Hi everyone, this is Bhatia and welcome to my channel Dreammask. So today we are going to do a quick revision of the chapter that is measures of dispersion. There are six topics in it which we will be completing quickly. There are handwritten notes in which you are going to get formulas essay but the formulas many summarize curfew liquid a cup of a pimpin learn who's a was the bottom questions carrying a questions make a decade question they take a system of the cons of formula cup lagana formula apply case a colonel calculation on apartment but you will be able to apply the formula by looking at the question and get the answer.
We will be doing revision like this. Then we will be doing interquartile range, standard deviation, mean deviation, all such things. If it is difficult to learn formulas, then I took it in the form of a chart so that you do not have a problem in learning here. By the end of this class, you will be able to clear all these formulas, all these questions, the whole chapter. Before this, we have done mean, mode, median, this chapter also quickly.
revision ki hai jisme saare formula sab kuch pad hai agar woh nahi dekha woh bhi deklo kyunki iss chapter mein mean median ke formulas use hongge to mean median aana bohot zaruri hai agar aapko measure of dispersion ka chapter karna hai to jo maine pehle revision karai hai mean more median ki uska link description me bhi mil jayega i button me bhi mil jayega wahan se jaake aap dekh sakti ho formulas tips pe hone chahiye stats easily ho jata hai so without any delay for amrita start karte hai aachi class that is methods of of measuring dispersion chapter yeah he had just one dispersion case a major career who he sorry cheese and we seek me a is the under main six but the hominid topics cover can add change is okay barry me John a key range case in a car to him in the hotel range you can see her to him mean deviation standard deviation coefficient of variation Lawrence of you sorry cheese I'm carrying a range a yeah I say I've got compulsory question but I'm a satsa TV but I think only range of the topic say compulsory question one which is a small question of 2 or 3 numbers. From here your big questions will be made. 4 number, 8 number, 16 number, from here big questions will be made. Ok, let's start today's class.
The first topic we are going to do is range. Super easy. See what is in range. It is super super easy to find the range. Now you know that we have 3 series in all the stats.
Individual series, discrete series, continuous series, according to that we do the formula. To find the range, formula is R is equals to L minus S. L means largest value, S means smallest value. So, if you have to calculate the range, the simple formula is R is equals to L minus S.
This formula remains the same in individual series, L minus S is same in discrete and continues in series. So, whether it is any of the three series, range ka formula change nahi hoga L minus S hi rega ye kaise question me kaise apply hota tino me tino series ke wabhi samjhaungi par ye yaad rakhna range ka formula tino series me same rehta clear hai cheez range ke saath saath ek aur cheez puchhi jaati hai that is coefficient of range yaha se compulsory question aana dhyan se dekh lo coefficient of range kaise nikalta hai formula is L minus S upon L plus S agar aap yaha pe values dal you will calculate the value of L and S, it will give you the coefficient of range. So in the range, only these two formulas have to be done.
Coefficient of range, whether it is of individual series, whether it is of discrete series, whether it is of continuous series, the formula remains the same. So basically in the range, only these two formulas have to be remembered. Range is equal to L minus S and coefficient of range is L minus S upon L plus S.
You... is clear. These two formulas should be learned in the class now. Now let's go to the questions. Super easy, learn the formula in the class.
Don't think I will do it later. And take a notebook with you that write the formulas that are there in your mind. You will never forget to write the formula.
Yes, let's come ahead, let's quickly do the questions. Five students obtained the following marks in the class. Find the range and coefficient of of range. He says, remove range and remove coefficient of range.
It is very simple. Now here you have not got 5 marks. Okay, this is an individual series. Absolutely because it does not have frequency.
What is the formula? Whichever series it is, L minus S. Which is the largest value? I can see 35 here.
35. Which is the smallest value I am getting here? 15. You also see 15. 35 minus 15. How much did the answer come? 20. So how much is the What to tell you? No, it's super easy.
Understand it carefully. This chapter is very easy. I will teach you the formulas carefully.
Next, what do we need? Coefficient of range. Coefficient of range formula is L minus S upon L plus S. How much L? we have means what is the largest value 35 smallest 15 below 35 plus 15 answer 2 by 5 that is 0.40 so if individual series is largest value smallest value is very easy to see.
See from here the largest number, the smallest number, minus both of them. That will give you a range and a formula for coefficient. Is it clear?
So it is very easy to find the range if it comes to the individual series. Is it tough in discrete series? No, let's see that too. Here we have a question given to us. Find the range and coefficient of range.
Okay, find the range and what to find? Coefficient of range. Marks and number of students. So if there is one x and what is that? So the first thing is which series should be taken care of.
We have a discrete series. Do it very easily, you will understand things very well. It is a discrete series. Now you have to find the largest value and the smallest value in it.
See the largest in this row, this one. Here two rows are given, in the individual, a number line was given, I found it from that. Pay attention to discrete.
We always find the largest and smallest from the marks above x. find from here the l will be the largest value from the upper row here the largest value is 70 so how much will be l 70 smallest value is 10 so how much will be s 10 so here the range will be 70 minus 10 that is 60 so if you give frequency x both in discrete series then you have to find l and s from x so if you have a series of x then you have to find largest value and smallest value. Similarly, the coefficient of range will be L minus S upon L plus S. Put values, answer will be 0.75.
You will get this whole PDF on the telegram channel. Link is in the description of the telegram channel. Just understand here, why this question is summarized, handwritten formula, you will get everything on the telegram channel.
Just focus here and read. Don't think of anything else. Give this time period to this chapter. Next, what we did now?
Discrete Now what we will do? That will be We will learn to find range in continuous series What is it saying? Find out the range and coefficient of range It has intervals If there are intervals, then it is continuous series This is x, this is f Where will we find largest value in this? Below or above? Here also we find largest value and smallest value in interval Where is interval starting?
Below or above? 5 se khatam kaha pe ho rahe hai? 30 pe. To yaha pe jo largest value hai, wo 30 rahene wali hai. Aur jo smallest value hai, wo 5 rahene wali hai.
To yaha pe kya hogya? That is, the interval where the largest value is ending, 25 to 30, the largest is 30, the smallest value is 5, L minus S, 30 minus 5, value is 25. So, range is 25. coefficient of range L minus S L plus S 25 upon 35 5 by 7 here also you can get the answer in point by calculating from calculator and write here. So some answers are given in points, some are left here. you can take out the answer in points and leave it. It is a calculator, we don't need time.
So, it is better to take out the answer in points and leave it. So, the first topic of this chapter is completed. That is range. The formula of range is, write notebook.
in the second chapter of this chapter, then the first topic was super easy, here comes the compulsory question, the big question does not come from the range, interquartile range is starting from here, very important things are starting, look carefully, interquartile range, quartile deviation, all these things will be read, before that I want to make you understand, the first thing is that Interquartile range, quartile deviation, in this Q3, Q1, all this has to be taken out. So first I will write the formula of Q1, Q3, then I will do these formulas. So first learn the formula of Q1, Q3.
Okay. You should know their formula before interquartile range, quartile deviation. Only then you will be able to do these formulas.
You see carefully, we have the same quartiles as we have the median. Q1, Q3. I have already done this topic in the start But I will tell you here I am revising their formulas so that you can do these topics properly.
How to calculate Q1 and Q3? First of all, we will see how to calculate Q1 in the individual series. See its formula.
how we will take out in the question I will explain there but first look at the formula formula to take out q1 is size of n plus 1 by fourth item if you remember the formula of median then So, there we used to write like this, size of this plus this, we used to do such things. Q1 means to divide in 4 parts. Quotiles means to divide in 4 parts.
So, Q1 is made from there. Okay. So, how will the value of Q1 come from there?
Size of n plus 1 by 4 comes because the meaning of quartile also means to divide in 4 parts. So, size of n plus 1 by 4th item. If Q3 is written, then a simple 3 will come here.
Or, Nothing else, the same formula is above, you just have 3 here. So if Q1 is the size of n plus 1 by 4, Q3 is the size of 3 into n plus 1 by 4th item. For whom is this? For individual series.
If we talk about discrete series, then the same formula remains. Whether it is Q1 or Q3 to remove the quartiles, the formulas remain the same for both individual and discrete. Come forward. What is the formula for the continuous series of n? Look carefully.
The formula for the continuous series of q1 is l1 plus 3. Here q1 is not 3. Wait a second. Wait. q1 is equal to l1 plus n by 4 minus cf upon f into i.
But if q3 is there, then here n is equal to 3. minus CF upon F into I. When you write these formulas, then you get a good mind. Otherwise, not just reading, you will sit with your hands once or twice. So, Q1, Q3 are formulas for individual and discrete series. But if I talk about continuous series, then Q1, Q3 are taken out like this.
