WEBVTT 00:02.290 --> 00:07.240 Now the next thing which we need to understand, is the chiefs of distributions. 00:08.270 --> 00:15.880 Now a data distribution shows all the possible values of the data and how when each value occurs. 00:20.200 --> 00:22.000 So what does of distribution? 00:22.180 --> 00:28.150 So let's say we have this particular data which is three, four, five, seven, eight, eight, nine, 00:28.150 --> 00:31.810 11, 12, 14, 15, 17, 18, 19, 19. 00:32.110 --> 00:38.190 So what we do here is we like this on a graph. 00:39.760 --> 00:42.310 And we try to create a call out of. 00:44.070 --> 00:51.930 So when three has one value and then four has one value, these values will have just a constant value 00:52.230 --> 00:55.890 and eight, because it has a higher number of values. 00:56.100 --> 00:59.700 The code will go up a little and then come down. 00:59.700 --> 01:02.880 The nine has one value, any living has one value and so on. 01:04.910 --> 01:05.450 So. 01:07.450 --> 01:10.360 These are the different type of distributions which we have. 01:11.290 --> 01:20.260 The normal distributed mean and median and mode are all equal and therefore are all appropriate measures 01:20.260 --> 01:22.690 of central tendency for skewed. 01:22.930 --> 01:26.790 The median may be a more appropriate measure of synchronous demands. 01:28.640 --> 01:31.040 So we have the bell shaped echo. 01:31.400 --> 01:38.330 So initially the smaller values have low values, low number of occurrences, and then the number of 01:38.330 --> 01:42.320 occurrences actually increase and then they go down again. 01:42.710 --> 01:47.420 It could be something like, let's say height of students in a class. 01:47.690 --> 01:54.860 So there would be less number of students with low height and less number of students with very high 01:54.860 --> 01:55.190 height. 01:55.700 --> 02:02.030 But then average height would be constant for the students it would bring in, you know, smaller number 02:02.030 --> 02:04.220 would mean a middle number. 02:05.740 --> 02:10.240 This is called the Bell Sheeple, which is also the normal distribution. 02:11.020 --> 02:17.050 Then there could be a triangular distribution, there could be a uniform distribution that all the values 02:17.050 --> 02:18.850 have seen the multiple sentences. 02:19.420 --> 02:21.490 Then there is the reverse GC. 02:21.760 --> 02:24.010 GC, right skewed. 02:24.850 --> 02:32.230 Right skewed because it is kind of stretched out and skewed out towards the right hand side. 02:33.010 --> 02:37.510 This is left skewed because it is stretched out towards the left hand side. 02:38.620 --> 02:42.790 Bimodal, which has two modes. 02:43.240 --> 02:43.770 Which is it? 02:43.780 --> 02:50.620 Which is it has two tips to it and multimodal, which has multiple things to it. 02:52.980 --> 03:00.300 Now for normally distributed data, which is basically this kind of data, the mean median and mode 03:00.600 --> 03:01.560 unseen. 03:03.010 --> 03:09.250 So what all of these mean median and what are appropriate measures of centers? 03:09.250 --> 03:15.340 And it's why even we talk about the left skewed or right skewed the mean value. 03:17.210 --> 03:21.230 And the mood value will be different from each other. 03:21.440 --> 03:25.310 So median will be a more appropriate measure. 03:25.340 --> 03:26.810 We'll see how that happens. 03:27.050 --> 03:32.400 But for now, you can understand that median will be a more appropriate measure of central tendency. 03:34.200 --> 03:36.330 Now let us look at normal distribution. 03:37.510 --> 03:45.010 So a normal distribution, sometimes called as the bagel, is a distribution that occurs naturally in 03:45.010 --> 03:46.180 many situations. 03:46.870 --> 03:50.770 For example, the BALTO is seen in scores of settlements. 03:51.520 --> 03:57.310 So when we are talking about schools of students, the bulk of the students will, for the average, 03:57.430 --> 03:58.300 see value. 03:58.930 --> 04:04.720 Basically, there would be a lot of students who will scored average value. 04:04.900 --> 04:11.200 While there will be a smaller number of Syrians who will score, be or B and there will be a very small 04:11.200 --> 04:14.170 number of students who will be scoring an F one in eight. 04:15.010 --> 04:19.160 So this will create a distribution which will resemble the double. 04:20.230 --> 04:22.480 America is symmetrical in nature. 04:22.840 --> 04:27.850 And half of the D doesn't fall on the left side of the mean and half of the data will fall on the right 04:27.850 --> 04:28.360 side of the. 04:30.020 --> 04:33.060 And many groups will follow this type of fight. 04:34.350 --> 04:38.880 So this is a highly used distribution, the normal distribution. 