 Hello, I welcome you all once again to my channel Explore Education, I am Dr. Rashmi Singh, Assistant Professor, Department of Education, Assistant Kanna Girls 2D College, University of Alhava. Nowadays, we are discussing and trying to complete the concept of educational statistics and the concepts over and under. So at this time, I am going to discuss with you Cartosis and Skewness earlier. I have already discussed the concept of NPC that is Normal Probability Curve and the concept of Cartosis and Skewness comes under NPC. In earlier lecture 2, I have discussed a brief about Cartosis and Skewness, but it is a different concept and questions have been asked from this very concept, so I have discussed it here also. Okay, so the lecture will be in bilingual mode and it must be useful for all of these students. NPC. You listen to the old lecture, what is the normal probability curve of NPC and your whole statistics is based on the normal probability curve, every time we say that if we follow the normal distribution, then it is like this, it is like this, what is the mean median mode, when is the mean median mode equal, so when you have to listen to the old lecture, if you have forgotten, then the symmetrical NPC, when it is completely symmetrical, that is, if you take it from the middle, then it is mirror image of the other, so Skewness and Cartosis are not there, when they are unsurmountable, when they are disturbed, then the concept of Skewness and Cartosis is added, its Hindi, then it is the same as Tirchha Paan and so on, so you read it with Skewness and Cartosis , there is no problem, so what are you saying, what is the meaning of Skewness and Cartosis, what is the meaning of Skewness and Cartosis, what is the meaning of Skewness and Cartosis, and in the last lecture, I covered the Skewness and Cartosis, but I was thinking a little more detail on the MAMD level, so I am covering it again, so what is Skewness, Skewness means lack of symmetry, as soon as your NPC's curve becomes unsurmountable, Skewness will be created, Tirchha Paan will come, it will be different from one side, in statistics, a distribution is called symmetric, if me, median and mode coincide, it is said that in the statistics, statistics are established, so in the statistics, there is only one dimension, when the medium, the middle and the middle are all in one place, coincide, otherwise the distribution becomes asymmetric, and as soon as they change their mind, your dimension becomes unsurmountable, so how is the name given on it, what is the meaning of it, there is a name given, when it will be negatively skewed, when it will be positively skewed, you will have to give your name, then you go inside it, so it is said that if the right tail is longer, look, we are taking this from here, so this is right,and this is left, everyone knows, so if the right tail is longer, look at this, if the middle is this, then this is in his right, and if he is in the middle portion, he is in his left, so he is saying that when the right tail is longer, this tail is small, and this tail is long, so if If the right tail is longer, we get a positively skewed distribution. It is said that when its right tail becomes long, then you call it positively skewed. Similarly, when the left tail becomes long, then you call it negatively skewed. So, this is only its name, you have to remember and understand. So, this also can be asked, what does it say when the right tail is longer? Positively skewed, there is no symmetry or negatively skewed. It is very simple, but it can be asked. So, you should know. Then, when there is a positively skewed distribution, then there is a bigger median and a bigger mean for it. Similarly, when the left tail is longer, then it is upside down. There is a bigger median and a bigger mode for it. You can see it. So, this also can be asked, when there is a bigger median and a bigger mean for it, then what is it? Is it positively skewed or negatively skewed? So, you should know. Because as soon as it becomes your sum-mit curve, the mean, median and mode will be the same. In all three NPCs, the mean is equal to median is equal to mode. But normally, we do not get the sum-mit curve of the NPC. You will get some skewness or cuts in it. Then, the example of the symmetrical curve, positive skewed curve, negative skewed curve are given as follows. Symmetry. See, you can see it. I forgot to tell you. See, it is sum-mit. This is the mean, this is the median and this is the mode. This is sum-mit. As soon as it becomes your sum-mit curve, if its right tail will be long, then you will say that it is sum-mit curve. If its left tail will be long, then you will say that it is sum-mit curve. What is sum-mit curve in sum-mit curve? That the mean is bigger than the median and the mean is bigger than the median. What is negatively skewed? The mean is bigger than the median and the mean is bigger than the median. Okay. Now, there are ways to get rid of it. Carl Pearson has a lot of statistics. And he has explained his formula very easily. Carl Pearson's coefficient of skewness. If we can get rid of it, then how much is the value of the skewness? He said that if you know the mean, median and the standard deviation from the three modes, then you can get the skewness. How can you get it? He said that the formula for skewness is mean minus mode upon standard deviation. Remove the mode from the mean and run away from the standard deviation. The value of this coefficient would be zero in a symmetrical distribution. If we are getting the skewness, then as soon as we get the sum-mit curve, then what will be the skewness? So, he said that the value of the skewness is zero in a symmetrical distribution. If the mean is greater than the mode, the coefficient of skewness would be positive otherwise negative. We have studied positive or negative. And Carl Pearson's skewness can be plus or minus one. As if all the skewness can be plus or minus one. Their value cannot be greater than that. And if the mode is not well defined, we use