N by 4, if Q1 is there, Q3 is there, then 3 N by 4. Note these formulas. Note what is I, what is CFF, what are all these things. I will explain you things in the question. So how to get Q1 and Q3 from the formula?
Now see what is our main topic that we have to do. Main topic is interquartile range. What is the main topic we have? Interquartile range. How to get the interquartile range?
Formula is Q3 minus Q1. What is the formula of interquartile range? Q3 minus Q1.
If you want interquartile range, First you have to get Q3. Q1 minus both of them, you will get interquartile range. How will you get Q1 and Q3? According to these formulas, it depends.
If individual is discrete, then we will get Q1 and Q3 from this formula. But if it is a continuous series, then we will be getting Q1 and Q3 from this formula. So interquartile range is Q3 minus Q1.
Next, what do we have next? Next is quartile deviation. Next, what do we have?
Quartile deviation. The formula of the quartile deviation is Q3 minus Q1 by 2. The formula of the quartile deviation is Q3 minus Q1 by 2. If you want to get the quartile deviation, you have to divide Q3 minus Q1 by 2. Next is coefficient of quartile deviation. The formula is Q3 minus Q1.
upon Q3 plus Q1. You will think, ma'am how to keep so many formulas in mind? When you are reading the formulas properly, you are writing it down by hand and when the question comes, you write the formula again and again. Not that the question comes and you apply it quickly.
You write the formula again and again, you put things on it, things sit in your mind. So don't worry, don't think that we can't do it. We have learned things till 12th grade, we have written in the paper, we have taken marks in college, we have remembered things sincerely If you write this seriously, then you will remember these things.
So, coefficient of quartile deviation is Q3 minus Q1 upon Q3 plus Q1. Start. The whole game is of formulas. The easiest subject is if the formulas are learned well.
Is it clear? So, how many formulas did we do on this page? On this page, we did three formulas which were of this chapter.
That is, which ones? Interquartile range, Q3 minus Q1. Quartile deviation, Q3 minus Q1 upon 2. And coefficient of quartile deviation. those extra formulas to write. Let's go ahead.
See this carefully. Any series or individual discrete continuous interquoted This will be the formula of the quartile range. This will be the formula of quartile deviation. The effect of individual discrete continuous will be on this that how to get Q1 and Q3. The effect will be on choosing its formula.
But in the interquartile range, each of which will have the same formula Q3-Q1 Quotient deviation will have the same formula Q3-Q1 by 2 I am repeating the formula so many times so that the formulas sit in your mind Ok, now let's do the question of this topic topic will also be completed. Let's start the question. First question of this topic.
See what the question is saying. Find interquartile range. We have to find this. Quartile deviation has to be found. And coefficient of quartile deviation.
Means I have to find Q3 minus Q1. And what to find? Q3 minus Q1 by 2. And what to find here?
We have applied this formula. Okay, we need all these things. We have to find these three things. These three things will be found when I have Q1.
Q3 aajay to sabse pehla kaam mera kya hai Q1 Q3 ko calculate karna. Teeke series kaunsi hai individual individual ke andar Q1 kaise nikaalte hai size of n plus 1 by fourth item. Mene aapko formula likhwaya tha n kitna hai ye dhyan se samajhna hai n kitna hai mere pass ye kitne hai ye 7 hai to 7 plus 1 by 4 that is fourth item kitna hua second item ke merenge 7 plus 1 by 4 8 by 4 2. second item.
What is written on second? 18. So, here what happened to me? 18. It is very simple to find out.
The number that will come from this formula. 2 came. Means pick up the second number.
18. So, what happened to me? Q1. Come to Q3. Here 3 into n plus 1 by 4. So, 3 into 7 plus 1 by 4. How much was made?
2, 3 into 2, 6. Means pick up the sixth item. How much is the sixth item? 4, 5, 6. 20. 28 so here my q3 is 28 the number that will come from formula like 6 came here whatever number you get by going to that number it will give you q1 q3 whatever it is one thing I am telling you very important whether to take out median or quartile first thing to do is to arrange data in ascending or descending order we do in ascending order most of the time but Here we had this data, not that you start removing the tile directly, no, first it was arranged in the sending order, that is, from small to big, 15, 18, 20, first arranged, then its Q1, Q3 is taken out. If we do not arrange, then the sixth item would be 30, what is the sixth item after arranging?
28. See, we needed the sixth item here, if we do not arrange, then what is the answer? 30, see, 30 is on the sixth number. What is the arrangement? 28 means arrange it if you don't arrange it then the answer will be wrong so it is very important in the quartile first arrange it then take out your q1 q3 once q1 q3 comes then just put it in the formula interquartile range q3-q1 we have 18 28 28-18 q3-q1 is 28-18 10 came then quartile deviation q3-q1 by 2 10 by 2 how much will come 5 will come. Coefficient of quartile deviation, add all the values.
What is the value? 0.217. So, like this you are doing questions easily.
Is the equation clear? Good? Sure? Let's move ahead. So, our quartiles behave like our median.
Like we arrange data in median. Before taking out median, similarly before taking out quartiles, we arrange data. One more thing, whenever we have frequency, whether we have to find the median or we have to find the quartiles, there we have to find CF.
I am repeating whether we have to find the median or quartiles, if the frequency is given in the question, it is discrete series or it is a continuous series, without finding CF, we cannot find the median quartiles. Understand carefully, calculate interquartile range, we have to find the interquartile range, quartile deviation, coefficient of quartile deviation, we have to find these three things. Interquartile range, coefficient I am writing the formula again and again, say Q3-Q1, this is Q3-Q1 by 2 and this is Q3-Q1 upon Q3 plus Q1.
We have to remove all these things. Means if we remove Q1 and Q3 first, then things will become easy. Which is this series? This is a discrete series. Why?
Because it has a frequency too. So, it has X and F too. This is a discrete series.
We don't have Q1 and Q3 here. nigaale. Discrete series individual series or series of then you can't work without CF. So, you have given this frequency.
If you remove the cotiles, then you can't work without CF. This is X, this is F, so let's remove CF first. The first one is same, then add it.
2 10 20 plus 10 30 30 plus 35 65 65 plus 42 107 inquire answer is 127 CF understand okay after understanding CF what to do now now you see formula of q1 what was size of n plus 1 by 4th item n what is 127 if we have frequencies then sum of frequency is n frequency If there is no frequency, then we will see like this, 1, 2, 3, 4, 5, 6, n will be 6. If you have not given frequency, then we will just count. But if you have given frequency in any question, n is always their sum. So, n is 127. Put it in formula. 128 by 4. Which one came? 32nd item.
How will we find this 32nd item? We will go to CF and find. Here, find a number bigger than 32. Is this bigger than 32?
These were smaller than 32. Find the big number from 32. Now which is the closest to these big numbers of 32? 65 is the closest to 32. This is far, this is also far. So what do we do in CF?
Let's find that number. If the 32 item comes, then we will find the big number from 32. And the closest one, what is that number? 65. The X in front of it gives you a quartile.
What is 40 in front of it? So there is 40 in front of 65. So Q1 is 40. Here whatever item is there, according to that, we find CF. The X in front of it is giving you quartiles. One more example, we also need Q3. Size of 3 into n plus 1 by 4. What will this be?
3 into n plus 1 by 4. We have already calculated this. How much did it come? 128 by 4. So 3 into 128 by 4 is? How much is the answer?
96th item. Now go to CF and see the big one and the one near 96. See the big number of 96. 107, 127. Now which one comes near 96? Who will get before 96? 107. Here is 107. Now go to the next X. What is it?
50. So my Q3 is 50. discrete series may as a cortis nickel to head jaha frequency or CF Nikala he padega a bar Q 1 Q 3 a gay up to formula manala interquartile range K formula mandalo quartile deviation the formula mandalo sorry question easily o dangere concierge are a body is a nickel sang Clear edges, so here the game is to find Q1, Q3. Rest, you have to put it in the formula itself, there is no problem. How to find Q1, Q3, you should know this well.
Okay, let's go to the next, whose next question is this? Calculate in Inter-quotile range, Quotile deviation, And coefficient this. So, we have to remove these three things. But this time, We have changed the series. Right?
This time, There are intervals in x. And below, There is frequency. What is there in x?
intervals, below frequency. If we have intervals then it is a continuous series. Okay, integral range means Q3 minus Q1.
Now you tell the formula. Quotient deviation means Q3 minus Q1 by 2. Coefficient of quotient deviation means what will happen? Q3 minus Q1 upon Q3 plus Q1.
