﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:04.20,Default,,0000,0000,0000,,>> I'm going to show you the answer to this, by doing it in a spreadsheet. You Dialogue: 0,0:00:04.20,0:00:08.95,Default,,0000,0000,0000,,could do all of these calculations, without any technology. And if you did that, Dialogue: 0,0:00:08.95,0:00:13.36,Default,,0000,0000,0000,,that's really great. It's always really good practice to calculate things Dialogue: 0,0:00:13.36,0:00:17.71,Default,,0000,0000,0000,,without using any technology, but just for the purposes of figuring out the Dialogue: 0,0:00:17.71,0:00:22.87,Default,,0000,0000,0000,,standard deviation, technology can really speed along this process. So I'm not Dialogue: 0,0:00:22.87,0:00:29.99,Default,,0000,0000,0000,,going to use any shortcuts here. We're going to do it exactly as we would if we Dialogue: 0,0:00:29.99,0:00:38.64,Default,,0000,0000,0000,,didn't have technology. So first we need to take the avearage of all of these, Dialogue: 0,0:00:38.64,0:00:47.46,Default,,0000,0000,0000,,we're going to sum them up. So we're taking the sume of all of these. I could Dialogue: 0,0:00:47.46,0:00:55.19,Default,,0000,0000,0000,,also just write equals a1 plus a2 plus a3 all the way to a10. And we'd get the Dialogue: 0,0:00:55.19,0:01:02.92,Default,,0000,0000,0000,,same thing. But why would we do that if we can simply write this. Now to take Dialogue: 0,0:01:02.92,0:01:10.88,Default,,0000,0000,0000,,the average all we do is divide by the number of values which is 10. So that's Dialogue: 0,0:01:10.88,0:01:18.65,Default,,0000,0000,0000,,just going to be 51,511.1. Alternatively, the nice thing about technology is we Dialogue: 0,0:01:18.65,0:01:27.07,Default,,0000,0000,0000,,can just do this. Take the sum, and divide by the total number. Do it all in 1 Dialogue: 0,0:01:27.07,0:01:34.56,Default,,0000,0000,0000,,step. So now we have the average. Now we're going to subtract the average from Dialogue: 0,0:01:34.56,0:01:40.78,Default,,0000,0000,0000,,each 1 of these values. Not the opposite, where we subtract each of these values Dialogue: 0,0:01:40.78,0:01:46.22,Default,,0000,0000,0000,,from the mean. That's an important distinction. In this case, it doesn't matter Dialogue: 0,0:01:46.22,0:01:51.48,Default,,0000,0000,0000,,as much but in other statistical concepts that's an important distinction to Dialogue: 0,0:01:51.48,0:01:58.23,Default,,0000,0000,0000,,make. So we'll write equals A1 minus. The mean. So I'm subtracting the mean from Dialogue: 0,0:01:58.23,0:02:05.63,Default,,0000,0000,0000,,each of these values. Now I could just do the same thing here and write equals Dialogue: 0,0:02:05.63,0:02:13.04,Default,,0000,0000,0000,,a2 minus the mean but that would be tedious. We can just drag this down. When Dialogue: 0,0:02:13.04,0:02:19.62,Default,,0000,0000,0000,,you do that, remember that there has to be a little plus sign there. That means Dialogue: 0,0:02:19.62,0:02:25.73,Default,,0000,0000,0000,,you're successfully dragging it down. If you went like this, it won't do Dialogue: 0,0:02:25.73,0:02:32.49,Default,,0000,0000,0000,,anything. It'll just highlight the boxes. So here, we have the deviations from Dialogue: 0,0:02:32.49,0:02:39.38,Default,,0000,0000,0000,,the mean. Here, in the next column We're going to square each deviation. Equals Dialogue: 0,0:02:39.38,0:02:45.39,Default,,0000,0000,0000,,b1 squared. And again, we're going to drag it down. So we have the squared Dialogue: 0,0:02:45.39,0:02:51.74,Default,,0000,0000,0000,,deviations for each of these values. Now remember that the variance is the Dialogue: 0,0:02:51.74,0:02:58.71,Default,,0000,0000,0000,,average squared deviation. So we could just write. Average of c1 to c10. But I Dialogue: 0,0:02:58.71,0:03:05.100,Default,,0000,0000,0000,,want to make sure we go through all the other steps in between. So let's again Dialogue: 0,0:03:05.100,0:03:13.67,Default,,0000,0000,0000,,practice calculating the average just for clarity's sake. So the variants then Dialogue: 0,0:03:13.67,0:03:19.83,Default,,0000,0000,0000,,would be the sum of c1 to c10. Remember that's how you start out taking the Dialogue: 0,0:03:19.83,0:03:25.64,Default,,0000,0000,0000,,average, and then divide by 10. So here's the variance, and then the standard Dialogue: 0,0:03:25.64,0:03:31.79,Default,,0000,0000,0000,,deviation is simply the square root of the variance. So we'll write equals SQRT. Dialogue: 0,0:03:31.79,0:03:37.70,Default,,0000,0000,0000,,That's the shortcut for square root. And then we can just see C13. So we know Dialogue: 0,0:03:37.70,0:03:43.73,Default,,0000,0000,0000,,that the standard deviation is 6557.16 approximately. Now I want to point out Dialogue: 0,0:03:43.73,0:03:49.100,Default,,0000,0000,0000,,something really important before we finish this solution video. Here I simply Dialogue: 0,0:03:49.100,0:03:56.95,Default,,0000,0000,0000,,said equals square root of this cell C13. Whereas here, I wrote out the Dialogue: 0,0:03:56.95,0:04:05.33,Default,,0000,0000,0000,,whole average. The reason for that is because say I had but this all here, A13. Dialogue: 0,0:04:05.33,0:04:12.85,Default,,0000,0000,0000,,Then, when we drag it down, we don't get the right deviations. And we can double Dialogue: 0,0:04:12.85,0:04:19.43,Default,,0000,0000,0000,,click on it, and see what it did. Here, it took A4 minus A16, whereas here it Dialogue: 0,0:04:19.43,0:04:26.13,Default,,0000,0000,0000,,took A1 minus A13, which is what we wanted. But we want it to always stay A13, Dialogue: 0,0:04:26.13,0:04:32.56,Default,,0000,0000,0000,,which is why we have to make sure this is a constant. And the way to make sure Dialogue: 0,0:04:32.56,0:04:38.51,Default,,0000,0000,0000,,it's a constant is by just writing it. Notice also that all of these values Dialogue: 0,0:04:38.51,0:04:44.27,Default,,0000,0000,0000,,changed when these values changed because all these values are dependent of Dialogue: 0,0:04:44.27,0:04:50.51,Default,,0000,0000,0000,,these values So when we change it back we should again get the correct standard Dialogue: 0,0:04:50.51,0:04:51.53,Default,,0000,0000,0000,,deviation.