hello guys hello hello hello what's up I hope everyone is well, friends. you will be good this is your envy sir and let as get started okay today we're gonna do are one shot of this chapter statistics okay it is a very important chapter if you If you look marks wise then there is one question here guaranteed you'll be asked okay so yes today actually we will do one shot It will definitely be useful for you for mains It will definitely be useful for you in mains and also in advance because If statistics are now in your portion It will be useful for you for advance also i.e. one One question of JE Main and one question of JE Advance You can guarantee both from here that is why this chapter is it becomes important right because you You are already doing the mains and syllabus wise Also if you compare then JE Main's There is a syllabus and there is a syllabus for JE advance It is synced now right so definitely You have the same syllabus, you have to study the same thing You have to work hard once in the mains also will get you four marks and finally in advance too It will give you four marks, yes so let us get it It started fine, how many hours will it last Because obviously someone is there in the chat He will write now that how many hours will Sir last Right, so let's assume this approximately. It will last for minimum two and half hours, yes definitely We will answer all your questions here as well Will practice a lot of previous We also practice questions in between we will do so that this chapter of yours is Its four numbers shouldn't go anywhere Infact you can do a lot by searching It would be an easy chapter, isn't it, if you have read one Have you studied the bar theory well? because I have seen maximum children what do you do, you study the theory properly No, you keep taking shortcuts sir I saw a one shot of statistics Some people had it for an hour and some people So, in 5 minutes, the statistics will be like this we do it and put it but ultimately if You have to read it in detail, definitely this particular one shot is for you wherever you go We mean everything in JEE Mains Advance We will secure four numbers for both of them along with obviously a lot of questions which that your recent previous year the questions will remain the same okay yes so let us get started ok turn on yes yes yes good evening good evening all of you and tell me How are you all? Have you come? Hope the preparation for JE is complete blessing It must be going on in a good way, it is the end of everything Definitely whichever children join here new If you are going then definitely you will go to the channel Also subscribe and yes here and You have too many one shots going on Like yesterday also we had a session where But whatever formulas you have in physics No he has a marathon session so tomorrow too he will have one You're going to have a marathon, okay, so will that. definitely you can see it if you I am facing problem in Physics, particularly Because nowadays in physics there are few Formula base questions are also coming right You know there's a lot of theory Physics has also started appearing in JE Mains these days If it has happened then it is important somewhere There are formulas on it, right? Direct questions would also be asked by you so that's why we also had another marathon yesterday You have kept it, Indrajeet sir is going to take it from you So yes, I think his session is already The schedule is done, you should check it once that will be your tomorrow ok yes p y q A lot of kids are talking about the series So yes, definitely that is also in the plan, right? I won't reveal it to you right now But yes, we added a little surprise element I have kept it for you guys, okay so yes P PYQ series for YQs also I am not talking to you but P Y Q You will definitely find something here If I am going to meet you then yes stay tuned definitely subscribe the channel p y cuz you That will be solved very well for you is my guarantee ok a little wait but you have to because it's up to him right now If it is working then start it ok let's start statistics ok We will cover all the concepts here one by one. We will look at the line, in this we have no theory If it is kept in starting then first it is empty You will read the theory and almost assume that I will give you empty theory in 30 to 40 minutes I will teach you and will answer all the questions at the end which is also a mixed question because in this Many come in the beginning Theory theory theory let's go and in the end your If all the questions are asked then you will understand the theory Read it well and only then we will come here If you start solving the question then No one will spam in between that sir Ask questions, get this done, get that done, everything it will happen just calmly, okay yes or no okay let's start okay okay Before We Start Kids Don't Know This is our final revision booster as well it has started then definitely if you It is in the last days, isn't it? Because you are getting everything in the test The series is booster sessions of P Y Q There is a discussion, there is a PDF and whoever is the highest All those lectures are quality lectures. You will get Physics, Chemistry, Maths all together and everything sorted out for you This is the only batch that you will purchase and everything will be sorted til there is infact you can see this You can also use it for main second attempt which the child can do till the first attempt that because in this we have done it priority wise I have posted your chapters, okay, bucket one, two. So let's say if you just started with bucket one And if you can complete only two then bucket Three ones you are Jee Main one after Jee Main you can use it for two as well ok So you will have access to the batch till the And then you can utilize it well okay you can let's start ok to start from the very basics I will try to tell you the first topic You must have understood the type just by looking at it data is ok statistics which is the chapter Somewhere these days you know as much as you want right Nowadays companies are also coming, so all There are database companies, can you tell me? ho, which are the companies nowadays which are very We use high data because Nowadays this is AI ML deep learning right? Artificial Intelligence, all these things A lot is going on and everything is happening somewhere There is a lot of use of data in Neither the branch that studies the data of mathematics, that is what is called This is statistics, everybody knows this much then statistics is basically the branch of mathematics which deals with the data Something about how to organize data How to remove interference data wise Because everything is connected to data No Done instagram2 is done what is in everything It is just data and nowadays you know that Those seem to be maximum packages like if you assume that because obviously a I have a dream of going to IIT After going to IIT, there were many such I know a lot of kids who are getting into IIT First do B.Tech and then do higher education For studies, go somewhere like US they are going somewhere so basically After doing BTech, you can do MTech Do MTech or MSc then one Specific branch B comes for doing B.Tech Obviously B.Tech comes after that then you Do you have to do it in computer science or civil? Mechanical, whatever branch you are running you can do it in that but after that when you You will go to do MTech or you will go abroad to do MSc From any foreign university or from India you can also do it from okay so there is one in it There comes a specific branch where you Specially, everything related to data things are taught okay where the data how to sort how to arrange its mean median mode would be a lot of things ok how to clean it up Because a lot of redundant data also comes right? yes or no so all those things are cleaned up how to do it how to sort it that's why everything is taught to you And its packages are also going to the highest Nowadays, if you look at IITs, you will see that most Who gets the highest package which is a data He is a scientist, his post is His name is Data Scientist, you can imagine That means some of your children will go on to become If you become a data scientist right here You have to look at the data all day and night ok yes or no but yes it means its that simple It does not happen here what we are going to read Because this is just 11th or 12th level JE JE level advanced level JE If there is statistics, it would be quite easy okay so that's what we're going to read here Let's look at your syllabus once What is there in the syllabus because obviously If your syllabus has been revised then you You should know, let's take a look that look at yourself in the syllabus whichever syllabus I am here, I will teach you everything, right? I do not want to listen to anybody who it is in the syllabus, you have to read it quietly yes and No and whatever is not in the syllabus, it will not be I will teach you that is also for sure okay and The syllabus for mains and advance is same If yours is same to same then there are no changes If not, then this is what you will get in statistics If you want to read then read it below If the syllabus of Probability is written then it Obviously we are not covering this in this video we will do empty statistics ok So what is it, it is the major of discretion Calculation of mean median mode of group Do you know what is data group data? There should be a group and then it is ungrouped If there is data then we do grouping like We have a lot of kids who have different If there are marks then we clubbed it, brother How many students have scored 30 marks How many students have scored 40 marks How many children have scored 50 marks in this We call it grouping or sometimes interval We can also do groupings based on how many brothers have children who are between 30 and 40 How many children have marks in their 40s and 50s? If you are getting marks in between then all this grouping is okay so group data so Basically the mean, median, mode of the group data is How to find out everything, you have to read it yourself Ungroup data Now let's assume that the data is ungrouped I mean we don't know how many kids there are Each child's name is written in front of him Marx wrote that brother this child is so number this baby its so many numbers this baby Its so many numbers, this is ungrouped data any type of grouping there we have If it is not done then how can it be found as mean, median, mode? Let's take out all that, you should know the syllabus Calculation of standard deviation is in How to find standard deviation How to find Variance, Mean Deviation and You have to read all this also for group data also need to read and also for ungroup data If you want to study then this is specially meant for JE I have seen it in mains, so the question is from here Infact they are coming in advance also from here The maximum question that comes is standard deviation mean deviation and variance if these three things You understood it well for group data and un group data also for both then Then this chapter is sorted Apart from this, it will take you a lot of time No need to spend four numbers Be sure that you are fine, whatever God says It is written that questions come but They come a little short but you never know the meaning If you are a JE then it is as if you had joined JE in 2023 It was not there till 22, it is there in 23, so okay yes Nowadays the trend keeps changing a bit that is why it is better that whatever It is mentioned in the syllabus only once You have to work hard in Mains and Advance, there is more work ahead If it comes then work hard once and you will reach the end It will be useful ok so let's get started As we talked about types of data, Ungroup data is ungroup data means children like for example simplest example which Everyone understands that this is the child's name his marks are in front of him brother this one kid its 50 marks right now just like you Test series was a test of Vora classes The series is going on, tests were conducted on Sunday 253 was the highest marks ok so Name of the child in front of his/her marks Name in front of his marks then this is ungroup The data is for ungrouped data now we You will study how to find the mean and the median how to remove the mode good The group data is of two types There are only two types in your syllabus And if you want to study then form a group The first in data is discrete data. Discrete Free Frequency distribution maybe a little bit if you If you have read it then you will have some idea So one is the discrete frequency distribution table that table was created right If you remember your childhood days, you have to read and One is continuous frequency Distribution Table to Continuous Data There are basically two types of discrete data if group data and ungroup data is ok then You have to read this one by one, everything in it is yours If you want to read good books then you should know what is the meaning of the words how to find out how to find out the median How to find the mode, you have to read it all means average median is somewhere Your middle observation center somewhere observation mode means whatever Observation Highest Number of Times Repeated The observation which is repeating is happening the most number of times okay this is I have given you a rough idea But let's read a little bit in detail Now suppose you have ungrouped data How to find the mean for ungrouped data Mean means average then how is it mean no, like for example here You have been given marks, right? Believe it or wait, some different people and his weight is 92 KG and one is 96 This one is of 104 kg, isn't it 10 This is KG's, everyone is waiting for you to take it out is the average mean for ungrouped data it is ungrouped look any type of If there is no grouping then how will you find the mean So what you mean is simply sum of Observations divided by number of observations yes it So everybody knows the number of observations Find out quickly how much it will cost 92 P 96 P 104 P 101 P 105 P 99 P 97 p 108 someone will calculate this divided By number of observations, what is it? So it is eight I think yes, you can count the total number of No, how many observations will it bring you can remove it from here ok Ultimately I will come from here now but this So it is very lengthy, see someone in the chat The answer is not telling why this is so This is the length method, you will have to add everything then Who will have to divide by 8 so much Sir, you will do it, but I don't feel like doing it If I did it in the exam then that's why it didn't matter give me some shortcuts, there is a shortcut for this And many more, your answer will be something or the other from here. It will come, you take it out, whatever comes I Should I tell you a direct shortcut? You won't do this, it's a rubbish method in the exam This is what normal kids do Some of the observations, we used to do this in childhood, 10th I am you are in 10th right now okay yes This happens but we do not use this method There is a smart way to do this look what is the shortcut shortcut it is Like all these observations are 100 You have to take an estimate of around If you have to do a miracle then make a guess What do you think after seeing all this? that how much will be the average then if I this When I look at all the numbers, it seems to me I am thinking that it should come around 100 You have to guess, this is also called guess method it is a guess category you have to guess ok if you want to guess then guess anything You can do anything as per your wish, your answer Still the result will be same, you can assume 99% guess I guessed 100 but still it is your answer My answer will be same, that is mathematics right that is the beauty of mathematics