the formula. He said that if the mode is known, then we can run away from the mean and run away from the standard deviation. But if the mode is unknown, then what will the median run away from? If the skewness is equal to the median is equal to three times and then run away from the standard deviation, then this is it. So, these are the easy formulas. You can ask these formulas. You can ask the formula-based numerical and competitive examinations. You can ask the MCQ-based questions. Because it is small. Then Kelly also said that when can you get the coefficient of skewness? If you have given the percentile or the decile number, then how will we get the skewness? We have read all the percentile deciles. If you write it properly, then it should come down from P to 90. But it takes a lot of time. So, you should understand that this is the percentile. So, the coefficient of skewness proposed by Kelly is based on percentile and decile. He said that if you know P90, P50, P10, that is, 90th percentile, 50th percentile, and 10th percentile, then you can get the skewness. You can ask the formula- S is equal to 90th percentile, 50th percentile, and the formula will be P90 minus 2 into P50 plus P into 10 upon P90 minus P10. You won't be asked this much, but you should know that the two most popular formulas to get skewness are Carl Pearson's, which is based on the mean, median, modal, standard deviation, and Kelly's, which is based on percentile or decile. That's it. Then comes the concept of cartosis. If we have the knowledge of the results of central tendency, which we have, in addition to these measures, we need to know another measure to get the complete idea about the shape of the distribution which can be studied with the help of cartosis. They are saying that if you know the measure of central tendency, skewness, then you can't know the whole way about the pattern, whereas if you don't know the shape of it, then we know the shape of cartosis. And what did Professor Carl Pearson say? Convexity of a curve. What is the value of a curve? What is the value of a curve? So, we are getting to know about the oil. How much time is there? How much is the lift? How much is the height? What is the shape of the bell? We are getting to know about the cartosis. The measure of flatness. How flat is the distribution? So, the degree of cartosis of the distribution is measured relative to the rate of a normal curve. The curves with greater peakedness than the normal curve is called leptocurtic. The curves which are more flat are called platicurtic. And the normal curve is called mesocurtic. As it was, it is not skewed. It is positively skewed and negatively skewed. Similarly, it is said that if your curve is becoming normal, then you will call it mesocurtic. But if it is more flat, as you can understand from the diagram, then it is called platicurtic. And if its peak is higher, i.e. its base is less, then it is called leptocurtic. This is your curve. This is your normal curve. So, this is mesocurtic. This is platicurtic. It is a little flat. That is why it is called platicurtic. Because the height is less. So, this is platicurtic. And this is leptocurtic. That is why it is called leptocurtic. This is the concept of cartosis. What is all this? Kaal Pearson's measure of cartosis. When you make it, it doesn't show. This is what it shows. Kaal Pearson also told us how to remove cartosis. So, he said, if you see now all these questions won't go to you. But at least you have to know the formula. There is no problem. So, he is saying beta 2. For beta cartosis, we will remove mu 4 upon mu 2 whole square. So, mu 2 the power 4. mu 2 the power 4 upon mu 2 the power 2. mu 2 the power 4 upon mu 2 whole square. So, this can be asked like this. Who was the leptocurtic? whose curve was higher. So, he is saying, if curves which are very high repeat have the value of beta 2 greater than 3. So, if you are given the value of beta 2 that is more than 3. And if you ask how will the curve be. Will it be mesocurtic or leptocurtic or platicurtic. You should know that when the value of beta 2 is more than 3. Similarly, mesocurtic when the value of beta 2 is equal to 3 then mesocurtic. And when the value of beta 2 is less than 3 then platicurtic. You can ask only conceptual questions. So that you know what is the concept of leptocurtic and platicurtic. If the value of beta 2 is equal to 3 then mesocurtic. If the value of beta 2 is greater than 3 then leptocurtic. If the value of beta 2 is greater than 3 then the purposa is nothing but nothing. The characteristic of a frequency distribution that a certain symmetry about the mean is called skewness. When we tell about the suckers of meaning if you do, then we tell about skewness. When purposa tells about the relative pointedness of the standard bell curve. The bell is pointedness. If it is more than pointedness then leptocurtic. If it is less than pointedness then platicurtic. It is defined by the frequency distribution. Skewness is an indicator of lack of symmetry i.e. skewness sammiti ki baat karega ki dono tarab jo daya aur baya issa hai, wo unequal hai central point ke isaap se, jabki kurtosis ke baata hai ki peak humari jada uchi hai ya flat hai with respect to the probability distribution. To ek sammiti ki baat kara aur ek shikhar ki baat kara hai. Skewness shows how much and in which direction the values deviate from the mean. In contrast, kurtosis explains how tall and sharp the central peak is. Skewness batata hai ki mean se dono dishaun mein jo data hai wo kitna vichlan kar raha hai, ke right mein vichlan kar raha hai, left mein vichlan kar raha hai. Jabki kurtosis ke baata hai ki, humari jo central peak hai, wo kitni tall hai, kitni sharp hai. To ye aapta kurtosis aur skewness mein difference ho kya agar push leh jaya, ye aapta push leh ye right short notes about how do you define, kya, how will you differentiate between kurtosis and skewness. So, thank you and don't forget to like and subscribe my channel Explore Education. I have done it from my side.