 Hello, I welcome you all once again to my channel explore education. I am Dr. Rasmussen, assistant professor, department of education, SS Kanna girls degree college, University of Allahabad. And in the series of discussing various issues on educational statistics, this time I am going to discuss with you all the concept of quartile deviation and standard deviation. Earlier I have discussed with you the measures of central tendency and how to compute mean, median and mode and measures of variability too. This time the concept of quartile deviation and standard deviation and in further videos I will discuss how to compute quartile and standard deviation. So, the lecture may be in bilingual mode and it must be useful for your conceptual understanding for various competitive teaching examinations as well as for your general BA MA and professional BA DEMED courses. So, let's start quartile deviation. Hindi meh bolin to chathur thansh vichallan, you know. But we have done that measures of variability measures of dispersion prakir nan ke mape or vichallan sheeltha ke mape. So, we have to know that central tendency. I tell you mean, median mode. I tell you an aspect. I tell you a thing like this. What is the possibility of the eyes around the central tendency. But how are the eyes different from each other? How is the difference? This is not We have to look at the results of variability for this. As discussed in the last video, both the eyes can be the same. But their distribution, their precision, their range can vary a lot. So, we should know that the mass of the eyes is different from the rest of the eyes. This is the deviation. So, we should know that there are two very important deviations. Quartile deviation and standard deviation. That is, Jatulthanj-Vichilan and Manak-Vichilan. So, first of all, we know Jatulthanj-Vichilan. What is quartile deviation? Quartile deviation is a measure. It is a kind of map that depends on the relatively stable central portion of a distribution. It depends on which. It is a map that is relatively stable central portion of a distribution. Similarly, the central portion, which is relatively stable, depends on that. Because the ends are generally extreme and outlier. According to Garrett. The book of Garrett's statistics is very important and very good. So, Garrett says that quartile deviation is half the scale distance between 75th, 75th and 25th percent in a frequency distribution. Quartile deviation is Jatulthanj-Vichilan. It is 1.25 percent or 1.4 percent. But the beginning of 1.4 percent is not the end of 1.4 percent. In fact, the middle 50th percent is the half of the quartile deviation. That is, half the scale distance between. That is, the beginning of 1 percent is 1 percent. If you divide it into 100 parts in your opinion, it is said that 25th, then 50th, then 75th, then 25th and 75th percent is the middle part of the quartile deviation. It is said that the entire data is divided into four equal parts. If you divide it into four equal parts, then what will happen to each part? 25th percent will be the value. According to Guilford, the semi-interquartile range is one half of the range of the middle 50 percent of the cases. That is, it is called SIQR, semi-interquartile range. That is, the half of the middle 50 percent cases is semi-interquartile range. That means, what is this quartile deviation? That is, semi-interquartile range is equal to quartile deviation. On the basis of ever definitions, it can be said that quartile deviation is half the distance between Q1 and Q3. That is, when your 25th is called Q1, similarly, when you reach 50th, then Q2 will be reached. When you reach 75th, then Q3 will be reached. So, if you divide Q1 from Q3 to Q2, then your quartile deviation will come. This is the same as IQR and semi-interquartile range. There is an interquartile range, that is, Q3-Q1. That is, Q3 is divided by 75th from 25th to 75th. That is, your interquartile deviation. And if you divide it by half, then the semi-interquartile range is half. Like the circle, the semi-circle is the same. So, what is the interquartile range? The range computed for the middle 50 percent of the distribution is the interquartile range. And upper quartile and lower quartile is used to compute IQR. That is, we consider Q1 and Q3 as IQR. And Q3, this is Q3-Q1 and IQR is not affected by extreme values. That is why extreme values do not affect IQR. Because we have taken the middle part. We have not taken the beginning and end part. Similarly, if we divide Q3-Q1 by half, then our semi-interquartile range will be the same. Half of the IQR is called as semi-interquartile range. SIQR is also called as quartile deviation. And QD, the formula for QD is equal to Q3-Q1 upon 2. That is, if we divide the interquartile range by half, then the semi-interquartile range will be the same quartile deviation. So, what is the quartile deviation? It is an absolute measure of this person. And it is expressed in the same unit as this course. When we were studying this person's measure, we had to study that there are two types of dispersion. Absolute measure and relative measure. Absolute measure where you have to find the actual amount. And relative, when you take out its 100, then who will always come in the 10th grade? The one who is called as coefficient of. That is, the amount of its amount, how many percent is its 100. So, the 100th grade will always come in the 10th grade. So, quartile deviation is an absolute measure of this person. So, what are the properties of quartile deviation? It is closely related to the median. See, what is the median? It is a part of the average. So, they are saying that your quartile deviation is much more than the median. They are responsive to the number of scores lying below it rather than to the exact positions. And Q1 and Q3 are defined in the same unit. The median and quartile deviation have common properties. They say that the average and quartile deviation are very similar. Both median and quartile deviation are not affected by extreme values. Both the maps are extreme. It does not depend on the different maps. In a symmetrical distribution, the two quartiles Q1 and Q3 are at equal distance from the median. And Q1 is equal to Q3 minus median. It is said that if you are completely symmetrical in the NPC distribution, then the Q1 and Q3 are at equal distance. So, the Q1 and Q2 and Q3 are like this. So, Q1 is equal to Q3 minus and Q2 is equal to the median. Q2 is equal to 50% of the average. So, you can see the median instead. Thus, like median, quartile deviation covers exactly 50% of observed values in the data. In other words, like Mathika, which is known as Chaturthansh Vichlan, covers exactly 50% of the average. In normal distribution, quartile deviation is called the Probable Error or PE. So, we are saying that, what is Chaturthansh Vichlan called as Probable Error? That means, the probability is true T. If the