Efficient Formula Revision for Statistics

Hi everyone, how are you doing? Sir, everything is fine, everything is fine. Friends, I hope all of you are preparing very well. And to put four stars on this preparation, I am bringing the formula revision series in the very wonderful way of my STATS. Friends, I had promised you that I will give you some notes during the exam time in which it will be very easy to revise the formula of STATS. Let's start. First of all, understand about this sheet. Listen, guys, the first thing I have given you is the formula revision sheet of STATS. Here. First of all, before writing this sheet, let's assume that there is only one sheet, take out 5 to 10 printouts of it, as per your provision. At regular interval, you have to fill this sheet so that the formula is retained for a long time. Guys, try to establish the link. See, the formula should not be written like this. If it is like this, it will be like this. As soon as I will make you write, make you make the linkage, you try to establish the linkage with the formula, establish the link of the formula with the concepts and questions. This is a very important area. Add practice questions. If possible, if you think that today I am going to do DPP, then first fill the sheet and do M.O.C.T.M.O.D. DPP. Fill the sheet of correlation, do the question bank of correlation. So whenever you are doing something, try to add some question bank. But this is not mandatory. It's like just if you have the time, then go for it. Come on friends, we are going to start the revision. Sir, here I will give you some basic tricks. How did I make this sheet? This is your concept handbook, which I have done all the questions and questions at the same place. It also has a summarized version. Designed one chapter in one page. So that you don't have to fill the whole sheet with me for the first time. And you have to take out 10-15 printouts of it. I have submitted you the whole stats of 6-7 pages in this form. Whenever you are empty, don't do revision again and again. You fill this sheet again and again. The more you fill the sheet, the more you establish with linkage. You believe that your whole stats will come in your hand. What is the field of revision you need to do? Guys, today for the first time see this sheet M.O.C.T After M.O.C.T guys, M.O.D is in one page After that friends, comes the core relation analysis The whole count is in one page Regression comes, regression since you have tension The way you have studied Similarly, formula sheet is there Aim 1, Aim 2 and Aim 3 Guys, we will fill everything After this, we have put questions here These questions will help you a lot in your revision We will cover all the questions Guys, after covering this whole Here I have designed a sheet on common property. We will revise the origin and scale where you make a mistake. Guys, my purpose is not to teach you. I have already taught and done revision. Now DPP is going on. We are just doing extra practice. And with that, I have an important role. I want you to do revision of stats formula. Sir, you can do PY, you can do it yourself. There is no such thing. I will do as much as time I get. But DPP is going on. It is as good as solving the same thing. So, how can I help you until you practice? I am tired of addressing this question. Guys, now let's start. Please, let's not waste time. Sir, the formula of mean. If there is an individual series, Sir, the formula of mean is, Aman sir, If there is an individual series, So, mean is summation of all the observations total divided by number of observations. Sir, it is discrete. Discrete means frequency is given with observation. Sir, our formula will be same. So, summation of FIXI upon N Sir, here the N is ours. Aman sir, here this is summation of FI. You can use two pens. Sir, send to Arya. Brother, buy any book of PYQ and start solving. Oh man, now please focus on this. You will disrupt it completely and leave it. Still I will send it. Come on. Guys, please, please, please. Continuous series. Summation of... F I X I upon n. But sir, it is a continuous series. Here class interval will be given. So here friends, here X I is midpoint. Guys, X I is midpoint. Come on. Guys, done. See, now I have here partition value friends. I have here mean, decil, percentile and quartile not bifurcated separately. Whenever you are filling, fill any one thing. Either fill median, or fill partition value. or fill, fill percentile and decile. So for today, let's do one thing. Let's not fill median in first revision. Everyone remembers median. Let's fill this partition value today for the quartile. Let's fill it for quartiles. Sir, this is an individual series. So there are 3 quartiles. So Kn into bracket is N plus 1 by 4th observation. Guys, do write this word observation. It gives you clarity that the outcome that will come from here The place where it is placed is our relevant quartile. Suppose its outcome is 3rd. So the place where it is placed is your quartile. There are 3 quartiles Q1, Q2, Q3. If you want to take out 2, then Q2 will be there. Here, instead of Kn, put 2. If you want to take out Q3, then put 3. If you want to take out Q1, then put 1 instead of Kn. Sir, suppose its outcome is in decimal. So guys, what you will do? For example, its outcome is here. For example, I will take an example. For example, suppose your outcome is 6.2. So guys, what we will do? Aman sir, we will do like this. 6th observation. Write 6th observation plus 0.2 times. Next one. 7th observation minus guys, 6th observation. Guys, 7th observation minus 6th observation. Sir, done. This is discrete series. Guys, in discrete series, same formula will be used. Sir, how can this happen? If frequency is given, same formula will be used. Guys, same formula will be used. Believe me. Kn into bracket. N plus 1 by 4th observation. Sir, what is the difference? How will we get N from summation Fi? Sir, but the interesting thing is, where will we check? Where will we check the outcome? Guys, we will check. Lie down. We will also calculate. Sir, here we have to make cumulative frequency. And check. outcome in CF and here we will check the outcome in cumulative frequency whether it is your number or your decimal wherever it is like, the corresponding observation will be your relevant partition value guys we are done with this Sir if it is continuous series guys write the formula of continuous series what will happen? guys this will be our L plus remember here, Kn N by 4 minus CF preceding Upon f into i. Friends, people say that continuous series is useless. I don't know if it is useful or not. I don't know. All formulas should be remembered. And at least, all the questions done by concept handbook in continuous series, you should remember them. Sir, how to proceed? Sir, how will we proceed in this? Aman sir, how to proceed? How will we proceed on this? I told you, what will be your first step? Your first step will be this. Guys, first step will be calculate. Guys, first step will be calculate. Calculate KnN by 4. Remember, friends? We used to call this mark the area. Mark the area. Guys, now tell me this. Take out KnN by 4. Friends, wherever KnN4 lies, we used to call it median class, quartile, partition value class. The upper cumulative frequency, the relevant frequency of the area marked, its class interval. Friends, if the series is not exclusive, then first do exclusive, then take class interval. Friends, do you remember the whole thing? Yes, yes, yes, guys we are done with. Sir, the formula of MOD, which is the number of observations occurs maximum times. Observation discrete having highest frequency. Friends, for this, the formula of MOD's continuous series becomes very important. Write it yourself and see if you can write the formula of continuous series. Yes sir, the formula of continuous series of mod, guys, LDR, I have written it there also. Mod is equal to guys, L plus FM minus F1 upon 2 FM minus F1 minus F2 into I. Sir, how to proceed? I have not written here. What will be FM? The highest frequency will be our mod class. Guys, FM, highest frequency, above that F1, below that F2, I and nothing else is used in the whole formula. Guys, is this point clear? I am not teaching you the chapter today, I have taught you and also revised it. I have designed a sheet so that you can revise the whole formula again and again. Write it down and establish the linkage. As I am saying, you will find this and that. This will be given in this question and this will be given in that. When you revise such a formula, then the speed of reading and solving the question will improve a lot. Your improvement will be 100%. Friends, should I move ahead? Guys, I am saying move forward. Friends, should I move ahead? Let's start. Sir, in GM, the individual series of frequency is not given. X1 into X2 into X3, all the observations have power 1 upon n. Sir, if you assume that the discrete series of frequency is given, then I had told you a shortcut that all the X observations are 2 and R is 5 times, then write 2 to 5 times and convert it into individual. Don't apply the formula. But still, the formula should be remembered. Please write the formula once. Sir, this formula was our anti log of summation of fi into xi instead of fi into log xi divided by n. Now, friends, we will write the trick of log and anti log up there. I have written it. In some important trips, we will write it there on the yellow page. Guys, we are done with this. Sir, same formula will be copy-paste for continuous. Here, guys, xi will be missing. Class interval will be given. Take out midpoint. The talk is over. Mid point, take out the point, the matter is over. Sir, now let's talk about harmonic mean. Friends, if you have an individual series, guys, if you have an individual series, so n upon 1 upon xy, guys, summation of 1 upon xi. Friends, if you have a continuous, sorry, if you have a discrete series, guys, what will be the formula? Guys, summation of fi, I mean, summation of fi, I will write n here, guys, n upon, Summation of FI upon X. 1 upon X is written because everything was coming once. The more times it was coming, the more times upon X. Friends, we used to calculate this whole thing in decimal. That is why I am establishing linkage. We used to calculate everything in decimal and check the answer in decimal. This is used when we need to compare the ratio. Sorry. Whenever we need to calculate something like this, which is derived from the ratio. Like we have speed, distance upon time. Whenever your units are made up of two things. In that case, you will calculate harmonic mean if the method is not mentioned. Guys, it will have same concept. It is silent because it is institutively. But I will complete this thing. X will be midpoint. Midpoint is taken out and rest whole formula is discrete. That's why I said that mean is this, this and this. Sorry, in all three places of mean, things are same. And here you have memorized both the formulas separately. What is the fun? Forget it. Friends, are you able to write the whole formula with me? Without opening the book? Are you able to write all the formulas today? Yes sir. If you are writing these formulas, then go to sleep peacefully at night and say, I remember everything. I just have to read the question properly, apply the method correctly. Now get yourself out of the zone of fear. Whenever you get scared, pull a sheet and fill it. I had told you in the class that I will do everything for you in free time. I am working on this only. Guys, come on. Sir. Combined, I said combined mean formula, combined partition value and combined harmonic mean concept is not there. Come guys, when combined mean is given as 2 groups, 3 groups and you have to merge both groups to get mean, observation is not known. So here the combined mean formula is x12 bar n1 x1 bar plus n2 x2 bar upon guys n1 plus n2. Sir, Then, Aman sir, you had asked us to do the formula of combined harmonic mean. H1, 2 is equal to N1 plus N2 upon N1 upon H1 plus N2 upon H2. Guys, N1 upon H1 plus N2 upon H2. Sir, in geometric mean, you have never asked us the name of combined geometric mean. I have not asked you any question. Nor has any question been given in your module. But, friends, if I ask you, does the formula of combined geometric mean exist? For example, a theory question has come. Yeah. which one of the following does not have the combined formula? It is of A, GM, and HM. It is not of partition value or mod. So, it is not that GM does not have the formula. The formula is there in our syllabus. So, for completion, I will write the combined formula here. GM12. Friends, the same formula is there. You know, the one of discrete. Anti-log. Guys, there are two series. So, guys, what will be the anti-log of? Summation of F. Guys, just a second. just a second, wait a minute, summation of, guys, just a second, sir, summation of n1, sir, this number of observation will be given here, n1 into log gm1 plus, guys, summation of anti-log of, guys, anti-log of n1, into log gm1 plus n2 into log of gm2 guys divided by n1 plus n2. Guys I want to tell you that if this question comes in the exam which one of the following does not have a combined mean formula then don't think that gm's combined mean formula doesn't exist. It exists. There are no questions in our syllabus. But it exists. Come on guys tell me. Have you written all the major of central tendency formulas in one place? Have you done all of them? Let me move on to the next practice. If you are forgetting anything, then just remember it here and finish it. Next time when you open the sheet, you can write it. Let's move ahead. Guys, relation between mean, median and mod. If the data is symmetric, all the observations are 5, 5, 5, 5, 5. So guys, mean, mod, median, everything will be equal. Here it is written mean is equal to median is equal to mod. Friends, if it is saying that it is positively skewed, then what sign will you put? Guys, it is positively skewed, so mean is greater than median. Guys, if it is saying that it is positively skewed, mean is greater than median is greater than mod guys mean is greater than median is greater than mod or negatively skewed guys mod is greater than median guys mod is greater than median is greater than mean And friends, if it is moderately skewed, then what is the empirical rule? Practical formula. If you know any mean or median, then you can find out the third thing. And the formula was, guys, our mod is equal to 3 times median minus 2 times mean. Guys, minus 2 times mean. Has everyone written it? Here, see, a good theory is revised and your practical part is also revised. If I want to highlight this, then this part is very important from the practical point of view. And this part is important from the point of view of theory. Guys, now, what is the relation between A and GM? If the observations are symmetrical, then all the arithmetic, geometric, and harmonic means will be the same. A is equal to GM is equal to HM. But if it is asymmetric, then sometimes it will not use the word asymmetric. Data are asymmetric. for the set of distinct, different positive numbers for the set of distinct, distinct means asymmetric for the set of distinct positive integer means he mentioned that I am talking about asymmetric all the observations are different, distinct positive numbers so when this happens, Aman sir in this case am is greater than gm is greater than hm but suppose in the question, if the question is silent that data is symmetrical or asymmetrical, the question should not be mentioned. Which one of the following option is true? But the observation is symmetrical, all the observations are same, it is distinct, it should not be mentioned. Guys, in that case, we have to satisfy this too and we have to satisfy this too. So, a condition comes here, friends. am greater than or equal to gm