WEBVTT 1 00:00:01.650 --> 00:00:02.993 Hello, students. 2 00:00:04.770 --> 00:00:07.410 Now we will go over a new problem, 3 00:00:07.410 --> 00:00:09.540 that is, problem 20. 4 00:00:09.540 --> 00:00:11.390 First, I'm going to read the problem. 5 00:00:13.170 --> 00:00:16.440 The following data are sample of white blood counts 6 00:00:16.440 --> 00:00:19.650 in thousands of cells per cubic millimeter 7 00:00:19.650 --> 00:00:21.210 for nine participants 8 00:00:21.210 --> 00:00:24.903 entering a hospital in Boston, Massachusetts on a given day. 9 00:00:26.490 --> 00:00:31.490 The values are: 7, 35, 5, 9, 8, 3, 10, 12, and 8. 10 00:00:33.930 --> 00:00:36.753 The question is, are there any outliers? 11 00:00:37.620 --> 00:00:40.560 And we need to justify our answer. 12 00:00:40.560 --> 00:00:43.080 So, as we know, to identify our outliers, 13 00:00:43.080 --> 00:00:46.440 we first need to calculate the Tukey fences. 14 00:00:46.440 --> 00:00:50.863 And in order to do that we first have to identify Q1, Q3 15 00:00:50.863 --> 00:00:54.060 IQR, and of course, part of the Tukey fences, 16 00:00:54.060 --> 00:00:57.510 we have to calculate the lower and the upper limits. 17 00:00:57.510 --> 00:00:58.953 So, let's get started. 18 00:01:02.490 --> 00:01:04.353 So the formula for Q1 is, 19 00:01:17.138 --> 00:01:19.080 as we know, K here will be 25, 20 00:01:19.080 --> 00:01:20.730 because we are looking at the Q1. 21 00:01:27.630 --> 00:01:30.780 And n is our sample size, which is nine. 22 00:01:30.780 --> 00:01:34.050 So when we do the algebra here, what do we get? 23 00:01:34.050 --> 00:01:36.060 We get 2.25. 24 00:01:36.060 --> 00:01:39.480 Now, as we know, 2.25 is not a whole number, 25 00:01:39.480 --> 00:01:41.310 so, as part of the formula, 26 00:01:41.310 --> 00:01:45.063 we have to go to the next whole number, and that is three. 27 00:01:46.470 --> 00:01:51.470 So now, the third value of the ordered set will be our Q1, 28 00:01:51.750 --> 00:01:55.050 and that is going to be seven. 29 00:01:55.050 --> 00:01:57.363 So, Q1 is equal to seven. 30 00:01:58.440 --> 00:02:00.283 Now we need to calculate Q3. 31 00:02:05.386 --> 00:02:06.540 To calculate Q3, 32 00:02:06.540 --> 00:02:11.160 all we have to do is replace the K, which we had 25 before, 33 00:02:11.160 --> 00:02:15.273 with 75, because Q3 is also the 75th percentile. 34 00:02:21.990 --> 00:02:24.600 So, again, when we crunch the numbers, what do we get? 35 00:02:24.600 --> 00:02:27.330 We get 6.75. 36 00:02:27.330 --> 00:02:30.960 As we know, 6.75 is not a whole number. 37 00:02:30.960 --> 00:02:32.640 So, what is the next whole number? 38 00:02:32.640 --> 00:02:34.230 It is seven. 39 00:02:34.230 --> 00:02:36.903 So, now let's go back to the ordered data set. 40 00:02:37.740 --> 00:02:39.750 What is the seventh value here? 41 00:02:39.750 --> 00:02:40.900 That is going to be 10, 42 00:02:43.740 --> 00:02:47.010 so Q3 is 10. 43 00:02:47.010 --> 00:02:50.670 So now, let's go ahead and calculate 44 00:02:50.670 --> 00:02:54.093 the upper and lower limits for our Tukey fences. 45 00:03:07.410 --> 00:03:09.690 As always, at first I'm going to write the formula, 46 00:03:09.690 --> 00:03:11.700 and I always encourage my students 47 00:03:11.700 --> 00:03:13.233 to write the formula first. 48 00:03:38.008 --> 00:03:39.300 And when we do the algebra, 49 00:03:39.300 --> 00:03:43.203 we get that the lower limit is 2.5. 50 00:03:49.380 --> 00:03:51.280 Now we will calculate the upper limit. 51 00:04:08.236 --> 00:04:10.270 Again, when we do the algebra, what do we get? 52 00:04:10.270 --> 00:04:11.270 We get 14.5. 53 00:04:12.720 --> 00:04:13.890 So now the question is, 54 00:04:13.890 --> 00:04:18.890 do we have a value that is below 2.5 or above 14.5? 55 00:04:20.190 --> 00:04:23.100 So, no, we do not have a value below 2.5, 56 00:04:23.100 --> 00:04:25.023 because our lowest value is three. 57 00:04:26.160 --> 00:04:29.730 However, do we have a value above 14.5? 58 00:04:29.730 --> 00:04:33.540 And that answer is yes, we do, and that is 35. 59 00:04:33.540 --> 00:04:37.650 Because 35 is greater than 14.5, 60 00:04:37.650 --> 00:04:41.010 we must identify that as our outlier. 61 00:04:41.010 --> 00:04:42.750 So we do have an outlier, 62 00:04:42.750 --> 00:04:45.603 and that is 35. 63 00:04:48.570 --> 00:04:49.560 I hope this helps, 64 00:04:49.560 --> 00:04:51.873 and I'm going to see you in the next video.