distribution is open class, if our distribution is open-ended, that means, we don't know from 0. It is said that it starts from less than 10. And the last number is more than 80. So, it is open-ended. So, in this way, if the distribution is open class and quartile deviation is the only measure of variability that is reasonable to compute. If it is open-ended, then only quartile deviation is possible. In an asymmetric or skewed distribution, we have studied that, when the NPC is not symmetrical, then it can be asymmetrical in two ways. So, skewness and kurtosis. So, we are saying that if asymmetry is asymmetrical, it is not equal. If there is no mean, median mode, then q1 and q3 are not equal from q2 or median. So, q1 and q3 are not equal from q2 to median. In such a distribution, the median of the IQR moves towards the skewed day. In this way, the skewed, the skewed tail, the degree and direction of skewness can be assessed from quartile deviation in the relative distance between q1 and q3. If you divide it into four parts, then the first 25% is q1, q2 is 50, that is the median, and q3 is q4 is the last two parts. So, what is your fourth equation, it is not affected by extreme scores. q3 minus q1 is called interquartile range, and when you measure it, then it is called severe interquartile range, and this is the quartile deviation. Okay. Then, the merits and demilitaries of what are the advantages and disadvantages of it. The merits are that quartile deviation is a better measure of this person than range, because it takes into account 50% of the data. The biggest of the range, the biggest of the range, the biggest of the range, the biggest of the range, the biggest of the range, the biggest of the range, that is the highest value and the lowest value. Then, secondly, quartile deviation is not affected by extreme errors since it does not consider 25% data from the beginning and 25% from the end of data. They are saying that why is extreme score not affected? Because the beginning 25% and the end 25% are taking the middle 50%. Then lastly, quartile deviation is the only measure of this person which can be distributed from the frequency distribution with open-end class. Then, what are the demerits? The value of quartile deviation is based on the middle 50% value, but it is not based on all the observations. You can also say this in the minus point that we are taking only 50% of the data and we are not looking at the rest of the 50%. Thus, it is not regarded as a stable result of dispersality. That is why, which is not a stable distribution which is not a stable distribution. Then, the value of quartile deviation is affected by sampling fluctuation. That is, the value of Vigilance is also affected by the fluctuation of sampling. So, this is the minus point. Now, on this standard deviation, the standard deviation is the most popular term in statistics. The term standard deviation was first used in writing by Carl Pearson in 1898. In 1884, Carl Pearson first used Manak Vigilance in his book. The standard deviation of population is marked by sigma and that for its sample is small s. So, he is saying that if you generally have mu in formula, it is used for standard deviation and it is used for sample phase. The standard deviation indicates the average of distance of all the scores around the mean. Standard deviation is the meaning of Manak Vigilance means that all the scores around the mean are in the mean and what we are doing is that it removes all the variables. It is the positive square root of the mean of standard square deviations of all the scores from the mean. When we take the mean in the middle, there are some branches at the top and some branches at the bottom, some branches at the bottom, some branches at the bottom, some branches at the bottom. So, the formula for removing the mean deviation is what it does. It is used for the minus sign. So, one way of doing it is mathematical blunder, that is why the standard deviation is used in a different way. He said that he does not combine all the variables. When you combine all the variables, the minus square root will also be in the plus. Then, we will get the same value of the mean deviation, which is the biggest mistake that we do not pay attention to the round-chins. So, to solve the same mistake, we have the concept of the minus sign. There are some round-chins and some round-chins. So, we will get the square root of the mean deviation. Now, we do not have to get the square root of the mean deviation, but we have agreed that the square root of the mean deviation is double. The standard deviation tells us how much the mean deviation is low. If the standard deviation is low, then that means if the standard deviation is low, it means that the data is close to the mean deviation. But if the standard deviation is high, the data is spread out over a large range of values, that is, the data is very tested. If we get a low SD, but if we get a high SD, that means the data is very varied. If the difference between mean and standard deviation is very large, then the theory being tested probably needs to be revised. They are saying that if the difference between the mean and standard deviation is very large, then the theory being tested probably needs to be revised. They are saying that the difference between the mean and standard deviation is very large. The mean with smaller standard deviation is more reliable than the mean with larger standard deviation. A smaller SD shows the homogeneity of the data. This data is proof of the data, that is, the data is very small. The value of standard deviation is based on every observation in the set of data is used in further statistical analysis. This means that the standard deviation is used in more statistical analysis. The merits of this are that it is widely used because it is the best measure of variation. We did not make any mistake in this, we first made a plus and then made a minus. It is based on all the observations of the data. It is based on all the accurate estimate of population parameter compared with other measures of variation. This is the most effective information of the population. This is very less affected by the fluctuation of sampling. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to calculate combined SD. It is also possible to is the most appropriate method to compare variability of two, variability of two or more distributions. So, this is how to compare variability of two or more distributions. So, this is how to compare variability of two or more distributions. So, this is how to compare variability of two or more distributions. So, this is how to compare variability of two or more distributions. So, this is how to compare variability of two or more distributions. So, in this video, I have discussed with you all the concept of quartile and standard deviation. So, thank you and don't forget to like and subscribe my channel Explore Education.