WEBVTT 1 00:00:01.140 --> 00:00:01.980 Hello, students. 2 00:00:01.980 --> 00:00:03.810 Welcome to problem 1d. 3 00:00:03.810 --> 00:00:05.490 In this problem, we are going to learn 4 00:00:05.490 --> 00:00:08.553 how to calculate the first and third quartiles. 5 00:00:09.720 --> 00:00:11.820 Now, before we start it, 6 00:00:11.820 --> 00:00:14.910 we have to arrange the numbers lowest to highest, 7 00:00:14.910 --> 00:00:16.083 so let's do that. 8 00:00:17.730 --> 00:00:19.833 That would be 147, 9 00:00:21.990 --> 00:00:23.403 175, 10 00:00:25.470 --> 00:00:26.823 180, 11 00:00:28.650 --> 00:00:30.033 185, 12 00:00:32.100 --> 00:00:33.483 194, 13 00:00:35.340 --> 00:00:36.633 196, 14 00:00:38.661 --> 00:00:39.494 223, 15 00:00:40.983 --> 00:00:41.816 225, 16 00:00:43.699 --> 00:00:44.532 and 240. 17 00:00:45.480 --> 00:00:47.160 Now, as I mentioned previously, 18 00:00:47.160 --> 00:00:50.670 very easily we can do this sorting using Excel. 19 00:00:50.670 --> 00:00:52.710 and I have actually video at the end 20 00:00:52.710 --> 00:00:54.690 which will show you how to do that. 21 00:00:54.690 --> 00:00:55.800 So now once sorted, 22 00:00:55.800 --> 00:00:58.710 we will use the formula we learned previously, 23 00:00:58.710 --> 00:01:00.550 which is L equal to 24 00:01:03.276 --> 00:01:06.587 K divided by 100 multiplied by n. 25 00:01:07.830 --> 00:01:10.650 Now n here is the sample size, 26 00:01:10.650 --> 00:01:13.890 and K is the percentile that we are trying to calculate. 27 00:01:13.890 --> 00:01:15.930 So for the 25th percentile, 28 00:01:15.930 --> 00:01:19.440 it's going to be L equal to 25 29 00:01:19.440 --> 00:01:23.943 divided by 100 multiplied by n. 30 00:01:25.740 --> 00:01:28.233 And the n here is of course nine. 31 00:01:31.200 --> 00:01:36.200 So when we do the algebra here, what we get is 2.25. 32 00:01:37.740 --> 00:01:40.890 Now as we know, 2.25 is not a whole number. 33 00:01:40.890 --> 00:01:43.890 So when we convert it to the next whole number, 34 00:01:43.890 --> 00:01:46.020 that will be three. 35 00:01:46.020 --> 00:01:47.693 So now the question is, 36 00:01:47.693 --> 00:01:52.140 what is the third number in our ordered set? 37 00:01:52.140 --> 00:01:56.220 So that is going to be one, two, three, 180, 38 00:01:57.600 --> 00:01:59.643 so 180 is our Q1. 39 00:02:05.670 --> 00:02:10.670 Now we have to calculate Q3, which is the 75th percentile. 40 00:02:10.920 --> 00:02:15.360 So again, here we are going to replace the K 41 00:02:15.360 --> 00:02:18.360 with the percentile we are trying to calculate 42 00:02:18.360 --> 00:02:22.710 multiplied by the sample size, which is nine. 43 00:02:22.710 --> 00:02:24.270 And what do we get this time? 44 00:02:24.270 --> 00:02:26.463 We get 6.75. 45 00:02:27.330 --> 00:02:29.880 Again, we are going to convert 6.75 46 00:02:29.880 --> 00:02:33.153 to the next whole number, and that will be seven. 47 00:02:34.410 --> 00:02:37.200 So again, we are going to go back to our ordered data set 48 00:02:37.200 --> 00:02:42.120 to find out which one is the seventh number in our set. 49 00:02:42.120 --> 00:02:47.120 So here again, one, two, three, four, five, six, seven. 50 00:02:47.910 --> 00:02:51.277 So the seventh number in the ordered set is 223. 51 00:02:56.820 --> 00:03:00.747 So our Q1 is 180, and our Q3 is 223. 52 00:03:01.999 --> 00:03:04.680 Q1 again is our 25th percentile, 53 00:03:04.680 --> 00:03:07.800 and Q3 is our 75th percentile. 54 00:03:07.800 --> 00:03:09.300 Thank you for your attention. 55 00:03:09.300 --> 00:03:10.950 I will see you in the next video.