that You can believe anything in your mind This is a hypothetical guess so assume that I guess I hope it should come to 100, you give the answer You can guess anything according to your own can you do any number you can guess I have guessed 100%, okay now whatever your guess is This is a Pisces, I just guessed it hit that mean cuz i got that feeling all the numbers some numbers somewhere something which is more than 100 something which is more than 100 If it is less then I think I will accept 100 Now all you have to do is just see this that this number 92 is less than 100 so How much less is it? 92 is less than 100 so how much less is -8 can do this -4 is + 4 why did you write more than 100 plus because it is too much how much is too much four is too much okay this is too much how much is too much is more than p5 or -1 -3 or p8 okay so write 100 here and then this Whatever you have calculated, just take their average. Just take their average, how can you take the average are the sum of observations divided by number If your observations are correct then take their average. Just add it here and your answer will come. What will be their average then see everyone's Make it equal, if we add all of these then this and this So it got cancelled, add some off If you add an observation then this will also get cancelled If this too gets cancelled then sum off observations how much is coming to No, if 5 - 3 becomes 2 then what is the sum of observations divided by the number of observations and that Add it to 100 and you will get the same answer 100 becomes 1/4 means 100.2 will become 1/4 If it is 0.25 then 0.25 out of 100 from here also If you take it out, this is what will be coming out, then this Do you have your own shortcut method or not? what do you do you can guess anything According to your calculation even if you guessed 99 Even if it happens, your answer will be the same The one that is there automatically adjusts You have to take the average of the one above The average of the numbers of the people above is a bit It can be time saving if there is anything like this if asked then okay one of the shortcuts You can say this is okay it happened For ungrouped data, ungrouped data means eight Marks of all the children are given to you individually but if it is not individually given then made a table like this Isn't it like there is a child who gets 10 marks? R there is 10 number then this one has 20 number There are three children who got 36 marks. So we will make a table like this, this is what we will call are discrete frequency distributions Why is table discreet called discreet because marks are different like 10 Marks, there is no interval being created in this do you see any such interval at night how many people between 10 and 20 have If you get your marks then this interval will not happen If the interval is not working then he should It is called discrete frequency Discrete distribution understood What is the frequency distribution here? marks are written on it and how many are these numbers The frequency of children's birth is written as There are four children here who got 40 marks There are three kids who got 50 marks, okay? If you are given this discreet table then how to find the meaning in it so what is the meaning in it To find out sigma a x a you have also done this I have read it in my childhood, right? I have read it but still write it down once mean mean will come si f x aa divided by sigma a okay so you have f and x here You will multiply it and then take its sigma So here this sigma f x comes from here Your answer will come from these 1779 calculations Obviously we won't do it because they want to learn If you haven't come right then you will find out the meaning If you have ungrouped data then sum off Observations divided by number of Observations If you are given some data like this in which marks are given frequency given then sigma f a a upon sigma a this also indirectly it is the sum of observations divided by number of Observations are fine and if continuous What is Frequency Continuous Continuous mean in which class interval is given This is called class interval like 10 How many children got marks between 25 and 30? Two children got 25 and 40 marks How many children got marks between There is a whole class of three children out of which We measured how many children there were Seven people who got marks between 40 and 55 What should you do here when children come? what happens is here you have to take the mid point isn't it because when you come to sigma f x if you do it then what is x aa in it x aa will be the mid point then take the average of these two Low average means 10 p 25 d ba 2 okay so how much will it cost 35 di ba 2 look at this 35 Divide this by your x = 35 divided by 2 similarly how much will come here come here will be 25 x 40 divided by that means take the average If you find the class interval given by x then How to calculate the average xi-xii / si f and if there is a continuous table You have given class interval, this is class The interval says something Nomenclature If you don't know I I'll tell you, it's like calling it class interval this is the one which gets completed They say this is called class interval What is the lower limit lower limit 10 upper What is the limit 25 and the difference between them that happens is called the range of the class Height is also called class height of class It is called size or also called range Sometimes it will be 25 - 10 i.e. 15 Class size: This is the lower limit, this is the upper limit This is the upper limit minus the lower limit Range or also called class size Now let's clear everything and move ahead Let's come to median, what is median Median is the middle observation but it So everybody knows about middle observation I know it, but what I don't know is That is, first you have to arrange the step one hota hai you need to arrange in ascending And descending order means whatever your data arrange that first arrange this You will have to either increase or decrease In order from smallest to largest you You can arrange it or even do it upside down here But it's the largest and there's Smollett You can arrange them in any order you like arrange in ascending or descending order two like for example which is the smallest number It is 92, right? Which one will come after 92? 97 will come 96 will come 96 has already come then 97 will come then 99 will come okay then 10 will come, then 104 will come, then 105 will come 108 will come and then you have to see that the middle Now see which is the observation Number of observations is even here If the number of observations is even then your Two middle observations will come, both of them look there is number three here three here three here three here there are two in the middle so whenever the number is off Observations will be either even or middle If two observations come then if two middle If the observations come then this is the median that this it is median what is called median then that In case tell me how many people you know is this the median or is this the median of these two None of these is median, their average is okay so this data has to be taken The median will come if the two middle observations are If they come then the average is taken, then the median this will come actually the median will be 100 okay Take the average. You have to take the average if the number of observations are even then two middle You will get observations, you will have to take their average We will get the median and if the number of observations If it is odd then only one number will come, whichever is The number in the middle is your median brightness. Yes, this is done again ungroup data For if there is ungroup data then you can do it like this but if there is group data then how will you do it So make a formula for that basically Now you need middle observation here The observation itself is eight, so you saw that Brother, yes these two are the middle ones three here, three here, this to you directly It is visible but if you assume a long list If so, I would give you 200 observations or 500 observations given to you in complete Excel I gave you the file, what will you do next? There must be some formula for this That's why the formula is that if the number of Observations are odd if the value of n is odd So your middle observation comes from what does the median mean your median If n is the number of observations, then The value of is even if the value of n is even then what will be the median if n of the If the value is even then the two middle observations will come and we will have to average them here Your mid observation will come and go one will come then another one will come n / 2 pv meaning okay this will come and divide by two You will have to do this observation plus this observation How to remember Divided by Two Do you know what is the way to remember? You are like this Remember that if n is even, it means it is divisible If it is by two then first divide by two let's do it and then do pv and here If n is odd then since n is odd then it is divided by two it won't happen so first we will float and Then it will be divided by two, so remember it like this do it the way to remember is done and by the way You can also understand it, like let's say only five Observation is a friend, you can get it if you There are only five observations, so which one? The median will be the median will be 5 p 1/2 n is nothing but 5 p 1/2 means third observation will come this is nothing but third Whatever your observation is, that will be The median is if there are five observations. The third one becomes the median similarly If there are six observations then the number is off Observations are even if 1 doti 4 pa 6 then There will be two middle terms in it so basically in this we will have to do n / 2, right 6/2, only then You will get 3 and n / 2 + 1 means 3+ 1 whatever The next one is him and his average is average If you do this, its median will be 3.5, so the median How do they get it out, I think it is clear It is done yes and no middle observation for you Now let's take it out and move forward Let's do this, now ungroup the data, see Mean, median, mode reading for all three is one Ungrouped data will come one discrete will come one The median of the ungroup will come to you continuously It is clear now you come to the discreet one How to find the discrete one from the discrete one The table is given to you where there are marks and There is a frequency in front so this will be given you have to remove it yourself because You will have to choose the frequency yourself. right so this table will give you 20 like 20 how many children does marx have six children 25 marks how many children are there like this 20 students are there who have 25 marks Similarly 24 students are there who have 28 If you understood these marks then this is the whole table You have been given data of total 100 students Complete data of 100 students is given to you If yes then first of all you have to take [ __ ] let We will have to find out the frequency to call it Coulter Frequency Coulter What is frequency again you know all this I studied a little somewhere in 10th if it is right then how can I get the frequency Let's find out the mean of cumulative frequency How many children are there who have less than equal Look, this is 20 marks. This is 20 marks. How many children have six children then less Then equal to 20 will also give six, brother 20 or how many are less than 20 you can see the complete table So number 25 is it, right? Its number 28 is 20 or How many children have marks less than 20? Similarly, children have 25 or less than 25 Up to 25 means less than equal to 25 lessons Equal to 25 how many children do you have so these 20 these are kids, they have 25 marks so these too You have to count yourself and these six should be 20 x 6 It means you will add both of them Frequency means the first six will come first This will come empty then add these two then Add these three, then add these four This will come out to be 6 p 20 26 in this Then add all three and add 24 to it. two this will become 50 then this comet Now you will have to find out the frequency Why calculate Cullet frequency Because the median is the middle Observation is done on how many children in total There are total 100 students in the class now Understand it carefully, you need to understand it a little It is not as if it was seen as a lecture and Consider it over because when the advance or If questions come in mains then they will be conceptual If he comes then consider it okay, total how many students are there 100 what should i take out that the child in the middle How many numbers are there in middle observation middle Observation is the median total 100 If you have 100 children in total, what do you think? you have to divide by n Because I have to find out somewhere if there are total 100 children then the 50th The child is there, where is he now but here but the value of n is even then the total number of Students are 100 then give middle observation Which all will come? One will come, 50 will come. If you share, then another one will also come If you get 51 then you have to average both. Only then will your median come, then you 50 observations will have to be found out and 51 Now you will have to find out 50 You can see the observation from here, you can see these 50 doesn't it mean there are a total of 50 children who marks is lesson equal to 28 There are 50 children whose marks are less Then equal to 28 so the 50th child will have How many marks will the 50th student get Like here there are six kids who got 20 marks. There are 20 kids here who have scored 25 marks. By this time your total will reach 50. Will you add all three of them? The total of these three how much is it if it is 50 then till here your 50 The next child will be complete now He who is next will get 28 marks, right? sorry the next kid has these marks and This frequency will be for the next child You will get 29 marks which means the one who scored 50 The child has 28 marks and the one who got 51 The child has 29 or 50 marks Observation is 28 and 51 observation is 29 And if you divide it by two then it will be 28.5 Your answer is what is the median of this table median will come did you understand it or not total There are 100 children out of 100 children you will get this You will have to look at these 50 students if you are arranging then when you arrange it then it is If there are kids who have 20 marks then 20 20 20 It will come six times like this, are you thinking it will be like this six Times will be written and then after that 25 25 like this It will be written 25 25 25 20 times and this 28 28 it must have been written like this 24 times, okay After that 29 will start directly, 29 will be written 28 times if it is written like this then it is complete I have my own determination in it, from here to here If you calculate till then it will come to 50 rupees. It means this is the 50th observation this. This is 51 observation 50 and 51 shone na 50 51 so yes your median will come from here good If Continuous Frequency If there is a distribution then there is a formula in it I happen to have seen this formula somewhere It looks like the median is being taken out Continuous frequency means that Continuous in which the class interval will be five There are children whose marks were zero and what does it mean Class interval is given Frequency is given So here you can see the cumet frequency again. You will take out 5, then 5 + 3, then 5 + 3 + 4 keep adding basically 1/2 inch frequency ok it will come here now how can median If you extract it, then this formula is continuous then you would get this Now you will have to apply this formula what is it so l plus all this is there in it what is L a is the lower limit of the median class now what is this median class The median class is the class whose culet Frequency is greater than equal to n / 2 So you have to find n/2. What is n? Total number of observations: How many children If he is in the class then see how much is n How many students are there in total? 