In this one lecture, I will tell you from the basics I will tell you everything till the advance and she is single The value that completes your data I give her a picture, I am the Major of Central I call it tendency in three ways Arithmetic mean, median and mode which you have been studying since childhood if Suppose your number of observations is odd The formula for mid value is n + 1/2 On observation remember the ascending or In descending you will have to change one Boss this is a promise of one shot video There is more to be done in this chapter after No I will have to wait hi how are you avery buddy welcome welcome welcome everybody then welcome later I will do it first tell me who has to do it Today in this video we will give you our class A very easy chapter of 11th which The name is Statistics Covering That too in one shot and I will make one more promise You may have read a little bit of this lecture. I haven't read much or I have left it that bhaiya will read it later but one thing I promise boss after this one shot video You need to do something more in this lecture. I don't need to do anything else You won't need to go anywhere for this one In this lecture, I will take you from basic to advanced I will tell you everything, skip anything I will not do it, okay, and it's obvious There are so many questions about maths There are questions even without questions Nothing happens now, yes friend, one miss Boss of conception formulas of this chapter I will have to repeat to myself that this is true somewhere But it is also wrong if you think that what is happening then formless again not a single word They get into your mind in the flow flow i will create yours in short sub Forget anything, believe completely what you You can see a monkey on the screen in front of you. But let's finish and sit with my pen and paper. Doing Calculations with Any in Statistics Friends, calculation is about to happen, let's go If you start then basically this chapter I will tell you what you read In this chapter, I give you guys These people are going to study Measures of Dispersion what is it why is it why do you take it all out I will tell you, let's start with some basics so that's a brush after reading class 10th things It's up to you, right? Let's go to statistics What is Statistics Basically? Friends, we talk about data what do people do in statistics What is data now about data Friends, data can be any information It seems like there are so many students in your school These are students, this is also a data of yours This is also how many male students are there in the school There is a data on how many students are there in your school Students are female, this is also a data How many females in your school have two braids? There is also this data in your school What is the weight of children? This is also a data So the data can be anything brother, you can Also read what type of resolution do you see in the phone There is data on how many hours you use your phone This is also data on how much time you waste Let's understand this is also data What am I talking about then statistics Mainly we talk about data now why do we do it so much There is a simple reason friends, today big A great statistic for businesses Ko is able to tell that the boss is an example I give it like I like watching videos like this on Facebook I like this type of videos If you don't like to watch then what do they do? They want you to do more of your work, Boss. waste more time here which do you do it or not please tell me if you do then you probably never notice it The kind of video you must have made today I saw that the next day too I was in the same condition suggests videos youtube2 big companies to friends like I told you data scientist or else Does data require a statistician? to collect to present to organize and So basically to interpret Statistics friends in these four words This ends here we can summarize the data Collect and then present Then organize and then data Trying to extract useful information from I do what you say Interpretation of data anyway what happens now it's very basic let's go with the very basic Suppose I have selected two schools Now please choose me one of these two schools Mathematics has to be taken forward in school For Olympiad, please use common sense what should I see I will see this I will see that brother Which child got more marks in school The school kids are coming good Are more marks better or school Understanding that more marks for children is better I came but friend, is it the same thing again that Brother, I want to see everyone's individual marks Everyone will get their individual marks here too I will have to look at that data after that I will play, see and understand and then I will tell you brother what is better, what is better no if it were like this for 100 kids Now marks are of 100 children I have to tell you after seeing it, brother how Students are good, average is topper It would not have been better if he was 100 To represent the marks of students there should be only one value that is one The value of marks of those 100 students It would be fun if I could tell you about it I go, you are understanding it brother, believe me Basically average speaking it was like a school DPS is that single value which means 100 There will be students but 100 students I extracted a single value which is a single what is the value that it represents I will tell you how I get the whole data. I will tell you, but that single value which is related to the entire data Give you complete information about I am representing value to him I talk about the data as if it is a school one is 60 for one and 70 for the other so you get this Friends, understand directly by looking at the single value In comes that boss 70 whose it is If you select school children then one Single value If you need to know more about the data If you are giving complete picture then it would be fun Isn't it boss, I talk about that single value only I am major of central tendency and she is single The value that you get about the data She gives him the complete picture, I measure it off I call it central tendency but three The arithmetic mean is calculated using this method Median and mode are what you have been studying since childhood yes you will also notice it sometime brother Finding the mean of the data, a single value came out A single value tells you everything about the data I understand that you took the median A single value came, that single value to you If she tells me about the data then I will understand it How to get started with data I am trying to learn about data. I'm trying to figure it out right now Friend, let's go a little basic that your boss Friends, there are three types of rough There are data, one is raw data which is You also talk about ungrouped data, friends This is your raw data, I will tell you everything There are so many doubts in your mind right now. will be continuous what is dispersion What is standard deviation variance I will clear everything up, trust me But just keep listening, have patience if you want 2x But look, it is your wish, but look completely isn't it okay friends there are three types of data There is one raw data which is called raw data. I can also say ungrouped data is a There is a discrete frequency distribution and one is continuous Frequency Distribution Firstly, I You need to use mean for raw data I would remind you once by finding the median mode what would have happened okay let's see Friends, mean and median for raw data How to find the mode first then the mean then you can denote the mean by x times. can you solve this what is its formula off of all observations what all Plus the observations, sum of all observations upon total number of Observations Upon Total Number of observations so let's sum it up 50 is gone, this has come, 60 is here, 70 is here 50 here you go 80 divided by one doti ch five okay so basically what is the data out off 100 marks 5 students ok i mean that If I am taking it out, will it come boss 50 + 60 110 180 230 230 + 80 310 friends yours 310 ba 5 So 5 si 5 1 b 5 * 2 62 of your data I got the meaning of your data, did I understand it? A single value is what tells you everything about the data. It is telling that the meaning is around this single value only five students will have marks What did he mean by saying fat? I have calculated the value around this single value fat-fat Roughly five children will have marks This single value represents all of these. It is about single value complete data I am telling you how to find the median Remember them boss, if you don't remember the median Median means mid value median what does boss median mean Now how to find the mid value of the data For this, you first have to Arrange in ascending or descending order If we have to do something then let's arrange it If the boss does it then the youngest one is in ascending You can make a difference to anyone it doesn't matter it wrote 50 it wrote 50 it wrote 60 it's good By the way, whoever knows this, please do a little please forward this video but my It's my duty to teach you everything starting from the basics I will tell you it is okay and everything is complete I will get it done, don't take any load at all, come on boss now First of all friends, find out the middle value For this you have to see two things, see one thing does it matter how many observations boss That is, we call it observations observation observation observation Observations or the data you collect that is an observation okay it's good itch Numerical value is called observation ok friends what will be the middle value You have to focus on n what is the number of what is the number of observations n Observations If your number of observations Odd if your number of observations is odd So there is a different formula to find the mid value happens and if the number of observations is even If yes then there is a different formula to find the made value it happens ok let's do it both ways If your number is odd then mid The formula for the value is n + 1/2 On observation remember the ascending or You will need to change in descending if If there is even number of observations then boss is mid The formula for finding the value is two mid The values obtained in this are n / 2h + n / 2+ 1h divided by 2 will give two middle values A middle value would be this one, this would be his Let's divide it by two, friends, this is yours If there is a formula to find the median then For example if I write in this query If I talk about particulars, boss, you can see it It seems that the middle value will be that middle Value means the amount on its right hand side There are observations on the left hand side as well If you have the same number of observations then 60 will be yours The middle value is you can also calculate it using the formula you will see that one will come 1 2 3 4 five five Observations are Odd 5 + 1 6 / 2 Third Third or three is not the median of the third observation The median is 1 2 3 Your third observation is the median and that is why I said the data You can arrange it in ascending or descending has to do I understood it, if you believe here friends If 90 was also written here 1 2 3 4 5 6 In that case both of these would be your mid values And by plusing these two you can upload You give it and the same thing is written here check how 1 2 3 4 5 6 so how much is 6/2 Done boss 3 third observation means 60 6/2 3+ 1 fourth observation then third + 4 / 2 That is what is written, I am telling you quickly because you already know this mode now How to find out median means mid The value of the data means everything Plus the observations upon the total number What does off observations mode mean? Meaning friends it has the most frequency The observation that you make most often akar is doing then 1 doti 4 friends if you look your 50 is coming twice 50 two Children's marks are 70 once, 60 once times 80 once which is the most repeated letter If it is your data mode then The mode of the data will be your direct 50 Mode Mast Frequency The version is clear now I am talking about the raw data I was doing one thing, okay, I would like to advise you I might do it, maybe you'll find fault You don't know how to find the median, have you forgotten? So please watch any of my 10th class lectures once Go there, you will have it available Fast forward in case you forgot how to find out how to find out the median It won't be much work, just a little work But either you watch this lecture or Let us recall a little bit about how For whom did we calculate the median and mean and mode for when the data is discrete or let's continue anyway let's talk further you stay stay stay keep going as if I told you that there are three types of data. RAW Data understood that now the boss is someone else Discrete Frequency Distribution What happens here is that the data is very large He is very big brother, he is here right now Friends, there were only five students, so five You have written the marks of the students separately Now suppose if many students come Let a lot of students come and many All the students come and do an observation You are seeing it being repeated many times that the observations are being repeated quite frequently Like that means 50 marks 10 Students have 60 marks 22 Students have 40 marks Students have 30 marks 12 Students have 20 marks nine Students have 10 marks at It is okay if the observations are of the students There are many and the observations are repeated If this is happening then in that case you are discreet Frequencies make up the meaning of discrete Every observation is different in individual How many times is Akar observing him? I say discrete frequency The mean of the distribution frequency is The observation is coming again, it is his The frequency is for example 40 The frequency is four, which means four times your 40 It is coming, meaning there will be four students like this Those who have 40 marks have frequency of 10 Eight means there will be eight students who have 10 If you understand the marks then it is yours Discrete frequency distribution is In case also mean media mode is different is removed if you don't remember you You can see, but anyway it won't work right now I also told you about the frequency distribution There are two ways, is there one Discrete is one Continuously, you should remember the raw data roughly. It has become discreet, now believe me it is even bigger data should come, many students should come or Then you can also think that brother observation It does not mean it is being repeated too many times there are 100 different observations so In that case you can use Continuous Frequency Dist is basically a class interval what do you do you do grouping yes you do grouping it okay my people friends grouped frequency What is also called distribution? We call this grouped frequency Distribution also says I am everything I will clear it, you just keep watching, see a lot It's going to be a lot of fun okay okay Now understand a few things here, friends. I have done grouping, it basically means what is good look by the way continuous There are two types of these too, he would explain it first hmm there are two types of continuous too if you Look, you can see the difference in both types. hoga ek hota hai exclusive continuous There is one meaning of inclusive Including both upper limit and lower limit Exclusive means