I have to remember this formula. Once I get it, I will easily calculate all these things. How to find the formula of the continuous series of Q1, Q3? We have learned its formula. That is L1 plus N by 4 minus CF upon F into I.
Now see how to work with this formula carefully. First of all, in this formula, N4 is seen. N by 4. How much is N? 60. First of all, you calculate N by 4. 60 by 4 is coming. is 50. Clear hoge cheez iss formula ke andar sabse pehle n by 4 calculate katey.
That is humare pass kitna aara hai wo 50. Kyunki frequency hai maine bola tha chai median ho. If there is frequency then CF will come out So here also we will take CF Here 4, 14, 29 all CF will come out Now see carefully Number 15th item, go to CF and find the one bigger than 15 and the one closest to everyone. All of these are bigger than 15 and the rest are smaller than 15. We don't need that.
We need the one bigger than 15. Okay. Bigger than 15. Which is the closest to the largest number? 29 This is going to help us a lot This will help us a lot This will get us all the CF, FL1 So the number that we have come from N by 4 The number bigger than that and the number near that Go and see in CF 29 Now come in front of it It has an interval It will give you L1 Because we want L1 in the formula This is the CF in front of you frequency F will give you in the formula you also need frequency F you need CF this CF has helped a lot but it does not take credit it will not be CF itself it will give CF to its superior what will we take CF 14 will take this thing very well understand it has helped us in getting L1 and F but when we have to find CF itself and put the value of CF then we take the value above that is 14 CF value will be 14 and if we take the value above and what is I? we have I that how much is its gap? here gap is 20, in 40-20 it is 20, in 40-60 it is 20 so the value of I will be 20 so put all these values, see L1 is 40 N by 4 we calculated is 15 CF we said 14 F we said 15 here into 20 you have to calculate this Q1's value is 41.33 If you have any problem, then say no, then here you have to calculate in the continuous series Q1.
Similarly, we will calculate Q3. Just like Q1, we will calculate Q3. What is the formula of Q3?
Q3 will come. Mistake. What is the formula of Q3? That is this 3n by 4 minus CF upon F into I. This is the formula.
First of all, what will we calculate? 3n by 4. What is the answer of 3n by 4? 45. Go to the table and find the value bigger than 45 and closest to it. Which is 49, come in front of it. This is your L1, this is your frequency, the value above is CF, CF29.
If you put all these values, you will get your values. See, the values are put here, see carefully. If you put F20, I20, how much is CF?
29. You will calculate everything. you will get Q3. Like this, Q1, Q3 both are found.
Just put in the formula, Q3 minus Q1, Q3 minus Q1 by 2. And here, you can calculate the answers easily from the calculator. Is this clear? So, with this, the topic of interquotile range and quotile deviation is also complete. So, we have to find the range and these two topics are also there.
Once we are moving ahead, I will do mean deviation. Before this, I will do two things. After 2 minutes, we have learnt the formula of range and deviation.
Apart from that, of the quartiles. See them properly once. Then start with me mean deviation.
Quickly. Now next look at mean deviation. This is the chart of mean deviation formulas.
It looks like there are many formulas. But trust me, super easy if you listen to me carefully. Mean deviation is of two types. Mean deviation can also be taken out from median.
And mean deviation. deviation from mean also can be taken out. So mean deviation from median means in question paper will be asked that if you take out mean deviation from median then you will use the median formula or if mean deviation from mean will be asked then you will use the mean formula.
So there are two types of mean deviation. Ok, see ahead, now what are the types of series? Three individual series, discrete, continuous, formulas are for all. First let's talk about three individual series.
deviation from median deviation the matlabhi hotel change minus to yahape minus hora hoga mean deviation from median a to median malakuch minus hora hoga to is me X minus M at the head X not of the question media who am muscle median to the mean deviation from median a to X minus M I got humming negativity person need to have more the other day more government Now I will explain how to work in the equation. We do not want anything negative in mean deviation. So what we put is mode.
The submission will come ahead because we write all the values adding. Upon n, this is the formula. is the mean deviation from median of individual series. If you have learnt the formula of individual series, then it is very simple.
Remember this well. Mean deviation from median means x minus m. Look carefully. The mode of x minus m is summation upon and you have to remember this.
If the deviation from mean comes, mean means median not mean, then it is the same formula. It will not be minus m, now it will be minus x bar from x. Because deviation is from mean, so change is coming from mean. minus b mean hi hoga to x minus x bar mod to aana hi hai summation aana hi hai niche kya aajega n aajega to individual series ke liye agar mean deviation from median hai to ye formula rahe If mean deviation from mean is there, then this formula will remain.
First tell me if any of these two formulas are having any problem. No, it's simple. Let's talk about individual series further.
Next is discrete series. What happens in discrete series? Frequency is the only thing that comes.
What to be afraid of? So it's the same formula. Just here in summation, an S is added because frequency comes. So in mean deviation from median, summation f x minus m upon n.
This is the mean division from mean. It is the same formula. What will come in the summation? f will come. Summation f x minus x bar upon n.
This is the formula. Clear? Let's move ahead.
If this is a continuous series, what happens in a continuous series? There is a frequency, there is no x here, there are mid values here. What happens in a continuous series?
There are mid values, there is M. So the same formula is discrete, the summation is the same, but instead of x, M will come because there are intervals in a continuous series. 0 to 10, 10 to 20, we don't use intervals.
we use mid values, mid value of 0 to 10 is 5, mid value of 10 to 20 is 15, so we use these mid values, so formula is same, here f was x minus m upon m, here f is small m instead of this x, mid values come, small m minus capital M upon n, this is the difference, mod f is same, if this is mean deviation from mean, then here fm minus, x bar upon n tell me if there is any problem in this it is very easy first of all what you have to do is you have to see which mean division you want which is the median or the mean it should be in mind if it is the median then x minus m will be there if it is the mean then x minus x bar will be there then see the series is it individual, discrete or continuous if it is discrete then you have to put the frequency if it is continuous then you have to put m instead of x this is the logic of this technique in formulas mind If you understand the logic, then you don't have to learn so many formulas, they become their own. This mode is definitely to be applied, this value is positive, keep this thing in mind. Frequency is outside this mode, but it is inside this summation.
Look carefully, frequency is not inside the mode, it is outside the mode, but the frequency is inside the summation. Keep this thing in mind. Okay, one more thing, we can't say its notation is so big, mean deviation from median. Believe me.
Clear? Mean deviation from median? Mean deviation from mean? Clear? Sure?
Let's move on. Next, look. Next is coefficient of mean deviation from median. Look, it's written here.
Whose coefficient do you want to get? Mean deviation from median. What do you have to do for coefficient?
the answer of mean deviation from median whatever answer you have here if you divide it by median then it will be coefficient of mean deviation from median to find coefficient the mean deviation from median will be The answer of mean deviation is, if it is a median one, divide it by the median for the coefficient. If you want the coefficient of mean deviation from mean, then whatever is above mean deviation from mean, if you divide it by the mean, then the coefficient of mean deviation from mean will be there. Understand very carefully, what to do for coefficient?
The answer you have above is of mean deviation. If it is of median, then divide it by median. If it is of mean, then divide it by mean.
You will get coefficient. This coefficient formula, whether it is individual series, whether it is discrete, series or continuous series or same formula will be that the answer of your mean deviation is dividing it. If it is of median then you will do it from median, you will get coefficient. then you will get coefficient.
This thing is clear, these three formulas are all same. The formulas to find the coefficient in all three series are same. The answer to the question of the coefficient, if the question is of the median, then divide it by the median. If the question is of the mean, then divide it by the mean.
You will get the coefficients. You have to learn the main formula above only. Because you will be calculating the mean deviation with this formula.
Clear? Now, take 2 minutes. Try to make a chart of formulas yourself You will be scared that you can make mistakes No problem, try it yourself Once you get the concept in your mind Then you will forget the formulas in the paper This thing will come out of your mind If you read the formulas with understanding, then you will never face any problem Now let's go to the next question But first you pause the video and do the formulas well What is the question saying here? What is the question saying here? Question is saying, calculate the mean deviation from mean as well as from median.
It says, calculate the mean deviation from mean as well as from median. And coefficient of mean deviation. And calculate the coefficient of mean deviation.
Okay, we will calculate all. It says, from the following data. This is the data given to us.
Whenever someone asks a question, the first approach, we do CBI first. We will do investigation. We will do investigation. What is the rule? SMF.
Whenever you have to do any question of start, first of all you have to check your SMF. S means check which is the series. Series is individual here.
What is the series here? Individual. Then it is said to check the method. In individual, we did not have a method. There was one formula.
One was mean deviation from median, one was mean deviation from mean. Sometimes it happens that there are three methods in individual series. If you can do the question of the series in the same way, then in the same way, in the same way.