greater than or equal to hm. I had also reminded you of this. Yes, Pooja, very good. But remember, we will use distinct positive words, not asymmetric words. So don't use greater than or equal words. Now we will refer to common property summary. Common property summary. We will do common property summary now. Tell me, we hardly took 15 minutes and I was explaining to you. If you write it yourself, you will not find it useful in 5-6 minutes. Shall we start with the revision of MOD formula now? Friends, are we starting to do the revision of MOD formula now? Tell me. Come on. Friends, along with me, there is an individual series. Guys, if the individual series... Why are there two tables here? If two tables are made by mistake, then there is no need to make it here. There should be only one. This should be only one. I will fix it. Come on. I will fill the sheet with the correct answer and send it to you. Now there are two answers. Listen friends, tell me what is range? Tell me what is the formula of range? Absolute measure or relative measure? Sir, all the observations are given in individual series. Largest interval minus smallest observation. If the frequency is given, then how many times someone comes, I have nothing to do with it. I will ignore the frequency. The formula will be same, L minus S. But friends, consider that it is a continuous series. If the series is continuous, then largest class interval minus smallest class interval minus lowest class interval. I am writing S, so that you can understand. I have used H as Highest Class Interval minus Lowest Class Interval Guys if you want to use the same word then what will be the result? What will be the result? This will be your result Guys Highest Class interval minus lowest class interval. Friends, remember this in continuous. Guys, series is not exclusive. Guys, if series is not exclusive, make exclusive. If series is not exclusive, make exclusive first and then move ahead. Sir, we are done with this. Sir, what is its relative measure? When we have to calculate in percentage, friends, L, guys, L minus S, whatever you have calculated, whatever it is, whatever it is, i.e. Indivolution, Discrete or Continuous, as you have calculated here, using the same information, largest L minus S upon L plus S into 100. And friends, if the quantity is 19, this minus this upon this plus this multiplied by 100. In a way, whatever you have calculated, divide it by total into 100, which is the formula of percentage, favorable upon total into 100. That is what we are looking for here to convert into relative measure. Friends, tell me, tell me the formula of mean deviation. Sir, the formula of mean deviation is, ultimately we satisfy the definition here. Sum of difference of all the observations from their arithmetic mean. Sir, this mean can also be this mean. Sir, how much do all the observations deviate from their measures of central tendency? Sum of all the observations. of that sum of all the division taken from their mean, median and mod. It can be anything, Aman sir. You write here A. We had made a general formula A upon number of observation n. Friends, I had written here that this can be mean, this can be median, or guys this can be mod. And friends, we had done the questions of median and mean in concept handbook. I had written the formula of discrete series here. discrete series formula, take summation of difference and multiply it with fi xi-a guys upon n since frequency is given, so kids know that n will be the summation of fi and there is no big deal friends, here in continuous, same formula will be used guys, if it is continuous just you have to calculate guys, same formula question will not come on this, will not come, will not come But I want to keep your completeness in your mind from your knowledge point of view. Same formula guys. Guys, xi will be equal to midpoint. xi will be equal to midpoint. Guys, is this point clear? And sir, what will be its relative measure? Sir, relative measure will be mean deviation about a divided by a into 100. Aman sir, this means, assume mean deviation about mean. So guys this will be mean deviation about mean. Guys mean deviation about mean upon mean into 100. Means mean deviation about all deviation from median. So mean deviation about median. You know the formula of median. Into 100. Guys is this point clear? Friends did you write both the formulas properly? With my help, without my help. Will you write it always? Yes sir. Come on next formula. Guys quartile. Children tell the children. Sir why you didn't make quartile separately? Aman sir, you made it here, here, here, why didn't you make it here? Friends, to find the quartile deviation, ultimately we have to find Q1, Q2 and Q3. If the series is individual, discrete or continuous, you will have to find the quartiles. And you know the way to find the quartiles, this is the way to find the quartiles. If it is individual, it is discrete, and if it is continuous, it is this. After finding it here, you don't have to do anything. Guys, you have to find the quartile deviation. Guys, quartile deviation is nothing. It is Q3 minus Q1 upon 2. Friends, here you will see in your concept handbook. So, I have written two things in concept handbook. Quartile variation and quartile deviation. Friends, for now, leave quartile variation. He did not consider quartile variation in the book of institute. Guys, so we will apply Q3 minus Q1 upon 2. And friends, what is the relative measure? Q3 minus Q1 upon Q3. plus Q1 multiply by 100. I want you to revise some things whenever you want. You revise with linkage and that is this. Guys listen, ultimately we are doing here also Q3 minus Q1 upon 2 whole divide by, we are doing here also Q3 Q3 minus Q1 upon 2 and here also we are dividing Q3 plus Q1 upon 2. And guys Q3 plus Q1 upon 2 gives us Q2 and this is our median. In short guys if you have given median so double the median and write here that will be your Q3 plus Q1 we have done the question on this so remember this is nothing guys, this divided by 2 is median if median is given then multiply it by 2 and pick up the earth your Q3 plus Q1 will be yours Friends, is this point clear? We have written this in concept handbook very well. If you feel, then see it once and repeat it here and say. There is no need to go to concept handbook again and again. Shall I move ahead, friends? Yes, I am answer. Now let's revise the formula of the standard deviation. Friends, if I remind you two formulas from the individual series. One is direct formula and one is indirect formula. Direct formula says, brother, there is no need to make table. Take under root, summation. X square divided by number of observation minus mean whole square. Guys, indirect method says that this formula is made up of definition. Summation of X minus X bar whole square. We will not take mod, but divided by N Divided by N Under root. Friends, what both formulas I have written. Friends, this formula is more memorable to people. But use is more. That is why I named it direct and I named it indirect. Sir, but if it is discrete series, then there is no change. Friends. you will find the mean according to the discrete series here you put F and here you put F your formula is discrete and there is no one for continuous guys, like there is no one for partition there is no one for formula, continuous always has one method find the mid point after getting the mid point your series is converted into a discrete series then the matter is over sir if I want to write the formula here then I will prefer this formula under root of summation of find the difference square it First multiply it by fi divided by n. And here n is summation of fi. Guys, here same formula. Aman sir, same formula. Guys, how to get xi? Mid point. Friends, now here comes, see below this, I have given 4a, 4b, 4a, 4b and 4c. Major of dispersion is 4, in 4 range of 4, mean deviation is there, quartile deviation is there, standard deviation is there. Guys, we call the square of standard deviation as variance. And friends, its relative measure is coefficient of variance. Remember, relative measure of standard deviation is not the coefficient of standard deviation. Guys, it is coefficient of range, it is coefficient of mean deviation, coefficient of quartile deviation. And we call it as coefficient of, coefficient of, of variance. variance word has come out that's why I told you variance first variance is nothing else, standard deviation and square it, that is the variance. Listen, coefficient of variance its formula is sigma upon mean as you find out, measure of central tendency multiply by 100. Now listen whenever you want data to check the consistency why is it used? This is used to check consistency guys care a more jitra can jitra coefficient of variance come data more consistent data is more consistent yeah the door so you can look at a discus door of the door the away company your company big big a dividend a dividend Nikala television maybe kia jiska coefficient of variance come welcome please dada consistent a pretty variant copy economy Guys, we are done with this. Sir, combined standard deviation. Sir, we remember, we remember, we will write. So, first of all, write with me. After that, you have to write by yourself. Tell me. Sir, n1 sigma 1 square plus n2 sigma 2 square plus n1 d1 square plus n2 d2 square upon amansar n1 plus n2. Children know that n1 is the number of observations in the first group. Sigma 1 is the standard deviation of the first group. Now comes the question of D1 and D2. D1 is the combined mean minus the mean of the first group. D2 is the combined mean minus the mean of the second group. Guys, is this point clear? If combined mean is there, then remember the formula of combined mean. X1 2 bar is equal to N1 X1 bar plus N2 X2 bar upon N1 plus N2. If you feel like doing it, then open the concept handbook next to it. and then hide the answer and then take out the answer in the calculator and that's it and then you will revise it like this one day before the exam here you write the formula and there you see the question here you write the formula and there you see the question that's it guys is this point clear? tell me is this point clear? friends I will move ahead friends everything is clicking everything is clicking I have written it very well if you get confused if you leave something I take assurance that nothing will happen. Guys, in miscellaneous point, I had to remember two shortcuts. What is the mean deviation of first n natural number? Sir, this is our n square minus 1. Guys, n square minus 1 upon 4n. Although standard deviation is under root of n square minus 1 upon 12. Guys, n square minus 1 upon 12. See once, as far as we have written this. Because I have written it wrong once that I will not record it again. So, I want everything to be proper. There should be no problem in clarity. Yes, under root of n square minus 1 upon 12. Sir. We have a ratio of QD, MD and S. Sir, tell me what is that ratio? 10 is 2 guys, that ratio is very important. 10 is 2, 12 is 2, 15. Remember this, first it is QD, then MD and then S. People often read it wrongly. First MD, then QD and then S. It happens because we read MD first while reading. So people think that first it is written MD. No. Guys this ratio belongs to QDMDS not MDQDS. Quartile deviation is to mean deviation is to standard deviation. If you know any one dispersion then you can use this ratio to find out the other dispersion. If you know mean deviation it means you know quartile deviation and standard deviation. If you know standard deviation and you don't know anything then you can use this ratio to find out the remaining two. This is the link to establish and repeat yourself. So now click the question once. Should I move forward? Guys is this point clear? Guys is this point clear? Should I move forward? Common property, come friends, summary, revise through summary. Guys we will revise through summary. I will revise the summary for you. What fun in life, forget it. Guys we are done with the, tell me how many minutes did it take? Do you think that we are revising the formula very effectively? Now there is no burden coming. that I need to change the concept of handbook I have also shortlisted that and given one chapter in one page Guys, we are done with the revision of this Come Aman sir, you will revise the core relation formula, make linkage and free us Guys, shall we start? It was very neat sir, yes I know Guys, let's start. Aman sir, let's start. Sir, we have read four methods to find R. Scatter diagram, Knarl Pearson, Spearman and coefficient of correlation. Guys, CCD, coefficient of concurrent deviation, I have written it wrong, I will change it. Coefficient of concurrent deviation. It will change, don't worry. I will send you updated PDF also, which will come after some corrections. Sir, show the second page. I will show you the second page and now we will start writing it. Sir. In Scatter Diagram, we know that if all the diagrams are increasing by 1, if 1x increases and y increases, then it is a positive correlation. If 1 increases and 2 decreases, then it is a negative correlation. This is what you had written in the form of the diagram. Friends, the more you increase x, the more y increases. The same proportion is increasing. Friends, this is called perfectly positive. Guys, perfectly positive. I am writing this in short, we should understand what we are writing and I know that I have taught you this, so whatever I say will hit your brain Guys, if the one who increased X, Y decreased, X increased from 10, Y decreased from 10 Guys, in the same proportion, there is movement in different directions, perfectly negative Guys, a curvilinear graph is formed, curvilinear graph, curvilinear is called R is equal to 0 In perfectly positive case, r is equal to 1. In perfectly negative case, r is equal to minus 1. Sir, here in positive case, r is greater. Sorry. R's value is from 0 to 1. Guys, in negative case, r's value is from minus 1 to 0. Sir, we are done with this. Is the scatter diagram revised? Is the scatter diagram revised or not? It took 5 minutes. Write it in full. What is the fun in exam? You blank the formula, blank the paper. What is the fun in it? There is no fun in failing you. Sir. Let's see Knarl Pearson. We saw two formulas in Knarl Pearson. When all the observations are given. Remember the first formula, it was written in the concept handbook. Children remember it. Same thing in everyone's language. N summation xy minus summation x. Let's change the pen. N summation xy. minus summation x summation y upon under root of n. Guys, n summation x square minus summation x whole square. Same thing, write y. n y square summation minus summation y whole square. Can you write this formula? Tell me, if the covariance is given, what will happen? If the covariance is given, what will happen? Write. Sir, do we remember the covariance formula? Sir, r is equal to covariance between x and y. Covariance between x and y divided by sigma x into sigma y. What fun if someone does something wrong in the world? Sir, here, our covariance, listen, your mind will go to the exam again and again, sigma x squared. Hey, idiot, that was our regression coefficient. This is talking about correlation coefficient. Done? Tell me, man. I have to write the next one. Shall I start? Yes. Sir. Covariance is discussed. We will write a very large number. We have written a little more and a little less. In the concept handbook. Summation of X minus X bar into Y minus Y bar divided by number of observation. Sir, there is something after seeing this. Not just one thing. That is covariance. Whenever you see this, understand. Question formula has come. Where covariance has to be taken out. And using covariance, there is a formula of regression. and using covariance, we will use coefficient