 Okay. If we look at our data, we can see we've got pretty smooth data because this is a large data set related to weight, which is kind of similar. I believe this came from the same area as we had with the height data where we had a very large data set. Because we're dealing with something that's in nature, you would expect then that we'd have this kind of distribution. If we have a very large sample, most of the items being in this center point and then it basically tapers off to either side in a fairly uniform way. Then we've got the variance and the standard deviation in formula format. So even though we entered the function in Excel and got the answer, sometimes it's relevant or sometimes useful to do the calculations and look at the steps along the way, if nothing else, to get an idea of what the function is telling us. So the variance is going to be represented by sigma squared. And here's the formula for it. You can see that whole variance is part of the standard deviation, everything under the square root. So as we calculate the standard deviation, we're going to basically be doing the variance along the way. So if we do this in more of a manual method but a way that we can kind of see what is happening, we can take each of these data points, which would be quite tedious because there's a long data set, but if you're in Excel, pretty easy to do. Take each of those data points and subtract it from the middle point, the mean, which was that 127.08 that we calculated before. This is the distance from each data point from the mean. Now, we've got this whole long data set. We snipped part of it, but if you added all of those up, there would be positive and negative numbers, and it would add up to zero. It doesn't here because we only snipped part of the data set. But remember that the characteristic here is if that's the middle point and I take every piece of data minus the middle point, that fulcrum point, then the sum of the differences will be zero. Again, you can't see any of the negative numbers here because we just have part of the data set. But then we're going to square the data, so we're going to square all of it, which removes the negative numbers and squares it. And then if we did our calculation down below, we're summing this up. Remember this is not all of the data set, but if I had all the data set it with some to this, you could check it out in Excel if you would like to see the full data set and work with it yourself. Square difference, there it is, and then we're going to divide by the count. The full data set had 25,000 points in it, so if I counted all the rows of the full data set, 25,000, and that gives us a variance of 135.97, and then if I take the square root of that, we get to the 11.66. So there's our 11.66 that we calculated using the function over here, 11.66, but you'll note that doing it this way gives you kind of a pretty nice intuitive sense of what is going on with the data set. In this data set, what I have done is taken the same data set of weight, but then removed some of the numbers in the middle, resulting in two data sets that are very similar, but different. And the reason this could be useful is because when we look at our statistics over here, note that when we look at the average or the men, quartile one, the median, quartile three, and the maximum, those give us a sense in and of themselves about the data set. But the standard deviation and particularly the variance oftentimes are more difficult for us to visualize in and of themselves and sometimes become more relevant if we're comparing two separate populations, right? So now if we had two different populations and we were to take these two numbers, then sometimes that's going to be a way for us to see where we might use those numbers like in practice, such as like a variance type of number. So remember the general idea with the standard deviation is the smaller the standard deviation, the less of the spread that you would expect around that middle point, the fulcrum point, the average, and the greater the number, the more of the spread. So in this case, I've removed a lot of the numbers like in the middle, the numbers that are closest to that middle point of the spread. So that's going to increase, you would think, right, the standard deviation and the variance. So let's check it out. So if I look at these two numbers and I compare the new data set versus the old data set, we come out to a pretty similar mean or average.