WEBVTT 1 00:00:01.860 --> 00:00:03.480 So hello, students. 2 00:00:03.480 --> 00:00:05.880 We are now with problem 1d, 3 00:00:05.880 --> 00:00:08.310 and here we are going to learn how to compute 4 00:00:08.310 --> 00:00:10.710 the first and the third quartiles. 5 00:00:10.710 --> 00:00:14.313 So we have already learned how to calculate the median, 6 00:00:16.320 --> 00:00:17.373 and basically, 7 00:00:18.810 --> 00:00:23.250 for the first quartile, 8 00:00:23.250 --> 00:00:27.930 we tend to denote that with Q1. 9 00:00:27.930 --> 00:00:32.930 And basically, that is the median of the upper half. 10 00:00:33.180 --> 00:00:34.870 Okay, so it is the median 11 00:00:37.080 --> 00:00:40.380 of the upper half, 12 00:00:40.380 --> 00:00:43.023 and again, for the ordered set. 13 00:00:53.010 --> 00:00:55.950 Okay, so here is our ordered set. 14 00:00:55.950 --> 00:00:57.870 Our median, again, is 194 15 00:00:57.870 --> 00:01:00.300 because we are using the same data set. 16 00:01:00.300 --> 00:01:04.530 So we are looking at the upper half, which is this part. 17 00:01:04.530 --> 00:01:08.910 So here we have four numbers above the median. 18 00:01:08.910 --> 00:01:12.120 So basically, to find the physical midpoint here, 19 00:01:12.120 --> 00:01:13.320 or the median, 20 00:01:13.320 --> 00:01:17.700 we have to take an average of these two numbers, okay. 21 00:01:17.700 --> 00:01:21.210 So it's going to be 175 and 180, 22 00:01:21.210 --> 00:01:23.110 so our Q1 will be 23 00:01:35.940 --> 00:01:39.720 177.5, okay. 24 00:01:39.720 --> 00:01:41.580 So it's basically, again, 25 00:01:41.580 --> 00:01:45.600 the physical midpoint of the ordered set, 26 00:01:45.600 --> 00:01:46.890 but at the same time, 27 00:01:46.890 --> 00:01:51.630 it is the median of the upper half of the ordered set. 28 00:01:51.630 --> 00:01:54.280 And what I would like to mention here is 29 00:01:55.470 --> 00:01:57.390 the method we are using in this class 30 00:01:57.390 --> 00:02:00.300 is what we call more of an eyeball approach. 31 00:02:00.300 --> 00:02:02.980 There are specific formulas to calculate 32 00:02:04.500 --> 00:02:05.820 first and third quartiles, 33 00:02:05.820 --> 00:02:07.950 but we are not using them in this class 34 00:02:07.950 --> 00:02:09.090 because we are still kind of 35 00:02:09.090 --> 00:02:11.580 in an introductory level bio statistics course. 36 00:02:11.580 --> 00:02:13.980 But there are specific formulas for this. 37 00:02:13.980 --> 00:02:16.480 So now, we are going to learn how to calculate Q3. 38 00:02:19.140 --> 00:02:21.330 For that, I'm going to use a different color, 39 00:02:21.330 --> 00:02:23.733 so it will be easier for us to see it. 40 00:02:25.740 --> 00:02:29.780 So here, this is basically that lower half, 41 00:02:32.010 --> 00:02:35.340 and we want to know the Q3 here. 42 00:02:35.340 --> 00:02:36.660 And what is Q3? 43 00:02:36.660 --> 00:02:38.650 Q three is our median 44 00:02:44.937 --> 00:02:46.354 of the lower half 45 00:02:52.530 --> 00:02:55.320 of the ordered set. 46 00:02:55.320 --> 00:02:57.873 That is what Q3 is. 47 00:03:01.530 --> 00:03:02.970 So Q3, here again, 48 00:03:02.970 --> 00:03:06.360 we have two numbers that we have to average 49 00:03:06.360 --> 00:03:07.980 to get our Q3. 50 00:03:07.980 --> 00:03:09.730 So the Q3 will be 51 00:03:14.310 --> 00:03:16.783 223 plus 225 52 00:03:18.570 --> 00:03:20.463 divided by two, 53 00:03:21.600 --> 00:03:23.673 and that will be 224. 54 00:03:25.020 --> 00:03:29.047 So now we have both our Q3 and Q1, 55 00:03:29.047 --> 00:03:33.210 and we are going to learn how to now calculate two events 56 00:03:33.210 --> 00:03:38.010 by using all these things we have found so far 57 00:03:38.010 --> 00:03:39.780 or we have calculated so far. 58 00:03:39.780 --> 00:03:42.990 So again, I want to reiterate, 59 00:03:42.990 --> 00:03:44.520 for Q3 and Q1, 60 00:03:44.520 --> 00:03:47.340 there are specific formulas that can be used 61 00:03:47.340 --> 00:03:49.113 to calculate these values. 62 00:03:50.070 --> 00:03:52.920 We are not using them here in this class. 63 00:03:52.920 --> 00:03:56.280 We are using more what we call an eyeball approach, 64 00:03:56.280 --> 00:03:58.350 and that's why you have to make sure 65 00:03:58.350 --> 00:04:02.760 that your data is an ordered set, smallest to largest. 66 00:04:02.760 --> 00:04:06.300 And basically, we are going by the physical midpoints here 67 00:04:06.300 --> 00:04:07.800 in terms of calculation. 68 00:04:07.800 --> 00:04:09.480 So for an ordered data set, 69 00:04:09.480 --> 00:04:12.630 your median is your physical midpoint. 70 00:04:12.630 --> 00:04:15.720 Q1 is basically median of the upper half, 71 00:04:15.720 --> 00:04:19.433 and Q3 is the median of the lower half. 72 00:04:20.700 --> 00:04:25.500 And another name for median is actually Q2. 73 00:04:25.500 --> 00:04:27.043 So we have Q1, Q2, and Q3.