upper limit exclude leave both here You include the same limits by the The left one is what you call the lower limit The right one is called upper limit here I think it was also written on the left side Consider the lower limit and the right one as the upper limit I have come okay now look at both of them what is the difference here upper limit is 10 So the lower limit of the next one is 10 and the upper limit is 10. Limit 20 and next one's lower limit is 20 Upper limit is 30 and the next one's lower limit is 30 upper limit 40 then the next one's lower limit Limit 40 is fine but it is not the case here The upper limit here is the next one There is no lower limit which is the upper limit here. The next one does not have a lower limit which is here There is an upper limit on this and the next one has a lower limit There is no limit, what is the upper limit here The next one's lower limit is set by mistake But do one here, if you understand then both are yours Class interval is just grouped data It's different, okay, now listen to me. Be careful friends as if a student If he had got 20 marks then I would have told him here shall I include it or include it here Where will I include you friends Will you include him here, why did I tell you You can not cross the upper limit in Exclusive Let's count brother, it's like 30 here as well there are 30 here also so the child whose You must have got 30 marks, where do you include it? You will include it here but not like this here why did i make it like this You can include upper limit in Exclusive I do not include both of you here You will assume that a child has scored 30 marks So it will be included here if someone has 21 That too will be included here for someone's 21 and 30 in between that too will be included here now one Let me tell you by giving an example, friends Suppose the frequency of this class interval is five This means there are five such students. Those whose marks are 10 or between 10 and 20 I am 20 no ok let's say its frequency is 11 so 11 There are students whose marks are 30 or between 30 and 40 what does it mean Suppose here I said 15 15 like this Brother, these are students of this class interval Frequency: There are 15 such students Those who have scored 31 or 40 marks i.e. both I understood what is in between I said that there are two ways to do your class interval The data is made exclusive inclusive and you always have to remember one thing that if you have been given inclusive data I need to convert it to an exclusive teach you how to do it I will give it to you, okay, okay friends, fat fat This is done for you. Ok, then call again. We will do three types of battles, RAW has become one Data observations are written separately of observations in discrete frequencies Frequency is written in continuous By clubbing multiple observations The frequency is written, now you understand it well Here are some basic things about class marks what does class mark mean friends The mid value is called the meaning of the class mark mid value t basically if I take this class If I ask you about the interval class marks, then something No Upper limit plus lower limit up to Upper limit plus lower limit up to what The mid value will be basically between 0 and 10 mid value is f if you don't understand it 0 p 10 10/5 its 30 p 40 70/2 35 its what will be the class mark 40 p 50 90/2 45 ok there is one class size class what does size mean it's basic The terms are in the stats which you should know No, class size means more friends Limit Minus Lower Limit Upper Limit Minus Upper limit minus lower limit, this is what you give just remember the formulas okay so if I Ask you about this class interval of 30 to 40 May I ask what the class size will be? limit minus lower limit 30 o sorry 10 ho okay it's okay you can denote it with small h yes usually usually usually It is clear, this is all your basics The basics are over now, this is your class These were 10th class matters, mostly in 11th class I'll tell you just one thing to do Should I explain it all in this one slide? what does dispersion mean pay attention friends if I tell you Find the mean of these three data. All three are raw data, if you mean all three You should take it out and check the meaning of all three. will come x times the mean of all three will not come friends you check it out you check it out If you say so, I will check all three and show you one by one. meen na how to look 11 p 10 21 21 p 30 38 45 45 ba a doti cha pa 45 ba 5 now tell me the mean median mode Single value is a single value that is not related to the data Give me a complete picture about this, what does it mean There should be a single value like this There should be a data for every value of the data. I am telling you about this single You can make observations of the data by looking at the values now if I can tell you about I would hide this data from you if I Let me hide this data in front of me, now I ask you Boss's five students will be five Students will be out of 20 marks When I calculated the mean, it came out to be nine So will you ever be able to guess that There will be one among these students who You must have got marks one or two brother, you are like this You will guess, right brother, if I tell you nine If I tell you then guess that Brother, whatever marks the student gets should be out of nine. They will be around, meaning a maximum of six will walk will go seven eight or bigger than nine 10 11 12 Do you understand what I am saying this By looking at the marks you will be able to tell that brother The observations will be around nine You must be around but you don't tell me You will find that you cannot even imagine that the boss is someone Someone might have got marks one also Someone might have got marks three also Brother, 17 must have also come because 17 is more than no it is far from 17 it is very far i understand what am I saying so the first thing is that I am single The value tells you something about the data You are not able to give this complete picture Think about it yourself, if I tell you Brother, this nine, this nine means for this It is best for this data because There are 7, 8, 9, 10, 11 around nine, but this nine is a Pisces. The best representative value for this data is why did it not happen because by not seeing you you You won't be able to tell whether anyone else has 17 or not marks came or infact for that matter also I understand what I am saying It's becoming clear what I am saying You can't tell someone's identity without looking at them marks three also came Brother brother now I told you about some school 50 out of 100 children went to school The meaning of marks is coming, that is coming 68 So will you ever be able to guess by seeing this? that some child may have even got two marks brother it means that just around it Your values will be all I have to say here But the meaning is that this single value represents your data that is Mean, median, mode are not enough for the data to give a complete picture about then which value should I extract from the data I will give you a complete picture about it Slowly we come to that thing and one more example Example Chotu sa, look what you are saying Friends it was as if some match had happened, the first match second, third, fourth, fifth, sixth, any one is ok cricket match happened ok in cricket match Virat Kohli believes that batsman number one Bhai sahib scored 30 runs in the first match and in that Whatever you create in it is fine, you can understand the data The other one who is the second batsman He is MSD brother, he is our Thala Bhaisahab na He scored this for you, now you There is no need to remove it but here first that is derived from the mean and median No brother this is raw data of their data Virat MSD's score raw data of Kohli's score if you find its mean median then Friends he will come exactly the same i.e. Virat Mean 53 is coming for Kohli too, MSD The mean for is also coming to 53 now its meaning What will happen? This will mean that the boss is a Both of them had met Marx around 53 What does it mean that you must have created a ruckus around me after seeing 53? Will you be able to tell that only Virat Kohli is on zero? Also got out is that boss Virat Kohli scored 117 runs Brother, it is not possible for you to hit any runs By seeing this you can tell that Virat Kohli scored 117 runs What I mean by run is my What I mean to say is brother this is two mean two Mean of different data is same but two different The second thing about data is whether both of them are data There are many differences between us, brother, if you look carefully what if i ask you Brother, which one of these two? How will you select a batsman from Brother will you tell me which batsman is more consistent If you select it, you will see it that MSD is more consistent MSD It is more consistent with what I say This means that these 53 are both data has a representative value but this is 53 is the best second data Representative value of first data Not a good representative value Because First Data is far from 53. Distant observations too are like 0 35 did you understand what i said I'm doing okay so looking at a single value You can't tell anything good about data Main median mode by looking at a single value from Now you can't tell by looking at this one slide Read it then we will start asking questions let's do it okay it follows from the above As much as I have discussed this till now, Told to discuss the central value Central values mean median mode which R Not tells you about data Sufficient to give complete information about a distribution mean median mode bhaiya There is no sufficient data about any Variables to give complete picture in R In the values variable means observations There is a lot of distance between the observations There is a lot of distance between us, one zero one 17 understanding in coming to terms with the values of the Observations of Given Data Gives Us Better Information about the data If you know this It may seem that our observations are one with each other How far is it from the other person then you will know the better You can get the complete picture, just keep listening so variable is another factor which is Required to be studied in statistics And that is why we call variable variable i.e. observations how far away that one single What did I say to Value about that one single from the value that you are extracting till now You have been taking it out till now if you come to know this Find how far away from that single value If there are distant observations then it is even better You will not get a picture about the data Now understand that if I told you that the one above The mean of the data is 53 but it is assumed that the I told you the number brother from above 30 is your dispersion value for the data For example, let's say it is 53 to 53 what does 30 with 53 mean 30 There are observations of your data even 30 minutes away And from this you will surely be able to tell that boss if 3030 is far away it could mean someone Marks of a batsman Marks friends, you also got 80, it's ok it is 53, add 30 to it, then 83 will work The batsman may have scored 83 marks also If you understand then variable variable now keep listening okay so if you need another Find the single value that best suits your data If you give variable then it will be more fun like Central values Mean Median Mode We have a single number single number to describe a single variable of a distribution With the help of numbers you can get information in distribution variables can tell this single number is called dispersion of the distribution is We call a single number as dispersion Like till now we mean single number median mode were talking with him if i Let me introduce another single number which If I say dispersion then this dispersion The boss will tell you that the boss is from that mean How far from the median is your mode? how far are your observations Observations there are and various methods various methods of Determining and Measuring the Dispersion called measures of dispersion friends this To find the dispersion value which Methods are used to measure it It is called dispersion and this is what you will learn in this chapter. I am going to read a single number which will give you this will tell you that your from the mode to your central value to your how far are the observations okay forward look the chapter is also starting i am all I will clear it, don't worry about major dispersion I told you guys basically dispersion Meaning, a single value that you can get based on the data I tell the variable as discussed above that The Di Spurgeon of the Major in the Values of the The variable it measures the degree here reat Do what measure does dispersion it measures the degree of scattering of the Observations in a distribution around the Remembering the Central Value Central Value That is, how far are you from the mean median mode How far are the rest of your observations? observations such as for example for Example friends if I type a random number Let me go through it for you so for data two mean or median so you have taken out the data to When you take out the dispersion for the data When you take out the dispersion for two, then Friends, that's something you need to do around five or six. You will see that single number, five or six. what do we understand from this now around that there are values around 53 but less than 53 If there are values even at a distance of five or six steps Brother add 6 in 53 to 59 and get around 59 You must also be seeing the values, I will understand So what am I saying, this single Introducing numbers will help you better understand the data There is better clarity about understanding I'm coming what am I saying okay now How do I find out this single number? I will tell you I will teach you friends, there are four methods Basically Range Cortile Deviation Mean Deviation Standard Deviation In this chapter we will discuss This is your syllabus for not studying cotyledon it is not a part of we will read this You will read this, which means you will basically read three things is the range standard deviation and mean deviation Let's just look at the mean deviation in the first 40 minutes. I will talk about the range is very easy let me tell you what is the range okay the range is very The range is easy, friends, there is a difference Between the two extreme observations But do you know the range of a good dispersion It is not major, the major meaning of dispersion is that tells you a scattering of data from the central value that that single value means How far is your data from the median mode How far are your observations? Range friends what is highest Observation minus lowest observation for Example if I ask you batsman B What is the range of batsman b1 then highest What is observation 117 Lowest observation what is ro to 117 minus 0 your friends 117 has arrived, okay so 117 is your data Range Aa 117 Your data range has arrived but do you know This is not a good major, I know why Because boss these are just two values considering everything else in the data Ignoring the values is good Dispersion measure is that which consider the values and go from 117 can we find out what can be found out from 117 that the boss can have values beyond 53 to 117 is more and can be less than 53 to 117 I am seeing you a little bit, I am understanding something is 53 some 60 70 away from 117 