53 in If you add up all of them, you get 53 then how much is the total There are many students, how much is this in total There is data of total 53 students. what you need to do is to divide n If you want to calculate it, it means 53/2 will come then this how much will it come it will come almost 26.5 So now you have to see whose have a Quelet frequency greater than 26.5 Which cumulant is greater than 26.5 this one is the frequency so this one which The class will be over, it will be yours Did the median class shine or not? class is that class whose [ __ ] frequency this is what is written look median class is that class whose [ __ ] Frequency is greater than n by 2 n by If the value of weight n is greater than I calculated how much it is, it's 20 26.5 Which number is greater than 26.5? It is 29, right? So the one with 29 is your median class. It's done now. What happens now? Is it the lower? limit of the middle class let's go into this we keep substituting in the formula okay so l is the lower limit it will come What is the value of 60 l 60 substitute This will give the value of 60 plus n/2 We just found that 26.5 is n / 2. what is cf what is cf the frequency of the class means the first class ok precy class to cumi frequency of the preci How much is the class one higher class is ok So that is 22 CF Culet the frequency of the Presidium Class Median Class Frequency Median Class Frequency Quelet not frequency so that is sen okay so this is sen and h what is a is the class size class size is upper Limit minus lower limit is your range if yes then what is the size of the class it is 1010 no 60 to 70 70 to 80 80 to 90 10 10 ki means if 10 comes here then from here also will come that will be your median median understanding If you need continuous If you want to find out then use this formula will have l is the lower limit of the median Class f is the frequency of the median Class I Qubit Frequency of the remember the presidio formula because It is mentioned in the clear syllabus that you will have to study all three One should know how to find the mean, median and mode for For Discrete as well as Continuous and also for ungrouped data then this the formula might make sense for you okay and moving forward I think now The median is clear to you, now we will come to the mode ok which mode will come in so in this mode will come okay so what is mode most repeating observation like suppose you see something Some observations are given 1 2 2 3 3 3 4 4 4 4 mode what happened whatever observation is like this which is repeated maximum number of times if that is your mode then what should be your mode jaega mode is that observation watch is Repeating the maximum number of times here But one confusion arises that Sir, if like This is four, that is four times, if you assume If I add three, one and three, then accept it I added another three now the three that is also four times and the one which is four, that too If it is four times then whom will you call mode now both are there means the definition is that most repeating observations then both are most The one that is repeated is four, that too four times and the three is also four times so If you go according to the definition then Both modes are okay so that means most Repeated observation happens basically here whatever observation, generally whatever question Only one of them will come in the exam There will be observation which is maximum number of times will be okay so if you you Ungrouped data is given for different children Marks are given so just see that Which is the maximum marks which are maximum The children have got those marks for which highest frequency is basically right so Even if you are given a discrete table how to remove g mode let's say Discrete Frequency Distribution Here marks are given and here Frequency given is five children who have 20 is number 6 and 18 is number 7 there are kids who got 25 marks okay nine There are children who have 35 marks and 10 children whose a should take the negative -5 marks are ok so basically what is the mode will go to -5 meaning the one whose frequency is the highest it is more, that is your mode, it has shone, right? The one which has the highest frequency If maximum number of children scores -5 then it is yours jaega mode is that observation watch is If repeated then you can remove it for ungroup also You can also take it out for discreet possible if such a discreet table is given then you can see that the highest frequency Whose marks are those then it will be mod minus f okay yes it shined good now if Continuous Frequency Distribution If the table is given then continuous means again like this This is a continuous table, it has class interval the size of the family is given and the number of Families are given that brother there are seven such families Suppose it is a city or a whole is it a district or whatever it is Data is given that there are seven such families Those whose family size is between one and three It is in the middle, which means there are maximum three members There are no eight such families in which three to five is a member There are two such families in which there are five to seven member and then these big families in which there are 111 members also okay so this Basically the data is given to you, if I If you want to remove the mode then how to remove it To find the mode, this is the formula basically again you should know l f1 - f0 your this whole thing what is l in this l is the lower limit of model class now this model what is class there median class there was model class model class is that The class which has the highest free frequency Whose frequency is the highest The frequency is the highest, you can see it all whose highest is this one's highest right so this Your model class is done this is model class this is called model class ok rest of you If you can take out all these things then this is basically What will happen to you, see it here f1, n and f2 are three things right, so this is your f1 it will happen the one with precy won't be f goes and the one who is sexy is f2 it goes, did you understand, one later, one first Now you will say that Sir if model class If the first one comes then take zero take it if you assume that this one which is right now then Your second class came in second position that model class has come, if the first one comes if this happens then the value of f would be zero It would have shined if it meant on the end points If it comes to extremities then I took zero Do yes or no, then this is f1, this is f no, this is f2 what is this, this is f1 The frequency of the model class f1 is the What is the frequency of the model class f0 Frequency of the precedent class to the model Class that the one with Presidium and the one which is f2 Successio will get the answer then will you do it what is the value of l, it is three right plus f1 - f1 is how much f1 is 8 - f0 is how much so f0 is 7 then two times f1 so 16 will go - f nine and f2 then 7 and 2 will come and What is the size of the class? 5 - 3 2 It will be okay, this upper limit minus lower limit There is a limit on class size here Two will come and you can take it out from here. Basically all the value has to be extracted by putting it So is it clear what is mean, median, mode? You can remove it even if there is ungrouped data You will find out the discrete frequency Even if there is distribution you can take it out and Even if it is a continuous one, you can take it out ok So all this is in your syllabus and further Let's increase one ampere cal formula Ampere Cal formula means experimental There is no proof or anything of this, it is just this If it happens, it happens, you have to remember it, okay? If it is then ultimately there is an estimate of the Emperor tomorrow's formula means an estimate that if You are given the value of mean, the value of mode is given and the median has to be found then this You can find out from the formula if any There are two givens, any two givens then there is a third can you take it out, now how can I remember it you will because it is very hard to remember If it is work then is there any shortcut to remember it Do you remember this sir because you read it It must be somewhere but I don't remember right I remembered it looking like this Pisces Who is Pisces? You are Pisces; I am not Pisces. If you are a Pisces then ok then remember me like this Who is Pisces brother, we should not think much about ourselves Pisces will say that we feel that in front You are Pisces right? So who are you? Pisces if you are there then you come here for that you are mean okay you are mean and plus mode mode The one who is there comes alone because he This one thing is enough, how can it remember the mode now? You will do it, you should see which mode it is, But we are standing alone, standing like this, remembering It is okay to take it, we are standing in the direction we are We alone are enough where we stand if the line starts from there then it is like this remember this and I remembered it like this that Three three kiss means this is the confusion It happens that who was efficient in what what was one what was two what was three so which This is the biggest word, look there are four in it There is an alphabet, it also has four alphabets Median M.E.D.I.A.N. is the highest If there is an alphabet then its co efficient too It will be the most, so remember it like this So the co efficient is also the highest so three Times median is equal to 2 means plus mode I mean remember it any way you can but remember it Yes and no are important sometimes such questions You will realize that the mean is given and the mode is given If the media asked then this would be there Formulas you should know There is a one of a kind formula for statistics ok now let's start the real class Let's do it, till now the revision was going on Understand it like this which is in NCERT which we prepare for basic board exam I read all the same things, but still the basis is working This was your real theory from here It will start and from here whatever you More questions will come from what will be taught If there are chances, then it's okay to listen carefully now then what is deviation deviation is basically x aa minus mean this is mean okay You can represent Pisces like this also ho so this is deviation from the mean It is represented, it can be done like this also yes sometimes I also do this, this is mean is syllabic representation either by m or by You can do it or you can do it x times also You used all these symbols in physics won't it be mean velocity mean average average We just do average everywhere, so it's okay this is a good deviation what is deviation So, how many marks did I get? Suppose I I got 50 marks in the test and the whole class The average is 60 then the average of the class is 60 and I only got 50, this is called deviation Deviation is how much less I got out of 10 marks If your average is less then your marks will be minus the What is your average marks? 50 marks What is the average of the class if it is 60 then the deviation What is the deviation of minus 10 Now why is this minus coming because you Be below average Whenever you are below average If yes then your deviation will be negative Suppose your marks are 100 and class If the average of is 60 then your deviation will be P40 means you are way ahead of the class You are an above average type of student, I understood Deviation means your minus the average that is There is deviation of any observation, If you can find out the deviation then it is called Deviation Now you have to read basically two things is one mean deviation is one standard deviation So what is mean deviation? Mean deviation This is the formula, this will directly give you If you know the formula then Mean Deviation what do we do first Deviation is found out by your observation, isn't it? Minus the average of the class and then modulating all Add them sigma sigma means take the turn Whatever the deviations of all, their modes are take their sigma two make them even and down comes the total number of observations this is the Formula for Mean Deviation in Mean Deviation Did you understand or not the meaning of mean deviation Remove deviation, take mode of all and add them and divide by the total number of observations For example let's take an example No, you will understand it a little better take the example, in my opinion you take the example yes there is p here so try this one As before, let us assume that the first five natural numbers okay the first five natural numbers You have to find the mean deviation about the mean Also look at the mean deviation, there are two types of mean You can calculate mean deviation about mean Or also find out mean deviation about median If you can then what is the mean deviation about the mean? Here the mean will be used for your marks Minus Mean Marks Average Marks If you If you want to find the mean deviation about median then Just i will come here x is minus Median here, just make the median, that much difference everything else happens the same total below number of observations rest everything will be same to this is mean deviation about median This is about median and this is about mean is the average mean of the average class which It is average and that is fine so here you can find yourself If you want to find the mean deviation about the mean then first First find the mean, find the average How to calculate average and sum off observations okay so sum of observations divided by number of observations so this How much will it come? It will come 5 * 6 / 2 / 5 It will come to 3, okay, means how much did it come to, three Once it has come, every single observation minus the mean from me okay every one The average of the observations is minus Do it, mean minus, then it will come to you Look at the deviation of this child What will be the deviation -2 it will become -1 will become its Ro will become its one and This will be done, did you understand the meaning of the class? The average is Thr and this child has the same number If the average of a number class is three then This kid is below average isn't he? Deviation is minus all these are deviations The mode of deviation has to be taken, add the mode by taking it do it, mod it, then do it sigma Meaning, add it and the total number of will come down Observation then total number of then from here you will get the mean deviation about the mean okay so how much is it + 2 4 4+ 2 6 6/5 It will go, meaning basically 1.2 will come out, the answer is clear What is the final answer 1.2 so how to find it is the mean deviation clear? is every one You can do it in the same way from observation Take all such observations and write them down Subtract the mean from this and you will get the deviation take the mode of deviation and add them below The total number of observations will be the same method is ok from here you can calculate mean deviation You can easily remove any tension related issue if mean deviation about median is If you have asked then from each observation you Minus the median Minus the median by taking the mod of whatever deviation and summing it up Below is the total number of observations. Well now Sometimes if group data comes in this then This is for ungrouping data. If group data is present then If it goes then the frequency will also come Basically just add one extra frequency two you're right here sigma f is aa no basically that's