of correlation formula and whatever is there this is the end of the discussion, we will make a chart for this and revise it Sir, we are done with this Spearman's formula, same thing in children's language 1 minus 6, summation di square upon n into bracket n square minus 1 everyone knows what di is, di is whole square of xi minus yi and xi and yi were the rank of the first observation and rank of the second category. Friends, if you have given sales and profit, don't take difference of sales. Take rank of sales and profit. The one who is the most, take first rank. The one who is less, take second rank. The one who is the least, take last rank. Okay? Guys, done? And what was the number of observation? Aman sir, coefficient of concurrent deviation formula. Guys, R is equal to plus minus under root of plus minus 2C minus M upon M. Guys, here C is our number of positive deviation. M is the number of observation. Write it here, guys. This is 1 less. 1 less than the number of observations. I had told you why it happens. I had told you everything. Now I am revising the formula. Number of positive deviation. The matter is over. Sir, when will we take positive? If you get positive by solving this, then both the outside and inside are positive. If 2C-M is solved and negative is there, then here also negative and here also negative. That's it. I explained the logic, why? Because in Maths, it is said that in under root, negative cannot be there. If it is positive, then there is no problem. But if it is negative, then there is a problem. So to make negative positive, inside is negative and outside is also negative. That's it. Guys, is this point clear? Should I move ahead? Friends, answer my questions. Give or not? Friends, should I move ahead? Guys, should I move ahead? Is the revise going well? See, I have already given you the summary chart of the probability. This is the summary of this chapter. I have already done the summary of the probability. When those 15-20 questions were done together in the last, when to think about what, when to think about whom, I have already filled that summary before that. Very good, Naveen. Come. Sir, let's talk about errors. Guys, tell me the formula of Probable Error. Sir, we have written it. We are not waiting for you. The formula of Probable Error is 0.6745 times. Guys, 0.6745 times Standard Error. Guys, now let's talk about Standard Error. So, what is Standard Error? Sir, Standard Error is 1 minus r square upon under root n. Sir, because of this, another jump comes in this formula. 0.6745 multiplied by standard error is 1-r square upon under root n. Now, this r is coefficient of correlation. This n is number of observation. Guys, here we talked about properties. If you take mod of r and take 6 times probable error. If 6 times probable error is more, take r and make it positive. Take 6 times probable error. If this is happening, So guys, your r is significant. And guys, if mod of r is big, guys, sorry, If your R is not significant, and mod of R is greater than 6 times probable error, my answer will be R is significant. Write it again and again. You will never forget it in your life. Sir, we are done with this. correlation of population. Remember? This is a world of knowledge. You should read it. Sir, you can find the probable error. There is a limit from here to here. Guys, there is a limit. R plus minus probable error. If you take R plus, then upper limit. And if you take R minus, then lower limit. From here to here, correlation of population will come. I have asked you a full-fledged question on this. I have asked you all the questions on one question on errors. By writing this formula. Don't just write it. Go and audit there. and you will see that yes, I had to do this and that, but you will not make a calculation mistake, you are mature enough, don't worry. Guys, done with this, shall I move ahead? Let's talk about important property. Guys, here you have to write a practical formula, I have to write a theory formula, theory also, theory question can also come on this. Guys, coefficient of determinant, sir, coefficient of determinant is considered more practical, more used, that is R square. Sir, we call this R square's theoretical formula, sir. It is explained variance, explained variance divided by total variance. Guys, explained variance upon total variance. Sir, coefficient of non-determinant, sir, this is 1 minus R square. And sir, we write this as unexplained variance. guys divided by total variance, done? guys done, sir coefficient of alliation you will remember it as 1-r square for this I have not made you remember any theory point under root of 1-r square and friends here first r square 1-r square coefficient of non-determination if we take its under root then coefficient of alliation guys here we revise in all the forms of correlation analysis tell me is confidence increasing? We are writing the formula without looking at it. We are enjoying it. You are still looking at it, if it is wrong or not. We will write without looking at it. I was sitting in the AC from morning. When I shared the sheet, I had to bring it to my target on one page. So I was sitting in the AC. It took time to design. It will be done. It will be revised in 20 minutes. Give the exam. Fill the log up. It has no stats. I will submit it on the question sheet. Otherwise, blow the notes of Tufaan Bash in 15-20 minutes. The work is over. Guys, let's move forward. Let's revise a long chapter, Regression Analysis. Will you support me? We have to see the common property. Let's move forward. We have to revise it in the next 10 minutes. Regression Analysis. I have written a small part. print out. I will zoom in and show you. In this chapter, our final aim is to estimate the value of one variable. As it is written, find the value of y when x is equal to 3. In this chapter, our aim is to find the value of one variable. When we already know the value of the other variable. This process is called regression analysis. To estimate the value of one variable, when the value of another variable is known, this process is called regression analysis. But to do this, how much God's grace would be there, if we get an equation here. It would be fun. Don't write this. It would be fun. I wish there was an equation like this. 2x plus y is equal to 10. I wish there was an equation like this. So here we would put the value of x and take the value of y. We call it as second aim. Sir, we need equation. So that we can calculate the value of one variable and get another variable. Sir, I wish we could do that. We need, no problem, I will give you regression equation. But the requirement of regression equation is regression coefficient. So friends, here first birth of regression coefficient is there. It is important to remember the formula of regression coefficient. So that you can make the equation. And it is important to remember the formula of equation. So that you can achieve your final aim. You know the value of one variable. and you can estimate the value of the other variable is this revision done? say, by making linkage, do you understand? in this chapter, whole world is mad We don't want to go mad. We don't want to go crazy. We want to establish this linkage and move forward. Friends, can I get some water? I'm a little tired. I don't know why today. 10 minutes. Friends, shall we start? Sir, sir, did you understand? To estimate the value of one variable. We have to estimate the value of one variable when we know the value of the other variable. Sir, for this, we need an equation. Sir, listen. We have two equations y on x and x on y. Sir, when and what should we make? When you want to find the value of y and you know the value of x, then make y on x. And when you want to find the value of x and you know the value of y, then make x on y. Sir, the value of the variable which we know is called independent. And the value which you want to find is dependent. If you want to find the value of y, then y is dependent. If you know the value of x, then it is independent. So that independent, sorry, that dependent and the value of y is known, whose value is known, understand, right sir. Sir, so here, when we will make this equation, when we need to find y, x is known. I am writing in short, sir when will we make this, when we need to find. x. Guys, y is known. Sir, the matter is over. I made a table and understood it. I wrote it in small. Yes. Sir, its general form is y on x. Guys, its general form is y is equal to a plus bx. Now see, if you want to find the value of x, x is equal to a plus by. Sir, when is this called general form? Guys, if you are writing x on y, then this is a general form and if you are writing y on x, then this is a general form. Sir, here we call a and b as regression parameter. Use this formula when a and b value is given or you can find it yourself. If you know the value of a and b, then put here y is equal to a. Suppose a is 2 and b is 3. y is equal to 2 plus 3x. Put here 2 plus 3y. This is x on y and y on x. So, use this formula when you know the value of a and b. or the question has given a way where you can't say a and b take it out and put it the equation is made so here put the value of x to 2 and take the value of y the final aim is this but to achieve this I need the equation sir here we call b as regression coefficient it has another form which we call point form if you want y on x then y minus y bar b y on x bracket x minus x bar we want x on y guys x minus x bar, b, y minus y bar. Sir, here the x bar and y bar is our mean. Sum of all the observations divided by number of observations. Or it can give you. But friends, here to put you will need b. And we call b regression coefficient. Sir, here. B, Y on X can be given. If you put given here and make your own, but you don't give and you have to remove, then you will get aim number 1. And friends, here comes aim number 1. We need equation so that we can, guys, we will write here. Sir, students usually get confused when to apply which formula. Guys, you have to think about the formula according to the information given in the question. Sir, there are three formulas to remove the coefficient. Will you write three formulas with me, guys? Will you write the three formulas with me? Guys, the first formula. Sir, the first formula. If all the observations are given, then the formula that will look like Knahl-Pierson will be used. That is guys, n summation x into y minus summation x into summation y divided by n x square's summation minus summation x's whole square. If the thing is ending at x, So, in all the formulas, in the denominator, it will be x. If it is ending at y, write the formula N summation xy minus summation x into summation y divided by N y square's summation minus summation y's whole square. Sir, think about this formula when you have all the observations given to you or when you have directly given this. For its practice, I have given a question. Find the regression equation. To put the regression equation, you need mean and b. And for b, I have given you all the information. X, Y, this information. So, here I have given you full-fledged question for practice. Listen. First, let's come here. Sir, if we have standard deviation and R, then your formula will be By on X, R, guys, Sigma Y upon Sigma X. And here, it will be R, Sigma X upon Sigma Y. Aman sir, if we have covariance, then covariance between X and Y divided by, guys, X is ending, so standard deviation of X whole square. Here, covariance between X and Y divided by standard deviation of Y whole. square. Friends, have you written the whole formula? You don't think so? You must be thinking that you have designed this chapter in 5 minutes. You are feeling it but believe me, it took me 4 hours to make it. Because you know how I have taught, how will the linkage start in your mind. I didn't want to break that linkage. That's why I designed it the same. I am moving ahead, friends. Now I am moving ahead. Can you promise me to do a question? I will do a big question Guys Let's do regression Guys Get the regression coefficient from these charts Get the regression coefficient I want you to get by on x I am doing revision with a question There are questions in charts and in Maths Get by on x Covariance between x and y Divided by standard deviation of x whole square Covariance is 121 standard deviation of x 15 square guys 15 square 15 into 15 sir this is 225 121 divided by 225 how much you have got 0.53 0.54 i am taking 77 guys b x on y how much will be co variance between x and y divided by standard deviation of y square 121 standard deviation of y is 14 14 square into guys 196 how much is it 121 divided by 196. Guys, how much is it? 0.612. Guys, I am taking 0.62. Yes, guys, we are done. Guys, we are done. What was he saying? Find the regression. Sir, you did not find the regression coefficient. You found the regression. Yes, I did not ask for regression. You found the regression. Done? You can find BX on Y as well as BY on X. You can find whatever you want. Guys, next question. The regression coefficient. Find the regression coefficient. What does it look like after seeing this whole thing? Listen, let's do one thing, let's stop at these questions because I have to revise this chart too. I have to revise this chart too. I had asked you to write this in class by hand. Now I have converted it into a chart. First let's see it completely and then we will go to that question. Listen, let's come. Sir, we have understood the name of this chapter. There are so many small formulas and we keep making up things in our mind. Because of these three formulas, your mind does not have proper linkage and you curse the formula. If you want to make a line, you need to find the co-variance of this and that. To make a line, you need to find this and that. You have a problem in linkage. You are trying to find the formula. Sir, in this chapter, you tell us why we call this chapter as correlation and regression. I told you two practical formulas for this. If you want to make a line, you need to find the co-variance of this and that. you know the regression coefficient, then you can find the correlation coefficient. Plus minus under root of b x on y multiplied by b y on x. Friends, second thing, sir, here we had written two formulas. b y on x is equal to guys r sigma y upon sigma x. And Aman sir, another formula was written. So the b x on y is equal to r. Sigma X upon Sigma Y. Aman sir, it depends on the question data that we will give, we will take out R. Now, many times when you write this formula, you know this, you have to take out this. So, standard deviation will give you. But standard deviation will never give you directly, it will give you information that you can take out. How will it give information, friends? Write here, Sigma X formula. Now, revise. Standard deviation formula. Go to MOD. Sir, in MOD, our formula used to be summation of. x minus x bar whole square divided by n. Sir, the formula of sigma y was under root of summation of y minus y bar whole square divided by n. Sir, is it done? I am making the linkage of the chapter. See, they are revising it. All the formulas that are found along with it are being revised. Sir, two practical points are done. Two theory points were written. Sir, if the value of r is plus minus 1, guys, it means regression lines. If the value of r is plus minus 1, guys, it means regression lines. then lines are identical guys if r is equal to zero guys lines are identical it is used to co-incide and friends if r is zero then lines are perpendicular till you write it again and again you will not remember friends lets move ahead sir here in important highlights you said about unity friends if we assume that one is bigger than one then the other should be smaller than one if this is smaller than one then this will be bigger than one one should