is 117 there is a little 117 at a distance if you understand Range is not a good measure, simple The reason is that all the observations Does not consider dispersion value While giving this answer I will talk about mean deviation If you don't want to memorize other formulas then like this Just as I am telling you the flow it's ok to keep going what are you saying Friends, there are three types of data: Raw data Discrete Frequency Distribution Continuous Frequency Distribution I calculate the mean deviation for all three data sets. Learn to calculate and remember the mean deviation What is the meaning of mean deviation Don't think that Pisces is Pisces Find deviation for ungrouped data and How to make individual observations What do I teach through mean deviation question bola dosto the scores of the batsman in 10 innings or this is for 10 innings Batsman's scores are given find the mean Deviation about the median, remember us guys What are you finding out that single value means be it the median or the mode from that single value how far are my observations from You will have to find out the single value, so He said find the mean deviation about How far from the median are your How far from the median are your observations? There are observations So first of all what are the three types of raw data then we will do it for discreet Then we will do it for continuous If we do it then first of all the median said find the median find the median then the median How do you take it out friend, you will know how do we find the median how do we find the does anyone remember the median hey friend it's simple It is simple boss, let's see it first First you can assign data to the data by ascending or descending arrange the raw data in the smallest order Which value is the smallest in my opinion? yours is 34 34 smallest 34 smallest 38 then what happened bigger than that boss 38 then Take out your 42, this is a bit boring but you will understand 42 then friends this is yours 46 If you want you can speed me up You will have to do it at that speed 4, ok even 44 isn't it so easy it became 46 and then it became 44 It's been 46, then yours is 48 in my opinion you are coming to my mind again 54 then 55 is coming 54 55 then 63 70 63 and 70 1 2 3 4 5 6 7 8 9 10 very great ok friends n your 10 your n is 10 means your n is even The number of observations comes in two mid values there is a n / 2h is one is n / 2+ 1h Divided by 2 this is your friends median comes let me denote it by A i am ok So what is n 10 10/2 Fifth Observation 1 doti ch 5 to 46 plus 1 doti ch pa 6 chhawa Observation 48 You calculate and you will get 6 only 10/2 5 p 1 6 then 46 p 48/2 friends will give you 47 so the median of the data is your 47 The median of the data is 47. Now you have got it. I want to take out the main aviation, that is, that single number to extract that tells you that your How far from the median are your observations Can anyone guess how long the ruffle should be If it is done well, observe good dispersion If it is major then how much ruffle should come from 47 Your maximum is 70 and your minimum is 23. Yours in my opinion friends my opinion Your dispersion should be around 15 Around 15 is the single number that you This tells you how far from the median your They are observations, not memorizing single numbers yes friend don't memorize it Babua it's ok right The single number that lets you know the median How far is it from your Let's go ahead and find the median now. what do you do take out x minus median and I will tell you its mode meaning ok Friends, 38 is how much more than your median of 47 It is far away -1 but apply minus mode 11 You have to take the positive value, okay 70 70 minus median so 70 - 47 is 23 you get 23 will go to mode of 23 23 is 48 - 47 1 mode of v friends only one is ok It is 34 - 47 brother your median is 47 right Your median is 47, so 34 - 47 will be 3 13 The mode of -1 and -1 becomes two 13 ok 42 - 47 -5 -5 modulo 5 becomes 5 okay 55 my 47 E mode of 8 8 is 8 which is 63 or 47 so 3 13 16 friends your mod of 16 will be 16 keep doing 46 - 47 -1 -1 -1's mode is 54 my 47 this is your 7 so 7's mode is 7 44 - 47 -4 sorry -3 -3 mode is 3 OK, so what did you basically find out? how far are your observations from your median How far is your observation from your median is far away and i turned the corner to sleep No need to cater to negative values Just listen, what do you have to do now Summation Or say n then n means number off Observations capital n mean number of observations let's take a look at this Let's check it friends 11 + 1 12 13 26 31 39 40 56 63 66 okay what does the formula mean Deviation Memorize the formula for calculating mean deviation Not there. Joe Deviation Came summation summation x a minus median upon If you make capital A then 66 up to 10 observations 6.6 Your answer has arrived 6.6 Your answer has arrived I will also check it once Just in case we are not doing anything wrong, right? Because it is a recorded video, nothing is wrong You should go to this chapter a little early what is it friend one second 923 That's right, this 23, my friend, I plused this 23. if it is then it should be 22 and plus 22 80 23 1 13 5 8 16 173 23 check it again friend 11 p 12 12 15 35 38 48 48 P 5 53 53 P 54 54 P 8 E 62 62 68 78 + 10 is coming to 88 friend why is it coming to 88 I am wondering if I am doing something wrong 11 + 23 ok is this a nine 4 ok Friend this must be nine friends 86 friend will come so I was thinking to check I will do it once please forgive me now next time I won't make a mistake with the bar, right? Anyway This is a calculation, you will understand this mistake here But you don't have to do this friends, this is your 86 I thought it would come, I probably remembered the answer Somewhere or the other, friends, this is your 8.6 Jayega sab kuch wahi hai 86/1 8.6 this single What the value is telling you is that it is higher than your median On an average all the values are this far apart On an average of all values from your median It's so far away, okay, let's go to the next one now friends We find the mean deviation about the mean from the same raw So first of all what do we mean for data? You have to take it all out first do I have to find out the meaning ok So how do we find the mean of 6 + 7? should I do the formula 6 + 7 directly 6 + 7 13 + 10 23 25 35 38 48 52 60 80 Friends, your number is 80. 1, 2, 3, 4, 5, 6, 7, 8, eight. it means your 10 has come it means your 10 has come What should I do now? Is that the same thing that I have done? Increase the value of your main through observation Minus it and turn it into mud okay so 6 - 10 is -4 I wrote it as 4 7 - 10 is -3 I wrote it as 3 10 - 10 is 0, I wrote it down 12 - 10 is your 2 13 - 10 is yours 3 4 - 10 is yours 6 4 - 10 Guruji -6 happens, see the mode is on 8 - 10 is 2, make it 20 - 10, now the same for everyone If you sum it then summation this summation sign is this we call it sigma okay guys It should be fine nowadays otherwise it will be cut x aa - boss how much will it be x times yours 4 + 3 7 9 P 6 15 18 20 30 each has to be done separately If there is a method then this is basically it friends what did i do sum of all deviation brother this deviation So this is what Davis brother means by observation Deviation is how far the observation is from the mean How far is the Six Mean from the Observation Mean how far is it from seven mean how far is it from seven mean 12 If you understand how far it is from Pisces then basically I am finding the mean deviation from the mean Deviation formula is the same as finding mean deviation what about x my summation x aa - x times up n number of observations then number of Observation comes from my side 1 Doti 4 5 6 7 8 and this is your 30 so overall my think your answer is 8 8 3 24 8 3 24 6 So from 8 56 sorry 8th 24 decimal place 7 3.7 something coming once Let's check if our people are together Also check so that it is not your mistake Friends, it will come at 3 p. Yes, that is correct. It will come at 3.75. okay so what does this mean that your from your mean means from 10 on an average which All the observations are 3.75 feet away from you You can also see the maximum distance from 10 that's 20 it's 20 so 3.75 is coming now you You will say that friend you are considering 3.75 as 10 median Sorry 10 is the mean so the deviation from the mean will be It is coming out to be 3.75 i.e. from the mean Your values could be at a distance of 3.75 At the most you will say Guruji 20 So I won't be able to understand this, brother I will not be able to tell you about the data 20 is also present in the data friends Meaning even dispersion of data is not enough To give a complete picture about but anyway anyway anyway more about this I will talk to you right now, okay, but you are fat Do you understand what I am trying to say No friends now we have to do the same thing What do you have to do, just find out the mean deviation But now I will do it for discreet, then If I do main deviation for continuous then Now main deviation for raw data is done Discrete Frequency Distribution Again the same thing, first of all about mean deviation You have to find the mean and see how the data looks given is discrete means three Observation is coming eight times nine observations 17 is coming 10 times 12 times 23 is yours bar 27 your five times let's do it okay how to do relaxed listening how to do okay okay let's go very comfortably so how do you mean you will remember me means remember me I want to know how to find out the fish first You will have to find out the mean deviation about the mean If you want to find out then you will have to find the mean, so f 3 8 24 these are the things of class 10th 9 10 90 17 * If you make 12 then 17 * 10 170 170 and then 34 I think your score will be 204 i.e. 23*9 23 * 10 230 230 if you subtract 20 3 then I think this will be your 207 27 * 5 so 27 10 270 halve it to 135 this is my calculation Now brother how to find out the mean Plus all the observations brother, this is it The sum of all the observations will come up to the total number of observations then call it summation f or say capital n it's the same thing okay so 8+ 10 18 30 this is your friends 30 p 9 39 44 this your 44 is coming do it please your 44 is coming will go 200 p 400 400 500 500 in 100 Plus 600 100 and minus 10, you get 590 in 20 ps 610 614 If you add sa to 618 618 then 625 630 660 will come okay now you If you can do it yourself then let's find out This was called the direct method of finding the mean ka this is called direct method here I will also write the basics of class 10th Maths was a direct method, friends. This is a good way to find out the meaning x b equation summation fi1 / 44 then 11 si 11 * 4 15 friends mean yours 15 has arrived Now find the deviation from the mean All observations in one flow Come on boss, what do you mean by observation? Take deviation and its mode of observation take the deviation from the mean and its mean okay So 3 - 15 - 12, I wrote it as 12 Mean of 9 - 15 observations taken will go 17 - 15 2 will come 23 - 15 friends 8 will come 27 - 15 friends or your 12 it will go okay now because here If the frequency is introduced then that's it What happens to you slightly different from these deviations You multiply these deviations by f ho friends you can know these deviations from your f We multiply yes you understand what i am saying you multiply your deviation by f Because boss, observation is eight, right? Dishes were taken out once from three, such that three came it is bar, if you understand then 12 a 12 a e you guys do you know 12 8 96 okay 10 si 60 12 to 24 9 8 72 5 12 60 and just a few No, this time you do it properly, just do the same isotropy f summation f x - x times i equal to what will come 90 p 60 150 156 P 4 160 P 20 180 120 P 60 So 180 something is wrong one second 90 p 60 150 156 160 180 180 P 60 240 240 70 P 310 312 here comes your 312 ok now what is the formula simple mean What is the formula for deviation about mean and what is summation f x a minus x times divided by summation f so this is yours 312 upon 44 solve this I have answer one I'll tell you after looking at it or you can do it yourself You can also do it 312 up 44 312 44 friends 7.09 will come, it will be fine, wherever it is needed I will show you the calculation So what is the mean of this data 15 and 15 on an average how far are you from Observations 7.09 is far away, you must be able to see it friends naa you will subtract 7 from 15 and get some three can go 15 in 7 plus will you do something 23 27 then the central value of If you join another value club with it then you will get it Giving a better picture about the data Is okay let me ask you a question now Discrete Deviation about Mean Now our mean deviation for frequency About Median Will Discrete Discrete take out the median everything is the same just the median I want to find the median, remember how to find it how to find the median for this remember the median mean mid value cummet How to calculate frequency of three same as before then next in three frequency plus kari then next in eight eight So friends this is the next 14 in 14 friends this your 21 8 out of 21 so this is your 29 okay and Summation f summation f that means capital A yours is equal to 29 This is clear, okay, then how is the median Friends, you will remember the steps By dividing n by n, that means 29/2, so 29/2 is 145 14.5 Just bigger cumulative frequency than 14.5 which one is 21 the one in front of him again I will tell you that this is a part of your class 10th Whoever does not remember, it does not matter, he took out the CA CF Niklaa We're Trite Find the Middle value of the data median of the data CF took out ok n ba 2 kara 14.5 se just There is a big comet frequency in front of it The observation with the least difference becomes your median Now it is clear what to do Take the median distance from the observation So how far is 30 from 15 - 15 is just 15 Will you tell me 15 is sorry, how far is 21 from 30 is 9 27 to 30 ti 30 to 30 g and 35 to 30 now what about the distance of pa because If the frequency comes then the same thing frequency to multiply f in one minus one minus The median is ok so 3 15 45 5* 9 45 6* 3 18 7 * 0 0 8 * 5 40 solve this Summation Summation f x my measure well be equal to well be equal So solve it boss 40 p 90 it is done Yours 168 108 P4 148 is correct now the formula is the same Mean Deviation Formula Summation f x - Mean Deviation take care of your summation f writing a little 148 by 29 Let's check the answers once friends If you check the answers simultaneously, then someone will There is no chance of making a mistake 148 ba 2 dec Will There Be Some Summer 5.13 I hope you do this basic calculation I can do it where needed I will give you don't take any load but it is very easy Friend, okay, okay, let's go, what's left now, raw Mean deviation done for the data Mean Deviation for Discrete is Given Mean Deviation About Mean Both Ways deviation about median now we Continuous Frequency Distribution or Then the grouped frequency distribution We will learn to find the mean deviation for and After that we will use standard deviation I will go into what the mean deviation is saying tell me about the mean then you have to find the median and then tell me the mean deviation, that's all What is the method to find the median? Will you do the class interval has come, how did you do it boss What is the given