WEBVTT 1 00:00:02.220 --> 00:00:03.090 Hello students. 2 00:00:03.090 --> 00:00:06.960 Now we are going to work on problem 1 E. 3 00:00:06.960 --> 00:00:10.110 Again, we are using the same dataset and the same problem 4 00:00:10.110 --> 00:00:11.310 but because it's been a while 5 00:00:11.310 --> 00:00:13.740 I'm just gonna read the problem again. 6 00:00:13.740 --> 00:00:17.610 A study is run to estimate the mean total cholesterol level 7 00:00:17.610 --> 00:00:20.370 in children two to six years of age. 8 00:00:20.370 --> 00:00:22.950 A sample of nine participants is selected 9 00:00:22.950 --> 00:00:26.580 and their total cholesterol levels are measured as follows 10 00:00:26.580 --> 00:00:31.580 185, 225, 240, 196, 175, 180, 194, 147 and 223. 11 00:00:37.140 --> 00:00:40.740 So one is asking us which measures the mean 12 00:00:40.740 --> 00:00:44.680 or median is a better measure of atypical value 13 00:00:45.750 --> 00:00:48.240 and we need to justify our answer. 14 00:00:48.240 --> 00:00:51.090 Now to answer this question what we have to do 15 00:00:51.090 --> 00:00:54.273 is we have to check for outliers. 16 00:00:56.700 --> 00:00:57.843 So how do we do that? 17 00:01:00.150 --> 00:01:02.910 To find out if we have any outliers or not 18 00:01:02.910 --> 00:01:06.720 we have to calculate the tukey fences 19 00:01:06.720 --> 00:01:08.853 for upper and lower limits. 20 00:01:10.680 --> 00:01:15.680 And here we are going to use some of the values 21 00:01:15.930 --> 00:01:17.940 that we calculated before. 22 00:01:17.940 --> 00:01:22.150 So basically for the lower limit of the tukey fences 23 00:01:23.640 --> 00:01:25.923 we will be using the formula. 24 00:01:27.570 --> 00:01:29.700 And again I always encourage students 25 00:01:29.700 --> 00:01:31.680 to write the formula first. 26 00:01:31.680 --> 00:01:36.680 So it's gonna be Q1 minus 1.5, and Q3 minus Q1. 27 00:01:38.340 --> 00:01:40.980 Now please keep in mind that another name 28 00:01:40.980 --> 00:01:45.363 for Q3 minus Q1 is the interquartile range. 29 00:01:47.160 --> 00:01:48.870 So here what is our Q1? 30 00:01:48.870 --> 00:01:51.630 We have already calculated it, so it is going to 31 00:01:51.630 --> 00:01:56.630 be 177.5, and this is the difference. 32 00:01:59.400 --> 00:02:04.133 So it's going to be 224 minus 177.5. 33 00:02:11.610 --> 00:02:16.610 So 177.5 minus 69.75. 34 00:02:19.800 --> 00:02:22.800 And this will give us the lower limit, 35 00:02:22.800 --> 00:02:24.587 which is going to be 107.75. 36 00:02:28.005 --> 00:02:33.003 And if we do round it up, it's going to be 107.8. 37 00:02:40.110 --> 00:02:41.820 Okay, simple. 38 00:02:41.820 --> 00:02:44.790 So now that is our lower limit. 39 00:02:44.790 --> 00:02:47.340 We need to calculate the upper limit. 40 00:02:47.340 --> 00:02:51.060 So basically the upper limit, it's very similar 41 00:02:51.060 --> 00:02:53.313 except the formula is a little bit different. 42 00:02:55.230 --> 00:02:58.200 For the upper limit we are going to use this formula. 43 00:02:58.200 --> 00:03:01.933 It's Q3 plus 1.5, multiplied by Q3 minus Q1. 44 00:03:15.810 --> 00:03:19.770 Now as I said before, Q3 minus Q1 has a name. 45 00:03:19.770 --> 00:03:21.120 And what is that name? 46 00:03:21.120 --> 00:03:25.770 That name is called IQR. 47 00:03:25.770 --> 00:03:30.770 So this is called IQR, our interquartile range. 48 00:03:33.720 --> 00:03:37.590 Now as you can see, looking at this formula, this part 49 00:03:37.590 --> 00:03:40.770 we have already calculated that from here, right? 50 00:03:40.770 --> 00:03:42.720 The only thing that's gonna be different here 51 00:03:42.720 --> 00:03:46.740 now we are going to add this part instead of deducting it. 52 00:03:46.740 --> 00:03:47.850 So let's do it. 53 00:03:47.850 --> 00:03:49.830 We don't need to recalculate that part 54 00:03:49.830 --> 00:03:51.603 as we have already done it. 55 00:03:53.040 --> 00:03:56.220 So here the Q3 is again 56 00:03:56.220 --> 00:03:59.673 we calculated it before is 224. 57 00:04:00.720 --> 00:04:05.720 And now instead of deducting we are going to add 69.75. 58 00:04:07.230 --> 00:04:12.230 So when we add 224 plus 69.75, what do we get? 59 00:04:13.440 --> 00:04:18.440 We get 293.75 and we round it up. 60 00:04:21.000 --> 00:04:25.173 It ends up being 293.8. 61 00:04:26.610 --> 00:04:28.650 Now there are no outliers. Why? 62 00:04:28.650 --> 00:04:31.800 Because if you look at our ordered set 63 00:04:31.800 --> 00:04:35.430 and we have done that previously, none of our values 64 00:04:35.430 --> 00:04:40.430 are below 107.8 or above 93.8. 65 00:04:41.100 --> 00:04:45.660 So the best measure here will be mean 66 00:04:45.660 --> 00:04:47.670 because we have no outliers. 67 00:04:47.670 --> 00:04:51.663 The best measure is mean. 68 00:04:53.820 --> 00:04:54.653 Okay? 69 00:04:55.800 --> 00:04:58.500 So the best measure of a typical value 70 00:04:58.500 --> 00:05:00.813 in absence of any outliers will be mean. 71 00:05:01.980 --> 00:05:05.493 Okay, now we are going to move to the next one.