be greater than unity and one should be less than unity about sign Sir, either BX on Y BY on XR both will be positive positive or both will be negative negative Sir, using both of them we can get R Sir, if both of them are positive then we take positive If both of them are negative then we take negative If both of them are positive we can conclude from here R will also be positive. And friends, if both are negative, then R will also be negative. It can never be that one is positive and the other is negative. Either both are positive or both are negative. Sir, we know that the regression lines Y on X and X on Y, they intersect at their mean. Intersect at mean. X bar and Y bar. Sir, what do you want to say? Guys, solve. Solve equation simultaneously. The point of intersection is mean. Guys, there is a question on this. Whenever both the lines collide, it collides with mean. If you solve both simultaneously, you will get the value of x and y. That is the mean. Guys. incorrect to correct incorrect to correct if you have given incorrect x on y or incorrect y on x then you have to correct it so the formula is correct b x on y you do reciprocal of incorrect y on x whenever you do reciprocal of incorrect y on x then y on x will give correct x on y and x on y is the reciprocal of incorrect correct b y on x you can write any one but I will write both correct y on x so do 1 upon reciprocal of incorrect b x on y friends, is this point revised? guys, I have also revised important highlights I have written one thing which is theory, practical, you are revising everything guys, is this point clear? friends, come Sir, if we want to know the regression line, how will we do it? We had written three steps. Guys, assume one. Guys, assume any one as x on y, other as y on x. After this, convert it to standard form. Take out b, y on x, b, x on y. you will get R you have taken out standard formula R after this you take out R by applying this formula if your R value is between minus 1 to 1 then your assumption is right or vice versa your assumption is correct or vice versa guys this point is revised did you understand how to write again and again now below this I have given a question I have put a big question on this whenever you revise this 1,2,3,4, revise all these points means revise 50% of the question Guys listen, I have revised all the formulas I have revised all the formulas You can do these questions, all these questions are in your question bank and concept handbook When you do these, you will gain confidence I have said that I am a teacher, I will come to teach you again and again I have taught you, I have called you to practice the formula Guys, should I move ahead? Tell me Come, I have made an important chart. How to think, how you should think about, see, what you should think when you see the following input. Whenever you see this, tell me, who should you remember by looking at this? Who should you remember by looking at this? Tell me. By looking at this, you fool, what will you remember by looking at this? Tejas, if you divide this by n, then you will get covariance. Sir, is codex we remember whose? Knowaranski's Sir how can we divide by n and see this and see this and see this and remember whose? Who should remember this? If this is the input in any question, Sir, I am not able to think. If you click something after seeing this, how will you think? Who should remember this? Yes, standard deviation. Sir, under root of summation of x minus x bar. Sir, divide it by n and add under root. Sigma x is here. Sir, divide it by n and add under root. Sigma y is here. Sigma x and sigma y is here. Covariance is here. So, what is your result? Your result is R. This will give you the order B. Take out whatever you want. Take out whatever you want. Sir, this will click us. Sigma X. After seeing this, it will come to Sigma Y. Friends, if the regression line is given. Listen. This regression line is given. I said that let's assume. I said this is X on Y. What can you find out by seeing this? What can you find out by seeing this? Tell me. Think. The line is of regression line. Sir, very good. Sir, if the regression line is of BX on Y. If you give two regression lines, then you give one BX on Y also. and B Y on X also came out. Friends, if these two are there, tell me, next box, if these two are there, means whose are they? If these two are there, Sir, how, how, how? Write it in standard format, how? Sir, if you are saying X on Y, then X on Y's standard format is X is equal to A plus B Y. Write it in standard format. Kneep X on one side. Minus 5 minus 3 Y. X is equal to minus 5 upon 2 minus 3 upon 2 Y. friends compare this x is equal to a plus by so this is b x on y 3 minus 3 by 2 compare the equation in a standard format and whatever is b will become b I am not getting into this, if I do I will go into teaching my motive is to make you revise the formula and the existence of these two means the existence of r end of the talk Friends, promise me that you will revise these formulas. You will practice these questions. I have asked you to do all these questions. Guys, here we are done with the revision of all the formula of the regression analysis. Will you revise the chapter of the first day of the exam in 10 minutes? I have taught you and made you understand. I cannot stop myself from explaining. What should I do? My attitude is to teach. common property revise, it will take 5 minutes sorry for making you study more guys, let me revise common property guys, let's do one thing let's do MOCT here, it will take 10 minutes 10 minutes, did you do it? 10 minutes, revise it, common property will be left you will study something else, right? whenever you give me 1 hour I will teach you something new, why will you repeat? come Sir, I am not telling you what is a common property. Guys, common property means the origin, change in origin and scale property. M-O-C-T, M-O-D, correlation and regression. It is written in four chapters. Listen, who is affected by origin and who is not. Listen, let's do it. Guys, it will just take 10 minutes. Along with the question, we will revise the question. It has no role without the question. Listen. Friends, I have given you the concept handbook by making pieces of it. Yes, I am just finishing it. Listen friends, Univariant data, Listen friends, Univariant data, Whenever we talk about single variable, Guys, that is called univariant data. Our M.O.C.T and M.O.D. talks about single variant. And on bivariant data, our chapter is correlation and regression analysis, Where two variables are discussed. Listen, Guys, whenever we change the origin or scale, Since there is only one variable, So, we change the original variable x and reflect it with y. How do we reflect it? With y. And since there are two variables here, the one we changed x, we reflect it with u and the one we changed y, we reflect it with v. Guys, did you understand? That's why there are two equations here and one equation here because friends, MOCT and MOD It is a single variable. So, the actual observation of X is represented by changing it from Y to U and Y to V. So, here the standard format is Y is equal to... y is equal to a plus b x. Understand. You have this x is original. Whatever you have multiplied in this, we call it scale. And whatever you have added in this, we call it origin. But friends, here there will be two standard formats. One is the changes you have made in x, which you have represented with u. And the other is the changes you have made in y, which you have represented with v. So here there will be two standard formats. One u is equal to a plus b. bx, v is equal to c plus dy. Listen, again friends, here is the origin, sorry, here is the scale, here is the origin, here in y, you have changed, here is the scale and here is the origin. Understand, many times people get confused, merge this property here. Brother, when you are talking about moct and mont, then this is the standard format, there is only one variable x and we represent the change of x with y. And here we represent the change of x with u, in correlation and regression, we represent the change of y with v. Listen, Sir, the difference between origin and scale is the measure of the measure of the central tendency. But in MOD, the difference is not only in the scale but also in the modulus. So, here the formula is made. First of all, you convert it in the standard format. Y's measure of central tendency is equal to A plus B times X's measure of central tendency. But here the measure of the measure of dispersion does not differ from the origin. Guys, Y's measure of dispersion is equal to guys. mod of B into X the measure of dispersion. Here guys this can be range, this can be quartile deviation, this can be guys standard deviation. But here the common property is not for your variance. Variance is not the part of measure of dispersion. Variance is the part of standard deviation. And this property is for measure of dispersion. This is not for your variance. There is a question on it, it has come, it is your request. Please revise the concept handbook question. Sir, listen. But friends now let's talk about correlation and regression. correlation, neither it differs from origin nor from scale. Guys it differs just from sign of multiplier. I also call it sign of scale. Friends, it does not differ from origin, it differs only from scale. And here we had made a formula, listen guys, B UV is equal to B X on Y. the magnitude will remain the same sin of b multiplied by sin of d now you all know that I have told you the meaning of b and d guys take the sign of x, the coefficient of sin of b and sin of d neither it differs from the origin nor from the scale and here we had written the formula b uv is equal to guys b x on y Multiplier of x divided by multiplier of y. We call it multiplier. Scale. And it makes difference only from scale. Guys, B, V on U. Guys, B, V on U. B, Y on X will be given to you. Guys, multiplier of Y divided by multiplier of X. That's it. Guys, is this point clear? Come to the questions. Guys, is this point clear? I have given you all the common properties at one place. Now, see. I have given you the relation. 2x plus 3y guys. 2x plus 3y is equal to 10. Okay. It is saying what is the mean of x. Guys sorry. And if the mean of x is 2 what is the mean of y. Listen guys. X's mean is 2. What is y mean? First tell me this. Is the mean the measure of central tendency or the measure of dispersion? This will talk about single variable. Single equation. Let's write it in standard format. Do y on one side. 3y is equal to 10 minus 2x. y is equal to 10 minus 2x upon 3 upon 3. Sir, why is it important to write in standard format? So that we can see actually how much origin we have changed in x and how much scale we have changed. Sir, this is the measure of central tendency. It will also differ from origin. It will also differ from scale. So, y measure of central, y range, what did you ask? y mean 10 by 3 a minus b x. How much is x, friends? 2. How much is this? Guys, this is 10 by 3 minus 4 upon 3. Guys, 6 by 3 will come up. Whatever will come, anything can happen. If there is a mistake in the fast, then this will also be 2. Guys, tell me, is this point clear? Guys, is this point clear? But now I have asked you one more thing. If the range of x is 15, what is the range of y? Now, the children know. I am doing it here to save time. Now, the children know that the range is the measure of dispersion. And the measure of dispersion. Here, the difference is not with the origin, but with the scale. That too, how? with positive sign guys so here first of all convert this Sir here is the scale y range is equal to mod of b 2 by 3 will be negative then also take positive into guys range of x, how much range of x have you given? 15 how much is it guys 3 5 15 10 answer is guys 10 Is this point clear? Is this point clear? Summary is revised. Major of MOCT and common property of MOD is revised. Practice is done. Convert to standard format. Major of central tendency and major of origin and scale. Don't take impact of both. And friends, if major of dispersion is there, then only take impact of scale and leave origin. Sir, now let's talk about correlation. Listen guys, here whenever we talk about correlation and regression, two equations will come easily. Because it is bivariant data. It is a bivariant chapter. Okay. Guys, u is u plus 5x is equal to 6. Second, 3y minus 7v is equal to 20. Guys, it is saying that if coefficient of correlation Rxy is 0.58, How much will be uv? Children know that Ruv doesn't matter between origin and scale but it matters with sign Sir, it will still be 0.580 but I have to multiply it with sign but before converting it into sign convert it into standard format How to convert it into standard format of bivariant? Where is the standard format? Sir, do u on one side and v on the other side I did u on one side 6-5x 3y minus 20 is equal to 7v so v is 3 upon 7y minus 20 upon 7 guys here the coefficient of x is negative here the coefficient of y is positive so guys here i will take negative and positive plus minus minus 0.58 so neither it got difference from origin nor it got difference from scale guys see what formula we have written guys we just have to consider the sign of b sign of d Guys just take the sin of x multiplied by sin of y and click quickly. Sin of x is minus, sin of y is plus. Guys 0.5 feet are xy multiplied by sin of x sin of y. That's it. 0.5 feet. Guys, is this point revised? Friends, is this question already point revised? Shall I move ahead? Is this point clear all of you guys? Is this point clear? Yes sir. Come. Regression. Sir, there is a relation between u and v and here u and v are already in standard format. I have given you a regression question y on x. B, guys, I have given you b y on x. How much? 2.4. You have to find out what is b v on u. Sir, b y on x multiplied by multiplier of y divided by multiplier of x. 2.4. Guys, what is multiplier of y? Sir, Y's multiplier is minus 3. Divide. Multiplier of X. X's multiplier is 2. Aman sir, solve this. 2.4 multiplied by 3 divided by 2. Minus 3.6. Minus 3.6. Guys, here we have the answer. Minus 3.6. We are done with this. Friends, here I have made all the common properties, all the formulas, proper linkage. I have revised all the chapters. Guys, we have successfully revised MOCT. We have successfully revised MOD, we have successfully revised correlation and we have successfully revised regression along with the linkage. We have revised the summary of the question and we have revised the common property. Here we are done with the quickest and fastest revision. Take out 5 printouts of this sheet, fill it 5 times, what is the fun of it, then there is no need to revise it. Sir, let's meet. I know your second page. Second page, second page, whatever you want to write. You are talking about this page, right? Second page, take this. Ayush, I will put this on YouTube, Revision. You can refer whenever you want. And all the students who are referring to it on YouTube, I will put the notes on the Telegram channel. Or you can go to the download section of the AKnC the Maths Learning app, and this sheet will always be available, the updated one. Because telegram keeps on running and it makes you lose your mind. I will change the updated notes at any time. So, the app AKnC, the Maths Learning app, its notes and DPP section contains updated notes. If any note is changed, it gets deleted and new notes are updated. Guys, bye bye, take care. Bye bye, take care guys. I hope you do the probability revision. Do something by yourself, my brother. When will I do extra practice? On one side you say sir, do PYQ, sir, do DPP, on the other side you say do revision. Do something yourself, then I will do something new. I will try my best, promise. Okay? Bye bye, bye bye, take care.

