WEBVTT 00:00.120 --> 00:05.100 Now that we have gone through descriptive statistics, let's start solving a few questions. 00:13.220 --> 00:18.830 You can see the question on your screen, and you will be able to watch the video. 00:19.100 --> 00:24.740 And after posing that, we do it can solve the questions and we will discuss a solution after that. 00:26.690 --> 00:34.760 You need to find out the meaning of these scores of 620 strings so you can see the scores are not sorted 00:34.760 --> 00:35.120 here. 00:35.150 --> 00:41.930 You can simply find of the men, the max, the range of these scores. 00:42.410 --> 00:50.360 The standard deviation, the variance, the mean median, all these calculations you need to do by hand. 00:51.050 --> 00:55.610 And after that, I will show you how you can solve this using byte. 00:57.170 --> 00:58.160 So let's go ahead. 00:58.580 --> 01:00.830 You can pause the video and find the solution. 01:02.570 --> 01:04.460 Now let's start solving the problem. 01:04.490 --> 01:07.550 I have taken all of these values and sorted. 01:09.140 --> 01:15.560 After sorting the values, the minimum value comes out to be for the maximum value comes out to be sixty 01:15.560 --> 01:20.150 six when we are trying to find out the median of the values. 01:20.360 --> 01:21.890 It will be the middle most value. 01:22.430 --> 01:28.610 So the minimum, most value will be, as these values are, even a number in the most value will be 01:29.330 --> 01:32.030 the average of 10 and 11. 01:32.510 --> 01:33.620 That will be a median. 01:35.540 --> 01:39.860 So the average of 15 and 17 here will be 16. 01:40.130 --> 01:41.690 So that is the median value. 01:42.890 --> 01:44.960 Now, how do we calculate the mean value? 01:44.960 --> 01:45.830 The mean value? 01:45.840 --> 01:53.720 We can be concluded by adding all of these values and dividing by the count of these items, four zero 01:53.720 --> 01:55.550 eight divided by 20. 01:56.750 --> 01:58.370 So let's take a some of these. 02:05.620 --> 02:08.800 And then divide it by the count of these. 02:16.040 --> 02:20.420 In Excel, you also do have divided function to average, so you can use that as well. 02:22.070 --> 02:25.760 Next, we let us find out the standard deviation for these numbers. 02:26.450 --> 02:32.330 So to find out the standard deviation of these numbers, we can simply find out the difference of these 02:32.330 --> 02:35.930 numbers from the mean value. 02:35.940 --> 02:40.940 So you've become a mean value, which will be fixed. 02:43.030 --> 02:51.460 So to fixing the value of what they're doing, the same here, and then we want to subtract each number 02:51.460 --> 02:51.880 from it. 02:53.740 --> 02:55.490 And why we do this. 02:55.510 --> 02:57.670 We also want to square these values. 02:58.090 --> 03:00.040 So let's square them simultaneously. 03:13.270 --> 03:21.320 Let's raise it to the father, too, so that we can be aware of these numbers. 03:34.690 --> 03:40.480 Now, these are the squared deviation of these number from the mean value. 03:41.290 --> 03:47.620 Now we also want to take the average of these what we can simply say save, even take some of these 03:47.620 --> 03:52.750 values and again, divided by the account of these values. 03:53.320 --> 03:56.890 So we can just simply copy the formula as well here. 03:58.270 --> 04:05.020 So you can see this taking the sum of all these values and then dividing by the count of all these values. 04:05.320 --> 04:07.870 So it comes out to be two fifty five point four. 04:08.890 --> 04:13.900 Now, if I simply take a square root of this value now, this is the standard deviation of these numbers 04:14.230 --> 04:16.500 and the variance will be square root of this. 04:16.510 --> 04:22.630 So I can simplify the square root and of this particular number. 04:22.960 --> 04:25.110 So it comes out to be fifteen point nine. 04:25.900 --> 04:31.780 So the mean for this num these numbers will be twenty point for the standard deviation comes out to 04:31.780 --> 04:36.810 be two fifty five point four, and the variance comes out to be fifteen point ninety. 04:39.190 --> 04:41.770 Now, this is how we solve it by hand. 04:44.080 --> 04:53.290 Now, let us try to solve this and let's try to find out how we can find the solution to this using 04:53.290 --> 04:53.620 byte. 04:58.060 --> 05:03.490 So here I have simply created a list of the numbers which we were given in the question, and I have 05:03.490 --> 05:08.620 created a data frame out of it, creating a data frame is simple in nature, and it provides a lot of 05:08.620 --> 05:10.240 functions we can use easily. 