There was no such thing in mean deviation. So, there is no problem in method in mean deviation. There is only one formula of individual series. There is one formula of mean deviation from median and one formula of mean deviation from mean. So, there is no problem in method.
Next, tell me the formula. Yes, let us tell you the formula of individual series. First, we will tell you the formula of mean deviation from median.
What is the formula? That is summation x minus x bar upon n. And mean deviation from, this is median, right?
So, here x minus m will come. Now, if mean deviation. deviation from median so what will come here that is M will come.
Keep this in mind. Mean deviation from median so X minus M. Mean deviation from mean so here X minus X bar upon N.
So it is very important to write formulas and to command on formulas. If you know the individual series then write the formula. Now according to this we have to question.
Formula tells us how to make the table. First what do we calculate? Mean deviation. Let's do median mean whatever you want first. Let's calculate mean deviation from mean first.
What I want is the mode of x minus x bar. So first I calculate x bar. If I want this mode of x minus x bar. I will make a table, I will make a column of x minus x bar. But first calculate x bar.
How will x bar be calculated? How is the x bar of the individual series calculated? Formula is summation x by And first x bar.
I will calculate the X bar. This is my S. How much is submission X?
405. So 405 upon 9. The answer is 45. What is my X bar? 45. It was not written anywhere that the mean has to be taken out. But the demand of the formula is that the mode of X minus X bar is required.
X minus X bar will come out then, right? First I will take out X bar. So what will be X bar?
45. Now this is the formula of X bar. I told you this in the quick series of mean, mode, and median. I have explained there how to get the mean of individual discrete continuous.
So I have made these formulas learn there. So you have to revise these things once from there. So you have got x bar.
Now x minus x bar will come out. So here we will get x minus x bar. Don't worry ma'am why we have written dx bar.
Now write in your simple language x minus x bar. So 20 minus 45. How much will the answer be? Minus 25. So it will be 22 minus 45. How much will be the answer? minus 23 but what I have is mode what does mode do?
this is mode right? what is there in the formula? there is mode what does mode do? it makes everyone positive so whether it is minus 25 or minus 23 I will write the answer positive because mode makes it positive so the answers will be 25, 23, 20 such answers will come Is it clear? If it is positive, then the answer will remain positive.
But the negative has to be made positive if you have a mod. So what did you get? That is x minus x bar. Will you add everyone?
What will come? This is summation x minus x bar. If you add everyone, then this is what we wanted.
How much value is coming? 160. So here we will write 160. And how much did you have? And is 9. So here 160 is 9. This will give you 9. mean deviation. Which mean deviation?
That is mean deviation from mean. This is its answer. 17.78 This is written. Its answer is 17.78 Clear? Now we have to find its coefficient.
How will the coefficient of mean deviation from mean come out? The answer which we got from mean deviation from mean, divide it with its mean. So 17.78 is mean say divide gear 45 answer get Nagya point three nine to yehama repass calculator game mean deviation from mean and whose cock office shit it is clear a same question me mean deviation from me median also asked, then we first see what was the formula, summation x minus m upon n, then first I have to find the median, it means you should also know the formula to find the median, size of n plus 1 by 2th item, I have also discussed this, here you will come to the 10th item, 10 by 2, 5th item, what will be the 5th item, you will see the number there, 5th item is 40 here, so this is your median, you have x minus m, column of minus m. They have calculated x-x bar and x-m in the same table. You can make a separate table.
First I will take out mean deviation from mean, then I will take out mean deviation from median. For that, you can make a separate table. By writing x again, you can make x-m.
Its summation will be 155. If you put 155 in the formula, then you will get 155. 55 upon 9 what you will get? that will be mean deviation from median so who is the game in this? that you should know how to get mean and median so that you can question 17.22 is the mean deviation from median we have to get coefficient for coefficient what we do?
the answer is mean deviation from median so we will divide the answer from median for coefficient we will divide from that with the help of which mean deviation is obtained mean deviation from median is obtained So, for coefficient we will divide it by median. That is by 40. Answer is 0.43. So, this is what? Mean deviation from median.
Tell me, is there any problem in this? No? Sure? Let's see things in a sorted way.
Listen to things with good concentration. You will understand very well. Don't keep your mind here. Bring it all here.
Let's move on to the next question. So, formula should come. According to the formula, mean mod should be taken out. That's all.
Next, calculate the mean deviation from median and mean. Here also, mean deviation is asked for median and mean. And their coefficients.
Coefficients also have to be taken out from the following table. This is x and this is f. So which series is there?
What is our first approach to question? I am telling you again and again. What is our approach? SMF. First of all, focus will go on series.
Which is the series? This is discrete series. Method, we have done the same formula in discrete series. We have done the method of mean deviation from median also.
We don't get the problem of method here when we take out mean deviation. Tell me the formula. Yes, let's tell the formulas of discrete series.
What were the formulas? See here. What was the formula?
Mean deviation from First of all, let's talk about mean. Only one f comes. Summation f x minus x bar upon n.
And if we have to take this out from median, then summation f mod x minus m upon n. It should be on these tips. Discrete frequency will come. If it is median, then x minus m will happen. Mean deviation x minus x bar will happen.
We will click such points in mind. If things are samji hai to. Teeke. To ye hamare formula hai. Formula se me direction mil jati hai.
X F note kiya. Teeke. Mujhe F into X minus. We need summation of x-x bar. Summation is after.
First I will make its column. f into x-x bar. When will its column be made?
First I will remove x-x bar. So first I will remove x-x bar. So first thing we will do is remove x-x bar.
First they have calculated median. I am doing mean first. We are discussing mean first. Here.
We are discussing about mean first, not median. Here we are talking about mean division from mean. So what do I want?
X minus X bar. When will X minus X bar come out? First, I will take out X bar.
So the first thing we will do is to take out X bar. Now X bar How does it come out in discrete series? Summation fx by n. So, first I wrote xf in the table. So, first fx will come out so that I can get mean.
So, fx came out. What is the value? 2460. How much is n?
60. Here I have mean 41. In one table, the whole work is done. We are talking about mean deviation from mean. Now what happens to us, we look at the table directly. Why did I take out fx? Here I don't need fx.
Because I had to take out fx because I need x bar for this. I need fx for x bar. That's why I had to take out fx.
We don't look at the table directly. Then the solution is never understood. Apply the formula.
Then see what you need. Start collecting it. Then things get linked.
Look ahead. We have fx. We have fx. Now I want x minus x bar. So what will I calculate here?
x minus x bar. That will be 20 minus. Here I have 41. 20 minus 41. Minus 21 should have come.
But there is a mode. Mode has made everyone positive. So here all are positive.
I want f into x minus x bar. So multiply the column of f with this x minus x bar column. 8 into 21. 12 into 11. All these are calculated here and the answer is given. What do we need for this? A.
Sum. submission submission head okay I'm a subco add gonna answer kidna 640 so you have a mechanic in this 640 put carrying a 640 by n Nietzsche and that will be 60 one sec it naiga 10.6 are clear ages I was one coefficient be chained up in the middle answer come in say he divide guru 10.6 seven four T one see her in heaven a coefficient of a doctor he do mean division cancer I have us come in say divide guru mean key helps in England I mean see Karen How much did it come from 5? 0.26.
So this is the coefficient of mean deviation from mean. This is how you do questions. If you are understanding the questions well, literally by posting here, quickly do the question yourself.
Keep the calculator with you. If you have done the question yourself with me here, trust me, you will not forget anything till the paper. Everything will be remembered well.
What did we calculate? Mean deviation from mean. Now what will we get? Mean deviation from median. Let's discuss the same procedure quickly.
If you know the formulas, then you will not have any problem. What is mean deviation from median? That is summation f x minus m upon n.
What is required here? Here we need the median. So, first of all, what is my work? To get the median.
This is a discrete series. To get the median in a discrete series, f is given, so cf will come out. Median without cf is not there. If the frequency is given, then that's why CF is taken out here.
Formula is applied here, see what is here, 30.5th item, The number greater than 30.5, the pass is 40, the value in front of it gives you the median, That will be 40, I have done this part of the median very well in the mean and median division. I have told you fast things here because it is done very well there. I repeat once again, whatever number comes from this formula, 30.5, greater than that, and the one closest to it is this, the x in front of it is your median, that is 40. I got m, now I want x minus m, so here I have taken out x minus m with mod, then I took out f into x minus m, then that is f into x minus m, its summation is 620. So by adding values in the formula, you don't have to be afraid of dm, it is x minus m only, you have to write the things that I have written in the chart, dm, you don't have to be afraid of all this.