why here sigma here f will come down and also down to sigma f that is n The limit f is what we call n, the total number of observations okay so in that case your The formula will be like this in that case This will be the formula this formula If we assume that tomorrow, discrete or any Group data given is basically discrete wala or continuous then this in it Formula will work if there is ungrouped data different data like these are 1 2 3 4 5 different You can do everything in it simply If it is clear from the formula then the mean The deviation is clear now let's move further and Now let's come to standard deviation and variance Pay So again mean deviation standard deviation You can find the maximum number of questions related to variance here. but it will be asked in the exam ok What is the standard deviation of this Again this is a simple formula, do you remember it? If you have to do all this, then how do you remember it? you will do it and the standard deviation is representing Sigma and its square it and that is called variance So just look at two small theories that's why I am getting started in the beginning I will do the theory and give you all the formulas Only if you remember it will you enjoy the next question We do all types of questions and also You will do whatever you can to get into JEE Mains no they will cover everything so definitely you Your statistics question will come outside of this. I can't, that's my guarantee, how can I whoever can make it will make it I will get it all done for you, outside of this the question will not be able to be made, if also there are p y cuz basically we have them too It is divided into different categories We will solve this now too but this formula etc. are important, you should know all this It is important to remember that variance is correct What is the formula, variance is sigma square this one just square this one root is root will be removed and this mean is written is this nothing but some observation divided by number of observations this is Remember the formula of Nothing But Mean Variance If you want to do it then do it like this, Sigma X A Sk divided by total number of observations minus mean square is this If you ever ask questions then I asked about Sigma Squad PM Scr there so this is gonna take the squad here shift sigma squa plus m The formula for square would have been even simpler that's all you have to do okay sigma x aa sk divide ba a ye m squa co If I shift it there then Sigma Scr PM screw this will come sigma x aa squa That means by squaring each observation Add it and the total number of will come down This observation is also very much in question Nowadays Sigma Squad is coming directly to you If I ask for help then don't sit down to take it out I have to go, what do many kids do? First let's take out the sigma sir, then I Then we take them both out and put them in square We will add it after doing this, oh brother why waste time I asked you what you are doing, just apply this straight away formula sigma x is the sum of every observation Square it and add it and give the total below Divide it by the number of observations Remember its direct formula sigma scale m m squa is directly this ok so Put this so it is clear, is it good Now this is the standard deviation for ungrouped data is ungrouped data then it contains If there is group data then it will come here The frequency will come, that would be the only difference if we assume that the variance is right variance what is the formula for variance The formula is sigma x a sk divided by n and minus sigma x aa Below is the total number of observations and its hole the square of the variance is what it means if the value If there is low group data then the frequency here f will come, f will come here too, then that's it this is the formula and this n is what you call n If you want you can write sigma f, okay n is nothing but it is sigma aa here too will go to sigma a so this is the formula for Group data If there is group data then it appears if there is ungrouped data then but Normally the questions that are coming are ungrouped data more of these come ok let's move on Let's move ahead, there is another special concept This is also specially for your JE Advance This topic is mentioned in the syllabus, you should see it The advance syllabus is mentioned separately there this is what is this this is the analysis of Frequency Distribution with Equal Mean For example, suppose you are given two types of data one is class A and one is class B both are The average marks are same here also Here also the average marks are same There is a mean but there is a different variance. it is different it is possible like this just assume that there is a class in which everyone is about 50 The numbers are coming, if someone is getting 51 then Someone is getting 49 but it is almost his People from nearby areas are coming now it is second class In which everyone is getting zero marks And if one is getting 100 then by averaging it If it is only 50 then it means he is a total out lier There are absolutely duffer kids and there are intelligent kids too and second This is a class where everyone is around average okay so the mean of both is equal but The variance will vary because there the deviation is very high right so that's why If you have two sets of data given whose The means are equal but the variances are different So how do we compare them here Look, a line is written, what is the line written that if the standard deviation of group A is less than the standard deviation of group B You can also call standard deviation or variance. If you can compare then standard deviation of group A is less than the standard Deviation of group B from group A is Considered more consistent and uniform which has less standard deviation We consider him more consistent than you So simply remember it like this that whose Deviation is low forget about the standard whose deviation is less means less than the average of all If the marks are close to each other, the deviation is less, right? I mean suppose there is a child and a If it is average of the class then it is average of the class That child has 60 marks, that's why he got 61 marks Deviation will be less where the deviation is less But all the kids are around average If someone's average marks are 50 then someone's is 51 Someone is 49, if there are kids around We call it more consistent and more uniform this is more uniform data so In this basically you have to read statement one questions with statement two because nowadays there are many If you are coming then you may have a question like that will give two sets of data then statement In the forest they will say that brother this data A set of data is more consistent and in the second statement we will say that this that's why what is the reason this is why Because its standard deviation is low yes So if the one whose standard deviation is less and is considered more uniform whose The standard deviation is higher, the less Is it uniform or less consistent? Is it okay? So you should know all these terms Questions like statement one and two are coming nowadays if you have started then you have to be prepared for everything ok and so on Let's move ahead and now let's talk about the efficient of what is variation again it is the same Variation type variation is more two sets of The data is let's say this is class A and class B is okay this is class A there is data and there is data of a class B ok I want to compare both of them so the variation I want to compare that brother there are more variations Where are you? There may be another class or two. There is a class in which everyone is around average The second class is the one in which there are absolutely no duffers There are kids too and they are very intelligent If there are kids too then average out their average It is the same so if you want variation here If we want to compare then there is a term called We call it the efficient of variation What is the formula for efficient of variation Its formula is sigma up m sigma what is the standard deviation and is the mean Sigma is standard deviation m is the mean into 100 now whoever has more, The more efficient the variation the more there are more variables like let's say its co The efficiency of variation is increasing The efficient of variation of a is more than co Efficient of variation of b then whose ko The more efficient the variation the more Variable is data that data is more variable that is less consistent that is less Consistent That Is Less Uniform Less If he is stable, he is less homo genius then all this You can use words whose variation what is it that is more variable This is known as Efficient of Variation I am not able to understand that there are too many variables Meaning, it also includes those kids who are absolutely who has zero marks and who has got 100 marks There is a child on both sides of the mark too The intelligent ones and the complete duffers too ok so there is more variation here More variation means less uniform Isn't it a uniform? It's not stable. if it is not homogeneous then all these things you Can you say that you understood this also should be clear let's go ahead and now look here I am Let me tell you some small There are shortcuts, okay, so these are shortcuts You also have to take care directly, right? Because this question comes up very often Find out the variance of first and natural numbers then if the first n natural numbers have If you want to find out the variance then you can directly use this remember that is n in these questions It will be very useful to you for a long time You will not need to do derivation directly You can remember this as n s - 1/1 variance of the first n natural numbers is n S - 1/1 if first n odd natural numbers or even natural numbers, then This is what happens in both cases, n s - 1/3 n s - 1/3 n s - 1/3 and whose formula is this This is variance, this is not standard deviation this is variance sigma square The value of sigma sqaure will be First n natural numbers can be remembered directly keep it because there is a direct A lot of direct questions are coming these days, so straight If you knew what formula you would use and the answer will come directly okay like for For example, suppose I tell you that no From to 10 Tooth Till 10 Their Variance If you find out their variance then If yes then directly these are the first 10 natural if there are numbers then 10 are mean 12 this is the Answer: If I tell you that brother odd The numbers are 1 3 5 7 9 find out their odds Find their variance, what is this number? it's number five right the first five are odd Natural numbers to first f to n square my divide ba 3 toy will come n screen my ba 3 and there n [ __ ] my ba 12 If it shines then we can use direct formula Remember for variances and move on what is a magic table good what is a magic table it's super important question about it Definitely it will come, that is confirmed isn't it so listen carefully to this magic table what does it say that if suppose I I added something to each of my observations has a set of observations x1 x2 x3 till xn2 + k xn2 if you calculate the sum of the observed values in each observation If you add k then you can remember it like this that Jo Mean Hota Hai Na Mean Is Very Mean So Jo You will do the same with every observation The same thing will happen with Pisces too, remember There is a trick, basically, if you want, then how can you do it you can also remember but ultimately whatever you You will do the same with every observation It will happen with you too, if you make every observation If I add some constant to the mean then also constant will be added if you If you substack some of your observations Every one of them will be substacked in the mean time If you multiply the observation by k then Mean will also be multiplied by K, every one If you divide the observation into Mean will also be divided by ke so whatever you You will do the same with every observation We will get along because Pisces is very Pisces okay so this is how I remembered it and standard What is deviation? Standard Deviation And by doing plus minus the variance the variance remains unchanged. It doesn't matter if you every Are you doing some plus in observation or not You are minus something in one observation If you are doing a minus then do a plus or minus the standard deviation from that, or Variance doesn't matter it will Standard does not change by doing plus minus Variance does not matter Yes If you multiply each observation You will multiply it by k k * x1 k * x2 So the standard deviation is Here the mode will come basically from mode it will be multiplied okay if you every one You are multiplying the observation by k then the standard deviation will be multiplied by mode is it not and every observation if you are dividing by then Standard deviation will be divided by the mode both have mode because it is the same If you route Sigma Squad then the mode will come Sigma squared is variance sigma standard deviation happens when you take the root If you do it then a mode will come, so pay attention to that mode also keep and there is a square here because Variance is obviously sigma squared to k will be multiplied by the square if the values such as Suppose you have a set of observations And I double checked every observation Tell me how many times the variance will be How many times will the original variance increase If I double every observation then The variance will become four times and one if every I tripled one observation If we multiply it by three then there will be variance nine times the square of 3 will mean The squeaky factor comes basically shine if you want then this table is for you take care directly because even this those are pretty good questions okay so Yes That Was All About Theory I've finished it completely, now whatever is after that All those are just questions, so as many as There is also a question, we have answered that too separately Everything has been done till here by dividing it into categories I understood something, before I doubted anything If it is there then you have to ask, we have seen till here All Mean Median Mode Mean Deviation We have read everything about standard deviation You have taken all the formulas and theories and you are finished it is there, whatever we do after this that is only questions and the questions that are there I have also divided it into different types so that's it we will read it type wise right What types of questions can come in total I think six to seven type of questions. The entire statistics chapter is written in this way If you do your research and see, six to seven types are there these seven types if you did it well outside of it If no question will come then there will be different categories By dividing into different types we can You will practice the questions Ultimately when you solve previous year questions You are also doing different types of Practice questions, not just one We are doing it in types because there are only one or two types which is mostly asked right so kids keep doing what you do The rest is missed and then the next shift If something different comes in then ours We suffered a loss, so we went and read something else. so that's why I had to type all of this it is necessary okay what is type one type one have two observations are missing this means this So infact you should understand it like this that Question if especially about JEE Mains If you do that then read a lot of previous years There are countless questions on this, meaning you can count them You won't get so many of these super It is important, you should repeat it most also Can you say this specially for JE Mains Probability of question coming from here that's too much you