05:10.570 --> 05:12.580 So I've created into a data frame. 05:12.970 --> 05:17.700 And now let view the data in a plot. 05:18.400 --> 05:20.820 So for that, you can simply say deer. 05:21.430 --> 05:25.630 You can see Pted dot data frame signifies a creation of a data. 05:26.800 --> 05:32.450 And yet I've given the column name as the F, the name of the data frame which we have created. 05:32.470 --> 05:40.690 So if I want to check the values so I can simplicity of both E and here, I can see all the values which 05:40.690 --> 05:41.290 we have given. 05:42.190 --> 05:52.270 Now, for that, if I want to plot these values, I can simply see the tornado plot and what these values 05:52.270 --> 05:52.690 voters. 05:54.410 --> 05:56.570 So here you can see these are the values which we. 05:59.660 --> 06:05.120 Now, further, if we want to create a histogram, we can simply instead of seeing plot thickens, maybe 06:05.120 --> 06:06.170 a first aid or test. 06:16.310 --> 06:17.480 This is the histogram. 06:17.480 --> 06:26.960 So you can see that the values are usually between zero and 20, and then that is a few values which 06:26.960 --> 06:27.880 are above 60. 06:28.790 --> 06:34.760 Next, we will go ahead and create a density plot for a better visualization so we can do the same thing 06:34.760 --> 06:38.510 and simply say density. 06:40.820 --> 06:42.530 It will give us a density block. 06:44.810 --> 06:45.110 Sorry. 06:50.090 --> 06:51.950 So this will give us identity plot. 06:52.880 --> 06:57.440 So here you can see the maximum values on No.20. 06:59.690 --> 07:03.490 And you can see the data is kind of normal still here. 07:03.500 --> 07:10.010 But after that, we have these values which are extra here, which makes this data a little skewed also. 07:11.360 --> 07:17.360 So let us go further and check the minimum, maximum mean median mode for this so we can simply say 07:17.360 --> 07:21.830 this is not a dog. 07:24.040 --> 07:28.040 Meaning that if we have seen this also, 07:32.180 --> 07:33.800 I copy this entire thing. 07:34.400 --> 07:37.910 What I can show you everything here, Max. 07:39.030 --> 07:39.040 I 07:42.560 --> 07:43.250 mean, 07:46.490 --> 07:48.680 then we'll see the median. 07:53.470 --> 07:58.400 But then let's also see the standard deviation antiquarians. 08:08.240 --> 08:12.290 So you can see the min value is four. 08:12.470 --> 08:14.000 Max is 66. 08:14.660 --> 08:16.610 Min is 20. 08:16.640 --> 08:18.650 Median is 16. 08:19.190 --> 08:22.100 The standard deviation is sixteen point three nine. 08:22.100 --> 08:24.490 And the median is to sixty eight point eight. 08:27.100 --> 08:30.520 If you want to see the more we can view the mood also. 08:37.780 --> 08:42.010 So there are three months, then 12 and 15. 08:44.830 --> 08:50.320 Further, if you want, we can view the skewness and doses of this as well. 08:51.160 --> 09:07.510 So let us find that as want to simply say, Dawn, you were skewness and not good for purposes. 09:08.740 --> 09:18.220 So here you can see that the skewness is one point nine six and the closest is three point seven two, 09:18.550 --> 09:22.450 which simply shows that there is skewness in the data. 09:24.110 --> 09:29.430 Now, because the causes is greater than three. 09:29.870 --> 09:38.720 We can simply say that this is left to go dig in nature that is which is clearly visible, that it is 09:38.720 --> 09:52.410 having a very slim peak, and the values and the edge in the fields are also left in the. 09:56.210 --> 10:02.630 So this is how you can simply find out, I mean, we didn't move minimax and everything that you want 10:03.140 --> 10:04.520 using Python. 10:04.820 --> 10:07.610 And just by using a single function. 10:07.820 --> 10:13.940 So this is not this overly complicated python makes it very simple for you to solving this. 10:15.240 --> 10:21.350 Now, there are a few things which we need to solve, whether we will be solving a few more questions 10:21.620 --> 10:28.310 so that you can learn how we can deal with data, with just presenting different forms to us. 10:28.610 --> 10:32.600 We might not always have data, which is as simple as this. 10:33.080 --> 10:33.560 Yes. 10:33.980 --> 10:42.020 There are a large number of rules when there are in sort of 20, if there are even one million or 100 10:42.020 --> 10:43.850 million, no matter what the number is. 10:44.090 --> 10:50.330 You can use the same function and find out the mean million more than all these enderlin lenses. 