So you have to write the things that I have written in the chart. we have to write f into x minus m, its value has come 60, 620 upon 60, answer 10.33. Now you want coefficient, what do we do in coefficient? The answer of this is divided, mean deviation from median, so the answer of this will be divided by median.
So what will it give you? That is coefficient of mean deviation from median. Is this thing clear? So we have calculated both here. Now let's go next.
What is next? See next question. Calculate the mean deviation.
mean deviation and It's coefficient from the following data. You have to calculate mean deviation from mean and coefficient from the following data. Here you have to calculate mean deviation from mean only, not median.
Look carefully in the paper. What was asked? If mean deviation from mean was asked, then you have to only calculate mean and not median. So, we have to only calculate mean deviation from mean and calculate coefficient.
Now, we will again put SMF here. What is S? Series.
Which series is this? This is a continuous series. Because what is in this? There is no problem of method, here in the continuous series there was only one method, we have only one formula. Which formula is there?
That is summation f here, here m minus x bar upon n. Because this is mean deviation from mean, so here the formula will be f m minus x bar upon n. So first of all, what will we do? We will note these marks, frequency, we will have to find mid values, mid values will be found. How do we find?
0 plus 10 divided by 2, 10 plus 20 divided by 2. divided by 2. All these mid values are written. Then I want m minus x bar. Then calculate x bar too.
What was the formula of x bar? We have done summation f m by and calculate x bar from it. 27 is coming.
Then what do you have to calculate? m minus x bar. Here is m minus x bar.
Then from which you have to multiply it? From f. It has been done from x minus m.
What is it doing here? It has been done from m minus x bar. This column is column to this column here sum is taken 472 by 50 will give you mean deviation from mean very simple you just have to apply formula means what you have to do formula should come then the formula will give direction according to the formula you have to work see here what is this Mean deviation from mean. Here I have put value 472.15.
9.44. What will we have to do for coefficient? This from mean.
We have to divide this answer from because without mean median we will not be able to find all these things so we should also understand all these things next topic is standard deviation most most important from here question comes from standard deviation so we have to do this carefully but before that take a break take 5 minutes and revise the formulas of mean deviation then after that I will do the chart of standard deviation for 10 minutes Do it quickly. This is the only topic of standard deviation. The one which is big, after that the variance, coefficient, all these things are very small topic of Lorentz curve. This is the only big topic left in this chapter.
Quickly revise mean deviation first and then we will do this. Quickly. Now next look at standard deviation.
Most most important, understand things carefully. It is not difficult at all. Super super easy if you do formulas after understanding.
How many formulas do you have to do in standard deviation? 7. It is not easy to do. We have to do 7 formulas in total. We will do 3 formulas of individual series.
We will do 3 formulas in discrete series. We will do only 1 formula in continuous series. We will do 7 formulas in standard deviation like this.
If you have to find standard deviation in individual series, then there are 3 methods of it. Actual mean method, assumed mean method and method based on actual data. This actual mean method is first one.
Second is assumed mean method. Third is method based on actual. This assumed mean method is also called as shortcut method. Keep this in mind.
So, we must be doing these three methods in the individual. This is also in discrete. Actual mean method, assumed mean method.
Third is not this, third is step deviation method. This is the most important method, step deviation method. In standard deviation, step deviation is important. For standard deviation, step deviation is important.
In the continuous series, we will do only one formula. Which is that formula? That is step deviation method. Understand things very carefully.
Which formula we will do here? That is step deviation method. So you have to remember this.
I will do the chart, from there you will remember better. So we have three formulas of individual, three of discrete and one will do continuous. Okay, let's go ahead. Let's go ahead. Now what is there in front?
One more formula is written here. Let's do this later. This is the note thing, let's do this later. Now let's see the formula of standard deviation. We will talk about the formula very carefully, lovingly and comfortably Because it is so easy, it is very good Let's go then, good means very simple What is there in the standard deviation?
First let's talk about the individual series Who will we talk about first? You will be doing the formula of individual series first. Okay, let's see. Which was the first?
Actual mean method. Which method was there in individual series? Actual mean method. Whenever you will do the formula of standard deviation, Under root has to come. So this under root thing is permanent.
See any formula, there is under root in sum. It is actual mean method. Mean will be used.
So what will happen here? x minus x bar If mean is to be used then x minus x bar What will happen of this? Square upon n It is so simple.
Root has to come. Clear thing is that I am telling you very simply. Mean will be used. will come? Its whole square.
What will be y? n. Inside this? Inside root. This is the formula for standard deviation.
Standard deviation is written with sigma. So sigma equal to root x minus x bar square upon n. This is the actual mean method.
Learn this formula in class now. What is sigma equal to? Here summation will come. Summation x minus x bar square upon n.
Summation means adding column. So, that will definitely happen. So, summation x minus x bar whole square by n. Learn this in the class right now.
This is actual mean method in the individual series. Is this clear? Next, see.
Next, what do we have? Actual mean method. Next is assumed mean method or shortcut method.
Assumed means a will definitely happen. Right? Assumed means a will definitely happen. A means there will definitely be deviation. there will be minus there will be deviation means there will be d so in assumed mean method d formula will come in assumed mean method d formula will come and if you have learnt learn here you have written the standard deviation here you have learned every formula if you learn this formula because this pattern is going on in every formula so what happens in assumed mean method we write summation here d square by n look carefully summation d square by n minus whatever is written here its whole square summation d by n whole square understand carefully d square by n minus this whole square summation d by n whole square Root is to be obtained because here is the formula of standard deviation.
Now what is D? Deviation. X minus A.
D is deviation that is X minus A. When I do formula, I am telling you very thoroughly. Because the question will be asked if the formulas are good.
In the question, you have to work according to the formula. But first the formulas should be good. So what is the formula?
Submission D square by N minus submission D by N whole square assumed mean method. Indeed, individual series guys maybe frequency native individual series a it's baby frequency kind of a green individual series a ticket to the facility this is the formula for as you mean method individual series next echo method based on actual data actual data matna me use Karun G na my happy deviation use can be actual data use Karun G same formula is written as x instead of d because we have to use actual data, no mean, no d, only the above is written. So here under root summation is x instead of d. minus here also see, only D is replaced by X, same formula is written here. So there are three formulas of individual series, actual mean method where square of X minus X bar is there.
Then after that is the assumed mean method, remember this pattern well, this pattern will remind you of all the formulas. Summation D square by N, then its whole square, minus in the middle. And then here the actual data is the same formula, just write X instead of D. Tell me, are the three formulas of the individual series clear? Next we have discrete series.
What we have? Discrete means here frequency will come. First we do actual mean method.
have but what will come in the submission frequency will come in the actual what will happen in the actual mean mean use will happen x y s x y square use will happen what will come in the submission frequency will come so the actual method of discrete series individual series is exactly the same, just the frequency comes forward, see the assumed mean method is the discrete mean method, the same formula will remain, just in the submission What will come? Frequency will come. So, actual mean method, assumed mean method is in both individual and discrete. The only difference is that here frequency does not happen, it becomes the formula of individual.
Where frequency happens, it becomes the formula of discrete. Come forward. In discrete, the formula of actual data does not happen.
Use of actual data does not happen. Instead of this, step deviation happens. In individual, there was no step deviation.
But in discrete, there is no actual data. There is no data. method is step deviation method. This is very important.
Step deviation method is very easy to learn. This is the same formula above. Same.
D is changed to D dash. D is changed to D dash. How does D dash come out? You must be explaining in the questions. The same formula is written instead of D and will come into I.
The same formula is here, the whole root one, D is changed to D'and you have to write into I outside the root. What to write outside the root? into I. How to find I? What happens?
I will tell you in the question. For now, see the formula. So, in the discrete series, the same formula of the zoomed in method, the same pattern, instead of D, D dash and into I.
Okay, so we had three individuals. Three formulas were in discrete series. Come forward to continue series. How many formulas were there in continue series? We had to do only one formula.
We had to do one formula. Here three are written. How to do one?
Now I will tell you. Discrete series, individual series is clear. In continue series, we have to do only one formula. That is step deviation method.
Only one formula in continue series. What is step deviation method? See the same formula discrete.
Whether it is discrete. whether it is continuous or same formula of step deviation fd dash square is same into i is same then why it is written differently because when we apply then you will understand the difference that d dash here is i here is i you will understand the difference in question but both have same formula whether it is discrete or continuous formula will be same when you apply how will i value come out only this difference remains then both have same formula discrete or continuous if you are doing that is step deviation method ok then why this formula is written above if we talk about continuous series talk about standard deviation we take out from this method continue series is given to us And we have to get standard deviation, we will apply step deviation method quietly. We do not use these two formulas.
