WEBVTT 00:01.570 --> 00:05.050 Now let us talk about descriptive statistics. 00:07.790 --> 00:17.000 Descriptive Statistics is a summary statistic that quantitatively describes or summarizes the data. 00:17.870 --> 00:25.130 So whenever we want to quantitatively summarize the data, we use the descriptive statistics. 00:25.370 --> 00:28.130 We don't want to find out something out of the data. 00:28.130 --> 00:30.230 We just want to summarize the data. 00:30.500 --> 00:33.080 This is all descriptive statistics. 00:34.630 --> 00:41.110 Now, while the scope of statistics is the process of using analyzing those statistics. 00:42.120 --> 00:48.210 So the script, the statistics in the process of using and analyzing those statistics, we are just 00:48.210 --> 00:54.990 trying to find out a summary of this in biostatistics, which we have, and we are trying to find those 00:55.230 --> 00:57.360 and analyze these values. 00:57.540 --> 00:59.610 We are not trying to do much out of it. 00:59.790 --> 01:01.670 This is called descriptive statistics. 01:01.680 --> 01:04.410 We just want to find out what type of data we have. 01:08.480 --> 01:10.190 Measures of central tendency. 01:11.380 --> 01:19.030 Mean is a calculated central value of a set of numbers to calculate a mean. 01:19.330 --> 01:26.350 We add all the numbers and then divide it by the count of the numbers, which we have added. 01:27.830 --> 01:30.920 The next measure of central tendency is the median. 01:31.700 --> 01:41.270 Median is the middle number in a sorted in ascending or descending list of numbers. 01:42.450 --> 01:46.740 The million is sometimes used as opposed to mean. 01:46.980 --> 01:52.770 Then there are outliers in the sequence that might skew the average of the values. 01:54.220 --> 02:00.070 Mode is a set of values in the values that appear the most often. 02:01.270 --> 02:03.790 Let us see what these are in-depth. 02:06.570 --> 02:09.360 So let us consider these odd values. 02:09.990 --> 02:18.390 These are sorted and we have values as one, two, three, four, five, five, six, seven, eight, 02:18.390 --> 02:19.290 nine and 12. 02:19.800 --> 02:21.870 These are total order values. 02:22.140 --> 02:26.250 The minimum value is one, while the maximum value is two. 02:26.250 --> 02:35.580 In the range will be the maximum value minus the minimum value, which is 12 -111. 02:37.260 --> 02:40.670 Now, let us go back to the definition of me. 02:41.740 --> 02:49.210 Means that we add all the numbers and divide the sum by the count of the number added. 02:50.080 --> 02:52.990 So we add all of these values. 02:53.440 --> 03:01.870 So we add one plus two plus three, four plus five plus five plus six plus seven plus eight plus nine 03:02.140 --> 03:02.740 plus two it. 03:04.270 --> 03:10.000 And then divide the sum by the total number of values which represent. 03:10.030 --> 03:16.510 So we have one, two, three, four, five, six, seven, eight, nine, ten, 11 values in total. 03:16.780 --> 03:19.270 So we divide the sum by 11. 03:20.450 --> 03:23.750 So here the mean is 5.60. 03:25.540 --> 03:29.500 Now let us find out the media as we have discussed. 03:29.800 --> 03:32.740 Median is the median most value. 03:33.750 --> 03:35.390 So that might be the most valuable. 03:35.400 --> 03:35.670 We. 03:37.510 --> 03:44.770 293847565 03:44.770 --> 03:46.390 is the middle most value. 03:47.260 --> 03:49.210 So out of 11 values. 03:49.660 --> 03:56.050 The six value comes out to be the middle most value, which is the median. 03:57.860 --> 04:00.380 The next value is more. 04:01.290 --> 04:07.170 Mode, as the definition says, is the value, which appears most often. 04:08.180 --> 04:10.760 So he is out of all of these values. 04:11.090 --> 04:14.660 Five appears twice, which is most often. 04:14.870 --> 04:16.190 So mode is five. 04:18.090 --> 04:27.450 Now please note that when we are calculating median for the old values, the median is the middle most 04:27.450 --> 04:27.810 value. 04:28.830 --> 04:34.380 I mean, is all a sum of all the values divided by the thought of the values. 