10:50.690 --> 10:55.550 But the only difference is if the data is given in some other way. 10:55.580 --> 11:01.250 So we need to learn how to handle the day that is given in some other way, no matter how large it is. 11:01.880 --> 11:04.460 It will still be as simple as this. 11:05.480 --> 11:11.870 So let's go ahead and have a look at another type of questions so that you can get what I'm trying to 11:11.870 --> 11:12.200 see. 11:14.750 --> 11:17.450 Now, let us solve this particular question. 11:17.750 --> 11:24.140 Now, if you see the difference between what the questions here, we had all the scores in hand. 11:24.260 --> 11:25.760 These are straightforward. 11:26.120 --> 11:27.760 We have the scores directly. 11:27.770 --> 11:32.270 So if we want to calculate the mean, it is simple in nature, we will simply find the sum of all the 11:32.270 --> 11:36.710 values and found of all the values and lower division for them. 11:37.550 --> 11:44.660 But then we have to find out the mean that we have scored and the frequency. 11:45.080 --> 11:47.420 Then it will be slightly different. 11:48.170 --> 11:58.580 You can see that the scores are not just 10, 15, 20, 17, but there are five students who have scored 11:58.580 --> 12:04.850 them, 20 for students who have scored 15, 20 children to have scored 20. 12:05.360 --> 12:07.940 So we need to handle it in a different way. 12:08.390 --> 12:15.050 Now, I give you some time, you can pause the video and try to solve this, I think, around how we 12:15.050 --> 12:16.730 can solve this kind of question. 12:16.730 --> 12:17.250 We have here. 12:17.270 --> 12:19.460 We have the score and the frequency. 12:19.790 --> 12:27.110 So the number of data points, which we have, the number of rows which we have is not actually the 12:28.430 --> 12:33.970 number of students which we have, but the number of students are given separately. 12:33.980 --> 12:40.610 So the number of students will be five plus twenty four plus 12 plus 12 plus extra 16 plus twenty one 12:41.000 --> 12:42.530 plus sixty six platform. 12:43.130 --> 12:50.270 So this is the number of students and the score for each student will be, say, five students will 12:50.270 --> 12:57.410 have been 24 students will have scored 15 to Astrid's will have scored 20 and so on. 12:58.760 --> 13:01.370 So let's pause the video for some time. 13:01.370 --> 13:03.080 Try solving it at your own. 13:04.120 --> 13:08.570 Think around it and then you can pause the video for resolution. 13:11.840 --> 13:13.520 Now, let us solve this problem. 13:14.120 --> 13:22.700 Now, when we want to see how many store how much force rooms have got, the total score for these students 13:22.700 --> 13:26.690 will be there will be five students who will have scored then. 13:27.020 --> 13:29.960 So the score for these five students will be 50. 13:30.800 --> 13:36.320 Then for 24 students who have scored 15, the total score would be 360. 13:36.950 --> 13:41.240 For 12 students who have scored 20, the total score would be 240. 13:41.480 --> 13:47.780 So this is basically then multiplied by five fifteen, multiplied by twenty four, twenty multiplied 13:47.780 --> 13:48.280 by 20. 13:49.070 --> 13:56.220 So this gives us the scores for each of basically the combined score for all the. 13:57.260 --> 14:04.610 Now we can take the sum of all of these values, which are product of school frequency, to get the 14:04.630 --> 14:10.160 total school, to get the combined score for all the students that we have. 14:11.210 --> 14:18.050 Now, what is the total number of students that we have for the number of students will be five plus 14:18.050 --> 14:24.890 24, last 12 plus twenty one plus twenty twelve plus explosive, six plus four. 14:25.550 --> 14:30.290 So if we add all of these values, you can see this is the cumulative frequency. 14:30.560 --> 14:36.500 So for five it is five, five plus twenty four comes out to be twenty nine five plus twenty four plus 14:36.500 --> 14:38.450 twelve comes out to be forty one. 14:38.900 --> 14:40.890 Some of these is sixty two. 14:40.920 --> 14:43.820 Some of then twelve is seventy four times one. 14:44.060 --> 14:47.720 So the total number of students that we have is one sixty eight. 