frequency? Frequency Yours 8 10 129 5 8 10 129 pa ok good curative frequency 8 P 10 18 P 12 30 P 39 44 okay you see the summation f means Capital A number of observations will be 44 only Just keep listening to one thing clearly, what now? Will do n ba 2 find the median for n ba Take out 2. Okay, so I took out n ba 2. what will come 1/2 friends 44/2 so 44/2 i 22 The cumi frequency just greater than 22 is the one in front of it would be the median but here So there are many values of 12 and multiples of 12. There are many values in between, friends. do you call this the middle class You used to call this the middle class You may remember this is your median class this is your median class understood this Your median class is included in these how does your median come from does anyone remember the formula by using the formula Does anyone remember the formula? Come and see the formula Grouped Frequency Distribution of Continuous Frequency Distribution to find the median for the The formula that is used is lower Limit plus n Batu - People above should always remember why this happens It happens sometime later you go and learn it but CF's You take the above value, it's ok If you already know everything else then lower limit So friends your load limit is 12, median class n batu yours is 22 22 cf yours CF Your Friends 18 Frequency frequency is 12 and h class size Class size is 18 x 12 x 6 6 1 6 to 22 - 18 4 4/2 2 friends 14 yours The median is 14 Your median is now what to do is to do the same thing is the median the distance of observation from the What is your distance from the median? Your median is 14 remember let's do observations what are observations what are observations so there are many when there are many observations then you know what Now take its mid value i.e. class mark Let's take it, do you remember the class marks, 0 and 6 mid value of 3 its yours no its yours 15 its yours 21 its yours 27 Now you understand, just take it out, right? So 3 - 14 i - 1 I'll write this as 11 mode The sum is 9 - 14 i.e. 5 9 - 14 - 5 Guruji please apply the mode, it's 15-14 1 21 - 14 is 7 27 - 14 is 7 7 14 Sorry 13 OK, now you know what to do If the frequency is given then from f to f Please multiply it 8 5 10 50 1 12 12 7 * 9 63 13 5 65 plus tax summation f x my median okay so 80 p 50 130 138 140 150 153 or 150 P 210 213 218 218 P 288 It is coming I think 288 is coming okay Let's check it once just in case 282 78 people are saying 80 50 12 once I will solve it again friends 130 138 140 150 210 213 210 213 218 200 why is 18 218 plus 60 8 written as 27 288 I said it will come to 2780, okay, just keep the same formula Is the formula for mean deviation is summation f a a minus median our summation f or cupit n tell me then 278 up 44 You will solve this, friends, it is yours Something of yours will come 6.31 6.31 is clear for easy continuous The median one is now done for continuous Mean Deviation About the Mean So first of all What you need to do here We will have to find out, let's find out the meaning Now friends let's find the mean of the class interval How to calculate mean for the question Do you remember someone used to have two methods Ajyu Mud Mean Method and Step Deviation Method I am using Direct Step Deviation Method I'll go, just let it become smaller yes here it is directly on your step On the deviation method okay let's go let's see let's let's c let's c let's go one second very good Friends, first of all, mid points will 10 and 20 come 10 + 20 hey class Mark nothing else 10 + 20 30/2 15 You can also see that it will be 15, it will be 25 It will be 35, it will be 45, it will be 55, it will be 65 and it will be 75 I think a lot has already been given in the beginning good 2 3 8 14 8 3 2 2 3 8 14 8 3 2 3 8 14 8 3 2 If there is a mistake here, it is right here There will be calculation mistakes and anything else Now what's a way to f* why should i go i do a little bit smaller Remember, in step deviation method you have u used to take out u aa what would have been x aa - a up h remember this formula x - a up h a It would have been great if you could imagine any of these When your Pisces comes, assume that you have Pisces on 45 I have guessed it, you should know it as if you I tried to find out the meaning of 45 The method is to use step deviation why do you lower your values Multiplication is a bit heavy on you You will say Guruji, if it is easy then anyone can do it There is no problem but when longer values and If the value is big then you should use this method will have to do it to make it smaller okay So friends what do you have to do u come one who is also x aa whichever is 15 - 45 - 30 by class size 10 so -30 ba 10 e -3 here I will come again and do a little for you Trying to understand the basics of class 10th This is maths, friends. This is ok. 25 - 45 - 20 upon class size 10 so this You will get -2 then 35 - 45 10 10 up class size friends -1 will come sorry -10 45 - 45 0 friends your 0 will come 55 - 45 55 Observation Minus Ajyu Mud Mean Observation Minus Azoom Mean 55 - 45 10 up Class size 10 1 Friends you have to calculate It will come in the pattern 1 2 3 Now you You Take out the summation f a u a friends, all of this Plus By doing this, we get 6 14 6 minus 20 plus all these plus 20 will come friends this is zero Zero is gone and it has come brother, very good zero it has come and how much should the summation f be? summation f i.e. capital A Pa 5 13 27 30 38 40 Your 40 Aa very good very good remember it now What was the formula to find the mean? The formula to calculate was lower limit plus sorry no lower limit ajyu mud mean plus Summation f ui5*h class size who doesn't remember Remember this here, class is important The basic formula of 10th is Ajum Step Deviation method is called step deviation Step Deviation Method to find meaning in it now don't think like this how many All the formulas are memorized by rote Whatever is going on is still the same, isn't it? Come on, friends, how much do you think I mean? guess 45 will come this is your row summation f Yours is 40 friends h yours is 10 friends your 45th is the mean How can I multiply anything in my memory brother? If you divide anything by , then your mean will be 45. What should I do now, what should I do now boss Now you have to do this, your Finding the mode of the distance of the observation from the mean you have the distance of your observation from the mean We have to find the mode of 15. Let's find it. distance from 45 - 30 but I give him 30 I will take 25 45 to 20 35 45 to 10 45 of 45 to 0 55 of 45 to 10 65 of 45 to 20 75 45 From If the frequency is 30 then multiply it So with frequency you're doing x - x times multiply 30 30 * 2 60 do it easily 20 * 3 60 10 * 8 80 0 * 14 0 10 * 8 80 20 * 3 60 30 * 2 60 okay guys do it Solve it quickly, it is yours Friends 80 60 200 p 400 has come 400 has come ok direct formula of mean deviation what happens to mean deviation summation summation f x aa - once divided by summation f this is yours 400 up 40 10 aa Your mean deviation is 10, check it also. takes I will check once, yes only 10 will come, did you understand? Easy, I have done this for your three datas For raw data For discrete data I mean you for Continuous ta Learn to find deviation with the help of mean Finding Median Mean Deviation with the Help of you guys learned okay two one last I will discuss this question on mean deviation I will solve it, you guys have to do it yourself, okay what are you saying calculate mean deviation about median okay so calculate Mean Deviation About Median Data Given to You you can just create one problem here that's boss 20 end at 21 start at 25 End, start at 26th what kind of data is this Continuous grouped one but there are two in that too Types are exclusive and exclusive friends that is exclusive why is sorry inclusive why on 20 It is ending, should start at 20 It was on 25, it is ending on 25, it starts on 25 This should have been your exclusive data this is data sorry this is your inclusive sorry do whatever comes out of your mouth by mistake For that, it is inclusive, I told you Told you to always be exclusive to inclusive how do you do it now Who all would have memorized this once in their childhood? Let me know in the comment box if you have already watching the video that I have memorized that brother let's subtract 0.5 from the lower limit 0.5 plus the upper limit There is a reason behind this, you don't always do this do this in the syllabus in your syllabus The questions are made in such a way that you get 0.5 To minus . understand the purpose is to do plus What happens is that you have to make both of these beans You have to make both of these the same. Both have to be made the same, which means whatever is above it There is a limit and the next one should have a lower limit Its upper limit should be having limits what should you do you should do both of these Do you see how much difference there is between these two? Whatever the difference is 5 10 1 100 4 lakh Whatever the difference is, usually one or two Whatever the difference is, it is it is of one divide it by two and it's over You will always divide one by two, so you will divide one by two 0.5 will come and so now 0.5 in 16 - 15.5 0.5 is added to this 20.5 is added to this 0.5 minus So 20.5 is 0.5 plus 25.5 is 0.5 ma then it came to 25.5 0.5 plus it came to 30.5 0.5 minus gives 30.5 0.5 times 35.5 it's gone and that's all that's left 5 6 12 14 friends The data will come and you can solve it yourself ok leave the decimal to us You are going but you don’t do it yourself You will handle it friend, you understood roughly, right? what am i trying to say let's move on So far we have talked about important matters Learned two majors of dispersion and also learned this What does it mean to find the measure of dispersion What is the mean of central value How far are your observations from the median mode This is the average, it tells you the dispersion measure We learned two ranges that are so good Dispersion is not major and I have one of your What did you learn about mean deviation friends? There is a problem with mean deviation This is just the main deviation that occurs In that I mean myself if you notice I apply the mode to the deviation myself Who told you to apply the mode bhaiya you see You must understand that brother, whatever your meaning Whatever you mean or whatever your mean will come You will get your observations from that You want to see how far it is from him To see how far your observations are Do you want this in this question also? Friends, in the question also from your median To see how far your observations are This is what you want, this is the whole purpose, dispersion How far is the exit from the observation post Sorry your median, mean and mode are correct but I am applying this mode myself So this became a limitation of this thing that BOSS Mean Deviation maybe there is some fraud in it that brother mode why did you apply any reason friend it's ok With mode you made the values positive So friends this is your mean deviation This is where your limitation arises Limitations are also written, ok plus Mean deviation about mean is more accurate as compared to mean deviation about median to This is something that you are here because of your limitations. You can see it is fat, right? I told you I already told you about that mode limitation remember and that's why I need a better major of If he needed dispersion I would tell him am standard deviation standard deviation I don't apply the mode myself, what will happen now this is how it happens let's go about it Let's talk Come on boss, now our people will learn friend Look, people have learnt mean deviation, right? with the help of mean median now you understand That's it, now we'll learn two more things And this is the last topic of your chapter. One way is to calculate variance and standard deviation. Is it okay to take out deviation? What happens? What is variance and standard deviation Simple as I told you this is for you Measures of dispersion means it gives you a They provide the single value that you need I tell you brother, your observations are yours What is the average distance from the central value But let's do it now, what is the standard deviation? I will tell you first what happens and then Let's talk about variances, okay anyway So the variance of a variate x now definition You may not understand, but I will try to explain I will do it ok The Arithmetic Mean Ariadman Whenever you say I have to take it, Aridaman means I have to take it Observations have to be plused upon total number of observations have to be done okay means I need to add some things to it total number of observations then who is plus by calculating the total number of observations of the Squares of all deviations in question I will do it and tell you, otherwise you won't enjoy it, okay well by the way these three mean Standard deviation becomes variance Individual for three types of data You can group this into discrete and continuous You also say individual, what does it mean here we are talking about raw data let's ask questions I will teach you by doing it, okay let's say what Finding the Variance I'm talking about standard deviation I will tell you what the question is first Look at the format given here is raw data Okay so first of all I will make it a table I will write it down, now I have understood it Find the biggest deviation first. What is it? you take it out you take out the deviation okay To find the deviation, Guruji first calculates the mean So you will have to find out, so just find out the meaning Come on, first of all, let us find out the meaning okay let's do p plus here 5 p 8 13 how much is p 8 13 p 8 is yours Friends 21 25 P 5 30 38 40 so this is yours 40 is 4 p 6 10 15 15 p 6 21 25 20 33 39 45 50 56 so your result is 560 okay That means basically sum of all your observations Friends, 560 has come, okay, so what about Pisces? what will be the formula mean your will go 560 my 1 friend's 6 sa 89 10 10 Observation means friends your score is 56 ok means yours is 56 we will check later We will also answer this, now let's find out the dish If you want to do it then you can understand it from your observation minus it but here this time we I will not apply the mode, okay why not I told you that it was a limitation, mud We were doing it on our own will, friend There was little reason for this, it was used uselessly so that we can turn negative into positive We could value it and make our calculation easier It could be possible but there must be some reason here But I will not apply the mode instead of that what am I going to do please listen carefully First, how far is 65 from 56 to the minus Now don't ignore it, 56 - 65 is Friends, minus 9 is 56 - 58, friends minus ka 2 okay well sorry I mean Observation is minusing from the mean Subtracting the mean from the observation 65 65 - 56 This is your 6 and 65 - 56 this is your 9 friends okay 6 58 - 56 is yours 2 68 - 56 is Your 12 is fine, 44 - 56 will be negative minus when 12 44 okay 48 - 56 is your minus 8 45 my 56 your 5 and 6 minus of 11 60 my 56 your plus of 4 62 - 56 i Your 6 60 - 56 e 4 50 my 56 e minus 6 OK, now you have your deviations. I want to square the deviation, okay so right? the square of is basically x aa - x times you what will we do square okay so 9 The square of 81 is the square of 2 is 4 12 the square of is 144 i write it properly I will give this to you 4 [music] No 144 