04:35.820 --> 04:37.080 Right now. 04:37.260 --> 04:38.610 Let us come to the end of the day. 04:39.930 --> 04:44.070 Now, here we have all the violence which will present in these old values. 04:44.280 --> 04:48.050 And additionally, we have an outlier value hundred. 04:49.080 --> 04:57.090 This outlier value means that this value is something very different from the original sequence, which 04:57.090 --> 04:57.540 we have. 04:58.920 --> 05:03.690 So for these values, the minimum number is one. 05:04.530 --> 05:06.540 The maximum number is 100. 05:07.500 --> 05:10.860 The range will be 100 minus one, which is 99. 05:11.310 --> 05:16.920 Mode still remains five because five is the maximum opening value. 05:18.190 --> 05:24.100 Now median is the by the mean of the middle two values. 05:24.340 --> 05:29.470 So the sum of the middle most values, which is five and six. 05:29.680 --> 05:31.570 Because these are even number of values. 05:31.570 --> 05:33.490 So there will be two values in the middle. 05:34.150 --> 05:35.380 So five and six. 05:35.530 --> 05:42.400 So we add five and six and divide it by two to find out the average of these two values, which is the 05:42.400 --> 05:45.460 median of the even values. 05:47.120 --> 05:54.620 So one thing which we find out is that median of even values is some of the median values divided by 05:54.620 --> 05:54.920 two. 05:56.270 --> 05:59.450 By median of the old values is the middle most number. 06:00.440 --> 06:08.750 Now, in case of finding out the mean, we saw that when we have these 11 values out of these 11 values, 06:08.750 --> 06:15.110 when we found out the mean, it came out to be 5163, because these values are near to each other. 06:16.170 --> 06:21.660 Now, just by the presence of one outlier, the mean value has changed a lot. 06:21.930 --> 06:23.550 I've added all these values. 06:23.550 --> 06:24.780 One divided by 12. 06:25.800 --> 06:28.320 To find out the meaning of these even values. 06:28.680 --> 06:31.080 So this comes out to be 13.5. 06:32.460 --> 06:35.460 Line here, the mean was 5.63. 06:36.430 --> 06:45.780 This means that presence of even one outlier causes a very huge change in the value of meme. 06:46.880 --> 06:56.780 So we cannot really explain the sequence using the meme because when I see the meme of these values 06:57.050 --> 06:58.940 is 13.5. 06:59.660 --> 07:09.080 I am kind of seeing that the median value is hit between 12 and 100 but is not correct because the majority 07:09.080 --> 07:12.500 of the values which are lying from values with. 07:14.090 --> 07:17.420 Should have been around 5.60. 07:18.570 --> 07:25.500 So which is the reason why we cannot really use these measures of central tendency to explain much? 07:25.770 --> 07:34.590 So when the value such as the mean is calculated in presence of an outlier, it cannot really depict 07:34.830 --> 07:39.840 the measure of central tendency more so in this particular situation. 07:40.080 --> 07:46.950 We will try to explain the sequence or explain the data using median value. 07:48.360 --> 07:54.420 Because the median value will not be impacted by the outlier much. 07:55.260 --> 08:01.260 So here when an outlier was added, still the median did not change much. 08:02.130 --> 08:03.740 It is still 5.5. 08:05.050 --> 08:05.640 I'm here. 08:05.650 --> 08:06.760 The median was five. 08:07.000 --> 08:13.930 So by adding one outlier, still the median remains almost the same and did not change as much. 08:13.930 --> 08:14.650 The mean that. 08:18.520 --> 08:20.440 Now which value to use when. 08:21.490 --> 08:24.430 So mean is highly impacted by outliers. 08:24.700 --> 08:26.130 Just what we saw here. 08:28.310 --> 08:37.010 I'm median is robust against outliers, which is the reason why we when we have outliers present, then 08:37.040 --> 08:40.940 instead of using me, we can better in the data using median. 08:42.720 --> 08:46.470 And what is the value that is most likely to be some? 08:47.400 --> 08:54.240 So when we are taking a sample of a population, then the value of the mode will be something which 08:54.240 --> 08:57.240 will be something the most number of times.