a C, but I'm going to put an X and it picks up the X and then sub I X sub I minus mu. Which is representing the mean. Close it up. And then we're going to put squared up top. So there we have it. It still doesn't recognize my N. What do I have to do? Excel for you to recognize. So I put my N here. Let's try to circle it. Say what? Why can't you see that? So it's still N. So there it is. So I circled it. There it puts the N up top. All right. And then let's put that whole thing.