04:39.240 --> 04:42.690 So let us see some characteristics of the vehicle. 04:43.020 --> 04:44.520 It is created on the bottom. 04:44.520 --> 04:46.710 He does mean and standard deviation. 04:48.470 --> 04:50.090 And it can be followed. 04:51.270 --> 04:52.710 For various purposes. 04:53.010 --> 04:55.380 LAKE Let us see scholarship distribution. 04:55.770 --> 04:58.190 So let us say we have this medical. 04:59.410 --> 05:00.580 This is the makeup. 05:01.030 --> 05:04.240 And in this makeup, we have this kind of a distribution. 05:04.450 --> 05:12.130 So the most number of screens will have the C rating and then there will be fewer students who will 05:12.130 --> 05:19.630 have to be A, B or B, and there will be a very small number of strings we got. 05:20.140 --> 05:24.640 Who would have got anything or everything right now? 05:24.730 --> 05:27.100 Let us say we want to distribute scholarship. 05:28.150 --> 05:36.340 Then what we can do is we can so you get all the students on the basis of the topmost ratings. 05:36.760 --> 05:44.710 So this has a distribution where the middle most, 80 of which is the mean value plus one standard deviation 05:44.710 --> 05:46.600 and minus one standard deviation. 05:46.600 --> 05:51.900 The area between this month's spray has 68.27% of the beta. 05:53.250 --> 06:01.710 While the meme plus y is standard deviation, I'm the mean minus twice standard deviation. 06:01.950 --> 06:12.030 This entire area has 95% of the entire data and mean minus three standard deviation and mean plus three. 06:12.030 --> 06:15.690 Standard deviation has 99.73% of the data. 06:16.290 --> 06:25.050 So what we can do is we can give the scholarship to any student who has scored more than plus standard 06:25.050 --> 06:25.650 deviation. 06:27.010 --> 06:31.780 Or let's say we want to fire people from the organization. 06:32.620 --> 06:41.830 Then we can put the people from a rating less than mean minus the standard deviation and do the. 06:43.590 --> 06:48.060 One of the things on where we can monitor the performance of the people at work. 06:50.840 --> 06:57.050 So the bellicose can be followed for various focuses like scholarship distribution, finding the best 06:57.050 --> 07:01.940 performers or the worst performers, or finding out the segment of a data. 07:05.940 --> 07:07.410 Now what is for doses? 07:08.610 --> 07:17.250 Gold doses is a statistical measure that defines how heavily the fields of our distribution differ from 07:17.250 --> 07:19.140 the themes of normal distribution. 07:19.470 --> 07:23.480 So we have this particular distribution and it has this same. 07:24.470 --> 07:24.790 Right. 07:25.100 --> 07:29.510 This deal is like a normal this deal frozen. 07:29.870 --> 07:37.370 Now, if the deal is highly extended or if the deal is not extended, it is a very small deal. 07:37.610 --> 07:42.680 So if you want to understand how the deal is, then we can use good doses for that. 07:44.300 --> 07:51.080 So Caduceus identify as whether the feel of the garden given distribution contains extreme values or 07:51.080 --> 07:51.350 not. 07:53.790 --> 07:56.100 So these are the types of producers. 07:56.310 --> 07:58.150 One is liptak a talk. 07:59.350 --> 08:01.210 We're just having a. 08:03.390 --> 08:12.810 Similar number of values in the go, and it is having a more number of values in the middle values. 08:13.260 --> 08:16.950 So in this, the middle most values will have a very high. 08:19.300 --> 08:23.200 While in case of normal distribution, it is just a normal distribution. 08:23.770 --> 08:30.270 And this is Lidegaard, which has a very large number of values in their veins. 08:32.360 --> 08:36.910 And the little convict has very few values in the state. 08:40.300 --> 08:42.340 Now let us discuss about skewness. 08:43.580 --> 08:50.630 We saw this is the image of the skewness we had left skewed and we had the right skewed. 08:51.440 --> 08:53.360 So let us discuss about the skewness. 08:53.960 --> 09:00.650 So skewness refers to the distortion or asymmetry in a symmetrical vesicle or a normal distribution 09:00.650 --> 09:01.700 in a set of data. 09:02.000 --> 09:05.450 If the curve is shifted towards the left or to the right. 09:06.800 --> 09:14.150 In this sad twist to the stillness can be quantified as a representation of the extent to which a given 09:14.150 --> 09:16.670 distribution varies from the normal distribution. 09:16.940 --> 09:22.910 So we have a normal distribution and we want to see how much this normal distribution has been pulled 09:22.910 --> 09:24.890 towards the right or the left inside. 09:25.160 --> 09:29.240 We calculate this using skewness a normal distribution. 