Hi everyone, how are you doing? Sir, everything is fine, everything is fine. Friends, I hope all of you are preparing very well.

And to put four stars on this preparation, I am bringing the formula revision series in the very wonderful way of my STATS. Friends, I had promised you that I will give you some notes during the exam time in which it will be very easy to revise the formula of STATS. Let's start. First of all, understand about this sheet. Listen, guys, the first thing I have given you is the formula revision sheet of STATS.

Here. First of all, before writing this sheet, let's assume that there is only one sheet, take out 5 to 10 printouts of it, as per your provision. At regular interval, you have to fill this sheet so that the formula is retained for a long time.

Guys, try to establish the link. See, the formula should not be written like this. If it is like this, it will be like this. As soon as I will make you write, make you make the linkage, you try to establish the linkage with the formula, establish the link of the formula with the concepts and questions. This is a very important area.

Add practice questions. If possible, if you think that today I am going to do DPP, then first fill the sheet and do M.O.C.T.M.O.D. DPP. Fill the sheet of correlation, do the question bank of correlation.

So whenever you are doing something, try to add some question bank. But this is not mandatory. It's like just if you have the time, then go for it. Come on friends, we are going to start the revision.

Sir, here I will give you some basic tricks. How did I make this sheet? This is your concept handbook, which I have done all the questions and questions at the same place. It also has a summarized version.

Designed one chapter in one page. So that you don't have to fill the whole sheet with me for the first time. And you have to take out 10-15 printouts of it.

I have submitted you the whole stats of 6-7 pages in this form. Whenever you are empty, don't do revision again and again. You fill this sheet again and again.

The more you fill the sheet, the more you establish with linkage. You believe that your whole stats will come in your hand. What is the field of revision you need to do? Guys, today for the first time see this sheet M.O.C.T After M.O.C.T guys, M.O.D is in one page After that friends, comes the core relation analysis The whole count is in one page Regression comes, regression since you have tension The way you have studied Similarly, formula sheet is there Aim 1, Aim 2 and Aim 3 Guys, we will fill everything After this, we have put questions here These questions will help you a lot in your revision We will cover all the questions Guys, after covering this whole Here I have designed a sheet on common property.

We will revise the origin and scale where you make a mistake. Guys, my purpose is not to teach you. I have already taught and done revision. Now DPP is going on. We are just doing extra practice.

And with that, I have an important role. I want you to do revision of stats formula. Sir, you can do PY, you can do it yourself. There is no such thing.

I will do as much as time I get. But DPP is going on. It is as good as solving the same thing. So, how can I help you until you practice?

I am tired of addressing this question. Guys, now let's start. Please, let's not waste time.

Sir, the formula of mean. If there is an individual series, Sir, the formula of mean is, Aman sir, If there is an individual series, So, mean is summation of all the observations total divided by number of observations. Sir, it is discrete.

Discrete means frequency is given with observation. Sir, our formula will be same. So, summation of FIXI upon N Sir, here the N is ours. Aman sir, here this is summation of FI. You can use two pens.

Sir, send to Arya. Brother, buy any book of PYQ and start solving. Oh man, now please focus on this.

You will disrupt it completely and leave it. Still I will send it. Come on.

Guys, please, please, please. Continuous series. Summation of... F I X I upon n. But sir, it is a continuous series.

Here class interval will be given. So here friends, here X I is midpoint. Guys, X I is midpoint.

Come on. Guys, done. See, now I have here partition value friends. I have here mean, decil, percentile and quartile not bifurcated separately. Whenever you are filling, fill any one thing.

Either fill median, or fill partition value. or fill, fill percentile and decile. So for today, let's do one thing. Let's not fill median in first revision. Everyone remembers median.

Let's fill this partition value today for the quartile. Let's fill it for quartiles. Sir, this is an individual series. So there are 3 quartiles.

So Kn into bracket is N plus 1 by 4th observation. Guys, do write this word observation. It gives you clarity that the outcome that will come from here The place where it is placed is our relevant quartile. Suppose its outcome is 3rd. So the place where it is placed is your quartile.

There are 3 quartiles Q1, Q2, Q3. If you want to take out 2, then Q2 will be there. Here, instead of Kn, put 2. If you want to take out Q3, then put 3. If you want to take out Q1, then put 1 instead of Kn.

Sir, suppose its outcome is in decimal. So guys, what you will do? For example, its outcome is here. For example, I will take an example. For example, suppose your outcome is 6.2.

So guys, what we will do? Aman sir, we will do like this. 6th observation. Write 6th observation plus 0.2 times.

Next one. 7th observation minus guys, 6th observation. Guys, 7th observation minus 6th observation.

Sir, done. This is discrete series. Guys, in discrete series, same formula will be used.

Sir, how can this happen? If frequency is given, same formula will be used. Guys, same formula will be used.

Believe me. Kn into bracket. N plus 1 by 4th observation.

Sir, what is the difference? How will we get N from summation Fi? Sir, but the interesting thing is, where will we check?

Where will we check the outcome? Guys, we will check. Lie down. We will also calculate.

Sir, here we have to make cumulative frequency. And check. outcome in CF and here we will check the outcome in cumulative frequency whether it is your number or your decimal wherever it is like, the corresponding observation will be your relevant partition value guys we are done with this Sir if it is continuous series guys write the formula of continuous series what will happen? guys this will be our L plus remember here, Kn N by 4 minus CF preceding Upon f into i.

Friends, people say that continuous series is useless. I don't know if it is useful or not. I don't know. All formulas should be remembered.

And at least, all the questions done by concept handbook in continuous series, you should remember them. Sir, how to proceed? Sir, how will we proceed in this? Aman sir, how to proceed?

How will we proceed on this? I told you, what will be your first step? Your first step will be this.

Guys, first step will be calculate. Guys, first step will be calculate. Calculate KnN by 4. Remember, friends? We used to call this mark the area. Mark the area.

Guys, now tell me this. Take out KnN by 4. Friends, wherever KnN4 lies, we used to call it median class, quartile, partition value class. The upper cumulative frequency, the relevant frequency of the area marked, its class interval.

Friends, if the series is not exclusive, then first do exclusive, then take class interval. Friends, do you remember the whole thing? Yes, yes, yes, guys we are done with.

Sir, the formula of MOD, which is the number of observations occurs maximum times. Observation discrete having highest frequency. Friends, for this, the formula of MOD's continuous series becomes very important.

Write it yourself and see if you can write the formula of continuous series. Yes sir, the formula of continuous series of mod, guys, LDR, I have written it there also. Mod is equal to guys, L plus FM minus F1 upon 2 FM minus F1 minus F2 into I. Sir, how to proceed? I have not written here.

What will be FM? The highest frequency will be our mod class. Guys, FM, highest frequency, above that F1, below that F2, I and nothing else is used in the whole formula.

Guys, is this point clear? I am not teaching you the chapter today, I have taught you and also revised it. I have designed a sheet so that you can revise the whole formula again and again. Write it down and establish the linkage.

As I am saying, you will find this and that. This will be given in this question and this will be given in that. When you revise such a formula, then the speed of reading and solving the question will improve a lot. Your improvement will be 100%. Friends, should I move ahead?

Guys, I am saying move forward. Friends, should I move ahead? Let's start. Sir, in GM, the individual series of frequency is not given.

X1 into X2 into X3, all the observations have power 1 upon n. Sir, if you assume that the discrete series of frequency is given, then I had told you a shortcut that all the X observations are 2 and R is 5 times, then write 2 to 5 times and convert it into individual. Don't apply the formula.

But still, the formula should be remembered. Please write the formula once. Sir, this formula was our anti log of summation of fi into xi instead of fi into log xi divided by n. Now, friends, we will write the trick of log and anti log up there.

I have written it. In some important trips, we will write it there on the yellow page. Guys, we are done with this. Sir, same formula will be copy-paste for continuous.

Here, guys, xi will be missing. Class interval will be given. Take out midpoint.

The talk is over. Mid point, take out the point, the matter is over. Sir, now let's talk about harmonic mean.

Friends, if you have an individual series, guys, if you have an individual series, so n upon 1 upon xy, guys, summation of 1 upon xi. Friends, if you have a continuous, sorry, if you have a discrete series, guys, what will be the formula? Guys, summation of fi, I mean, summation of fi, I will write n here, guys, n upon, Summation of FI upon X.

1 upon X is written because everything was coming once. The more times it was coming, the more times upon X. Friends, we used to calculate this whole thing in decimal.

That is why I am establishing linkage. We used to calculate everything in decimal and check the answer in decimal. This is used when we need to compare the ratio. Sorry.

Whenever we need to calculate something like this, which is derived from the ratio. Like we have speed, distance upon time. Whenever your units are made up of two things.

In that case, you will calculate harmonic mean if the method is not mentioned. Guys, it will have same concept. It is silent because it is institutively. But I will complete this thing. X will be midpoint.

Midpoint is taken out and rest whole formula is discrete. That's why I said that mean is this, this and this. Sorry, in all three places of mean, things are same.

And here you have memorized both the formulas separately. What is the fun? Forget it.

Friends, are you able to write the whole formula with me? Without opening the book? Are you able to write all the formulas today? Yes sir. If you are writing these formulas, then go to sleep peacefully at night and say, I remember everything.

I just have to read the question properly, apply the method correctly. Now get yourself out of the zone of fear. Whenever you get scared, pull a sheet and fill it. I had told you in the class that I will do everything for you in free time.

I am working on this only. Guys, come on. Sir.

Combined, I said combined mean formula, combined partition value and combined harmonic mean concept is not there. Come guys, when combined mean is given as 2 groups, 3 groups and you have to merge both groups to get mean, observation is not known. So here the combined mean formula is x12 bar n1 x1 bar plus n2 x2 bar upon guys n1 plus n2. Sir, Then, Aman sir, you had asked us to do the formula of combined harmonic mean. H1, 2 is equal to N1 plus N2 upon N1 upon H1 plus N2 upon H2.

Guys, N1 upon H1 plus N2 upon H2. Sir, in geometric mean, you have never asked us the name of combined geometric mean. I have not asked you any question. Nor has any question been given in your module. But, friends, if I ask you, does the formula of combined geometric mean exist?

For example, a theory question has come. Yeah. which one of the following does not have the combined formula?

It is of A, GM, and HM. It is not of partition value or mod. So, it is not that GM does not have the formula. The formula is there in our syllabus. So, for completion, I will write the combined formula here.

GM12. Friends, the same formula is there. You know, the one of discrete.

Anti-log. Guys, there are two series. So, guys, what will be the anti-log of?

Summation of F. Guys, just a second. just a second, wait a minute, summation of, guys, just a second, sir, summation of n1, sir, this number of observation will be given here, n1 into log gm1 plus, guys, summation of anti-log of, guys, anti-log of n1, into log gm1 plus n2 into log of gm2 guys divided by n1 plus n2.

Guys I want to tell you that if this question comes in the exam which one of the following does not have a combined mean formula then don't think that gm's combined mean formula doesn't exist. It exists. There are no questions in our syllabus. But it exists.

Come on guys tell me. Have you written all the major of central tendency formulas in one place? Have you done all of them? Let me move on to the next practice. If you are forgetting anything, then just remember it here and finish it.

Next time when you open the sheet, you can write it. Let's move ahead. Guys, relation between mean, median and mod. If the data is symmetric, all the observations are 5, 5, 5, 5, 5. So guys, mean, mod, median, everything will be equal.

Here it is written mean is equal to median is equal to mod. Friends, if it is saying that it is positively skewed, then what sign will you put? Guys, it is positively skewed, so mean is greater than median. Guys, if it is saying that it is positively skewed, mean is greater than median is greater than mod guys mean is greater than median is greater than mod or negatively skewed guys mod is greater than median guys mod is greater than median is greater than mean And friends, if it is moderately skewed, then what is the empirical rule?

Practical formula. If you know any mean or median, then you can find out the third thing. And the formula was, guys, our mod is equal to 3 times median minus 2 times mean.

Guys, minus 2 times mean. Has everyone written it? Here, see, a good theory is revised and your practical part is also revised.

If I want to highlight this, then this part is very important from the practical point of view. And this part is important from the point of view of theory. Guys, now, what is the relation between A and GM? If the observations are symmetrical, then all the arithmetic, geometric, and harmonic means will be the same. A is equal to GM is equal to HM.

But if it is asymmetric, then sometimes it will not use the word asymmetric. Data are asymmetric. for the set of distinct, different positive numbers for the set of distinct, distinct means asymmetric for the set of distinct positive integer means he mentioned that I am talking about asymmetric all the observations are different, distinct positive numbers so when this happens, Aman sir in this case am is greater than gm is greater than hm but suppose in the question, if the question is silent that data is symmetrical or asymmetrical, the question should not be mentioned.

Which one of the following option is true? But the observation is symmetrical, all the observations are same, it is distinct, it should not be mentioned. Guys, in that case, we have to satisfy this too and we have to satisfy this too. So, a condition comes here, friends. am greater than or equal to gm greater than or equal to hm.

I had also reminded you of this. Yes, Pooja, very good. But remember, we will use distinct positive words, not asymmetric words. So don't use greater than or equal words. Now we will refer to common property summary.