okay then my 12's square again Friends 144 Square of 8 Again Friends Your 64 The square of your 121 11 becomes 8 12 becomes 4 square is yours square of 16 6 is yours 36 4 square e your 16 6 square I will count your 36 one doti ch 5 6 7 89 10 Okay, if you add all of these together, you get 6 6 12 18 24 25 29 33 37 38 42 so this Write your T here, write it here no 42 so let's put it here pat up 4 so 4 p 8 12 12 p 4 18 sorry 16 20 26 28 29 30 33 36 okay 3+ 1 45 45 6 662 is coming so your summation x am x times the whole square your amount is 662 now some formula no friends there is no formula What did he say Arimilli? Standard Sorry Variance Whatever variance you get, friends you You denote by this sign Let's do it, it will come to you summation summation x a me a times square Your Competitive and Simple Deviations are as follows: square them okay square them and If you find out their meaning then plus them all 62 662 Your capital is coming from my evil 10 is 66.2 your answer of variance is given ok i'll check it once This will be your answer of 66.2 i.e. your variance answer wait a second okay together with your Let's check as well, yes 66.2 is the correct one Answer is very good friends this is yours The definition was written here, Isra Dhyan take note hey where have all these buses gone yes this Look whose square is to do aridaman all The Deviation is ok but where is the difference from the mean From the Arithmetic Deviation Taking You From the Mean It is okay not to take it from the median, friends. which we call variance x or denotes the variance of x Or do you denote it with this sign What is Standard Division Standard divisible by nothing but the variance of x Take the square root of the standard deviation. you take the square root of the variance x okay but the positive square root is positive square root of variance x then standard How do you find out the deviation friends, this also Your discussion is how can you find the square root of this will you do it i will tell you look at your What is the variance of your variance x or Then this is your 66.2 standard What will be the deviation, root of variance x How much will be the root of variance x friends this square root of variance square root of 66.2 Good by the way of Standard Division sign this is why brother [ __ ] root off If you do this, the standard deviation will be reduced This is the sign of this, this is what you have written here It must be right here, it is written somewhere look it's written got it okay it's just You all have your symbols, well by the way now how to find the square root of this i will tell you a In this question the square root of this I teach those who know how to take it out Those who don't know the good thing, see it once how do you do it 66.2 you wrote it comfortably Once you learn the method, see what you do Do you pair with the right side? Right side pairing or grouping with grouping But in two parts, friends here so with two if you look from the right side there is no one to pair with two So you put zero, okay you accepted it Take double zero, if it works then it's ok, otherwise No problem, you can do it from the right side Pairing this, this and this, if you want double If you apply zero more then it will be a very good thing The pairing has been done now what will happen this pairing Why do I do this, friends, all this together it comes down to why does this happen what happens leave it, it's the method to take it out, it's ok well by the way you know its square Why will the answer of the root be greater than eight? so the square root of 64 is 8 Square root of 8 is greater than 8, its answer is 8 A big one will come now see what they do 66 start from the left side Just less than or equal to 66 what is the perfect square number 64 so you you write 8 8 64 ok what do you do now Pay attention 66 is just smaller than perfect square or equal to 64 so whose 64 The square of eight is eight so you wrote eight 8 likha t likha t likha at likha at likha at wrote 8 wrote now what 66 - your 2 has come Now listen to them both together below. If you take out the decimal, it will reach your top Look, 8 point some answer is coming and here But what do you do that you have written here? You add that here again + 8 is yours 16 I understood, this is your first step Now here you make the box and here You also make the box and remember this The same number comes in this box The same number comes, meaning if there is one here then one here two here so here two here But three, so here three and single digit What does it mean that you will get the number 220 if need it then 160 box something like this friends 161 * 1 161 It will be done but if you do 160 2 * 2 then Friends if this goes beyond 220 then You will do 161 * 1 here friends 161 came out of 10 and 9 went away this is your 11 11 became 6 friends 5 this is your 0 59 and this Double zero will come down together, remember do you understand what happens here But it is the same, if you plus here then Here you come 162 and make the box again and make the box here again what can I say, the same number will come in the box I will get the same number in the box 5900 If you want then buy 162 coaches into coaches for Rs 5900 Now I have to go to two to two decimal places always take it out okay so it does one thing I took 3 and 3 so 3 3 9 3 * 2 6 3 6 18 3 1 3 4 48 69 4 4 Will you do more? if it goes then write 4869 Write 4869 and you can solve it It does not matter how much you have here And here also it was 8.13 on approx yours Answer: So friends, your standard deviation is 8 P13 has come, this is your standard division I will check the answer once as well It will come ok it was very easy ok come now The data is the same, it is raw data, it is raw data Variance Standard Deviation is to be found I am telling you the second method, it is a simple and easy method okay now here i am friends i am also a mean person I will not find out the meaning I will not find out the meaning I will accept what I said, I am not mean I will take it out, I will consider it as mean, I will remain in the mean I will consider it a mean and then I will tell you I will tell you a formula, you can also use that formula You can take it out friends I will take it out d d means x i - a this is also a deviation brother Minus the mean from the observation to do minus from it is amazing it means just that You can take any of these as your meaning I mean I guess I did what I did I will do the same here I will take it friends, I will do 48, right? reason bng my calculation will be correct if you Whatever you use, your answer is correct I will come sorry, I am reasoning by looking at it like this Boss, it's simple, we have to correct the calculation So, I mean I have already thought about everything I have kept it like that so that it would be in the middle of the class What is statistics usually about when you're walking so fast in the lecture Sometimes this kind of calculation happens If there are chances of making a mistake then I hope you don't sing you guys don't mind that you guys mind that no i am joking If you mind it, I will do it anyway anyway yes let's take a closer look no friends so I guessed it means This is what Ajum Mean from Observation Minus R brother, this is just a deviation this is just a deviation so remember do it maybe it's called D for deviation This can happen but let's do it anyway friends So 38 - 48 is minus 10 of 70 minus 48. 22 48 mi 48 e 0 34 mi 48 e minus 14 42 into 48 and minus 6 55 into 48 7 63 my 48 so friends this will be your 15 ok is 46 over 48 and this is your minus 2 over 54 over 48 e your 6 and 44 my 48 your minus 4 Remember to square the deviation I always squared d. Find the square quickly, okay, so -10 square is 100 square of 22 is 4 44 I think it will come 22 22 2 * 2 4 2 2 4 2 4 2 4 484 will come Sorry, 484 will come, right? Square of 0 is 0 - 14 sqaure 196 6 ka - 36 7 ka 49 15 ka 225 2's your 4 6's your 36 and then I will check your 60 once. Are all the values correct or not 96 36 49 225 4 36 and 16 okay friends if you understand all these If we sum the square of the deviation then this you will get something 11 46 if i am not wrong you can check it out okay now What is Direct Formula? Formula You just need to remember the formula okay you guys still need this calculation You can see what the formula is, standard Variance to calculate sorry variance x What is the formula to find it, just remember it Keep Summation d square a n minus summation d / n period remember this formula for square summation d s what is coming 1146 up n 1 2 3 4 5 6 7 8 9 10 10 minus summation d so friends calculate summation d also You will have to do summation and calculate what will come out If you do then friends with minus minus If you do plus plus then this is your 10 24 30 32 36 so minus 36 comes out to be 22 plus 22 is going to be 44 50 50 14 friends your 14th is coming if i am not your color is coming 14 let me check it also I will take it very good ok now what about this will be summation d means summation d means summation d is 14 n 10 friends this is your square Let's solve this quickly 1146 / 10 - 196 / 100 solve it and get 100 Your LCM will come or 11460 -196 is equal to 11460 then 11460 I will do some calculation 196 6 out of 10 got 4 9 out of 15 got 6 3 divided by 2 1 2 64 so this is your 11 264 up 100 then 11.6 Your variance has arrived, let's check it 112.5 your variance is absolutely correct i understand what am I doing standard How to find deviation Standard Deviation To find AD standard deviation you'll need to do the square root of this square root of 11 2.64 I will solve one more and give it to you You guys will solve it yourself later, right? 11 2.64 let's see how to do it so 112 wrote 64 written grouping from right side If you want to pair then put double zero If you want then don't use it, but use it only when it works group it from the right side group it I am left alone, leave the banana, no problem No need to worry, now the forest should come first if you want to do it okay friends then just one Smaller one is equal to perfect square one If it is just 1 then it's 1 wav, okay if you want One can take all three of these together as well there is no problem it is 1 1 1 now what is written here friends Do plus here two has come here box Box here friends this is your zero and Here below you have got 12 down Your 12 is over, it is clear, now pay attention listen carefully to what is happening here Listen to what is happening to you here. is one 9 * 9 Is there anything wrong here? There was no problem Yes No Nothing there is no problem ok now pay attention ok guys now look 12 is here If the same number appears in the box 12 below, If I do 21 * 1 then 21 will become 12 more than that If it comes out then do 20 * 20 and make it zero it will be 20 * 0 will be 0 so friends yours This zero has come here and your 12 has gone down okay below now listen to what is written here Plus it so it comes back to 20 here. Make it box and because you take down now 64 If you are going to then your decimal point will go up your decimal has landed on top okay box The box is clear, it's clear once again Look what is going on here, look at everyone First one is written 1 1 1 1 - 1 0 If I do plus then two come in the box box the same number will come now if you want 12 then one and 21*1 cannot exceed 12 If zero should come then 20 * 0 will come 12 0 12 Now 64 will go down and your decimal will go up It will go and whoever comes here is an add So these 20 boxes have arrived now what will be the next 20, boss here 20 If you want box 20 or box 12 then 64 friends take it 6 si 36 603 6 2 12 36 ok i think 206 is coming here this is your six here Your six I think 10.6 is a very You can leave your closed answer here 10.6 I will answer your standard deviation by a I check it again 10 p yes 6 is yours The answer to the standard deviation is fine, you can choose then take out upto two decimal places, don't want to you can also do that, there is no problem, it is the same look here 206 what would you add here Six, whatever box you get, you add the same If you do this then your 212 will come here The box will come and the box will come here too I'll go friends, there's nothing left here well by the way 206 * 6 how much was coming 12 2 36 was coming I think so 1 2 36 You will minus whatever comes here, it will be dubbed here It is ok to take the dub off here then it is 10.6 1 It will come easily, I learned it both ways Look, don't get confused, what is the deviation Square it and find its arithmetic mean And here I have said direct mean no I took out the fish and made it amazed and then Later Deviation Mean Deviation from Observation Just square it, the formula has changed Because I have asked Pisces something ok guys let's ask another question another question on this on this okay now this time I will teach you through the UI method, okay? and friends this is called shortcut method and does it work for you They say shortcut method, shortcut method I will tell you the formula, first you can find the solution Look brother, your discrete frequency Your brother is distribution, this is discreet frequency distribution or a function Why don't you do it through shortcuts? I will first tell you about it through the normal method So brother, we have just given the discreet We were doing RAW, now we are doing RAW were now let's do discrete okay It is very easy to do it brother, first take out the fish So, you will get the direct way to find out the meaning I already know the formula, so it's given to me Friends, to find out the meaning you okay let's find out the meaning here, my answer is fine then 2 4 6 4 4 16 6 5 30 8 15 15 8 e 120 10 8 e 80 12 5 e 60 14 4 e 56 16 5 E 80 either find the mean or accept the mean now I am doing it by finding out the meaning right now like I did it assuming it to be mean okay so here So the formula remains simple, six is six 6 p 6 p 6 18 so yours is 18 or 8 will come ek do pa 6 sorry ek do pa sa 13 plus 8 21 26 34 3 P 4 3 P 4 7 748 yours is coming sumation f x yours is coming 748 ok sam How much will it cost? Take out Summation A i.e. Capital A4 p4 8 ps 28 36 40 50 your 50 has come ok very much Fine, let's go then what will happen to you? x times your summation will come f x ap sum f equals equals 748 b a 50 solve If you do it friends, I will get 748 or 50 Did I do something wrong? I got 450 It has been like this here, these people, good friends sorry it will be 4 to 8 friend that's why I I am checking the calculations so that there is no mistake 8 16 30 120 80 60 this 50 is coming it's ok 56 no it's ok 80 friends you 450 It is coming, this 450 of yours is coming, how is that so maybe let's do it yes no or 450 If you are saying right then yours will be 450 and up to 50 sorry calculation 450 up 50 this will be yours is ok i mean its ok now what is the same Find the deviation and square it So the deviation is x aa - x times okay so let's go x - x times one is what multiple of two this minus tax minus sa four out of minus na minus five out of six from not minus minus of three aa from not minus minus one out of 10 is 9 minus one out of 12 from 9 minus 3 14 from 9 minus 5 and 16 9 minus the square of the deviation from It's always the same thing as variance deviation If I want to square the deviation then I have If I square it, mine is 49 and yours is 25 this is your name this is your name this is your name this is your name this is your name Y your 15 and this is your 49 Now since there is frequency as well, that's it multiply by the frequency a - x b kaal squa to 49*4 bhaiya this is a little It will be a long one. Do it 49 * 4. It will give 196. 