We do not use these two formulas, but it is given in many books, that's why I have written here. They say that continuous deviation is a problem. and discrete will be same formula. See, this and this both formula is same. Mid values are required in continuous.
Just M E is to be applied instead of X. This is not a formula. Formula is there. But if you want standard deviation continuous, in the continuous series, then the question is from the easy step deviation.
So when all the questions are done from the step deviation of the standard deviation, then why should I remember these two formulas? So that's why this formula is not considered. In the continuous series, we will apply this formula in the standard deviation.
In many books, the formula is given, instead of this X, M is applied. The same formula is loaded, instead of X, M is to be done. Here there is no X which I do M, so the same formula is there.
I have not written these two formulas here, so that there is no confusion in your books. Whether you have written this formula, if you want to get out the standard deviation of the continuous series, you will be getting it out of this step deviation method. We will not use these methods. Methods exist, but if all this works, then why should I remember three methods?
This will work with one, there is no need to remember these two. Did you understand the thing? So you will do it very simple and very easily. Continuous series.
series k bhi 3 method ho sakte the simple x ki saag m hi to karna hai par iss se question karne ki zarurat nahi hai iss se sare question ho jate to mai zyada extra ke wyaad karo clear hogi cheez total 7 formulas hai 3 iske 3 iske aur 1 iska formula batawa standard deviation clear hai pakka chale aage agar standard deviation clear hai See one more formula, quickly, this note one. If someone asks the coefficient of standard deviation, then you have to divide the sigma, which is your standard deviation, from X bar. The formula of coefficient of standard deviation is sigma upon X bar.
What is it? Sigma upon X bar, coefficient of standard deviation. Okay, take two minutes, quickly revise the formula of standard deviation once, so that we can do the questions quickly, quickly. Quickly revise, then I have to make two more formulas.
I will do it from here. Quickly revise this chart once. Then I will also do the formula of combined standard deviation.
But first revise the chart quickly. Now what we have to do next? That is combined standard deviation.
Just like we had taken out the combined mean, we will also take out combined standard deviation. sigma 1 2 what happens n1 sigma 1 square n2 sigma 2 square n1 d1 square n2 d2 square upon n1 plus n2 is in the whole root what happens to d1 x1 bar first code Combine the standard deviation, so data will also give us 2, x1, x2. Combine means to collect 2 data.
So we will also be given 2 series. So what will be the D1? x1 bar, the mean of the first series minus its combined mean.
If we want to get D2, what will we do? The mean of the second series minus x1 2 bar. So you have to keep this in mind, that is the formula of combined standard deviation and how to get D1 D2.
And once again, we will see the same thing in the next class. plus the same n1 with d1 square, the same n1 with d2 square, below n1 plus n2, d1 d2 come out like this. Clear?
Both are mean in d1 d2. If d1 is there, then x1 bar minus combined one, if d2 is there, then x2 bar minus combined one. You have to keep these things in mind. There is a formula for variance in front of us, we are not doing that now.
When there will be questions, we will come to that. we will do it only then, we are not doing it now. OK, the formula of standard deviation is complete.
Now let's quickly do the questions. We will put the approach, SMF must be working. See what is written, calculate the standard deviation from the following data. This is here.
We have to put S, M, F. Which is the series? Individual. Which method should be put in the individual? We have to think here. Because here there is not one method in the individual.
How many methods were there in the individual? There were three methods. So we have to think about the method too. They didn't tell anything, from whom to take it out. So we put the simplest method.
That is, I have chosen the actual mean method. Because it is the simplest, it is the first. So what method did we choose?
Actual mean method. Because the first method is the first. Tell me the formula.
Let's write the formula. What was its formula? Sigma equal to under root will be.
Summation x minus x bar square upon n. This is the formula. So, you got to know these three things.
Question is done. Now, let's work according to the formula. What do I want? x minus x bar whole square.
So, first let me get x bar. Then only I will get x minus x bar. What is the formula of x bar? Summation x by n. table may fell a X note Kia submission X Ketana hi 200 a Ketana 20 200 by sorry a niche attend hey take it up and Jega 20 X bar Ketana gaya 20 hamid say a X minus X bar casque alex my next bar Nikala T no G fell a X minus X bar Nikala 16 minus 20 minus 4 20 minus 20 0 18 minus 20 minus 2 sorry happen to a yeah happy morning the he had a more Are you a goat or No, it is simple x minus x bar.
So, negative will also be the value. If there is a mode, then we do positive. There is no mode in this. Simple x minus x bar is there. And then what to do with x minus x bar?
Square. Do 4 minus 4 square is 16. Minus 2 square is 4. It will be like this. Minus 2 into minus 2. Minus into minus becomes plus. That is all done.
I want its summation. I wrote it down by adding. I wrote it down by adding.
98. So, 98. 98 upon 10, we have to do root of that. It is very simple. Look carefully.
98 upon 10, look. Here is the root of 98 upon 10. 3.13. Tell me, why is the question difficult? If your SMF approach is fine, no one can stop you from taking number in stats. Let's go to the next question.
Let's move on to the next. Let's apply the SMF approach on the next. What is it saying?
Blood serum cholesterol level of 10 persons are under. We have been given the data of 10 people. Calculate standard deviation with the help of assumed mean. It is said that standard deviation is obtained with the help of assumed mean.
Again, SMF approach. Which series is this? It is an individual series.
Which method to apply? I don't have to think about that. He only said that apply assumed mean.
So, which method is there? That is assumed mean. Now after that apply formula. We will apply formula also. What was the assuming?
Under root will come. What was in under root? Assumed mean is D. Summation D square by N minus summation D by N whole square.
Tell me any problem? No, right? How D comes out? X.
minus a say to my love who's a happy be scared say a X minus a car to you do this to you many car loony a guy assumed mean Cassie Nicole there is X Mrs. center value Lilo yeah we have a value Logan Chodi, ye dono chodi value, ye wali chodi, yahape center value ye dono hai, 255, 288, hum upar wali lete hai, toh main a kya lenungi, 255, toh yahape x minus 255, toh yahape x will be 25. What is this? It is D. Right? X minus 255. I will do all the calculation. I want D.
See, I want submission D here. So, I will be getting submission D below. I also want submission D square. So, I will also get D square.
I will also add the square of the values that will come out here. I will put it here. I already have the value of N. What is the value of N?
10. In formula, it is same. We have to put all the things carefully. Here, submission D square is there. So, whatever answer you will get, suppose I am not taking 2, 6, 8, 9. Upon N. How much is N?
10. Minus submission D by N. How much is submission D? 1 by N.
What is its? Whole square. So, its whole square will be.
What will this be? It will be root. Okay, you will put value and answer here. Your standard deviation will come. Now, here.
I have taken A255, he is taking X-264. What did I say? Take X-255. How much is he taking?
X-264. How is he taking A264? No problem. You ask the question from A255, the answer is same. I am telling you after solving it myself.
We can't remember what A was taken in the book. We have found only one way to take A. That the values we left above, see the values in the center.
One way to take A is to take A. If you get one, it's a very good thing. If you get two, then pick the one above.
So here we got one, we will take 255. To solve the question, your standard deviation will be the answer. No problem is coming, so don't worry about it. We have to take 255, 268 is there any problem?
No, we can't follow everything in the book. If your concept, your questions are correct, then your answers match the book. It is not necessary to take 264 because they have taken it. We know our 255 is there, question it, this is the answer. answer you have the solution so there will be no problem.
Is it clear? Now what we have here is standard deviation. Now see next question what is it saying? Next it is saying calculate the standard deviation from the following series. Let's calculate, this is the data given to us.
Now what is done here? We have to apply SMF approach. Which series is still individual? Which method?
We have practiced two methods, that is, which is the actual mean method and we have assumed So we use the remaining one, that is, actual data We had the same third, we use that too so that this time it is practiced You have to do it from the first, you can do it from the first method also, there will be no problem What was the formula? The formula was that is Summation x square by n minus summation x by n whole square This is very simple, you have given the question in x, what is the formula? What do you need? You need summation x square. So you will do x square.
Here are all x square. You will add them. You will get summation x square. You already have summation x. 200. You will put all values.
You will get your solution. See this data, this sorry method has been used here. First thing is here are values. Here I am adding values.
Here I am adding summation xk. Summation xk is 4098 by 10. Minus summation x by n is whole scale. Summation x is 200. 200 by 10 is whole scale. Solution is 3.13.
If we say so, then along with this we have done the three formulas of the individual series of standard deviation. Now let's move ahead. Next what we have is calculate the standard deviation from the data take assumed mean 6. He has said assumed mean 6 low.
First thing is SMF. S is series. Which is series?
X and F are given. So, this is discrete series. Absolutely.