can say that because the previous question is obviously It's too much, okay, two observations are missing What does this mean, you must understand it What will you do, for example, let's say 10 observations If there are 8 observations out of 10 observations then I will give it to you, suppose it is not there, it is there -3 it is how many are there five or six or seven And there is eight, right? Consider this as zero and give me two more. Observations will be missing, they will not give They will ask you to find out their value They will tell you that there are 10 observations. out of eight here are you take out two and here But the mean and variance give you the question We will give it means it is a reverse question basically mean will be given variance will be given Observations will be missing, you will have to remove them These two observations will be missing only two will be missing and so you will get two equations Create two variables and get the value of x and y These short length questions will have to be removed If so, such questions arise In the exam you will read this a bit later you can do it in round two because If there is statistics then it is a little lengthy It will be fine, how can we say yes or no Look at this question, let's try this Yes, this is the question of JEE Main 2023, right here This is saying that the meaning of six observation so you have six observations here is t 4 5 and look these two You made the x disappear and that's it, total six If there is observation then sum of numbers divided by number of numbers and this is given to you right The meaning of six observations is fi ye mean You are given five so this is the first equation From here the value of x + y will come from this is your value of x + y from here once taken out x + y will come right From here x + y will come out how much will it be 9 and the value of x + y will be 10 12 18 Is it shining or not, this is an equation of its own So here it comes right, I mean, I put myself in question. If given is then mean is sum of observations divided by number of observations one The equation comes x po and the other one is Variance is given to everyone, the formula of variance is known to everyone Do you know that variance is sigma? up n my mean square mean so question I am given, brother, I mean, it is given, right? the square of minus mean this is equal to Variance and variance also given in question then the second equation will come from here basically square each observation If you add them, then the square of 1 is equal to 2. sqaure 4 sqaure 5 sqaure x Square Total Number of Squares How many observations are there? six is minus 25. shift it over there it will become 35 or not 25 p 10 if i let him go there From here basically you will get the x swap If you get the equation then what is x square It will come once, take it out, calculate 35 * It will become 6 and all of them will have to be sent there So take out x sp sqa from here how much comes and then again two equations did you understand the variable, right? this is an equation The equation is this: you need to find out x and y So find out how much is xs + ys coming out to You guys will have to do this calculation properly yes or no did you understand this or not We have applied the formula for variance, so every Adding an observation by squaring it Below is the total number of observations minus the mean square of equal to variance is okay How much will the variance formula come here remove x s + y s from here x remove x + y so I removed x + y You do this calculation, how much is coming it's 164 it's coming it's 164 it's coming okay now after this look i.e x and va I will have to remove it, after this I have seen it A lot of kids keep doing this Meaning after this, different types of methods are used Everybody like a child will do that sir this Two equations, two variables, these need to be solved no sir then what will I do Take out the value from here and put it in I will substitute it, I will solve it like this Sir now this method is not workable from here Obviously x will be quadratic and the sum of x The value will come, if x comes then put it in you will do it, it will come, it is not wrong, some children Some kids keep doing this as well, what do they do isn't it here because x is square and if x is also positive then it would apply the identity is the hole square of x pwa i x pwa s p 2 xva okay 2 xva then its you know its value you know its value then we will take out x inva from here first x If the new one comes then we will take out the x myva If one Miva comes then what is the use of Aqua x miva two equation two variables from there If you solve it, then all these are lengthy methods. don't do all this in the exam You don't have to do all these [ __ ] ways What I am trying to teach you is that It is hit and trial, meaning you will see it no you are 18 then 10 more what did you think are you brother square of 10 p square of 8 It is 164, how many people saw it? If you want to score well in the exam, you should They say that toppers do very fast calculations. He does it, everyone who has the numbers can see it It appears that his mathematics is strong If it goes right then you should just see it So the values of x and y are 10 and 8. guess it directly because it is 18 Neither 18 means 10 more nor we can do 11 more can do seven different permutations Now try the combination, right? Then we can understand which ones and which ones I haven't gone yet, which means I can basically do 10 + 8 11 P 7 can be done 12 P 6 can be tried If you do 12 x 6 then you will get the square of 12. If you add 144 and the square of 6, you get 36. 164 will come otherwise your basically x and wa is that 10 and aa and if x and wa The value of is given, which means every observation is given gaya one has t is fur there is not 45 and x and the value of wa is 10 and 8 and now you get What is the asking mean deviation about Now what is your mean? Mean Deviation If you want to find out then subtract the mean from each one If you want then it means five, what does it mean is five so subtract five from everything If you subtract five from one observation How much will it come -4 This will come -3 will come -1 will come 0 will come 5 will come 3 it will come, mode them all and add them, ok Mean deviation shines or not, everyone's mode Then add it and ultimately how much will it cost This will become sa and one aa 8 and aa 16 and what will be the total number of observations is the total number of observations so this is will go your mean deviation okay so mean Final answer of deviation 8/3 is clear 8/3 The Final Answer Option C Option C has arrived Option C will ask you for mean deviation in the end so in the end all your both When the observations came, all of them came from all The mean has to be minused and modulated and then added Very clear, another question we will do in the same way will practice ok jee main 2021 This is the question, such questions are asked every year also hold your ear, there is such question Definitely you will get multiple questions We will meet, it's not that one or two is fine If we can get three of them then this is also the same is the mean and variance of six observations So there are six observations here like 10, 11, 15 a and b are ok divided by total observation right six observations and their Mean how much given is 10 right mean and Variance given so mean is 10 and variance 20/3 so the value of A P B will come from here And the second equation will sound like this to everyone square it and make it d so the square of 11 Square of A Square of B square divided by 6 minus the mean of square this is equal to variance okay so you're always removed from here Do the value of a p b What is the value of a p b Tell me you will go and throw me out from here The value of sp b s is an equation This is the equation and then you have to guess It is not that you sat down to solve it directly You should assume that the value of a and b What will come, tell me how much will come how much is a pb coming from here to anyone did you find the value of a p b a p b Has anyone calculated the value of what is the value of aps be once Take it out and tell in chat that 134 is writing is anybody coming on 17 17 It's coming and it's out of here Extracting by cross multiplying etc. You will have to get an ASCII scan here from and from here a p b will come okay this is a P B so 17 is coming A Sk P B Sk how much is coming is a scr ps b scr i think 145 will come, you try it, 145 is coming Then the sum of A and B The value is now obviously 17, not 10 or so 10 and 7 will not make the deal right because 10 plus 7 will give 149 And if this doesn't work then try something else try this and the square of 9 8 is not na 8 p 9 17 so square of 8 is 64 na square yes it will become 145 just look Basically 8 and neither a nor b has the value 8 and 9 8+ 9 8 s 9 s shine then a The value of 8 and the value of B is just this And what did they ask you? Basically, both of them If you asked about the difference, then the answer is absolute difference will go one okay finally option d is the You will answer, that means basically all the answers There will be two observations given that All you will be missing is the variance and mean You will have to do the calculation using the formula It's okay for you to go ahead and this is the next one This is a question, you should try it in your homework isn't it because it's the same again to you Like there are six observations mean given Variance is given and four observations are given then take the values of x and y and you know the rest yes it is right then you can do this as your homework Now let's go ahead and come to type two Type two is shortcut question then shortcut There is also a shortcut which is the magic Here is a table, see what the magic table says The magic table says that if you Add anything to the observation, subtitle anything Enter your variance and standard there is deviation it remains the same isn't it if we add anything in all the observations x aa + k Add or subtract the standard Deviation and variance are the same remains and does not change right then its A lot of questions come up about this Interesting questions come through direct shortcuts Put it on, see what it does to you, give it to you will give like here it is given that the limit x i - The value of p is 3 and x is the times square of p Its value is 9 and you will be asked standard deviation and so on If you have a question then what do you have to do is simple Here, the value of p is taken as zero. because you each mean you x i - p Find the standard deviation of or empty or take it out because if I have to get out of here If you want to go here then you have already done the P.P. I take the value of x aa - p as standard If deviation occurs then you have made every observation I just said p p this is nothing But - p + p will cancel each other out so to get from here to here I just plus p so when you do every one Do you plus or minus anything in observation? do you do any standard deviation from that It doesn't matter so that's why it depends on p He doesn't do all this, so whatever questions There is a case in which you took p as zero. do it, remove it, means basically your The question became whether Sima xi6 will become the value of limit x as you get 9 is given and the standard deviation of This is what the formula is in the formula substitute x–xii The value of s is 9, the number of observations Look, it is going from 1 to 10, so the number is off Observations R 10 sigma aa value of 3 is the number of observations is 10 and its Whole square so how much will come from here Here up and down are basically from zero to zero Multiply it, meaning this 90 - 9 becomes 81 will go down to 100 9/1 is the answer shone 9/10 is the answer then directly you Simply Substitute in the Formula Don't worry about that P and look like this there are many questions like this one too What you need to do here is remove this right just shoot him sigma x a given you have n and sigma x is square this gives you Given n * a and the number of observations how many are there going from one to n so the one which The number of observations is n, got it? What is Standard Deviation? We have to find out the formula of standard deviation Look, I keep writing to you again and again, but There is also a need to write formulas in the exam There is no need to enter the value directly but here I I will write it again and again to explain it. sigma x aa square divide by n - sigma x aa up n ka hole square right this is is the formula so sigma x is a sc n in a number of observations n sigma x aa is given n is right below the number of observations n and its whole square is ultimately under root off this will get cancelled a-1 okay Option Option D will come, its answer is yes or no This shortcut shined, right? It was a direct shortcut give it to me Your NV style will work okay remove the f in this too remove this I will simply write the standard deviation How to calculate standard deviation under Just put it in the root of the formula sigma x square your number of observations minus it comes look a its hole square okay so ultimately sigma x aa squa how much given is 45 number of observation r Na yay 9 up 9 ka hole squa to kitna aa will go to come ok standard Deviation, keep in mind what is asked If the variance of the standard deviation is If asked, the root standard deviation will not come If I asked if I would come to Easley route then in two and four Do not be confused whether two or four is correct or one And it's a small question, but it's still a good question If you do it here also then it will be the same If you neglect it, the variance will come The variance will remain the same, its variance You have asked that basically the variance would have remained the same then the variance is basically sigma x a s up n this is the formula of variance The root will not change in the variance, that is the only difference then take out the variance from here sagma x i What is 40 Number of observations 10 Limit x i 10 Number of observations 10 Its hole square then how much is it coming three is coming this is the variance telling you that I and lad are mean and variance to lad The value is 3 and the variance is 3. okay then the one which has three is yours This is the answer, it means it got rejected The value of pass lada is 3 variances same will remain the same because variance will not change But the meaning changes now this attention If you want to find meaning in it, keep it, don't look at it carefully here if I divide this I will give you 10, you should use simple mind that which x is - 5 its sigma is given to you how much 10 so if I get the mean of x i.e. - 5 If you want to find out then this sum of observations Divide by the number of observations then one will come i mean this is your mean this shines The mean keeps changing, the variance will remain the So here I have taken the mean of x and - 5. took it out and how much is that it is one so now you tell me what will be the mean of x aa How much will the cost be or just tell me straight away You basically need to find the mean of x = 2 - 3 Right -3 then what will be its mean? look if I have to go here how much I will have to add, I will have to do plus two no brother if you have this and you are in it If you do plus two then it will become true So if you want to go from here to here then If you have to do plus two then go from here to here If I also have plus two then its mean brightness will be 3 It means that as you do with every observation Do the same to Pisces as you would do with me So when you did plus two, then there also plus two if you do it then you will also get the answer Option A: Did that one shine or not? This one is shining It happened because there is a