25 * 4 25 * 4 is 100 5 * 9 is 40 5 * 9 = 45 15 * 1 is 15 8 * 1 is 88 5 * 9 is 45 4 * 15 is 60 5 * 49 is 196 ok you can understand this multiply the square of the deviation by the frequency There is no need to memorize the sum by multiplying it by memorize in a pattern memorize in a pattern If you remember it in a pattern then friends I can see it from here somewhere I might have even calculated it Let's check it 196 100 45 15 8 45 60 all something is right 245 how is it coming this is good faw hai woh four tha yes this 245 aga na dis will be 245 okay so I've looked at the stats Friends, I had already written the solution so that There should not be any problem in the end friends Yours 74 will come 754 ok now what about deviation Average Mean to Standard Variance of Square will be varied x sl this will come to you 754 If you want to write a formula then use summation f x a my x times the square of n upon n So 754 up 50 then this will 754 up 50 will be 15.0 and standard deviation slush his sign you can easily remove it in homework can some 3 p something will come as far as I know something 3.88 will come ok let's go ok next now look again data discrete yes your data is discrete but now I can do this for you by shortcut method I will show you what the shortcut method is now. You have learned almost all the methods but now you Learn shortcut methods also but for this you will need The formula may seem a bit odd, but I I will try to make it easier for you so the size off item is given frequency given size off item given frequency given okay now take a look now i am in two ways either I'm doing it or I'm finding fault and then find the deviation and square it If there is a frequency then I am multiplying it, shall I say it again or So I am finding the mean and then the deviation I am finding the mean deviation and then its I'm squaring it and then I'm giving it a frequency If frequency is available then multiply by If yes then I am doing the second method without any mean but I am doing it with a mean mind if I I am not taking any mean action, it means consider me mean If you need it, I will just look at a question I just assumed that it was a question I considered it to be mean in which case I took out d and I applied this formula now I am going to get u Now I will go to the method with a question u will go for the aa method friends i have a question okay now take a good look first of all you come u direct u He must have kept it as his friends kept one second this is what your 3.5 y Went 4.5 Is there something wrong here pe one second one second one second yes no no everything is fine everything is fine come on Anyway we do it ourselves I don't think I have the calculations It is available let's see friends I believe I believe I Suppose I accepted this Ajoom mean okay let's go Subtract 3.5 - 5.5 and find what your h is You will go and look at this between these two How much is the difference between these two Friends, the difference among all is your class There is only one difference in size from one Divide it, okay divide it by one only two okay let me say it again so x is 3.5 - 4.5 - 2.5 up 1 so friends your result will be -2.5 only -2.5 will come only, it is clear after that After that your 4.5 - 5.5 so 4 sorry -2 Will it come - I am saying it will be 2.5, I am fine 4.5 - 5.5 -1 up to 1 so your -1 will remain These friends, your zero will come here 6.5 - 5.5 1 up 1 and come 7.5 / 6.5 2 / 1 Friends this will be your 3rd number this will be your 4th number will go to square the deviation okay So ui11 this is yours four this is yours four this is yours 9 this is yours 16 1 2 3 4 5 6 7 1 2 3 4 5 6 7 okay now you what do you do you do ui5 to f and f to you multiply by ui2 and then I I will tell you the formula then f*ui5* 8 * 4 E 32 f u come [ __ ] karo means these two Multiply check if i did any mistake 380 yes that's right do both of these 3 4 12 f * u s 7 1 7 22 * 0 e 0 60 * 1 e 60 85 * 4 85 * 4 so 85 * 4 4 20 4 8 32 34 340 it has arrived yours is ok 32*9 so 32*9 2 18 9 27 28 288 yours has arrived 288 very good 8 * 16 16 8 f * u [ __ ] 16 8 8 6 48 8 1 8 128 This is yours 128 What should I do now? Solve these problems then the summation f ui2 plus all these plus all these do it then 170 + 60 230 230 I 100 330 330 minus 6 so 324 becomes 2 Plus 326 336 3 356 this is yours 356 if I am not rang if i am not r okay let's f this screw so f this screw Friends this is your 17 ok sorry 356 a little You will get only 356 out of 356 you will get 15 minus sorry you will have to minus 13 then 356 353 343 yours will come 3 43 343 Let's check it again 230 330 4 mine 334 320 Do something wrong and do the calculation again I take it, there is no problem 230 330 4 minus 3 26 two plus 328 338 358 358 13 in 358 minus 13 in 358 Mine 345 Come 345 now that's right look at these this is yours 19 ago If we add these then 60 plus this is 400 600 688 688 688 plus 12 gives 700 700 In 828 835 okay son are you watching what is dangerous This is the way, I just got the correct answer for it Answer friends available answer will be available But this method is not available, right? Now let's just see the method formula What is this called shortcut method What is the formula Standard Day Sorry What is the formula to find the variance? here h s do h s h s is class What is the square size of the class will go one by one you will consider your class size and nothing else is ok what comes inside yours inside Summation f Summation f Upon a whole square this is your friends If you apply the formula then h size is 1 square sum f u square e 835 upon capital n how much is boss kapit n you Take out 40 40 125 1 35 45 55 65 75 85 85 195 197 217 Bhai saheb 217 strange number is not coming Let's check it once 217 is strange I don't have a number, no, okay, 217 is coming There is no problem, it is coming only 217 Anyway let's solve it further so this is yours 835 up 217 minus a a a y i a a u i i.e. 345 up 217 ka ho hole square bhaiya sahab very big very big answer It will come okay, do something like this, it will definitely solve it Friends, we can do this much with a calculator. who will do it it will cost so much ok let's go so if I take out the calculator Let me show you the thick and thick, I have to teach you what is going on calculator pay attention give me 8 35 divided by Bye 217 3.84 79 3.84 79 So 3 p 84 let's see 79 minus minus 345 So 345 in 345 11025 11025 C 217 in 217 47089 47089 ok then 90 25 divided by 47 089 088 9 2.52 your 2.57 is coming 2527 just do something like this and solve it This is 3.84 79 3847 9 - 2.57 2527 1.32 1.32 is your variance I think this is The answer is as bad as I think I am Friends, this will be your answer, well my answer It is not written near me but friends it is fat This is the answer you are getting, this is your answer it will come ok it is clear and just standard You will find the square root of the deviation do 0 point something something today Let's go, this was your shortcut method No friends, you guys have asked the same question here you can do it too or your homework will be exactly the same This is a question, it will definitely be your homework. Same question, exactly same, just your class here size class size your two will become 10 Which shortcut should be done using shortcut method only? Method From Do it using shortcut method or UI method Okay basically this is your table view. anyway let's go ahead let's go ahead ok there is one last question, right, we guys asked We looked for the data I have looked at it once for discreet Let's do it for continuous I want to find out I want to find out the standard deviation For the following distribution then mean I have to find out, I have to find out, okay, fine The meaning has to be found out, standard dish friends You guys can figure out the meaning yourself You guys can take it out yourself, I will help you Finding the standard deviation of variance Let me calculate the standard deviation, brother. We will have to find the variance for this, okay what will I do friends I will use that method without any meaning I will use it if you find out the meaning you can do it, it's very easy, without any reason How will you pay the most attention to him For that first of all you have to go through its middle value of x aa friends your value is 25 will go 35 will become 45 55 65 75 85 okay now what did you do you came nikaala what is y up h up what is e x aa - a to Capital A you are 55 I can even see you I accept what I believe so that If our calculations tally then so that What about us? I took 55 in my opinion. I have kept it for Rs 55, okay, move ahead Let's see brother, 25 - 55 is minus 30 Minus 30 / 10 is minus 3 35 - 55 20 ba 10 my ka 2 friends I am telling you hmm this -1 will come this cry will come this one will come this This will come, I have already told you this Then what do you do with whatever deviation comes square it and then here you go again f i ui2 make everything the same everything is the same ui5 1 0 1 49 f 13 * -1 is -'s 13 15 * 0 is yours 0 14 * 1 is yours 14 5 * 2 is yours friends 10 and 4*3 is your 12 is great then f ui2 then 3 * 9 7 of e 20 6 * 4 4 of e 20 13*1e13 doing nothing f*ui2 this is your f so okay 15*0 0 14 * 1 is yours 14 5 * 4 is your 20 and 4 * 9 is your 36 plus them plus them okay He would have checked the values once and would have told you I am this much -9 12 14 10 12 27 24 13 14 20 36 okay friends this is your summation f ui2 will appear here your summation f ui2 summation f square okay put the formula here you will get your answer if my If I have the answer present, I will let you know hmm okay friends whatever answer you get the answer you give It will come, whatever answer you get, that will be t will be 223 The answer to the variance will be 22.22 Okay and standard deviation of Answer B 14.9 Check once ok to take it is easy, in my opinion it is too easy I'll just go back once again that you guys should be able to understand that by memorizing the formula There is no need to look at three types of data Is raw data discrete and continuous? How to do it easily for raw data See Variance Standard Deviation The first simple method: remember two things You can also do this by finding the mean and Can you also just remember these two things? If you want to keep it, you can do it by removing the mean You can do it by assuming or by finding the meaning You can do it by assuming it to be mean It is very easy to take it out and see how here Observations are written, find the mean from the mean Find the deviation and the square of the deviation whatever the square of the deviation is Come plus take them meaning their ariam mein Basically 662 by your number of observations did it then what in the next question please pay attention to the question same here hey raw is standing but i am without any reason I will take it out, I will do it considering it as a mean I am not making any mistake here I believe Pisces and from that my brother Pisces If we take deviation then take all the deviations Just square the deviation here. What happens if the formula changes? friends formula summation d s / n - summation the hole square of d/n this will give your Standard takes out standard sorry variance you can take out the pension ok now see what happens the same data the same discreet but in this Who will you guys do this to again and again? Sorry, it's not the same it's discrete right now we're talking about raw data Now we're looking for discrete data If you look at it, what does it mean for discreet take it out and do it, take it out and do it, brother, that's it by direct method you found the mean from fi5 f you found the mean Then you calculate the deviation from the mean. square of because the frequency was So multiply it and then did you read it directly with capital n I divided it, that's your answer directly Your direct is absolutely correct but If you want to do a little crazy method then Look, you've been given the discreet once again. You can do it discreetly without any meaning You can see it using the u i method without any meaning You can calculate it using Ajud Mean Method Or you can do the step deviation from u to aa I have given it to you with aa, look how it is Discreet means I believed what I believed 5.5 is the deviation from the mean Remove it is ok ok, do it without finding the meaning, so I did it without finding the meaning Let us calculate the deviation of the mean. I squared it, f a u f u square I took it out and applied the formula Diya, did you understand it, it is so easy, so very easy There is one last question on this, I will tell you this I will give you my homework but why discuss it? Listen to all the questions that I had till now There Marx is written straight away It is written size of item, it is written variable It is written now Sani what happened in this question Friends it is written here wages upto what does wedges up to mean what does wedges up to mean This up to 15 means you should think that boss this If data is given then up to ₹1 means up to ₹1 12 workers are earning up to ₹10 and 30 workers If you are earning then basically these ₹1 12 workers It is not written that they are earning 0 30 workers Kamara re I did not write it like this ₹5000000 is written, it is written like this, up to 15 up Two 15 up to 15 means 0 to ₹ 1 now to 30 means 0 to 0 now 2 45 means 0 to 45 now two 60 then 107 workers from 0 to 60 earn money It is written from 0 to 75, friends Now you will have to change the gap to normal look there is a gap of 15 30 45 15 15 now you can see this Think about it friends, it is very easy, it is very easy, okay how to do it once you learn it take if you look at the 15 from the row you cry from the 15 start from 0 to 15 only 15 is given If so, then there is no problem for you now I want 15 to 30 I want 15 to 30 how take it out remember for 15 to 30 15 to 30 He said, look at 30 from zero and 15 from zero So zero to 30 is your 30 people. zero to 15. You have 12 people from zero to 30 from zero 15 people must also be coming brother, from zero to 30 Meaning workers who earn from Rs. to Rs. 0 There are 30 such workers who earn 30% from zero Workers earning from zero to 15 per cent If there are workers then 12 out of 30 are already there It is included, if you subtract it then what is left is 18 These will be 18 workers who are earning Rs 15 to 30 You must have understood what I said now 30 to 45 see what to do 0 to 45 Look, there are 65 workers. 