WEBVTT 00:00:00.012 --> 00:00:04.197 >> I'm going to show you the answer to this, by doing it in a spreadsheet. You 00:00:04.197 --> 00:00:08.949 could do all of these calculations, without any technology. And if you did that, 00:00:08.949 --> 00:00:13.362 that's really great. It's always really good practice to calculate things 00:00:13.362 --> 00:00:17.709 without using any technology, but just for the purposes of figuring out the 00:00:17.709 --> 00:00:22.873 standard deviation, technology can really speed along this process. So I'm not 00:00:22.873 --> 00:00:29.985 going to use any shortcuts here. We're going to do it exactly as we would if we 00:00:29.985 --> 00:00:38.639 didn't have technology. So first we need to take the avearage of all of these, 00:00:38.639 --> 00:00:47.458 we're going to sum them up. So we're taking the sume of all of these. I could 00:00:47.458 --> 00:00:55.191 also just write equals a1 plus a2 plus a3 all the way to a10. And we'd get the 00:00:55.191 --> 00:01:02.922 same thing. But why would we do that if we can simply write this. Now to take 00:01:02.922 --> 00:01:10.884 the average all we do is divide by the number of values which is 10. So that's 00:01:10.884 --> 00:01:18.654 just going to be 51,511.1. Alternatively, the nice thing about technology is we 00:01:18.654 --> 00:01:27.070 can just do this. Take the sum, and divide by the total number. Do it all in 1 00:01:27.070 --> 00:01:34.563 step. So now we have the average. Now we're going to subtract the average from 00:01:34.563 --> 00:01:40.776 each 1 of these values. Not the opposite, where we subtract each of these values 00:01:40.776 --> 00:01:46.216 from the mean. That's an important distinction. In this case, it doesn't matter 00:01:46.216 --> 00:01:51.481 as much but in other statistical concepts that's an important distinction to 00:01:51.481 --> 00:01:58.227 make. So we'll write equals A1 minus. The mean. So I'm subtracting the mean from 00:01:58.227 --> 00:02:05.630 each of these values. Now I could just do the same thing here and write equals 00:02:05.630 --> 00:02:13.044 a2 minus the mean but that would be tedious. We can just drag this down. When 00:02:13.044 --> 00:02:19.621 you do that, remember that there has to be a little plus sign there. That means 00:02:19.621 --> 00:02:25.734 you're successfully dragging it down. If you went like this, it won't do 00:02:25.734 --> 00:02:32.486 anything. It'll just highlight the boxes. So here, we have the deviations from 00:02:32.486 --> 00:02:39.383 the mean. Here, in the next column We're going to square each deviation. Equals 00:02:39.383 --> 00:02:45.394 b1 squared. And again, we're going to drag it down. So we have the squared 00:02:45.394 --> 00:02:51.742 deviations for each of these values. Now remember that the variance is the 00:02:51.742 --> 00:02:58.709 average squared deviation. So we could just write. Average of c1 to c10. But I 00:02:58.709 --> 00:03:05.996 want to make sure we go through all the other steps in between. So let's again 00:03:05.996 --> 00:03:13.670 practice calculating the average just for clarity's sake. So the variants then 00:03:13.670 --> 00:03:19.829 would be the sum of c1 to c10. Remember that's how you start out taking the 00:03:19.829 --> 00:03:25.637 average, and then divide by 10. So here's the variance, and then the standard 00:03:25.637 --> 00:03:31.793 deviation is simply the square root of the variance. So we'll write equals SQRT. 00:03:31.794 --> 00:03:37.695 That's the shortcut for square root. And then we can just see C13. So we know 00:03:37.695 --> 00:03:43.730 that the standard deviation is 6557.16 approximately. Now I want to point out 00:03:43.730 --> 00:03:49.998 something really important before we finish this solution video. Here I simply 00:03:49.998 --> 00:03:56.953 said equals square root of this cell C13. Whereas here, I wrote out the 00:03:56.953 --> 00:04:05.325 whole average. The reason for that is because say I had but this all here, A13. 00:04:05.325 --> 00:04:12.849 Then, when we drag it down, we don't get the right deviations. And we can double 00:04:12.849 --> 00:04:19.432 click on it, and see what it did. Here, it took A4 minus A16, whereas here it 00:04:19.432 --> 00:04:26.126 took A1 minus A13, which is what we wanted. But we want it to always stay A13, 00:04:26.126 --> 00:04:32.564 which is why we have to make sure this is a constant. And the way to make sure 00:04:32.564 --> 00:04:38.507 it's a constant is by just writing it. Notice also that all of these values 00:04:38.507 --> 00:04:44.267 changed when these values changed because all these values are dependent of 00:04:44.267 --> 00:04:50.507 these values So when we change it back we should again get the correct standard 00:04:50.507 --> 00:04:51.530 deviation.