shortcut here My 5's Sum of Observations Divided By Number of observation one will come i.e. that Its mean is x a my 5 asked for x Aa mine 3 so when we have to go from here to here So you will have to do plus two, so plus two there too Whatever you do here, you should do the same there too it happens it is not right to do this or that we have understood and move forward type three which You won't even find it in books It doesn't mean what you say to it It's a bit underrated even in books It doesn't happen but it's a super important type if this type of question comes then You guys will enjoy it a lot, specially Kids are attending this one shot Because I want to tell you something very good I am going to answer your questions quickly You will go there and then you will get the solution of the book. I want to see that and I want its photo It is ok to send it, it will not appear in the photo The solution of the book should be so long and you can do it with shortcut, okay so this Very close to my heart ok Aerith May What is the progression type three? look listen carefully you got a will give a means a padi a pd like this is ok a p 3d is working like this app suppose n my 1d something like this ok an a caught Now we will give you the variance of this A or else You will be asked for its standard deviation tell me if there is some 11 number in a There are some 20 numbers which are in A, you can Find the Variance First Term Common Difference If I give you all this then you can be clever here because we know what to do variance does not change plus minus So if I do that in every observation from - a let me tell you each and every observation - Make a difference in each observation - Make a difference in each observation Two out of every observation I Should I do it directly - do a here what will be left a - a 0 this my eddie will be left 2d at last n - 1d will be left of this also The variance will be whatever its variance is The variance will also come because you have calculated every I have just given a minus from one observation Adding plus or minus does not change the variance it happens okay and then what do you do here so here basically I have done -a and from here to here right now what do you do divide by If you do d then this row will come / d 1 will come 2d / d so 2 will come here okay and By doing this we get n - 1 in the end Now you can take out the variance here But keep this in mind here, like Suppose the variance here is v okay You can calculate the variance of this The last one because its variance If you find it easy to calculate its variance You should find out its variance. It will be easy, just find out the variance of this its variance if v comes now you reverse Come on look, remove all this, you will be shocked If you want to go from here to here then what do you need to do to multiply by d It will have to be written with d in every observation, right? You will multiply only then you will move from bottom to top you will be able to go and then if you want to do it then when you if you go from here to here then you will get d square you will have to multiply it because if you Multiplying each observation by d If yes, then the variance is related to d square. We had read that it will be multiplied that brother every observation should be marked with K If you multiply, the variance will be your k scale it will be multiplied by ok and here if d s v comes then d s v will come here also Because doing plus or minus makes no difference when you went from here to here you you did plus a, there is nothing in doing plus a it remains the same so you just follow it take it out and then keep going up and up and up This means you have to walk in reverse, well now. This is done, this is one of the concept There is no shortcut to this, there is a shortcut to this I'll tell you right now if you have There is n from ro, right? Like we had read one. 1 to the first n natural numbers then its The variance is n - 1/1 If it is 1 to n then this is the variance. You can directly remember it by rote you can kill me basically if it is desi what does it mean They say that if it is said clearly then Just remember this, it will be useful in the exam and remember this as well if If n is zero then its variance is nn2 di ba 12 you can remember this directly ok this is the interesting thing look at this your questions will become a little faster because You will remember other people directly you might not remember it okay and the rest of the people will remember it If you don't know the concept then this is a little can you fast how can you fast I'll tell you that right now, like for For example, this is the question of JEE Main, right? The only question is that you should see its solution You will see it long in books etc. whatever happens we don’t read into it So we basically discuss ourselves Basically, the first term you need here is Nine is given and then there are seven like this x1 x2 x3 till x7 so the first term is nay okay the first term There's nine and it's all in A with common difference d common difference d given then the first what is the second term 9+ d then 9+ 2d and doing this what will be the seventh term 9+6d will come, this will come so this is an A first term second term is seventh term or not first term second term third term seventh term then seven terms are there this is basically r x1 x2 x3 and this x sen and what do you ask yourself I am asking myself that this thing which is from x1 x7 is the standard deviation of all of these Standard deviation is given to you by four Right Standard Deviation is Given as Four well its standard deviation is given and You have to figure out the meaning, now all this will come only when If a common difference comes then ultimately what will you do? first you do it, first do everything to the nine If you substantiate it then it will come, see it is there Subtracting nine from one observation I gave naa as minus and then d as divide it so divide it by d It comes down to dividing each observation by d I have done it, now what is its variance I just told you the formula, brother 0 to n then n n+ 2 / 12 ok so n n + 2 divided by 12 then it will come to 6 * 8 / 12 So now you should do the cancellation etc. 6 * 2 4 will come out to be its variance It is coming out, how much is it coming out yes four is coming out variance is ok This variance is the standard deviation it does not happen, this is variance, then variance Four is coming out from here to here now If I want to go, then multiply it by d The variance d will be squared, so its The variance will be 4d S and if you go from here to here then nine becomes plus now if you want to plus nine then you can add it to plus If the variance from yours remains the same then its How much variance will come here? The same will come in 4DS and Standard If deviation is given then what is the variance standard sigma square is square of 4 so basically you have the variance The 4D scale you found is the variance How much is given in the question square of 4 16 is given variance then common from here The difference will come, the common difference is gone 2 will come and why will u come plus minus 2 why not because look here you I told you that it is increasing a to negative I don't want to take that one anyways it's plus minus two It will come but it is increasing so understand If it went then the value of D came from here and if d If the value of has come then now you have everything, right? Now what do you have to find out? You have to find the meaning it is and take out x6 n x6 first what is x6 sixth term okay a p 5d that's it right Firstly, how much common difference is there in the first term If you take out how much now, it will come to 19 ok it is x6 which is x6 x times that is what I asked right so this is 19 ok how do you mean If you take it out then don't take out its mean also So this is a very bad way to find out its meaning How much will be its mean after giving this last There is a line in this, its meaning will come to all of you if you will do it then one to 6 0 p 1 p 2 p 3 till 6 then 6 * 7 / 2 and number of observations sen if it is then its mean will come to three so this is its The mean is three then from here to here If you multiplied by d then here also d If you multiply it by this the mean will be 3d and then if we do 9 then its mean will be 3d + 9 ok 3d will come first one is the line its mean and the value of d is two then 3d how much is it 6 + 9 15 will come i.e. 15 It has come so ultimately how much has it come 34 ah went and see this is your question means shine or else you will get a lot of trouble here do not use that dangerous formula You will read it and you can do it here as soon as possible If you can, take it out whenever you can If it happens then do this smart thing immediately get to the bottom, their variance, their mean, Take it all out and then go upstairs You just have to multiply and divide Ultimately it's okay and let's move on to another one the question is try it let's do it okay Just chase him away once and that's it, it's over do it fast fast so here is number six If the number is in A then you will believe it like this a a p d a p 2d such dot dot dot a p 5d hey chamka yes so this is six numbers are in a to You immediately do it like this, brother here 0d will go upto 2d 5d and then divided by d So do it 0 1 2 and 5 and their variance what is this last line Its variance is the variance n + 2 / 12 okay so its variance will come you Take it out somewhere on the side that n + 2 divides by n 12 means its variance will be 35/1 The variance is 35/1 Okay, that's how we figured it out. I will not tell anyone the direct form n n + 2 divided by 12 so its variance comes out And whatever variance comes, if you If you want to remember it directly then its variance comes to 35 meaning whatever its variance is * d You can also make a shortcut for this If the variance comes to 35/1 then it will definitely come into common Remember the square of the difference directly Taking the variance of the bottom one out by d squared multiply it by ok then above The variance of the same has arrived and the same will be given to you You have to find the same variance in the question I have just asked you about the variance now See, variance will only come when the value of d is and to find the value of d, a This equation is given to me brother The equation is given a p a3 a3 will be a p 2d okay this is equal to 10 means 2a p 2d equation 10 so one equation is this and the other The equation is the mean of the six observations If you have given then it means you have given 19/2 Now how do you find out the meaning of it again don't find the meaning of it find the meaning of it What is its mean, add all the values you will get So 5 * 6 / 2 and below is the number of observations If it is 6s then it will be 5/2, that means all of them are fine, right? Add and divide by the number of observations diya now if we have to go from here to here then Multiply by d and go from here to here So + a so in this also you multiply by d Do it first see, this means multiply by The value of d and a is given to you 19/2 So the second equation comes from here 5d p 2a = 19 so two equations two variables okay Take out these two equations and the two variables d So 2a + 5d = 19 Subcut 3d = 9 The value of d is 3 and the value of d is 3 then It is ok to substitute here into 3 ka squad this sigma squad has arrived and you have been asked about 8 sigma sqaure so from 8 Multiply it, you have to figure it out yourself Will you calculate how much it will cost Just do the calculation here with A3 cancel it four cancel it with four two so 356 will come which is how much 210 will come will go in my opinion 2110 ok option b is the answer b for Bombay is ok yes or no then I hope that It's clear okay so is it clear or not Aye which type was this it was my type three Which types have we read once you can revise it as well, it was the first type when Two observations are missing maximum comes anyways it's ok second one Type is shortcut it used to come earlier meaning 2021 I came around a lot and it might get extinct again It's okay, but you can still come back anytime You can see it is available in 18 also, it used to come earlier disappeared a bit around 23 then came back its time will come alright arith that The progression is a little bit every year It does not come all at once, it comes little by little If it comes then its trend will gradually increase If it increases then it will be good for us Is it not so because we understood it well it's alright now let's move on to another one The question is will you do this as your homework or not? Come on, do it quickly, try it quickly This includes the variance of the terms of increasing a so basically there are 11 terms so I will write b1 as a I assume ok next b2 will come a + d then a + 2d and in the last there is 11th term then That's a p 10d and the variance given to you is 90 in All of them have a variance given of 90 Okay, so now you If you subtract a from this, then 0d, 2d and 10d and similarly it will come here 012 till 10 So find their variance. Their variance If n is 2 divided by 12 then 10 10 p 2 di 12 10 will come basically so What is their variance 10 and if here 10 If yes then its variance is given by you in the question given it will become 10d scale then zero zero cancel d e 3 will come because increasing A I have said it, that is why P3 if decreasing If it would have been -3 plus minus, it would have been okay is it absolutely clear or not i hope it is It has also shone and now we move forward are type four on type four what is type Four is the magic table again it's the same thing that if you plus or minus anything If you do, then variance and standard deviation If there is no change then these types of questions You are asked again and again, okay magic table so you must remember that table This is the table you want, especially this one focus on the portion that if you eat every Add or subtract anything to the observation If you do that, your standard deviation is the variance. Even mean deviation is there or mean deviation is there Same as standard deviation This is the same table for mean deviation which is happens with standard deviation only It happens with mean deviation also okay so All that will remain unchanged, it will be the same It will be ok, look at it, what is the question so here you have a set given x attention look at x you have natural numbers from 1 to 17 1 2 3 dot dot dot till 17 ok these are all natural numbers then what is y what is capital y so y is a A p b then each observation is divided into a subset of a x + b will come next a * x + b a * x + b Every observation shined with a have to multiply and plus b have to do a multiply p by a multiply p by a b will come last like this multiply by a and p b then it will come look it shines x and y so this is given to you in the question different sets and then it's saying that the mean and the variance of y elements of y which is The elements having mean and variance are you are given 17 more 216 this means you are given how much 17 and How much variance is given to you 216 So what is his next step to take out himself? It is good for you to find the value of a + b ok then how to find the value of a + b Tell me then find its mean and variance Firstly how to find the mean of x sum of observations ok divided by Number of Observations So this will come 17 * 18 did ba 2 / 17 means 9 will come, this shine will come, then n+ 1/2 will come its mean will be nine and For variance, you can understand it like this: These are the first n natural numbers, then n s - 1/1 is n s - 1/1 is straight The variance is 17. In this you are 17 - 1 16 17 + 1 18 / 12 Cancel it with four, ok then how much will it cost 24 will go and it will come, it is his who