Right? Next method is assumed. mean there a family calls a method on such a day he assumed mean method on say Jonathan garden formula get a human method car sigma equals to under root submission D square by n minus summation D by n car whole scale it is the and oh yeah my past discrete series a formula frequency hoogie So, put frequency in summation.
Assumed is deviation. D will be there. Write D. If it is discrete series, then frequency will be there.
Put F. This is its formula. If assumed mean is given in question, we have to take question. We don't take the mind from ourselves.
If there is mention in the question, then we have to take the same assumed mean. So, what we have to take as A? We have to take 6. Now we will calculate all these things.
I want FD square, FD all this. So, first you take out D, then only all this work will be done. So I noted xf, so first I take out d.
What is d? x minus a. 1 is 6. If 6 is minus from every x, then d will be found.
Here is d. x3 minus 6, minus 3. What did we get? d was found. What else do I want? I want fd and fd square too.
So first I take out d square too. See, I took out d square too. I want fd.
Here is fd. I want things that have submission after it. Submission FD is required, FD is taken out. Submission FD square is required, FD square is taken out.
Just put all the things in the formula. How to put things in the formula? Now see carefully what values we will be putting. See here carefully.
What values do we have? See, I have formula. Submission FD square, what is the value? 139. Put it. What was the value of n?
46. Put it. Submission FD minus 31. Minus 31. And what is n? 46. put the value here.
What is happening of this? Square. So, it must have divided the square of 31 and the square of 46. You have got this answer.
It is inside the root. After solving this, how much did the answer come? 1.602.
So, if you know the formula, then you get the direction, then there is calculation which is done easily by the calculator. So far, things are clear. Let's go to the next question.
Now see what is next. What is next saying to us? Next question is this. Calculate standard deviation from the following data.
And we have to calculate the deviation from the following data. method is given. No method is given.
So what we will do is we will put S, M, F. Which series is this? It is discrete because frequency is also given and X is also given. Which method is applied? We have three methods in discrete. First method, we have actual mean method.
Second method was assumed mean method. Third was step deviation. Here X is 12.513, 13.514. So, I am not seeing any x properly. It means it is like 1, 2, 3 or 12, 13, 14. Point-point are visible.
When the data is slightly tilted, then you choose step deviation method. Because step deviation method makes the question easy. So, I am using step deviation in discrete series. Because this data is not looking straight.
What was the formula? That is under root. What was the formula?
Why am I writing the formula again and again? So that you remember. square by n minus summation fd dash by n whole square into i. This was the formula.
We will be working with this formula. Whatever is written here, we need the same. Now look carefully. Now let's work according to the formula. I want first note xf.
I want fd dash. All these things are required. we have to find D before D'so how to find D? from X-A from here we choose assumed mean we left one value here from here we will see which center is the center of the value value is 14.5. So, A is 14.5.
So, you first subtract D. Here, I subtracted D. 12.5 minus 14.5 minus 2 came. 13 minus 14.5 minus 1.5 came.
13.5. Calculate all these terms. Now, we need D'.
D'is a very good thing. It makes data simple. How do we subtract D'?
D'always subtracts D by dividing it by something. By what? Now we have D, now who do you divide it from? Understand carefully, there are two things to see, whatever you can understand, you consider it.
Now I have to divide it, how did I know? First of all, see this number which divides all of them, such a number which can divide all of them. Most of the time what happens is that who is the smallest number among all of them, not zero. The smallest number is 0.5. So you divide all these by 0.5 and you will get D'.
Or you can see how much difference is there in 0.5. So you can divide it by 0.5. So D'makes the odd number of D simple. Point numbers are to be made simple. See, there were some points.
So, which is the smallest number? Don't look at the sign, don't look at the zero. Point five.
You all divide by point five. Divide two by point five. Minus four will come. This sign has to be written. If you do 1.5 with 0.5, you will get 3. If you do 1.5 with 0.5, you will get 2. All these answers will come.
Or you can also say that it is 0.5 C because the gap between them is also 0.5. So, that's why we divided d by 0.5 for d'. As soon as d'became easy, we need fd', so you take fd'. I also need fd'square, so you can take d'square first.
There is nothing like that I took fd'and after that I can make column of d'square. Absolutely, you can make it. There is no problem, the column will be back and forth.
You saw that first I want fd', so first you take fd'. You know what I mean? If you want FD-Square then you make a column of D-Square again.
After that make FD-Square. Column can be in front or back as you need in the question. Then they have already taken out because they know the need of D-Square.
Then D-Square is already taken out. FD-multiplied by FD-FD-Square multiplied by FD-Square You solved all these. Added the columns.
All submissions were given. Then you will get work done. and what is I?
I is the thing from which you have divided here. I divided from what? From 0.5. So what will be the value of I here?
That is 0.5. All these values have been put here. This has become with you.
The one who is coming, see FD dash minus 124. This is D dash square 544. Solved all the values. Answer is 0.719. It will come easily from the calculation.
Question. clear hua? Achche se?
Pakka? Chalo, then next pe chalate hai. Now, next question kya kera hai?
Dhyan se dekhna. Next is calculate mean and standard deviation from the following data. Kya ta mean calculate karo aur standard deviation. Mean toh main nahi calculate karo ki, aap karoge. Hum sirf standard deviation ki baat kar rahe hoge.
Firse SMF approach. S, M, F. Series kaunse hai? Continuous series hai. Kyun? Kyunki intervals hai.
Method kaunse legayenge? Agar aapko standard deviation nikalna hai. Ka?
It is a continuous series. You don't have to think of method. You have to apply step deviation.
We will apply step deviation. What is the formula? I am writing the formula again.
Here is a continuous series, X does not work, here mid values work, so D will not be X minus A, D will be M minus A. Why? Because it is a continuous series, so X will not happen, what will happen?
M. So what will we get out? M.
Then M minus A, how much is the center value from this? 35. You got M minus A. Now what is D dash when we divide D? What is the smallest number among this? 10 is there and see their gap also, the gap of interval zone here.
How will D'come out? D by 10. After that, you need FD'in the formula, you need the square of FD'You have to put the values. Tell me where is the difficulty here?
Tell me which thing is there that you think will bother us? Nothing. You have to put all the values here, calculate everything, the answer will be 15.69.
It is clear, you must be questioning like this. If once you know the series, method, formula well, you are revising, before going to the paper, you are revising the formula sheet, then it is super easy. Next, what is next saying? that is mean and variance. We are not doing variance now.
Come to the next question. We will do variance now. Don't worry. Next, what is he saying?
Two samples of sizes, 100 and 150. Two samples are there. Their sizes are given. Their mean, the away and on case tender deviation do sample in case sizes means standard deviation big a find the mean mean me Carlo and standard of combined sample of size 250 who hum since the capuchin mean oh standard which I combined will a black combined mean and combined standard deviation puts not Sarah hey so much Eric Ashley can mean a standard Nika Lou combined what level capuchin a combined mean and combined combined standard deviation push.
Clear? Now how are you doing? See, what was the two sample of size?
If there are sizes, then N1 and N2 will be. and 100 and 250 mean a 50 60 to a co-worker x1 bar X 2 bar little a little one echo to the enemy standard deviation of the Sigma one Sigma to Lilo a Muslim mean be put a combined well a the formula this is the formula of mean combined put all the things in this formula you will get combined mean how much is coming? 56 is coming ok, then what he asked he asked to take out combined standard deviation ok, standard deviation is taken out combined What is its formula? This is it, I just learned it.
Put all the values. But we don't have D1 and D2. So first calculate D1 and D2 before putting values in it.
You are not seeing why it did D1 and D2 first. We saw our formula, D1 and D2 are missing in it. So even after writing this formula here, first take out D1 and D2 and then put it in the formula. There is no problem, it is not going according to the book.
Write the solution like this and the person in front understands some things who is checking the paper. This formula will... d1 d2 missing, now take out d1 d2 first. How was d1?
x1 1 bar, x1 2 bar. First value bar was given in the question. Combined one, you just calculated 56 above, so how much did this answer come? Minus 6. D2 will also come out like this, plus 4. If you put all the values, you will get the combined standard deviation that is 7.46. Tell me if there is any problem in this.
Is there any problem? No, sure. Let's move ahead.
This is the combined. combined standard deviation. With this, the topic of standard deviation is also completed on which we have talked about formulas and combined.
Okay, this was the topic of standard deviation. After that, we are going to do very small formulas. Take a rest of 2 minutes and quickly post the video for 2 minutes. And quickly revise the formulas of standard deviation. After that, I have to do 2 more formulas.