Common property summary. We will do common property summary now. Tell me, we hardly took 15 minutes and I was explaining to you. If you write it yourself, you will not find it useful in 5-6 minutes.

Shall we start with the revision of MOD formula now? Friends, are we starting to do the revision of MOD formula now? Tell me.

Come on. Friends, along with me, there is an individual series. Guys, if the individual series...

Why are there two tables here? If two tables are made by mistake, then there is no need to make it here. There should be only one. This should be only one. I will fix it.

Come on. I will fill the sheet with the correct answer and send it to you. Now there are two answers.

Listen friends, tell me what is range? Tell me what is the formula of range? Absolute measure or relative measure?

Sir, all the observations are given in individual series. Largest interval minus smallest observation. If the frequency is given, then how many times someone comes, I have nothing to do with it.

I will ignore the frequency. The formula will be same, L minus S. But friends, consider that it is a continuous series.

If the series is continuous, then largest class interval minus smallest class interval minus lowest class interval. I am writing S, so that you can understand. I have used H as Highest Class Interval minus Lowest Class Interval Guys if you want to use the same word then what will be the result? What will be the result?

This will be your result Guys Highest Class interval minus lowest class interval. Friends, remember this in continuous. Guys, series is not exclusive.

Guys, if series is not exclusive, make exclusive. If series is not exclusive, make exclusive first and then move ahead. Sir, we are done with this.

Sir, what is its relative measure? When we have to calculate in percentage, friends, L, guys, L minus S, whatever you have calculated, whatever it is, whatever it is, i.e. Indivolution, Discrete or Continuous, as you have calculated here, using the same information, largest L minus S upon L plus S into 100. And friends, if the quantity is 19, this minus this upon this plus this multiplied by 100. In a way, whatever you have calculated, divide it by total into 100, which is the formula of percentage, favorable upon total into 100. That is what we are looking for here to convert into relative measure.

Friends, tell me, tell me the formula of mean deviation. Sir, the formula of mean deviation is, ultimately we satisfy the definition here. Sum of difference of all the observations from their arithmetic mean. Sir, this mean can also be this mean. Sir, how much do all the observations deviate from their measures of central tendency?

Sum of all the observations. of that sum of all the division taken from their mean, median and mod. It can be anything, Aman sir. You write here A.

We had made a general formula A upon number of observation n. Friends, I had written here that this can be mean, this can be median, or guys this can be mod. And friends, we had done the questions of median and mean in concept handbook. I had written the formula of discrete series here.

discrete series formula, take summation of difference and multiply it with fi xi-a guys upon n since frequency is given, so kids know that n will be the summation of fi and there is no big deal friends, here in continuous, same formula will be used guys, if it is continuous just you have to calculate guys, same formula question will not come on this, will not come, will not come But I want to keep your completeness in your mind from your knowledge point of view. Same formula guys. Guys, xi will be equal to midpoint.

xi will be equal to midpoint. Guys, is this point clear? And sir, what will be its relative measure? Sir, relative measure will be mean deviation about a divided by a into 100. Aman sir, this means, assume mean deviation about mean. So guys this will be mean deviation about mean.

Guys mean deviation about mean upon mean into 100. Means mean deviation about all deviation from median. So mean deviation about median. You know the formula of median.

Into 100. Guys is this point clear? Friends did you write both the formulas properly? With my help, without my help. Will you write it always? Yes sir.

Come on next formula. Guys quartile. Children tell the children.

Sir why you didn't make quartile separately? Aman sir, you made it here, here, here, why didn't you make it here? Friends, to find the quartile deviation, ultimately we have to find Q1, Q2 and Q3.

If the series is individual, discrete or continuous, you will have to find the quartiles. And you know the way to find the quartiles, this is the way to find the quartiles. If it is individual, it is discrete, and if it is continuous, it is this. After finding it here, you don't have to do anything.

Guys, you have to find the quartile deviation. Guys, quartile deviation is nothing. It is Q3 minus Q1 upon 2. Friends, here you will see in your concept handbook. So, I have written two things in concept handbook.

Quartile variation and quartile deviation. Friends, for now, leave quartile variation. He did not consider quartile variation in the book of institute.

Guys, so we will apply Q3 minus Q1 upon 2. And friends, what is the relative measure? Q3 minus Q1 upon Q3. plus Q1 multiply by 100. I want you to revise some things whenever you want. You revise with linkage and that is this.

Guys listen, ultimately we are doing here also Q3 minus Q1 upon 2 whole divide by, we are doing here also Q3 Q3 minus Q1 upon 2 and here also we are dividing Q3 plus Q1 upon 2. And guys Q3 plus Q1 upon 2 gives us Q2 and this is our median. In short guys if you have given median so double the median and write here that will be your Q3 plus Q1 we have done the question on this so remember this is nothing guys, this divided by 2 is median if median is given then multiply it by 2 and pick up the earth your Q3 plus Q1 will be yours Friends, is this point clear? We have written this in concept handbook very well.

If you feel, then see it once and repeat it here and say. There is no need to go to concept handbook again and again. Shall I move ahead, friends? Yes, I am answer. Now let's revise the formula of the standard deviation.

Friends, if I remind you two formulas from the individual series. One is direct formula and one is indirect formula. Direct formula says, brother, there is no need to make table. Take under root, summation.

X square divided by number of observation minus mean whole square. Guys, indirect method says that this formula is made up of definition. Summation of X minus X bar whole square. We will not take mod, but divided by N Divided by N Under root. Friends, what both formulas I have written.

Friends, this formula is more memorable to people. But use is more. That is why I named it direct and I named it indirect. Sir, but if it is discrete series, then there is no change. Friends.

you will find the mean according to the discrete series here you put F and here you put F your formula is discrete and there is no one for continuous guys, like there is no one for partition there is no one for formula, continuous always has one method find the mid point after getting the mid point your series is converted into a discrete series then the matter is over sir if I want to write the formula here then I will prefer this formula under root of summation of find the difference square it First multiply it by fi divided by n. And here n is summation of fi. Guys, here same formula. Aman sir, same formula.

Guys, how to get xi? Mid point. Friends, now here comes, see below this, I have given 4a, 4b, 4a, 4b and 4c.

Major of dispersion is 4, in 4 range of 4, mean deviation is there, quartile deviation is there, standard deviation is there. Guys, we call the square of standard deviation as variance. And friends, its relative measure is coefficient of variance.

Remember, relative measure of standard deviation is not the coefficient of standard deviation. Guys, it is coefficient of range, it is coefficient of mean deviation, coefficient of quartile deviation. And we call it as coefficient of, coefficient of, of variance. variance word has come out that's why I told you variance first variance is nothing else, standard deviation and square it, that is the variance. Listen, coefficient of variance its formula is sigma upon mean as you find out, measure of central tendency multiply by 100. Now listen whenever you want data to check the consistency why is it used?

This is used to check consistency guys care a more jitra can jitra coefficient of variance come data more consistent data is more consistent yeah the door so you can look at a discus door of the door the away company your company big big a dividend a dividend Nikala television maybe kia jiska coefficient of variance come welcome please dada consistent a pretty variant copy economy Guys, we are done with this. Sir, combined standard deviation. Sir, we remember, we remember, we will write. So, first of all, write with me. After that, you have to write by yourself.

Tell me. Sir, n1 sigma 1 square plus n2 sigma 2 square plus n1 d1 square plus n2 d2 square upon amansar n1 plus n2. Children know that n1 is the number of observations in the first group.

Sigma 1 is the standard deviation of the first group. Now comes the question of D1 and D2. D1 is the combined mean minus the mean of the first group.

D2 is the combined mean minus the mean of the second group. Guys, is this point clear? If combined mean is there, then remember the formula of combined mean.

X1 2 bar is equal to N1 X1 bar plus N2 X2 bar upon N1 plus N2. If you feel like doing it, then open the concept handbook next to it. and then hide the answer and then take out the answer in the calculator and that's it and then you will revise it like this one day before the exam here you write the formula and there you see the question here you write the formula and there you see the question that's it guys is this point clear?

tell me is this point clear? friends I will move ahead friends everything is clicking everything is clicking I have written it very well if you get confused if you leave something I take assurance that nothing will happen. Guys, in miscellaneous point, I had to remember two shortcuts. What is the mean deviation of first n natural number?

Sir, this is our n square minus 1. Guys, n square minus 1 upon 4n. Although standard deviation is under root of n square minus 1 upon 12. Guys, n square minus 1 upon 12. See once, as far as we have written this. Because I have written it wrong once that I will not record it again.

So, I want everything to be proper. There should be no problem in clarity. Yes, under root of n square minus 1 upon 12. Sir. We have a ratio of QD, MD and S. Sir, tell me what is that ratio?

10 is 2 guys, that ratio is very important. 10 is 2, 12 is 2, 15. Remember this, first it is QD, then MD and then S. People often read it wrongly. First MD, then QD and then S. It happens because we read MD first while reading.

So people think that first it is written MD. No. Guys this ratio belongs to QDMDS not MDQDS.

Quartile deviation is to mean deviation is to standard deviation. If you know any one dispersion then you can use this ratio to find out the other dispersion. If you know mean deviation it means you know quartile deviation and standard deviation.

If you know standard deviation and you don't know anything then you can use this ratio to find out the remaining two. This is the link to establish and repeat yourself. So now click the question once.

Should I move forward? Guys is this point clear? Guys is this point clear?

Should I move forward? Common property, come friends, summary, revise through summary. Guys we will revise through summary. I will revise the summary for you.

What fun in life, forget it. Guys we are done with the, tell me how many minutes did it take? Do you think that we are revising the formula very effectively?

Now there is no burden coming. that I need to change the concept of handbook I have also shortlisted that and given one chapter in one page Guys, we are done with the revision of this Come Aman sir, you will revise the core relation formula, make linkage and free us Guys, shall we start? It was very neat sir, yes I know Guys, let's start.

Aman sir, let's start. Sir, we have read four methods to find R. Scatter diagram, Knarl Pearson, Spearman and coefficient of correlation.

Guys, CCD, coefficient of concurrent deviation, I have written it wrong, I will change it. Coefficient of concurrent deviation. It will change, don't worry. I will send you updated PDF also, which will come after some corrections.

Sir, show the second page. I will show you the second page and now we will start writing it. Sir. In Scatter Diagram, we know that if all the diagrams are increasing by 1, if 1x increases and y increases, then it is a positive correlation.

If 1 increases and 2 decreases, then it is a negative correlation. This is what you had written in the form of the diagram. Friends, the more you increase x, the more y increases. The same proportion is increasing. Friends, this is called perfectly positive.

Guys, perfectly positive. I am writing this in short, we should understand what we are writing and I know that I have taught you this, so whatever I say will hit your brain Guys, if the one who increased X, Y decreased, X increased from 10, Y decreased from 10 Guys, in the same proportion, there is movement in different directions, perfectly negative Guys, a curvilinear graph is formed, curvilinear graph, curvilinear is called R is equal to 0 In perfectly positive case, r is equal to 1. In perfectly negative case, r is equal to minus 1. Sir, here in positive case, r is greater. Sorry. R's value is from 0 to 1. Guys, in negative case, r's value is from minus 1 to 0. Sir, we are done with this. Is the scatter diagram revised?

Is the scatter diagram revised or not? It took 5 minutes. Write it in full. What is the fun in exam? You blank the formula, blank the paper.

What is the fun in it? There is no fun in failing you. Sir. Let's see Knarl Pearson. We saw two formulas in Knarl Pearson.

When all the observations are given. Remember the first formula, it was written in the concept handbook. Children remember it.

Same thing in everyone's language. N summation xy minus summation x. Let's change the pen.

N summation xy. minus summation x summation y upon under root of n. Guys, n summation x square minus summation x whole square.

Same thing, write y. n y square summation minus summation y whole square. Can you write this formula? Tell me, if the covariance is given, what will happen? If the covariance is given, what will happen?

Write. Sir, do we remember the covariance formula? Sir, r is equal to covariance between x and y. Covariance between x and y divided by sigma x into sigma y.

What fun if someone does something wrong in the world? Sir, here, our covariance, listen, your mind will go to the exam again and again, sigma x squared. Hey, idiot, that was our regression coefficient. This is talking about correlation coefficient.

Done? Tell me, man. I have to write the next one. Shall I start?

Yes. Sir. Covariance is discussed. We will write a very large number. We have written a little more and a little less.

In the concept handbook. Summation of X minus X bar into Y minus Y bar divided by number of observation. Sir, there is something after seeing this.

Not just one thing. That is covariance. Whenever you see this, understand. Question formula has come.