the variance is 24 it shone we saw it I found the mean, found the variance, and then y is its mean and variance is given by So now you think that if I have to convert x to y If you want to go, what will each one have to do? Look at each observation with observation I multiplied it by A and got B plus Now if I add it then there will be no difference in the variance It doesn't matter, think about the variance first Its variance is 24 Its variance is 216 So when you have started with A in every observation If we multiply it, then the variance in the The square will multiply and it will give you 216 given is the new variant that shone no here the variance is 24 when If you multiply by a it will be a square. will be multiplied by plusing any If it doesn't make any difference then just click on A from here. The value will come, how much will it come, you can know this by 36 and no it came the value of A will come to 3 it shone Anyway I told you Ae Positive Again Plus No minus is to be taken, the value of A is and If the value of A is r now look at its mean Isn't it so and in every observation you have started with A If we multiply it and add b then what This is the mean, multiply it by A as well Add b and you will get the new mean It is given that it has shone, so just put the value of A do this then The value of 27b will be minus 10. So A has come, B has come, I have asked you A P B What is the value of APB which has shone from mine So if you know all that, not n school my ba 12 n p 2 divide by 12 so all these you will be able to give the answer quickly, so that is this how you can do it fast statistics It is lengthy but I remembered a few things if I go then it won't happen, otherwise all this will happen Shortcuts have to be taken out or not let's move on to the next question Try this, what is it saying In this it is being said that a is a set of 2 a terms okay so there's a set in which What is the number of terms 2n that a terms are a good so a which number of terms is a such a a a a such It is written a number of times it flashed no it must have shone meaning the total number is off terms t a write n times a out of them is written and the remainder is n terms That is - A then - A - A - A this is also n number of terms are there isn't it which is n number of The terms are - A and this is the n number of terms is that is a right so there is a set like this In which total 2n number of terms are there how many in total this is total 2n okay now this saying that if b is added to all the a Terms I added b in every term I have added b in all these terms. did it by adding b to each a + b Given in the last also a + b here - a + b - a + b added b to each one okay if Each and every term is added by b than the mean is five so now the new mean is Five is the good old mean of it. What will be the mean Obviously here it is Pe + A And - if there is A then they cancel out among themselves If you go then the sum of observation will become zero If it goes then how much will the mean be? The mean will be zero. Its mean is zero and what is its mean Five is given to you in question so when you If you go from here to there then you have every What did each one do with the observation If we add plus b to the observation then the mean if you add p b to it then it is zero and If you put 'b' in it then this new meaning will come means basically the value of b will be five. It's gone, it's shining, this is the old Pisces I put a plus B in it because every Whatever you do in observation will mean the same thing I also have to do it right so I understand this now a where will the value come from then the value of A is for that I am saying that its standard deviation You are given 20 standard deviation of this 20 is given so its amount will also be 20 What is the standard deviation because 20 By doing plus minus on standard deviation It doesn't matter, it just did a plus We have added a plus to every observation If you go from here to here then I have minused it So ultimately it doesn't matter plus If by minusing it, its standard deviation 20 then its also 20 now standard What is the formula of deviation? It will tell you I know every observation is square You will add all these observations square a square you will square a a s a s how many times will this happen 2n number of Times will be divided by the total number of How many observations are there? It is also 2n, okay? What is the square mean of the minus mean rho 0 The square of and its root is the standard Deviation and its value is 20 given to you If it is in question then it will be cancelled From here basically the value of a is 20. will go and asked you a sc p b s then a How much will it cost 20 5 sk Meaning basically 425 will come, the answer is 425 is the final answer whether it shines or not then that's all You should know where you are brother What is added, what is the mean, what is the variance okay the magic table the magic table is actually very very important and let's move on And the question is again from JEE Main 2020 Meaning this shortcut will make you longer The method of cutting needs to be done No, because it is saying that the variance of the first a natural number has 10 variance What is the first n natural numbers Smy is 1/1 this is given to you 10 then From here the score of n will be 121 so the value of n The value has come to 11 ok its over and Similar Variance of even natural numbers to an even number What is the variance of then m scale 1/3 and its value is 16 given, then From here the value of m square will be 49 so The value of a came to be 7 and you are asked to calculate m if yes then 18 is the answer then it is ok tell me if you know something i mean neither you will be able to do it very quickly, otherwise you same every one first you will write to a 1 to a Then you will square everything and add 1 square p 2 square till n square is the variance Standard deviation is in all these exams You don't have to sit to take it out, you know it beforehand all this should happen so that you can do it It's fast clear and let's move on So it is a favorite of JE people, isn't it a mistake? We will say that we made a mistake by making a variance We took it out and got this variance but on rechecking On rechecking it was found that there was some Error so brother why do you do the error first in the exam If there are errors in it too then it is all JE's It is a favorite when it comes to color observation I will delete it and replace it With correct observation, this also has a If there is a shortcut then I will again show you the shortcut I will tell you about your question Obviously it will get a little faster, okay? First see how to do it and you will understand So what should I tell you about this, like will give you something like this x1 x2 x3 There are some observations, their meaning is given to you Suppose there are 10 givens and their variance is This is also given to you for example some If you can take values also then give all this will give and then tell you to on rechecking it was found that a mistake was made by mistake The one who was supposed to take a six took a nine okay so what do you need to do I look at you from here na border x–xii So whenever such questions come, be careful now. Listening to me is like a shortcut for you I am going to tell you something which will make your answer a little easier It will come fast whenever you get such questions What to do, first you have to take out Sigma X I have to get it from here Sigma X Aa Take it out and from here sigma x comes take out the [ __ ] like sigma from here X will come, this number of observation will also come given will be in question that 10 is pa is ch Whatever it is, it is okay, so find out its value. and take its value from here Now whatever correction you want to make For example, suppose you accidentally forget an observation I should have taken it, I should have taken 12, whatever Correction has to be done in Sigma X Correction has to be done in Sigma X Aa and in sigma aa squa If you need to make a correction then this is the shortcut that whatever correction you need to make For this, first of all you need to know Sigma X You will have to find out sigma x aa sqa Take it and make corrections in it. Now make corrections. How will you do it, suppose you are told that You took it by mistake, you should have taken it 12 So whatever mistake you have made, do it right You should have taken it, add it and it will come down New Number of Observations Because sometimes it is said that a mistake We will have to remove three observations from remove right five remove four this is three I had taken the observations wrongly and one Sometimes you should have taken observation Such questions also come when you ask three questions Get the observation removed and get another one inserted If you make a new add then ultimately accept that First, let the number of observations be There were 15 initially, initially these 15 I was going up to, let's say for example, 15 got three reduced from 15 So how many are there? 12 and one more add If you get it done then now the new number is off Do you know how to divide observation by that? If it happens basically it will come to you Similarly, if you want to find out new variance then use Sigma Whoever makes corrections in x aa square By mistake, their squares got wrong minus it and what actually happens I should have added his square The new number of observations will come down which will be new The number of weight is that and the minus which is This is a new meaning, make it a new meaning and its square so from here you get the variance You will get it, just try asking a few questions. only then will it shine right like for example this The question is to try this do the question first read the question What is it saying that Mean and Standard Deviation of 10 observation number of Observation is 10 ok means you have given 20 mean is 20 standard deviation then Write down the variance, 64 will be sigma It's squared, basically the variance is okay Now I have explained to you that first of all you Sigma X Aa and Sigma X Aa Scr Extract take sigma x diva ba 10 i mean and sigma x a sk divided by number of Square Equation of Observations Minus Mean 64 So take out sigma x from here first If you get time quickly then this 200 more will come You can take it out from here x as much as you want it will come 464 and put a zero on it So 4640 will come, right? So I took this out. I have removed it, now if you want to remove a new one Mean New Mean to New Mean Formula So what happens is this sigma x aa Now I have to make a correction in it If any correction needs to be made then there will be a question for that If you read it, it is saying let it on was observe that one observation was Recorded as 50 instead of 40 to 40 I wanted to but what did I do? Whatever was done by mistake, minus that which was done correctly should have done that plus now an object What was the initial number of observations 10 If one out of 10 is removed and one is installed then still What is the even number of observations? 10 out of 10 If yes then this is your new mean, Sigma Write XA, I have made a correction in it Do it and enter the new number of observation bus below This is the answer, solve it as much as you can hoga ts your answer 19 will come so this The new mean will be your 19 and asked for new variance give correct variance Are you asking how to correct variance? we will find out variance new variance new this how to find out this sigma x aa sk It happens that we need to make corrections in it How do you make correction in this then it will be 50% square minus will add the square of 40 we will do that which is the new number of observations 10 is okay which is the new number of observations Divide that by 1 and minus whatever is new Mean is its square so look from here You will get the answer from here whatever aayega that will be your direct answer this Whether it shines or not, whatever Sigma shines x a sk is there in which by mistake any remove the mistake and do what is right You should have put it down, number off observation new one and then minus new The square of the mean is the sigma expression aa s ba n up divide by a minus mean of Square variance will come new one is ok After doing this calculation, your B option It will come means 13 will come you can do it from here You should get 13 so check by doing the calculation take it t obviously you can do it right next Let's move on to the next question, ask yourself this once Try it once, there is an answer to it The final answer is absolutely full and final to me tell me what will be the final answer, its ok yes Everyone's answers came in the chat in a flash should go right in line yes then how will you do this mean end Standard Deviation of Marks of 10 What is the number of observations of students? 10 right were found to be so mean and Standard deviation from mean is given 50 and If standard deviation is given then sigma square will become square of 12 will become 144 If it goes yes or no then it becomes a variance basically right standard deviation is 12 so The variance will be the square of 12 144 ok now consider yourself as the best basically First take out sigma x aa sigma x how much limit will come x–xii How much will this cost? It will cost Rs. 2500 and plus 144 is 2644 Zero is it coming look once If the calculation is correct then it will come will go and if it comes then now in these If you make correction then you will get new mean and new variance Both will come first, obviously to you you will have to find a new meaning to remove whatever happened by mistake tha it was later observe that to marks this and this were rangali read means this is wrong If they are wrong then remove all those who are wrong and what is the correct one a 45 well we reversed it into 45 and 50 The ones who are there are the wrong ones, basically read a little bit in english He is saying that two marks are 20 and 25 Rangli read age 45 and means she wants to read It was there but he read it by mistake Right then 45 and 50 is the mistake, this mistake he should have taken it from this and since you removed two and added two then Still the number of observations will remain the same so your mood will come from here now this Will you calculate that whatever comes is okay Can anybody figure out how much it will cost? is 50 and this is 95 and 45 - 5 will it become 45 Is it coming, check it, whatever it is This is your new mean and new variance For that, correction has to be made in it We will make correction in this: square of 45 becomes 50 Of Square of 20 Square of 25 The number of observations below is still the same and minus the square of whatever the new mean is so it will come from here okay whatever from here That's the answer that you deserve, did it shine or not So basically I told you the method. Calculation Obviously you put a - b Take it there, it is a little easier ok Isn't it calculation wise? So if you give this answer then 269 will come here. You will get the answer of 269 calculations, you need it to manage is ok but this shortcut is clear no how how quickly you just have to do this You have to do it and you just have to do it in the exam have to do this do this answer will come if new If you have asked for variance then you will have to do this also Sometimes there is only a new meaning in the question If you ask then your answer will come by 45 only If you go then see what was asked in the question is wether they are asking the correct variance If correct variance is asked then one step Otherwise you will have to do some more calculation You will have to do it but if you ask the correct meaning if it is then it is even easier right now it is you are going to try it in your homework so right now we Let's go, this is also the same, isn't