14:51.050 --> 14:55.060 And the sum of all the scores will be sum of all. 14:55.150 --> 14:59.290 These numbers, which we have yet 50 plus 360 plus to 40 in all of this. 15:01.390 --> 15:10.840 So if we find out the mean, the mean will be some of all the scores divided by the number of students. 15:11.260 --> 15:17.020 So some of all schools will be what it will be, the sum of scores multiplied by the frequency. 15:17.440 --> 15:20.380 So 50 plus 360 plus 240. 15:20.390 --> 15:26.240 This some of all of these values will be four, two, three, nine, divided by the number of students. 15:26.320 --> 15:28.810 What is the number of students, the number of student? 15:28.810 --> 15:33.550 Does the sum of all the frequencies which comes out will be one sixty eight. 15:33.820 --> 15:39.820 So the means for all of these students is actually twenty five point two three. 15:40.720 --> 15:43.810 So this is the means for all of these students. 15:48.690 --> 15:56.310 Now, if you want to find out the median score, then the median score will be a lot different. 15:57.030 --> 15:58.800 How do we find out the median scored? 15:58.800 --> 16:07.080 The median score will be the score, the middle most scored of these scores, which we have now, the 16:07.080 --> 16:08.130 middle score. 16:08.160 --> 16:13.980 You cannot find out directly from here, but you will have to find out the score of the middle, most 16:14.160 --> 16:16.470 stringent in the sorted order. 16:16.770 --> 16:19.680 So it will be half of one sixty eight. 16:20.340 --> 16:22.230 Now, what is half of 168? 16:22.230 --> 16:27.000 Half of 168, is it before 168? 16:27.000 --> 16:28.440 Divided by two is 84. 16:28.770 --> 16:34.440 Now, where do we get the cumulative frequency as a before it is here? 16:37.020 --> 16:42.280 I scored 27, so I scored 27. 16:42.300 --> 16:46.140 The cumulative frequency is around 80, 84. 16:46.320 --> 16:51.720 So the median score is 27. 16:52.080 --> 16:55.170 While the mean is twenty five. 16:55.260 --> 17:02.460 So you can clearly see how the values are spread out, how it is very different. 17:02.460 --> 17:09.120 If you consider me and median, if you consider median, you get the middle most value. 17:09.390 --> 17:16.260 While when you're trying to find out the mean, you get the value, which is an average value of value 17:16.500 --> 17:24.360 is of the words, though, if is not impacted, which is actually impacted by the outliers. 17:27.910 --> 17:35.980 So let's go back now, let's solve a little question here now considered here this question where we 17:35.980 --> 17:39.670 have the asymptotes instead of the score itself. 17:40.120 --> 17:46.300 So here I had the exact score, which is the mean given distribution. 17:46.300 --> 17:49.750 So we have then 15 dwin like this. 17:49.750 --> 17:50.700 We have the numbers. 17:50.710 --> 17:57.150 But now what we have is we have these mean of we have the class interval. 17:57.160 --> 18:05.020 So we don't know the exact scores of these students, but we do know that the scores are ranging between 18:05.020 --> 18:08.590 zero and eight, eight and 16, 16 and when differential. 18:09.130 --> 18:10.920 So we have a class in Berkeley. 18:11.300 --> 18:16.150 Now, when we have class interval, the calculation somewhat remains the same. 18:16.600 --> 18:21.430 But you will have to make slight changes to the approach which you are following. 18:21.880 --> 18:24.130 Then we are given class interval. 18:24.580 --> 18:29.410 You will not be given the class interval mean, but you will have to calculate the class interval. 18:30.370 --> 18:34.930 So I have calculated the class interval mean for you in advance. 18:35.350 --> 18:38.560 But now it is completely up to you how you solve this question. 18:39.190 --> 18:46.420 So it is somewhat in the same terms of the last question, but you just need to get the understanding 18:46.420 --> 18:48.190 what we are doing and why they're are doing it. 18:48.490 --> 18:52.870 So just try this particular question and try to find out the mean value for this. 18:53.440 --> 18:58.570 You can also find out the standard deviation and variance and all of the matrices. 18:58.870 --> 18:59.230 Right. 18:59.440 --> 19:02.260 That is an additional practice which you can do. 19:02.440 --> 19:06.040 But the main question here is, if you want to find out the mean, how would you do that? 19:06.310 --> 19:11.650 So you can pause the video and then find out the values you can unbossed to see the solution. 