Where covariance has to be taken out. And using covariance, there is a formula of regression. and using covariance, we will use coefficient of correlation formula and whatever is there this is the end of the discussion, we will make a chart for this and revise it Sir, we are done with this Spearman's formula, same thing in children's language 1 minus 6, summation di square upon n into bracket n square minus 1 everyone knows what di is, di is whole square of xi minus yi and xi and yi were the rank of the first observation and rank of the second category.

Friends, if you have given sales and profit, don't take difference of sales. Take rank of sales and profit. The one who is the most, take first rank. The one who is less, take second rank. The one who is the least, take last rank.

Okay? Guys, done? And what was the number of observation?

Aman sir, coefficient of concurrent deviation formula. Guys, R is equal to plus minus under root of plus minus 2C minus M upon M. Guys, here C is our number of positive deviation. M is the number of observation. Write it here, guys.

This is 1 less. 1 less than the number of observations. I had told you why it happens.

I had told you everything. Now I am revising the formula. Number of positive deviation.

The matter is over. Sir, when will we take positive? If you get positive by solving this, then both the outside and inside are positive.

If 2C-M is solved and negative is there, then here also negative and here also negative. That's it. I explained the logic, why?

Because in Maths, it is said that in under root, negative cannot be there. If it is positive, then there is no problem. But if it is negative, then there is a problem. So to make negative positive, inside is negative and outside is also negative. That's it.

Guys, is this point clear? Should I move ahead? Friends, answer my questions. Give or not? Friends, should I move ahead?

Guys, should I move ahead? Is the revise going well? See, I have already given you the summary chart of the probability.

This is the summary of this chapter. I have already done the summary of the probability. When those 15-20 questions were done together in the last, when to think about what, when to think about whom, I have already filled that summary before that. Very good, Naveen. Come.

Sir, let's talk about errors. Guys, tell me the formula of Probable Error. Sir, we have written it. We are not waiting for you.

The formula of Probable Error is 0.6745 times. Guys, 0.6745 times Standard Error. Guys, now let's talk about Standard Error.

So, what is Standard Error? Sir, Standard Error is 1 minus r square upon under root n. Sir, because of this, another jump comes in this formula. 0.6745 multiplied by standard error is 1-r square upon under root n.

Now, this r is coefficient of correlation. This n is number of observation. Guys, here we talked about properties. If you take mod of r and take 6 times probable error.

If 6 times probable error is more, take r and make it positive. Take 6 times probable error. If this is happening, So guys, your r is significant. And guys, if mod of r is big, guys, sorry, If your R is not significant, and mod of R is greater than 6 times probable error, my answer will be R is significant. Write it again and again.

You will never forget it in your life. Sir, we are done with this. correlation of population.

Remember? This is a world of knowledge. You should read it. Sir, you can find the probable error.

There is a limit from here to here. Guys, there is a limit. R plus minus probable error.

If you take R plus, then upper limit. And if you take R minus, then lower limit. From here to here, correlation of population will come. I have asked you a full-fledged question on this. I have asked you all the questions on one question on errors.

By writing this formula. Don't just write it. Go and audit there. and you will see that yes, I had to do this and that, but you will not make a calculation mistake, you are mature enough, don't worry. Guys, done with this, shall I move ahead?

Let's talk about important property. Guys, here you have to write a practical formula, I have to write a theory formula, theory also, theory question can also come on this. Guys, coefficient of determinant, sir, coefficient of determinant is considered more practical, more used, that is R square.

Sir, we call this R square's theoretical formula, sir. It is explained variance, explained variance divided by total variance. Guys, explained variance upon total variance. Sir, coefficient of non-determinant, sir, this is 1 minus R square. And sir, we write this as unexplained variance.

guys divided by total variance, done? guys done, sir coefficient of alliation you will remember it as 1-r square for this I have not made you remember any theory point under root of 1-r square and friends here first r square 1-r square coefficient of non-determination if we take its under root then coefficient of alliation guys here we revise in all the forms of correlation analysis tell me is confidence increasing? We are writing the formula without looking at it.

We are enjoying it. You are still looking at it, if it is wrong or not. We will write without looking at it.

I was sitting in the AC from morning. When I shared the sheet, I had to bring it to my target on one page. So I was sitting in the AC.

It took time to design. It will be done. It will be revised in 20 minutes.

Give the exam. Fill the log up. It has no stats.

I will submit it on the question sheet. Otherwise, blow the notes of Tufaan Bash in 15-20 minutes. The work is over. Guys, let's move forward.

Let's revise a long chapter, Regression Analysis. Will you support me? We have to see the common property.

Let's move forward. We have to revise it in the next 10 minutes. Regression Analysis. I have written a small part. print out.

I will zoom in and show you. In this chapter, our final aim is to estimate the value of one variable. As it is written, find the value of y when x is equal to 3. In this chapter, our aim is to find the value of one variable.

When we already know the value of the other variable. This process is called regression analysis. To estimate the value of one variable, when the value of another variable is known, this process is called regression analysis. But to do this, how much God's grace would be there, if we get an equation here. It would be fun.

Don't write this. It would be fun. I wish there was an equation like this. 2x plus y is equal to 10. I wish there was an equation like this. So here we would put the value of x and take the value of y.

We call it as second aim. Sir, we need equation. So that we can calculate the value of one variable and get another variable. Sir, I wish we could do that.

We need, no problem, I will give you regression equation. But the requirement of regression equation is regression coefficient. So friends, here first birth of regression coefficient is there.

It is important to remember the formula of regression coefficient. So that you can make the equation. And it is important to remember the formula of equation. So that you can achieve your final aim. You know the value of one variable.

and you can estimate the value of the other variable is this revision done? say, by making linkage, do you understand? in this chapter, whole world is mad We don't want to go mad. We don't want to go crazy. We want to establish this linkage and move forward.

Friends, can I get some water? I'm a little tired. I don't know why today. 10 minutes.

Friends, shall we start? Sir, sir, did you understand? To estimate the value of one variable. We have to estimate the value of one variable when we know the value of the other variable. Sir, for this, we need an equation.

Sir, listen. We have two equations y on x and x on y. Sir, when and what should we make? When you want to find the value of y and you know the value of x, then make y on x.

And when you want to find the value of x and you know the value of y, then make x on y. Sir, the value of the variable which we know is called independent. And the value which you want to find is dependent. If you want to find the value of y, then y is dependent. If you know the value of x, then it is independent.

So that independent, sorry, that dependent and the value of y is known, whose value is known, understand, right sir. Sir, so here, when we will make this equation, when we need to find y, x is known. I am writing in short, sir when will we make this, when we need to find. x. Guys, y is known.

Sir, the matter is over. I made a table and understood it. I wrote it in small. Yes. Sir, its general form is y on x.

Guys, its general form is y is equal to a plus bx. Now see, if you want to find the value of x, x is equal to a plus by. Sir, when is this called general form? Guys, if you are writing x on y, then this is a general form and if you are writing y on x, then this is a general form. Sir, here we call a and b as regression parameter.

Use this formula when a and b value is given or you can find it yourself. If you know the value of a and b, then put here y is equal to a. Suppose a is 2 and b is 3. y is equal to 2 plus 3x. Put here 2 plus 3y. This is x on y and y on x.

So, use this formula when you know the value of a and b. or the question has given a way where you can't say a and b take it out and put it the equation is made so here put the value of x to 2 and take the value of y the final aim is this but to achieve this I need the equation sir here we call b as regression coefficient it has another form which we call point form if you want y on x then y minus y bar b y on x bracket x minus x bar we want x on y guys x minus x bar, b, y minus y bar. Sir, here the x bar and y bar is our mean. Sum of all the observations divided by number of observations.

Or it can give you. But friends, here to put you will need b. And we call b regression coefficient. Sir, here. B, Y on X can be given.

If you put given here and make your own, but you don't give and you have to remove, then you will get aim number 1. And friends, here comes aim number 1. We need equation so that we can, guys, we will write here. Sir, students usually get confused when to apply which formula. Guys, you have to think about the formula according to the information given in the question.

Sir, there are three formulas to remove the coefficient. Will you write three formulas with me, guys? Will you write the three formulas with me?

Guys, the first formula. Sir, the first formula. If all the observations are given, then the formula that will look like Knahl-Pierson will be used. That is guys, n summation x into y minus summation x into summation y divided by n x square's summation minus summation x's whole square. If the thing is ending at x, So, in all the formulas, in the denominator, it will be x.

If it is ending at y, write the formula N summation xy minus summation x into summation y divided by N y square's summation minus summation y's whole square. Sir, think about this formula when you have all the observations given to you or when you have directly given this. For its practice, I have given a question.

Find the regression equation. To put the regression equation, you need mean and b. And for b, I have given you all the information. X, Y, this information.

So, here I have given you full-fledged question for practice. Listen. First, let's come here. Sir, if we have standard deviation and R, then your formula will be By on X, R, guys, Sigma Y upon Sigma X. And here, it will be R, Sigma X upon Sigma Y. Aman sir, if we have covariance, then covariance between X and Y divided by, guys, X is ending, so standard deviation of X whole square. Here, covariance between X and Y divided by standard deviation of Y whole.

square. Friends, have you written the whole formula? You don't think so? You must be thinking that you have designed this chapter in 5 minutes.

You are feeling it but believe me, it took me 4 hours to make it. Because you know how I have taught, how will the linkage start in your mind. I didn't want to break that linkage. That's why I designed it the same.

I am moving ahead, friends. Now I am moving ahead. Can you promise me to do a question?

I will do a big question Guys Let's do regression Guys Get the regression coefficient from these charts Get the regression coefficient I want you to get by on x I am doing revision with a question There are questions in charts and in Maths Get by on x Covariance between x and y Divided by standard deviation of x whole square Covariance is 121 standard deviation of x 15 square guys 15 square 15 into 15 sir this is 225 121 divided by 225 how much you have got 0.53 0.54 i am taking 77 guys b x on y how much will be co variance between x and y divided by standard deviation of y square 121 standard deviation of y is 14 14 square into guys 196 how much is it 121 divided by 196. Guys, how much is it? 0.612. Guys, I am taking 0.62.

Yes, guys, we are done. Guys, we are done. What was he saying?

Find the regression. Sir, you did not find the regression coefficient. You found the regression. Yes, I did not ask for regression. You found the regression.

Done? You can find BX on Y as well as BY on X. You can find whatever you want. Guys, next question. The regression coefficient.

Find the regression coefficient. What does it look like after seeing this whole thing? Listen, let's do one thing, let's stop at these questions because I have to revise this chart too. I have to revise this chart too.

I had asked you to write this in class by hand. Now I have converted it into a chart. First let's see it completely and then we will go to that question. Listen, let's come.

Sir, we have understood the name of this chapter. There are so many small formulas and we keep making up things in our mind. Because of these three formulas, your mind does not have proper linkage and you curse the formula. If you want to make a line, you need to find the co-variance of this and that. To make a line, you need to find this and that.

You have a problem in linkage. You are trying to find the formula. Sir, in this chapter, you tell us why we call this chapter as correlation and regression.

I told you two practical formulas for this. If you want to make a line, you need to find the co-variance of this and that. you know the regression coefficient, then you can find the correlation coefficient.

Plus minus under root of b x on y multiplied by b y on x. Friends, second thing, sir, here we had written two formulas. b y on x is equal to guys r sigma y upon sigma x.

And Aman sir, another formula was written. So the b x on y is equal to r. Sigma X upon Sigma Y. Aman sir, it depends on the question data that we will give, we will take out R.

Now, many times when you write this formula, you know this, you have to take out this. So, standard deviation will give you. But standard deviation will never give you directly, it will give you information that you can take out.

How will it give information, friends? Write here, Sigma X formula. Now, revise. Standard deviation formula. Go to MOD.

Sir, in MOD, our formula used to be summation of. x minus x bar whole square divided by n. Sir, the formula of sigma y was under root of summation of y minus y bar whole square divided by n.

Sir, is it done? I am making the linkage of the chapter. See, they are revising it. All the formulas that are found along with it are being revised.

Sir, two practical points are done. Two theory points were written. Sir, if the value of r is plus minus 1, guys, it means regression lines.

If the value of r is plus minus 1, guys, it means regression lines. then lines are identical guys if r is equal to zero guys lines are identical it is used to co-incide and friends if r is zero then lines are perpendicular till you write it again and again you will not remember friends lets move ahead sir here in important highlights you said about unity friends if we assume that one is bigger than one then the other should be smaller than one if this is smaller than one then this will be bigger than one one should be greater than unity and one should be less than unity about sign Sir, either BX on Y BY on XR both will be positive positive or both will be negative negative Sir, using both of them we can get R Sir, if both of them are positive then we take positive If both of them are negative then we take negative If both of them are positive we can conclude from here R will also be positive. And friends, if both are negative, then R will also be negative. It can never be that one is positive and the other is negative. Either both are positive or both are negative.