09:29.240 --> 09:30.800 We have skewness zero. 09:32.720 --> 09:40.310 So here we have negatively skewed, normal, skewed or positively skewed a normal distribution has no 09:40.310 --> 09:40.760 skew. 09:40.970 --> 09:45.110 So for this, the mean median and mode will be at the same value. 09:46.510 --> 09:49.060 And this is a perfectly symmetrical distribution. 09:49.840 --> 09:55.270 When we have the negatively skewed, it is skewed towards the negative towards the left. 09:56.080 --> 10:00.970 And here we have the positively skewed where it is skewed towards the right hand side. 10:01.630 --> 10:09.730 So when we have the negatively skewed distribution, so here the mode will be higher than the median 10:10.150 --> 10:13.390 and the median will be higher than the mean value. 10:14.310 --> 10:22.110 Why in case of positively skewed, the mean will be greater than the median and the median will be greater 10:22.110 --> 10:23.490 than the more divided. 10:30.590 --> 10:36.560 Now the next thing which we need to talk about is correlation and obedience. 10:37.280 --> 10:39.350 This is a very important topic. 10:40.360 --> 10:49.030 So both the measures they measure the relationship and the dependency between two variables. 10:49.900 --> 10:52.290 So let's see, we have two variables. 10:52.300 --> 10:56.500 One is age of a person and another is the income of the person. 10:57.190 --> 11:02.890 So in an ideal situation, as the age of the person will increase the. 11:03.860 --> 11:06.260 Income of the portion will also increase. 11:07.250 --> 11:14.150 So here there is a positive relationship between the age and the income. 11:14.900 --> 11:15.590 Why? 11:15.800 --> 11:17.240 When we talk about. 11:18.450 --> 11:26.460 The age and the health of the person as the age of the person will increase, the health will deteriorate. 11:27.450 --> 11:29.490 So what are these measures? 11:29.490 --> 11:31.230 Correlation and obedience. 11:31.500 --> 11:35.760 They measure the relationship and dependency between two variables. 11:35.760 --> 11:42.150 In the two variables are dependent on each other or if they are changing together or not. 11:42.870 --> 11:49.440 Covariance indicates the direction of a linear relationship between the variables, so equal medians 11:49.440 --> 11:55.440 will be giving if the values are changing towards positive direction or they are changing towards the 11:55.440 --> 11:55.880 negative. 11:55.890 --> 12:00.630 That action and correlation will give the direction also. 12:00.810 --> 12:04.710 And along with that it will also give the strength of the relationship. 12:05.040 --> 12:11.550 If the values are very highly dependent on each other and they are strongly changing together, or that 12:11.550 --> 12:17.370 is a very minor relationship between the change in the values dependent on each of other. 12:18.540 --> 12:26.820 So here you can see that we have these dual values and here the correlation coefficient has a values 12:26.820 --> 12:31.320 0.9996, which is very, very high value. 12:31.590 --> 12:36.510 So here there is a strong was too lenient correlation. 12:36.840 --> 12:41.100 So these values are changing together and they're changing very strongly. 12:42.260 --> 12:42.670 Okay. 12:42.860 --> 12:44.630 Positive that way. 12:44.630 --> 12:46.730 Here the value is negative. 12:46.730 --> 12:47.680 Z 2.19. 12:47.690 --> 12:52.640 So it is a strong negative negative because it has a negative sign. 12:52.910 --> 12:56.360 So when one value increases, the other value decreases. 12:57.390 --> 13:05.550 And here in strong positive relationship, when one value increases, the other value also increases. 13:06.660 --> 13:12.170 And if the value would have been close to zero, which means that the values I have a weak relationship 13:12.180 --> 13:12.600 with meaning. 13:13.350 --> 13:15.300 So if the value is lower. 13:16.710 --> 13:20.000 It is 0.64 and it is 2.99. 13:20.220 --> 13:23.460 So a lower value means that they have a weak relationship. 13:24.090 --> 13:31.260 Strong relationship is depicted by a higher value, close to one or close to minus one. 13:31.800 --> 13:40.230 While a weak value would be closer to 0.5 or something like if the value is very close to zero. 13:40.470 --> 13:44.640 This will mean that there is no linear relationship between these two values. 13:46.430 --> 13:52.820 So here at -0.58, it means that there is a negative relationship, but it is weak. 13:53.830 --> 13:57.700 Here the value the relationship value is 0.64. 13:57.700 --> 14:02.740 So the there is a negative, positive relationship, but it is a weak relationship. 14:04.630 --> 14:08.590 So this is about the descriptive statistics. 14:09.430 --> 14:09.760 Thank you.