0 to 30, 30 workers. If you subtract it, you will get 35, did you understand it now? You saw that 45 to 60 workers means basically What I am trying to remove is 45 workers Sorry how many workers earn money from ₹ 5 to 0 If you are then from 0 There are 107 workers earning Rs 6 from zero to 45 What did I say, whoever asked, he got zero. 65 workers earning from zero to 45 There are people somewhere who earn from zero to 0 There will also be people earning from zero to 45 coming in From zero to 0 earners, now 45 earners start earning from Rs. People will also be coming so from this you have I minused it friends, this is your 42 So there will be 42 workers who are earning Rs 45-60 Yes friends, I have given this to you directly Write P here 15 18 42 15 18 35 42 15 18 35 42 right 15 18 35 42 or you go ahead Then you can do everything else yourself It's the same, everything else is the same Do it by shortcut method or by finding the solution You can do it in two ways, either take it out or don't take it out okay once I would also check on hmm 15 18 sorry two 12 it is there friend forgive me This is 12, right friends? This is 12 12 18 35 it is 42 right this is your 12 sorry so I will check here again and again, okay how did 12 come hey look 12 out of 15 They are just workers, I had written 15 So here is your chapter's standard Deviation and variance both end it ends okay so we have three Why did you learn Measures of Dispersion? Let's find the dispersion as a single value that tells you that your observations from your central value i.e. How far is the mean from the median from the mode Range cut deviation will not be learned later we will learn it in next classes after that You have studied standard deviation, variance and Your mean deviation is only three Range Range Mean Deviation and Standard Deviation Range Mean Division Standard Division Standard Dishon To take it out you just have to take it out, let's go Let's move ahead Come on now friend, don't misunderstand that we Of all the variance formulas I saw, Formulas mean why do these questions arise First you should see the formula and then There are four or five questions that I want to ask you I will get the standard deviation, variance and these it is related to everything because your It is given in Miscellaneous in NCERT Just pay attention to the first stand you see When I looked at the formula for variance, I saw that Look at that the summation x minus x times the whole square up n Very important formula which you need right now It will work fine as well Boss what is this square deviation of deviation the square of the deviation of the square of its amet mean removed ok second formula Here, if you want to do it only by taking x, then you Remember the word we just used in the question I did not do it, just your second formula says this that brother summation is very important summation x up n - summation x i up n time Squa, let me tell you where you get this formula from come, you will understand, you will understand easily Look what a formula we saw then boss that if f comes, if f comes then our One formula also became that boss if f comes if it is basic then add f to it If you want to do it in a proper way by finding out the meaning it has to be done by finding the meaning it has to be done by finding the meaning if it is then it is ok then this is your summation x ah sorry summation f x aa - x bar's square upon capital a okay it's Which formula is this, who is this by finding the mean This is a formula, which one is this by finding the mean There is a formula to find the mean without finding the mean Without finding out the meaning, actually this means I will take it out but this is without any meaning. Now a formula without any mean what was the boss Summation summation ok squa up Minuses Summation Samedi Upon a Capital A Ka Hole square okay i remember now see the one with y Just take your shortcut method formula what is it You friends please write this summation in this summation y square upon capital a minus sum y aa with capital a S and outside friends what did you feel here let's give you the square of a okay right in this If you get A in both of these then You put nothing or your standard of deviation Summation Eddie [ __ ] Upon Capital A Minus Summation Eddie Look here, I have a hole square in my cup two summation f y a square up n min Summation Summation f on ui2 this u aa containing method has u aa Remember in the method, multiply by h square Now listen to which of these you must do Such formulas where you don't care Okay, friends, this is one of them. The formula where you don't care I would have to take out this one of yours from where You don't need to find fault, this is your Where you don't need to find fault, this is your Both where you do not have to find fault ok these two will take your meaning away The formula is ok, I understood it clearly Now listen to what I say which will be useful to you right now you are going to remember this formula and Remember what this formula said I put a star here Now I'm going to ask you a question about Just remember this one formula and one Remember this formula but these formulas So you can understand these formulas a little bit Do you understand what is written in the variance? Formula summation x aa my mean whole square you please pay attention okay pay a little attention pay a little attention Give me one this one and one which one of sa variance summation x up n sum x up n square now Friends, think about it and see what is happening can you tell me what is this summation sum of all observations bro what is x observations to sum of all observations upon Total number of observations sum of all observations upon total number of observations so can I say that that this is nothing it just means so summation x Sum of square of s/n observations Squares of Observation to Observation Square the sum of n and find the sum of all the sums. Minus friends your mean square This formula is very important, this formula Very important, this is going to be useful to you right now this is going to be useful to you right now and it It will be useful to you right now guru ji How to remember all the formulas We will keep it in a pattern, everything will happen, remember one follow the pattern, you will remember everything, it's ok anyway what to remember for now this one this one You will use this the most First understand what is the formula for variance What is the formula for variance? Summation of Square of Observation Upon Capital A of the Square of Observation Total number of observations minus mean square minus mean square this is you what gives you variance what gives you variance gives you the variance variance variance Variance Variance Variance Let's ask what the questions are saying The Mean and Variance of Seven Observations in Just do as you said, okay? You may be asking yourself this question Nothing happened after I told you Understand these as the mean and variance of seven Observe Vesh R 8 and 16 friends you You have been given total observation seven Total observation capital and given to you from What you get is the mean, that is, the value of x times is the mean you've been given eight really great and you Variance is given 16 okay if five of these are this and this I have given you five observations, friends. Observation is two, one is four, one is 10, one 12 a 14 Find the Remaining Two Observations There are total seven observations, five are given Let us assume the other two to be x and y and this is what you get Removal What should we do about the two things in the question The one being talked about is Pisces And another one is variance, use their formula Let's do it okay so what is the mean formula brother Brother, did you say mean or variance? If we use the formula then we will get the mean formula Everybody knows that 2 + 4 is 10 + 12 + 14 + x + y / 7 so the mean given to you friends is 8 so 8 8 7 8 7 your 56 equals 2 + 4 6 + 10 16 + 12 28 + 4 32 42 42 + x + so this is your 42 + x + y so from here you get the form of x + y I see an equation 56 - 42 = 14 x + y friends you are seeing 14 Only one question came, where will the other come from We used mean because mean is given Now there is no need to think anything if you believe it is new If there is a question then the mean of the mean is given The formula ended and we found out which of the variances Which formula is used for variance? should I apply it, I just told you what Which formula of variance will you use? summation x up n my mean square If we calculate the square of minus mean then we get the variance You are given 16 easy steps to do the summation x What does [ __ ] mean observation square and sum the observation two is his square kara observation four his square kara observation six he it's not six but 10, make it square Observation 12 Square it Observation 14 Square it Observation x square it Square the observation y and divided by total number of observations Seven and mean are given to you friends 8 8 Square of 64 another equation will come from here yes or no, take it out quickly now don't put this here take it away don't do this childish maths first minus 64 goes there then 64 will be 16 friends your 80 came 80 * 7 Should I write 560 directly? Is there any problem? okay the square of 2 is 4 p 16 P 100 P 144 p p 196 p x swa sk abe do plus this Brother, let's make the situation worse, let's do it in our mind ok so add cha to 196 200 240 340 440 444 450 460 friends x love yours 100 has come, children's maths, everyone so much Now we can calculate these two equations here How do I solve this, please tell me a trick hmm let's see a simple way is it x or y take out the value from there and put it here And by substitution method we find out x and y I will tell you another way, brother. The children's method has now come to class 11th ho tell me everybody who's boss x pw the square of x - y is 2 * x s s can be written equal to y s So which formula did you remember brother? hey look there's no problem look when you You will open it comfortably when you open it x s + y s + 2xy x s + y s - 2xy t + From 2xy - 2xy will be cut off x s + x s 2x s y s + 2y s this is what will come why did I say this do this because I know x + y is 14 so 14 square of friends here it becomes 196 x - y's hole square like that you know no x s + y s you know 100 then Friends, you have got Rs 200, now what is the benefit? This is where your x - y square comes from Four more values of x - y are obtained. -2 ok so roughly what do i want to say you know x + y 14 with her Yours x x – y is given to you and you get x + y is known 14 You are given x - y -2 in You solve both the equations I will get your x and y values I'll say it again I'll say it again I will say it again, this was an equation This is the equation but what did I do what did i do, use this thing From here you saw another equation, meaning If these are two equations in themselves then first Replace this with the equation given below and the previous one Just taking this as a minus along with the question Please solve it friends if you are plus in these If you do this, it will get cancelled plus this cancel this your 2x equals 16 x your 8 more if one comes wawa 6 ek aa then y6 aaa look here if you both of them if If you plus then again this will be cancelled, this is yours 2x equals 12 times 6 times 6 so what is your answer The same answer is coming from both places friends x6 y x8 y6 or x6 y8 both answers It is possible, you understood it clearly, very good Let's ask the next question, same question If you use a little bit of mind then the meaning and Variance of six observations are eight and 16 so the boss kapit n gave you six mean given you eight and and and variance You've got a variance of 16, okay? if each observation is multiplied by 3 ok boss you might have some observations accept it a1 a2 a3 a4 a5 a6 It is okay if each observation is given through If it is multiplied, it means this is your 3 a1 3a 2 3a 3 3a 4 3a 5 36 then the new mean and Tell me the new variance, new mean and new Tell me the variance, it's simple brother, let me see Given the mean and variance, I know the formula I'll give it a try and let's see what comes out okay so guys i know what is mean I know the formula, what is it, totaly it so kids kids know so mean you It is given how much will be the sum of eight friends your a1 + a2 + a3 dot dot dot + a6 total your total is six i think there are six observations right yes 68 48 so Basically friends your a1 + a2 dot dot dot + a6 your 48 has come what should I do with its pickle Should I post it or let it be written, what is happening Who knows, this matter of variance might be useful to you so what is the variance friends also told about summation x as up n my mean square so the variance given to you is 16 summation x s how will you do it friends summation x Squa means square of observation Basically this is your a1 s a2 s p a3 s dot dot dot friends a6 smeen What is the mean of your x times then x times Square good by the way capital n e 6 pisces ka square is 64 so again -64 goes there so 80 80 * 480 so your a1 + a2 becomes 480 s + a3 s dot dot dot a6 s what should I do, put pickle of it, hey wait This is something that came to you from here, which was given to you it happened that you took it out from there okay Now you will talk about the new variance and the new mean. do friends let's see the new mean then if If I talk about new meaning then new meaning means hey 31 p 3 a2 dot dot dot 36 all I multiplied it and the total remained 6 So if I take the common a1 p a2 dot dot dot a6 now up 6 3 and 3 to friends a1 p a2 ps dot dot dot a6 you already know 48 is equal to you 48 times yours or yours 24 So new Pisces New Pisces Your 24 Hours How to get the new variance New Variances note down the new variation from there Summation X Up The square of A minus the mean is just this new mean You can also write it here does new summation x come with your capital a Minuses Square of new mean to new variance I have to find out how much new it will cost friends You will have to square the observation square to square of 31 square of 32 dot dot dot p 36's square capital n Yours is 6, what is the new mean of 24, so 24 square is 576 ok solve it now how will you do this Brother if you take three commons sorry friends this is not a 3 a1 s this is a 3 a1 hole square is of 3 a2 square is of 3 a6 The whole square is the square of observation So observation 3 a1 is its square so If you look, the most common one will be nine. What will be left is a1 s + a2 s dot dot dot this is yours a6 divided by 6 - 576 then 3 * 3 3 * 2 is the value of this thing to you You already know how many are coming, 480 is coming There was a problem, so here you got 3 * 480 up two - 576 This is yours 240 720 - 576 so 720 20 is 120 144 coming My new variation 144 is coming once Let me check it, it's ok, it's my new variance I thought 144 would come, I would check it hmm wait a second yes that's right new Variance 144 understood how to do nothing give the same I will use the formulas that I told you I am doing this, I applied the formula and understood it I found that six observations were added to make 48 New variation is coming, sorry variation I applied the given formula and understood something like this The sum of the square of observation is 480 annas and these two things are the new mean and be used to derive a new variance Let's go, good question, what are you saying in the question Focus carefully put a star on it friends star mark this what is it saying Remember the mean and the standard deviation Standard Deviation Given Variance Not Given What does standard deviation mean and what does variance mean okay No, there are 100 observations, 40 and 5.1 are given. It is a very good boss, I have given it to you 40 capital n you have 100 and standard Deviation will give you 5.1d Friends you will get it immediately Calculate Variance and Standard Deviation square it and nothing else then 5.1 if you square it then I think will get 26.0, let's check it once Math Calculator 51 * 5.1 26.0 Why I calculated the variance because I am in the variance formula I know how to play, what did you say now brother a good respectfully by a student Student has given your mean and standard Deviation measured by mistake 