Sir, we know that the regression lines Y on X and X on Y, they intersect at their mean. Intersect at mean. X bar and Y bar.

Sir, what do you want to say? Guys, solve. Solve equation simultaneously. The point of intersection is mean. Guys, there is a question on this.

Whenever both the lines collide, it collides with mean. If you solve both simultaneously, you will get the value of x and y. That is the mean. Guys.

incorrect to correct incorrect to correct if you have given incorrect x on y or incorrect y on x then you have to correct it so the formula is correct b x on y you do reciprocal of incorrect y on x whenever you do reciprocal of incorrect y on x then y on x will give correct x on y and x on y is the reciprocal of incorrect correct b y on x you can write any one but I will write both correct y on x so do 1 upon reciprocal of incorrect b x on y friends, is this point revised? guys, I have also revised important highlights I have written one thing which is theory, practical, you are revising everything guys, is this point clear? friends, come Sir, if we want to know the regression line, how will we do it? We had written three steps. Guys, assume one.

Guys, assume any one as x on y, other as y on x. After this, convert it to standard form. Take out b, y on x, b, x on y.

you will get R you have taken out standard formula R after this you take out R by applying this formula if your R value is between minus 1 to 1 then your assumption is right or vice versa your assumption is correct or vice versa guys this point is revised did you understand how to write again and again now below this I have given a question I have put a big question on this whenever you revise this 1,2,3,4, revise all these points means revise 50% of the question Guys listen, I have revised all the formulas I have revised all the formulas You can do these questions, all these questions are in your question bank and concept handbook When you do these, you will gain confidence I have said that I am a teacher, I will come to teach you again and again I have taught you, I have called you to practice the formula Guys, should I move ahead? Tell me Come, I have made an important chart. How to think, how you should think about, see, what you should think when you see the following input.

Whenever you see this, tell me, who should you remember by looking at this? Who should you remember by looking at this? Tell me.

By looking at this, you fool, what will you remember by looking at this? Tejas, if you divide this by n, then you will get covariance. Sir, is codex we remember whose?

Knowaranski's Sir how can we divide by n and see this and see this and see this and remember whose? Who should remember this? If this is the input in any question, Sir, I am not able to think.

If you click something after seeing this, how will you think? Who should remember this? Yes, standard deviation. Sir, under root of summation of x minus x bar. Sir, divide it by n and add under root.

Sigma x is here. Sir, divide it by n and add under root. Sigma y is here. Sigma x and sigma y is here.

Covariance is here. So, what is your result? Your result is R. This will give you the order B.

Take out whatever you want. Take out whatever you want. Sir, this will click us.

Sigma X. After seeing this, it will come to Sigma Y. Friends, if the regression line is given. Listen. This regression line is given. I said that let's assume. I said this is X on Y.

What can you find out by seeing this? What can you find out by seeing this? Tell me. Think. The line is of regression line.

Sir, very good. Sir, if the regression line is of BX on Y. If you give two regression lines, then you give one BX on Y also.

and B Y on X also came out. Friends, if these two are there, tell me, next box, if these two are there, means whose are they? If these two are there, Sir, how, how, how? Write it in standard format, how?

Sir, if you are saying X on Y, then X on Y's standard format is X is equal to A plus B Y. Write it in standard format. Kneep X on one side. Minus 5 minus 3 Y.

X is equal to minus 5 upon 2 minus 3 upon 2 Y. friends compare this x is equal to a plus by so this is b x on y 3 minus 3 by 2 compare the equation in a standard format and whatever is b will become b I am not getting into this, if I do I will go into teaching my motive is to make you revise the formula and the existence of these two means the existence of r end of the talk Friends, promise me that you will revise these formulas. You will practice these questions.

I have asked you to do all these questions. Guys, here we are done with the revision of all the formula of the regression analysis. Will you revise the chapter of the first day of the exam in 10 minutes?

I have taught you and made you understand. I cannot stop myself from explaining. What should I do? My attitude is to teach.

common property revise, it will take 5 minutes sorry for making you study more guys, let me revise common property guys, let's do one thing let's do MOCT here, it will take 10 minutes 10 minutes, did you do it? 10 minutes, revise it, common property will be left you will study something else, right? whenever you give me 1 hour I will teach you something new, why will you repeat?

come Sir, I am not telling you what is a common property. Guys, common property means the origin, change in origin and scale property. M-O-C-T, M-O-D, correlation and regression. It is written in four chapters. Listen, who is affected by origin and who is not.

Listen, let's do it. Guys, it will just take 10 minutes. Along with the question, we will revise the question.

It has no role without the question. Listen. Friends, I have given you the concept handbook by making pieces of it. Yes, I am just finishing it. Listen friends, Univariant data, Listen friends, Univariant data, Whenever we talk about single variable, Guys, that is called univariant data.

Our M.O.C.T and M.O.D. talks about single variant. And on bivariant data, our chapter is correlation and regression analysis, Where two variables are discussed. Listen, Guys, whenever we change the origin or scale, Since there is only one variable, So, we change the original variable x and reflect it with y.

How do we reflect it? With y. And since there are two variables here, the one we changed x, we reflect it with u and the one we changed y, we reflect it with v. Guys, did you understand?

That's why there are two equations here and one equation here because friends, MOCT and MOD It is a single variable. So, the actual observation of X is represented by changing it from Y to U and Y to V. So, here the standard format is Y is equal to... y is equal to a plus b x.

Understand. You have this x is original. Whatever you have multiplied in this, we call it scale. And whatever you have added in this, we call it origin.

But friends, here there will be two standard formats. One is the changes you have made in x, which you have represented with u. And the other is the changes you have made in y, which you have represented with v. So here there will be two standard formats. One u is equal to a plus b.

bx, v is equal to c plus dy. Listen, again friends, here is the origin, sorry, here is the scale, here is the origin, here in y, you have changed, here is the scale and here is the origin. Understand, many times people get confused, merge this property here.

Brother, when you are talking about moct and mont, then this is the standard format, there is only one variable x and we represent the change of x with y. And here we represent the change of x with u, in correlation and regression, we represent the change of y with v. Listen, Sir, the difference between origin and scale is the measure of the measure of the central tendency. But in MOD, the difference is not only in the scale but also in the modulus. So, here the formula is made. First of all, you convert it in the standard format.

Y's measure of central tendency is equal to A plus B times X's measure of central tendency. But here the measure of the measure of dispersion does not differ from the origin. Guys, Y's measure of dispersion is equal to guys.

mod of B into X the measure of dispersion. Here guys this can be range, this can be quartile deviation, this can be guys standard deviation. But here the common property is not for your variance.

Variance is not the part of measure of dispersion. Variance is the part of standard deviation. And this property is for measure of dispersion. This is not for your variance.

There is a question on it, it has come, it is your request. Please revise the concept handbook question. Sir, listen. But friends now let's talk about correlation and regression.

correlation, neither it differs from origin nor from scale. Guys it differs just from sign of multiplier. I also call it sign of scale. Friends, it does not differ from origin, it differs only from scale.

And here we had made a formula, listen guys, B UV is equal to B X on Y. the magnitude will remain the same sin of b multiplied by sin of d now you all know that I have told you the meaning of b and d guys take the sign of x, the coefficient of sin of b and sin of d neither it differs from the origin nor from the scale and here we had written the formula b uv is equal to guys b x on y Multiplier of x divided by multiplier of y. We call it multiplier.

Scale. And it makes difference only from scale. Guys, B, V on U. Guys, B, V on U.

B, Y on X will be given to you. Guys, multiplier of Y divided by multiplier of X. That's it.

Guys, is this point clear? Come to the questions. Guys, is this point clear?

I have given you all the common properties at one place. Now, see. I have given you the relation. 2x plus 3y guys.

2x plus 3y is equal to 10. Okay. It is saying what is the mean of x. Guys sorry.

And if the mean of x is 2 what is the mean of y. Listen guys. X's mean is 2. What is y mean?

First tell me this. Is the mean the measure of central tendency or the measure of dispersion? This will talk about single variable.

Single equation. Let's write it in standard format. Do y on one side.

3y is equal to 10 minus 2x. y is equal to 10 minus 2x upon 3 upon 3. Sir, why is it important to write in standard format? So that we can see actually how much origin we have changed in x and how much scale we have changed. Sir, this is the measure of central tendency. It will also differ from origin.

It will also differ from scale. So, y measure of central, y range, what did you ask? y mean 10 by 3 a minus b x. How much is x, friends? 2. How much is this?

Guys, this is 10 by 3 minus 4 upon 3. Guys, 6 by 3 will come up. Whatever will come, anything can happen. If there is a mistake in the fast, then this will also be 2. Guys, tell me, is this point clear?

Guys, is this point clear? But now I have asked you one more thing. If the range of x is 15, what is the range of y?

Now, the children know. I am doing it here to save time. Now, the children know that the range is the measure of dispersion.

And the measure of dispersion. Here, the difference is not with the origin, but with the scale. That too, how?

with positive sign guys so here first of all convert this Sir here is the scale y range is equal to mod of b 2 by 3 will be negative then also take positive into guys range of x, how much range of x have you given? 15 how much is it guys 3 5 15 10 answer is guys 10 Is this point clear? Is this point clear?

Summary is revised. Major of MOCT and common property of MOD is revised. Practice is done. Convert to standard format.

Major of central tendency and major of origin and scale. Don't take impact of both. And friends, if major of dispersion is there, then only take impact of scale and leave origin. Sir, now let's talk about correlation. Listen guys, here whenever we talk about correlation and regression, two equations will come easily.

Because it is bivariant data. It is a bivariant chapter. Okay.

Guys, u is u plus 5x is equal to 6. Second, 3y minus 7v is equal to 20. Guys, it is saying that if coefficient of correlation Rxy is 0.58, How much will be uv? Children know that Ruv doesn't matter between origin and scale but it matters with sign Sir, it will still be 0.580 but I have to multiply it with sign but before converting it into sign convert it into standard format How to convert it into standard format of bivariant? Where is the standard format?

Sir, do u on one side and v on the other side I did u on one side 6-5x 3y minus 20 is equal to 7v so v is 3 upon 7y minus 20 upon 7 guys here the coefficient of x is negative here the coefficient of y is positive so guys here i will take negative and positive plus minus minus 0.58 so neither it got difference from origin nor it got difference from scale guys see what formula we have written guys we just have to consider the sign of b sign of d Guys just take the sin of x multiplied by sin of y and click quickly. Sin of x is minus, sin of y is plus. Guys 0.5 feet are xy multiplied by sin of x sin of y. That's it. 0.5 feet.

Guys, is this point revised? Friends, is this question already point revised? Shall I move ahead? Is this point clear all of you guys? Is this point clear?

Yes sir. Come. Regression. Sir, there is a relation between u and v and here u and v are already in standard format. I have given you a regression question y on x.

B, guys, I have given you b y on x. How much? 2.4. You have to find out what is b v on u.

Sir, b y on x multiplied by multiplier of y divided by multiplier of x. 2.4. Guys, what is multiplier of y? Sir, Y's multiplier is minus 3. Divide.

Multiplier of X. X's multiplier is 2. Aman sir, solve this. 2.4 multiplied by 3 divided by 2. Minus 3.6. Minus 3.6. Guys, here we have the answer.

Minus 3.6. We are done with this. Friends, here I have made all the common properties, all the formulas, proper linkage. I have revised all the chapters.

Guys, we have successfully revised MOCT. We have successfully revised MOD, we have successfully revised correlation and we have successfully revised regression along with the linkage. We have revised the summary of the question and we have revised the common property.

Here we are done with the quickest and fastest revision. Take out 5 printouts of this sheet, fill it 5 times, what is the fun of it, then there is no need to revise it. Sir, let's meet. I know your second page. Second page, second page, whatever you want to write.

You are talking about this page, right? Second page, take this. Ayush, I will put this on YouTube, Revision.

You can refer whenever you want. And all the students who are referring to it on YouTube, I will put the notes on the Telegram channel. Or you can go to the download section of the AKnC the Maths Learning app, and this sheet will always be available, the updated one.

Because telegram keeps on running and it makes you lose your mind. I will change the updated notes at any time. So, the app AKnC, the Maths Learning app, its notes and DPP section contains updated notes.

If any note is changed, it gets deleted and new notes are updated. Guys, bye bye, take care. Bye bye, take care guys.

I hope you do the probability revision. Do something by yourself, my brother. When will I do extra practice? On one side you say sir, do PYQ, sir, do DPP, on the other side you say do revision. Do something yourself, then I will do something new.

I will try my best, promise. Okay? Bye bye, bye bye, take care.

Transcript for:Efficient Formula Revision for Statistics

Transcript for:
Efficient Formula Revision for Statistics