19:13.600 --> 19:15.970 Now, let us look at the solution. 19:16.330 --> 19:24.820 So here I have copied the class interval and the respective values for, you know, we just converted 19:24.820 --> 19:25.570 this into. 19:31.580 --> 19:37.760 So I have converted this into the glass in Deauville form, and I have gone through the glass in Deauville 19:37.760 --> 19:38.450 mean for you. 19:38.960 --> 19:40.700 So this is the interval mean. 19:41.090 --> 19:47.480 So when we were talking about the propria problem there, we had the exact course. 19:47.840 --> 19:50.270 We were calculating based on the exact spot. 19:52.400 --> 19:54.290 So we have the most value. 19:54.560 --> 19:59.540 Now, this model, most value is just the mean of the glass interval. 20:00.020 --> 20:05.660 So this particular value can be the same as a score of which we had earlier. 20:05.900 --> 20:10.760 So in sort of taking the entire value in one value at a time, we're just simply saying that there were 20:10.760 --> 20:16.130 five students who have the score, which is having the mean value of food. 20:16.130 --> 20:21.040 And then we are doing the same calculation which we were doing in the case. 20:21.380 --> 20:23.360 So we just simply find out the product of this. 20:24.080 --> 20:27.200 So this will be this. 20:37.160 --> 20:38.840 So we do the same here. 20:39.590 --> 20:40.850 Now, this is the product. 20:41.210 --> 20:45.650 Now we we need to find out the some of the frequency. 20:45.680 --> 20:49.010 So we need to know the total number of students that we have. 20:49.490 --> 20:50.900 So it will be equal to some 20:58.430 --> 20:59.300 of these. 21:02.090 --> 21:05.480 So basically, these are the total number of students that we have. 21:06.170 --> 21:09.230 And these are these two are a total of the scores. 21:10.130 --> 21:13.730 But frequency and when we add these up, we get the 21:16.790 --> 21:19.310 total score for fifty nine students. 21:19.670 --> 21:28.820 And if you want to find out the mean, we can simplify it down by dividing the sum by the sum of the 21:28.820 --> 21:29.630 frequency. 21:31.190 --> 21:39.290 So what did we do, B, for each class in Doval, we multiplied it with the frequency to get the score 21:39.290 --> 21:41.330 for that particular frequency. 21:41.330 --> 21:46.250 That is five students high school as four. 21:46.340 --> 21:51.860 So we multiplied it to get the score for our total school for that five students. 21:52.130 --> 21:55.340 And similarly, for 10 students, the class interval was 12. 21:55.640 --> 22:00.380 So these 10 school student scored on an average around 12. 22:00.680 --> 22:04.970 So that is why we say 120 is the total score for the student and so on. 22:05.270 --> 22:08.540 So this is the score, but the frequency. 22:10.250 --> 22:13.750 And when we are these up, we get one, four, six, eight. 22:13.760 --> 22:16.880 That is a total school for all these orders. 22:17.270 --> 22:22.730 And these all students are nothing but fifty nine in number, which we got by adding the frequencies 22:22.730 --> 22:23.240 together. 22:23.720 --> 22:30.380 And when we divide the total score by total number of students, which is the normal formula for me, 22:30.810 --> 22:37.130 the guilty by means court for this particular class. 22:38.420 --> 22:41.810 So this is how we solve that particular problem. 22:42.470 --> 22:49.230 In case you faced similar kind of problem, in case of data frames, or even if you have a huge data 22:49.310 --> 22:58.910 there, you have this kind of problem, you can simply find out the frequency and use similar approach 22:59.210 --> 23:00.500 on your data frames. 23:01.130 --> 23:04.250 Let's go ahead and learn inferential statistics. 23:04.550 --> 23:11.230 And once we are going through the influential statistics, we will pick up different problems. 23:11.240 --> 23:12.980 We will pick up different data sets. 23:13.310 --> 23:20.480 And you can apply these methods on that particular dataset to find out the mean median, more outages 23:20.480 --> 23:25.250 and all the values so that you get a handle on how you solve these problems. 23:25.850 --> 23:31.010 So the problems will be slightly more difficult in case of inflation statistics. 23:31.310 --> 23:39.500 So that is why it is important to have a clear knowledge of descriptive statistics so that you can understand 23:39.500 --> 23:41.870 what is going on in influential, sarcastic.