50 Instead of 40 for one observation now done What the 100 observations he made He calculated its mean and If you calculate standard deviation then it is standard devin came here this means event This will come to you but what did he say that The child mistakenly included one of those 100 observations took 50 for one observation while it was should take 40 that is, what he meant by 100 observations He took one observation in it wrongly what did he take he took 50 Whereas he should have taken 40 again and again I will tell him that he will understand and he should take 50 while he took 50 while he got If you should have taken 40 then tell me what was his The mean or its variance or standard deviation Deviation came, it might have been wrong, yes or no it must have come wrong yes or no because He took the mean and st deviation variance by taking 50. He took it out when he should have taken 40, understand came came now what are you saying what is the Correct Mean and Standard Deviation Correct what is mean and standard deviation Let's do what we know will happen, let's see you know this incorrect means you know this Employees of Incorrect Standard Division If the incorrect standard variance is If I talk first, let me talk first Ekas bar ok pay attention this is your 40 so x bar you know friends problem or else do this summation x come up n friends x times yours is 40 this is your 100 summation x friends this did you get your 4000 or not what is summation x come your 4000 tell me one thing this summation This summation is equal to this summation is equal to this summation x Yours is incorrect brother why is it incorrect he took 100 observations only brother when you To find out the meaning, you use two things be sum of observations upon total number of observations because when he scored 100 When he must have plused the observation to 100 Add a plus to your observation it must be that he got 4000 but in this 4000 Somewhere he has crossed 50+ whereas He had to make it 40 plus again, yes or no I will tell you that he figured out the meaning and it cost 40 If I look at it this way, then all his The sum of observation is 4000 but in this 4000 He has crossed 50 somewhere or the other Brother, his sum of observation is wrong Why didn't he come because he has crossed 50 when I had to do 40 plus then I Correct, so what did I correct? how to find correct mean correct summation x How do I calculate it brother, I removed 50 from 4000 gave it because I had done 50 plus and If I add 40 then it is basically 4000 to 50 If you subtract then this is your friends or your total 3990 will come y your correct summation xi Now friends, how will the correct meaning come Tell how do you correct me aayega correct means will be correct some of the Observations upon capital A to 39 990 up 100 so correct mean your result is 39.9, understood? Now let's talk about variance, pay attention Let's talk about Dena variance guys What is the variance that is coming? summation x come upon upon upon n minus mean Now listen to me attentively So this is about your incorrect variance Why did the incorrect variance come Boss Incorrect The variance is 26.0 this is yours you don't know this is yours This is 100 and I mean you took 40 That's why your incorrect variance came Let's solve this, friends, this is your 40 here 40 6.01 66.1 summation x ask your 100 100 up so 6601 some x s yours has come tell me it It is wrong brother, the mean is wrong, the variance is wrong If it is there then it will also be wrong, how can it be correct Now you think I did something wrong So I didn't do it, let me take a look here But I haven't done anything wrong how is curry 1600 coming good yes a no there is something wrong i am the one who is trying to solve this problem That's big, it's a square of 40, isn't it, friend? Is it the square of 40? I checked the calculation. I was doing this, I saw my mistake brother Means whatever is the square of 40, now we will do it this is square of 40 so 1600 1600 if you come here 1600 plus plus plus plus plus plus plus you do one thing to this 20 would have done this Let us go 26 Or just keep doing this and it will be easy Our purpose is to make calculations easy toy friends 26.0 Equals Sum of X Squared Minus 1600 goes up by 100 and then two more zeros come You went 100 now 100 here so this is your 2601 equals summation x s y x s mean observation I squared it and made it even with the minus 2 3 4 If you bring it here then it's yours 1 2 3 4 2601 1062 6 16260 16 16 2601 this is your summation x s ok i will check it once i am 16 2601 right now tell me because this there is incorrect variance because this is incorrect If it is Pisces then this will also come out incorrect, now this What does incorrect mean? What does incorrect mean? What do you mean friends, what is this observation? Square the sum of the given numbers and make them equal observations which will be 100 observations which will be 100 There will be observations, square them and I made them equal and squared them and their equal tax But when I did the observation If you had squared it, I would have done 50 square measure while the square of 40 will be You should have done it friends this is incorrect yes or no this is incorrect yes or no this is incorrect yes or no very good so correct see how to remove it correct correct summation x a s will be 16 16 2601 16 2601 my 50 sqaure + 40 [ __ ] of Ok 16260 square of 50 2500 or your 1600 If you subtract, you get 50 Square and your friends yes 6 is gone na 900 900 you get minus in this If you want to do it then how much is the minus 900 16260 900 you minus it So 0 out of no goes to 9 out of 16 7170 161 70 If you check the calculation once, then 161 70 very good so now it's right now you Can find the correct variance What is the formula for correct variance yes will go correct summation x ask up n minus minus the square of the correct mean so that's it Correct, yours has arrived 161 701 n yours is 100 correct mean how much is coming Friends your correct mean is 39.9 Now you can solve the square of 39.9 So, this is basically yours 161.3 will come, square 39.9 here Come on let's go so this is your discipline tool math Calculator 399 Multip 39.9 15920 And I feel I have made some mistake again I feel I have done some mistake I have done it again, yes I understood it, but friends 1661 7.01 minus how much is it coming friends I forgot it was 1592 39.9 Multi 39.9 159 2.01 159 2.01 Solve it If your correct variance comes then it will be 16 17.01 15920 this is yours 5 out of 11 9 is gone two 0125 too many nice 1025 is the correct 1025 is the Correct Variance is correct 105 Friends sorry 25 is the correct variance 1025 I am saying correct, check it once Let's take 25 Aga very good so just correct Standard deviation is asked, is it correct? If asked about standard deviation then correct What will be the standard definition correct? Standard Deviation Will Be Squared You will understand the root of variance This is your answer and this is your correct answer Mean Correct Standard Division as before how much was the standard diesel 5.1 was 40 it was a bit more because I had made 50 rupees I had taken 40 Place is easy, there is a similar question in NCERT please do that as well let's do this one ask a question it is a very good question and its Afterwards we will finish the session with your what are you saying with your homework what are you saying If each of the observations is in question x1 x2 x is increased by an amount a denominator If you increase the observation by an amount do it ok then x1 p a x2 p a x3 p a dot dot dot Ok comma ok where a is a negative and positive number ok anything can happen then show that the Variance remains unchanged Show that the variance Your unchangeable will show that variance Yours unchanged This question will remain which one should I use friends I will tell you, okay, just pay attention Let us first check the Pisces what would the mean be if you made every observation If you increase it by A, what will it mean? check it out so if I talk about Pisces first mean your x1 p x2 p x3 dot dot dot P xn2 + a + x3 + a dot dot dot dot dot xn2 + x2 + x3 dot dot dot the terms xn2 x2 x3 taken together a I took it with me now you know this what is this what is this you all friends do you know friends once this is your new They would have written your new change or new are new Pisces New Pisces New Pisces, the new Pisces that will come will be your ex-wife x times only x1 p x2 + x3 d x up n this is your x bar this is your x bar so this x times plus who told this to aga a How many times did I add a if I made a 100 If I add times then 100 * the answer is If I add a 500 times then 500 * a The answer is if I add a 1000 times if I do it then the answer is 1000* if I do it n times n times right Just first with second with third then add a to n times a So n up n n to n friends your a is left Meaning, the new mean that you got is from your A Its rough meaning is that it will increase Boss, I believe some of your observations Mean was coming four lots of observations It must have meant that your four were coming now He said that if you consider every observation Incrementing each observation by five if yes then the mean will change what will be the new mean nothing which was coming earlier means which was coming earlier Mein was coming in it you said five, five ads If your new mean doesn't come then do it as before mean was coming just add a to it this is yours How will the new mean become the new variance How will I find the new variance? Let me teach you to pay attention here. What is the formula for variance that I use? I will use this variation, you will see Remember the formula summation x aa - x times hole Square Up n is ok So can I call it like this x in place of X is a P a that reflects your observations yes this is your old one isn't it your old one variance this is your old variance Old Variance If I talk about new variance If I talk about new variations then what should i do summation whose summation ax minus in place of x x p instead of x aa it will be x + a and instead of mean New mean instead of mean then new mean then minus mean what is the new mean in place of yes understand friends this is your divided by n and its square now see what is the benefit what happens is if you open the brackets then ् begins with a mine a will be cut dos your summation x aa - x Only the square of the bar is left upon what capital n Now what happened that new variance The new variance is the same as the old variance the same as This is the new variance, the old variance brother What will be the old variance? Old variance What will happen to the old observations Minus Mean Square Sum of Deviation What is your variance? There is a formula yes now I have made an observation If I increase a then x will come in place of aa f what will you write there four variance remains unchange variance Remains Unchanged Clear It is clear, it is correct, it is very similar Using the same formula in the pattern is perfect In a similar pattern I will give you this one I am afraid I am giving the question in homework no it is very easy question, given that given that what is given is mean and good Wait, let me tell you what this is has given got given that proves the mean end vari of or a12 a aa lalala friends take it x times ok you take x times given that x times sl x bar given that sl x bar and here but you can also do it like this a x times okay so what has been said given that x times means and this is your variance, an observation of x1 x2 proven like xara questions that what is happening this time prove that the Mean and Variance of the Observations If you Multiplication of a in your observation Do it, I just added a, now you If you multiply a then the new result will be The mean will come and will be multiplied by a In the old mean a got multiplied and the A new variance will come with a score multiply It will happen, look, this was the old variance in that a score will be multiplied by one You have to ask this question in an exact way In the same way you have to ask the question I just told you You will find a new meaning in the old one What is variance old variance old Variance Summation X aa minus x times the square of your capital A new variation, what will happen? Please pay attention what is the new variation please pay attention new Variance will be summation If there is multiplication in it then a X A X Your observations became minus Pisces your friends Pisces your friends change k x times came when you do it then a x Your time will come here friends This Aye take this as x friend more this smaller take x it will cost too much or wait a bit Small x to variance Variance Equal to Some the square of x aa minus x times capital a y your friends old variance new Variance New If I New Variance AV Key If I talk about it then instead of summation x aa this is yours x has come in a i.e. call it a x the x minus the mean instead of the mean friends A x x times x times yours has come divided by its whole square divided by Bye n ok now what did i think of j new variations just in case you notice new Variance will be summed if you take a common so a common came a sc common basically brother In square a you will put a square outside I took it out and inside my friends, yours is inside Your save x aa Inside you save x aa - once Apna Capital y your square okay you a square out So if you take out a [ __ ] So summation summation x a mine x bar your Capt this will save your square friends this what was this thing what is this your old If this is the variance then the new variance is is the new variant a scale in the old way How do you multiply and find the new mean okay ok i did it anyway Your statistics end here friends. there is another small topic but That is why it is not in your NCERT now we will not discuss that, that is efficient of variation there you basically How much is there in each of the two data sets It is a variable, you can find out but Anyway it is deleted from our NCERT we're not going to go to that thing okay yeah So brother, first of all you should tell me this How did you like the lecture, what all things were, click here Look I know what happened in this chapter There are lots of formulas but if you You will go to memorize the formula, I am 100% saying what to do if you forget the formula I don't have to remember the formula You have to understand and remember it in a flow Keep that boss mean deviation taken out the most First calculate the mean deviation for the raw data First for Discrete then for Mean In Continuous for Deviation Continuous also two types exclusive exclusive Inclusive always means exclusive Deviation is calculated in two ways: mean Deviation about mean and mean deviation about mean By finding the median, mean, deviation, median Taking out the mean deviation and then the variance of what was the standard deviation boss i Told you to first find out the variance, then How do you find the standard deviation? Remember, you have to memorize individual and not formula Data is given, either find the mean or If you find the meaning without finding the meaning then who will also find its meaning then through observation square of the deviation by the frequency Di then multiply it and its arimilli have fun chill do what you want to do Just don't harm anyone, tata bye bye love you all and take care i hope you You must have enjoyed statistics, did you understand it? hoga love you bye bye