it brother Letter on one student is increased good one Children means that one is there in school The child went to the teacher and said no no i have very low numbers you are very few Increase it and he will become the teacher's favourite I was a student so the teacher gave me 8 marks Tell me you have scored 12 marks, ok 8 to 12 It happened, his numbers went up, okay, this happens He was there in school, so obviously this is the same person Variance will also change now one's number If you increase it, everything will change, then the same thing will happen This is the situation, okay let's move ahead type and the rest type six and type seven okay so what is type six type six is Use of Bano Miyal means by using Bano Here questions arise in statistics There are a lot of good questions in which you can make miyal has to be used bano miyal use it What does it mean you have a table like this I will give it to you for example here what is given consider the data on x then The value of x is given to you and in front of you Its frequency is given, which means it is the same x If the table with f is ok then the value of x is given by it is 0 2 4 8 and keep doing it like this Power n and its correspondingly Basically I gave it in AC and A terms This is the only difference, rest everything is same so this is f given to you x given to you and you have to find f x a because The ultimate meaning of the data is given to you In the question, by comparing the value of A If it comes right then calculate the mean, how much will it mean ok first of all what is the total frequency will come Sigma does all these then the power of T is A Everybody knows this, so whose is it The value has arrived this is sum of all the frequency sigma a The value of sigma a will come to this and f x will come to this Now take out f in x aa, here it is zero aa. will go here nc1 will come to the power of 2 1 it is nc2 in 2 power 2 will come here nc3 * 2 the power of 3 will come here n s a n to the power of 2 n now how will you add all of these To add some Bano Miyal If we add all these we will have to invest funds See what will come out, what ultimately means that is what it is sum of sigma f one a This is the formula, the sum of observations divided by number of observations then number of observation so 2 to the power n is that You have already seen this from here which will have to be found out which is nc1 * 2 to power 1 nc2 * 2 to the power of 2 and so on till n becomes n * power of 2 n okay so here you get What should I do if I am missing a term If you look carefully you will see nc0 because here it became zero so a When the term with S is over, he You will have to recreate one more ad here subcut two AC and two power 0 to this I added it and also subcut it at the end I will give you the power of betting by doing this at last n s eight to the power a and what I I added that in the end, I will subcut it too Now what is the benefit of this, see the benefit of this that from here to here it is basically The expansion is done now, it would have happened like this only sv to the power of x and nc2 to the power of x The expansion of a to the power of p2 is written as how many people saw this e 1 p 2 expansion to the power a and this one which value hey this is nothing but one and below is the bar of two A means ultimately it has come to the power of 3 n - 1 up to the power of 2 n and in the question you have given 728 divided by 2n so this will cancel out will ultimately become 3's power n will become 729 will you come from here 3n this -1 goes there so 729 so the value of n 6 will come from here hey did n's shine or not Did you understand that the value will be 6? Is this 1 game ultimately an expansion or not? the power n of x in which the value of x is put to the power n two just happens like this nc0 p nc1 nor one power 1 nc2 * power 2 of one if you pay attention if you look at it from the top you will see that in place of x t is seen as x to the power of 1 and 2 power 1 to the power of x to the power of 2 to the power of 1 Whose expansion is this 1 ps 2 to the power of a is ok it shines So these are some of the questions from Bano Miyal I can ask you though there are very few such There aren't many questions and this is the last one This type is also very famous, okay Again many questions regarding this come up Understand carefully what it takes Observations are divided into two groups And it comes like there is a class, there is a class there are some boys and some girls now who Boys have an average, they will give it to you I will give you the average of girls then will ask you to find the average of the whole class or Give the standard deviation of boys We will give the standard deviation of girls Will give the standard deviation of the whole class If you take it out, this is that type of question, right? Seven is those questions where observations are divided into two groups so this also Again he is very famous in JE Mains and Tell me a shortcut or formula for this too Whatever you say, I'll give it to you put this on so just life jinga lala okay means all questions will be formed okay so see if You will get questions like this in combined form Like there is a class in which there are some boys There are some girls, like this whole class You have to make such a diagram in the exam You will make such a diagram in the exam, right? You will get clarity, as if you are a complete there is class in it let's say 20 r boys and 30 are girls 20 boys 30 girls now who are boys average marks of is 40 and the The average marks of girls is 50 which is ok if yes then it is given to you by their means also and which Boys, their variance is given to you Suppose there are three and the girls The variance is given to you by dividing it by sigma. do [ __ ] and sigma to [ __ ] and then will ask you to tell the mean of the whole class or Tell me the variance of the whole class of boys Variance given is the variance of girls boys mean given hai girls mean given hai If you calculate the whole class then just get this formula If we want to find the mean of the whole class then in n1 it would be just like in physics The center of mass has to be averaged out basically nothing else n1 move n2 mat divided by n1 plus n2 and if you get Finding the variance is the responsibility of the whole class is the formula okay here sig maw [ __ ] will be 3 sigma 2 [ __ ] mean There is a variance for girls, right? This is the variance n1 n2 is the number of observations and the bar bar is the mean x1 bar is basically the mean of the boys and it means marks of all the Girls substitute all these values When you get the answer, remember these two formulas will have to be done and will have to be done means questions come up do not say that sir I I can skip I don't have to do anything ok can't skip anything look How to question about it If it is in 2023, then it will definitely come in 2024 could right like for example like this make a diagram, you are fine, one like this box another such box and a complete It is necessary to make this box diagram like this right in questions like this right in questions like this Make a diagram so that it can be understood Come let me ask you what question you want to ask What do you want to say in the question? and variance of a set of 15 nature 15 numbers are 12 and ok so let's say number 15 right there are 15 observations what do they mean hai that is 12 and variance variance means sigma square that's 14 okay up to here So okay the mean and variance of another set of 15 numbers then there is another set which has another 15 numbers The number is what their mean is 14 Sigma 2 Squad Is Not Given To You basically that's sigma square given okay is if the variance of all the 30 observations All of these 30 observations Adding the variance, that is 13 so total Class basically means the whole class which The variance is 13 so you just need this one You want to find out the variance of girls Understand it like this, okay then how will you do it with everyone First find the mean of the whole class How to find the mean of a class? I have already told you the direct formula u1 + n2 mu2 Divided by n1 p n2 okay so how many boys are there 15 and their what does it mean 12 ok 15 girls what does it mean it will come down further n1 p n2 so this basically 13 will come or else it will come 13 will go and 13 will come Now you can use this formula You will do the variance for the whole class How much is the variance given by Then over here and Sig Maw Square and and 15 sigma square e 14 n2 n2 e 15 sigma 2 sqaure is basically this and it will come down n1 p a2 means it will come down to 30 okay plus now look here n1 a2 your n1 p a2 the hole square of k then what is n1 a2 15 and the hole of n1 p a2 will come down square so square of 30 and the sum of both The mean is minus them and then square them Okay, so minus the mean, this is 12 and This is 14 or 12 -1 square from here You will find out its value, just have to find out one This is the variable okay so from here take it out then come It will go from here, you just have to remove it that's what you asked, take it out from here and see how much it's coming okay take out sigma from here So you can do the calculation again to see how much you are getting Is Some are getting 10, some are getting 12 Someone is getting 11, how come everyone is getting different Whatever it is, take a look at it but calculation you will have to do it right it will become sigma The square will come from here whoever comes try the calculation and see ok next question this Try this one, it's the same It is also being said that mean and the Standard Deviation of Marks of Class A So there is a class A, right, there are 100 in it. students are there Suppose this is class A, it has 100 students are there and their meaning and How much standard deviation is given to you how much given is it mean i given s 4 and Standard Deviation is Given then Variance Eliminate Standard Deviation Alpha Given right here alpha is written so The variance will be the square of alpha. will go and similarly there is another class which is the mean and standard deviation of the class B of A students well the number here of students is that n is right r Respectively, how much does it mean that it is mean is 55 and the standard deviation is given by How much will the variance come The variance will come to 30 mine alpha's hole square ye will come variance and then saying that if the mean and variance of the combined class is 100 of 100 plus means the combined mean of all these and The variance is 50 and 350 so the mean is 50 And it is said as variance only, isn't it Standard deviation said variance said this time times the variance is 350 times the variance is 350 so All these things have been given to you, This is from the class which will become the whole class After combining both of them, again, first of all Find the value of n How to find the value of n So the total mean is that is equal to n1* mu1 + n2 in mat divided by n1 p n2 n1 p n2 aa If you get 100 rupees you can take it out from here How much will this 5000 rupees cost? 50n e 4000 p 55 A so the value of A from here is 200 Will it come or not, the value of A has come to 200 I mean this is ours oh this is ours here comes 200 There are 200 students in this and 100 in this means total 300 students are there then one so we have that mean grouped mean okay You have placed that one and now place this one, this one is bigger. the formula is sigma sqaure how much is sigma squa 350 look given 350 this is equal to n1 and alpha squa+ n2 30 - alpha times square and below n1 + n2 okay what goes down here look you get n1 + n2 so 100 = 200 okay How many total students 300 will come here plus n1 n2 our n1 plus n2 that's 300 its whole square and here 100 and 200 and then minus the mean If you subtract, how much will the hole of 40 - 55 be square so from here basically you get alpha I will get it okay will you take out this alpha After solving the equation completely, you will get alpha will have to take out So Alpha will come so I am just asking you this have then find out the sum of the variance to some of the variance as soon as the alpha comes then you this take it out, take it out and then the sum of both ok we have to find out alpha square 30 Mine Alpha's hole will have to be removed [ __ ] and then asked sum of the variance right or no then this yes what torque is 25 crore what is this 25 Crore Statistics 25 Crore a child is saying something like this okay right so yes that is it means here But we all have our own type I have completed it. How many types were there in total? There are seven types in statistics now whatever Your question will come from among these seven I won't go beyond seven, okay? Definitely you should read them carefully, right? Whatever question is to come, it has to come from here. I will not go out, that is for sure, it is okay So with this your whole It is a chapter that gets completed, it is ok The kids definitely stayed till the end It is a great thing that you completed the whole chapter. kiya and yes definitely now you can be very very sure now a little too obviously Practice the questions on your own So that confidence comes from within you, how much you You will also read it after that by yourself at the end You have to practice questions because unless you do it with the teacher then You will feel that yes it is very easy It is easy but until you practice yourself If you do it, you will not gain that confidence That is why I would recommend that you type wise some previous year questions you Identification it will come that yes friend this one from me The question is if they are being made then one of the theory can you make something like a short note so that Because there are a lot of formulas in it. Like just last time we used this formula If you read it, it is possible that till he is 24 By the time January comes you will have forgotten everything no and then revise it again in the last Brother, will you remember this formula then? So that's why make some short note type thing So at that end moment you can revise it can you go okay yes or no yes okay let's go ok then let's end it with this Today's class is another class tomorrow of people in which you are a physics major His formula is that the marathon will run right then Definitely you can attend that too If Indrajeet sir is going to take it then yes Definitely you should attend that too Because nowadays in physics it is based on formula A lot of questions are coming, so those who These are at least formula based questions. You will be sure that almost one like this Your third paper is today because in 2023 It had become a trend that very much There has been theory, specially meaning chemistry this happens in maths and physics There are still numericals though, okay but If you know a little bit about physics then you need to know the formula If you come here then you can ask your questions carefully you will be able to do it because maximum questions are It happens to you like that in round one if you get all of them knocking knocking There are shortcuts, assume there is some formula There is no direct result that you will get If you know it directly then you can directly go to the exam If you try and come, your number will be there Definitely you can attend that too It's tomorrow so I think that session is already going to start. If it is done then you put an end in it and It's okay to attend to him tomorrow as well Let's end with this and the rest is obviously You have to like this in between I forget to speak like this but I am sure that all means all the kids must have done it that you didn't do it, please like the session and Subscribe to the channel now and go ahead are also planning things okay so we will meet again, isn't it ok then