The chapter will be completed. See you in the next video. quickly revise the standard deviation formula then we will do further quickly are you not done yet?
quickly revise the post then I will do the variance quickly now next is variance this is very simple, it says don't work for me how to find variance? standard deviation square every formula of variance is standard deviation formula square or say the answer of standard deviation is squared then it gives you variance. understand my point very carefully.
suppose in this question standard deviation is given. also asked variance also asked so what will you do calculate the whole standard deviation square the answer of it, it will become the answer of your variance if the standard deviation variance is asked in the same question, then okay, suppose someone's standard deviation is 2, then how will its variance be that is standard deviation square that is 2 square square, explain something with an example, then let's go ahead, then the question is question curtain is the question carrying a coaches coefficient of variation game potent a house equation at a other DC question make coefficient of variation put your scope formula out there standard deviation upon mean into hundred chaotic standard deviation upon mean into hundred coefficient of variation car formula yeah last formula has the class car so don't worry up for the first equation goodness okay tell you start let's complete the variance first hmmm here was the variance question I told you that I will do it later where is standard deviation mean, standard deviation mean and variance, here it is see the question, calculate the mean and variance you will calculate the mean, what will I tell you how to calculate the variance The same approach will be there that is SMF series is continuous series. Which method we will use?
I know that we have to find the variance. Variance means that we have to find the standard deviation only. So, I am here in continuous series so I use the step deviation method only.
Now, do you know this thing? What is the formula? That is, carefully, sigma is equal to under root summation fd dash square by n minus summation fd dash by n whole square into i.
This is our formula to find standard deviation that is in continuous series. Now, understand one thing very carefully. You have two things here which you can do.
You apply this whole formula and find standard deviation. one answer of that will come. Sigma equal to something.
Okay. By applying the whole formula, take out the whole standard deviation, one answer will come. And then later, what will you do? And then later, you will take out the variance by squaring this answer.
Now, I understood today, before doing two ways of this question, I am telling that you have seen that there is a continuous series, there is a step deviation method, you know that for variance, standard deviation is to be taken, you have calculated the standard deviation completely and the answer of standard deviation comes in the end. square it and you will get the variance. Okay, this is one way. What is the way? What is done in books?
Before applying the formula, square it. See how we had the formula of standard deviation. Summation. again writing this formula is minus summation FD dash by Erica whole square into I this formula was whose was this of standard deviation what is the variance we have variance is sigma square so square this formula what do you do square this formula when I square what will happen by square this what will happen if I do square this whole what will happen by this square this whole square will be cancelled what will happen that will be summation fd dash square by n minus summation fd dash by n this is done, this root is removed and this will be square of i also into i square means you haven't solved it yet you have already squared the formula of standard deviation before solving it What is the question to be done? That first solve the whole problem Then square the answer Or square the formula first Your direct answer will come So in many books they square the answer after taking out the whole answer In many books In many books, the formula is already squared.
So if it is squared, then this formula of variance is formed. The root is removed from it and this is I square. Will you do the whole square in the multiply? This will also be square, this will also be square. If this is square, then the root will be removed.
If this is square, then what will happen? I square because I is outside the root. If this is square, then this will become I square.
So you can do this too. So here the question I have brought, In this, the formula is already squared. Now work according to this formula Now when you work according to this formula You will get the direct answer You will not have to square at the end So both methods are fine You can square after removing the whole standard deviation Or you can first write the formula of variance by squaring the formula This thing is clear Now according to this you will work FD dash square you know to remove You can do all these things Clear thing So this was the question of variance Next question is from the prices of shares X and Y given below state weather which is more stable in value.
You have prices of X and Y shares. This is X and this is Y. He is saying which is more stable.
Which is more stable. Is X more stable or Y. Which is more stable.
It is not written anywhere in the question that we have to get the standard deviation, mean deviation, coefficient of variation, nothing is written. We gave two shares, asking which one is more stable. If such a question comes, then you have to get the coefficient of variation. If such a question comes, then what to get?
Coefficient of variation. We will also get the coefficient of variation of X. We will also get the coefficient of variation of Y. And then we will see the value of which one. is more stable.
If we want to check which one is more stable, we will find the different coefficient of variation of both. First we will find the x. Now understand things carefully.
What is the formula to find the coefficient of variation? Sigma upon x bar into 100. Whose coefficient of variation is this? X's. How will the coefficient of variation of x be found? Sigma upon x bar into 100. to 100. First of all, what do we get?
We get X bar only. How does X bar come out carefully? X bar is individual series.
Summation X by NSA will come out. Summation X is here. See. Summation x is 448 by 10 is 44.8. Tell me, is x bar clear?
Sure? Let's move on. Look at the x.
What do I want? I want sigma. Sigma means standard deviation.
standard deviation of individual series I have three methods actual mean method, assumed mean method and use of actual data first method is actual mean method its formula is used summation of x minus x bar square upon n this is its formula here x minus x bar is happening understand this carefully x minus x bar x bar is my point 44 point If I take out x minus x bar, it will also come in points. So, my question is that it will become point and I will have to do more calculations. So, I am skipping the first method which is the actual mean method.
Because x bar is 44%. we have to minus the point, so we leave that method. The second method was assumed mean method. Summation, what was here? d square by n minus summation d by n whole square.
This method can be used. How much assumed mean we took from here? 45, so what will you remove here? You will remove d. Here you will take out D and what you want submission D square also you will take out D square also.
You will get all these values here, you will put values here, you will get sigma. Why is DX written here? Because we are calculating this sigma for X series.
So here X is written with D. There is no D here, it is the same formula D. Because we have calculated Y with Y.
calculate d then d y will also have to be written. So both are working on the same table to show d separately. So here d x is written or d x k is written.
You can also do this, let d remain here, there is no problem. You make the table of both separately. When you are calculating the coefficient of variation x, then you make its table separate. When you calculate y, then make its table separate.
By that you will get this d y d y. You can write by making a separate table of d and d square. They had to do only one table, so they wrote dx dx that this is of dx and this is of dy.
But you don't have to do this. First make a table of x with coefficient of variation. Take out the values completely.
Then make a table of y with coefficient of variation. Calculate it. Then you will do it separately like this.
Then you will not have a problem of x and y. Okay. What is here?
Sigma for x is equal to 100. Let's move on Here all values will be calculated, you will put the value, see here your answers will be coming like this, You will not have to write sigma x, for x, the whole calculation will be taken, for y, the whole calculation will be taken, This is not writing dx, dy, write simple d, you have such a coefficient of variation, write here, How much is the coefficient of variation of x? 7.25%, this is written in percentage, how much is the coefficient of variation of y? That is 3.03%, This is also written in percent. Who is stable? Stable is that whose coefficient of variation is less.
Its coefficient of variation is less. 3.03 So, y is more stable. Whose coefficient of variation is less, that is more stable. So, here y is more stable.
Is this clear? Let's move on to the next question. Last question, last topic of today's class. That is Lawrence curve.
Very easy and very simple to understand Draw a Lawrence curve, we have been given income and number of persons, we have to make a Lawrence curve. Don't do any formula like this, only this question will understand things. First of all, the income has been given, let's note the income, all the income is taken. You have to get the cumulative income of that income.
The cumulative means first as it is, then 200 plus 100, 300, 400 plus 300, 700. 5 plus 7 is 12, 12 plus 8 is 2000 Means the cumulative income is to be taken out Like CF is taken out, first add the same Then the percentage of this cumulative income Cumulative percentage How does it come out? The last one is always the total in cumulative You check its total, it will be 2000 only So, the last one is always total. So, the percentage you have to write this total below.
What Saab has written is above into 100. What Saab has written is 300. Total 2000 into 100. What Saab has written is 700. Total 2000 into 100. You have taken such cumulative percentage. So, cumulative income was given as cumulative percentage. Same with the number of persons.
What you have to do in this is, why you have to write it below. 80 to 70 plus 80 150. You have written all these. Then what do we do for percentage? The total of the below is 250. So what will we do?
80 upon 250 into 100. 150 upon 250 into 100. 200 upon 250 into 100. You will write all these. All these answers will come. Tell me is this table clear? Sorry, tell me is this table clear?
Tell me, then we will move ahead. Now what you have to do is write here income percentage and here you have to write percentage of persons. What you have to write is income and what will come below? Persons. Wait for a second so that the data is also there, there is also a problem in making us, let me explain to you easily.
Now what we will do is, here is income and here is percent. Now see carefully, here is 32% and here is 5%. We are looking at the percentage.
percentage of income and percentage of person percentage is 5 in front of 32 so here 32 will be here and 5 will be here somewhere above this, 5 will be here in front of 32 see this is 30, so 32 will be in front of 32 in front of 5 here. So this point will be somewhere here. How much is 15 in front of 60?
15 in front of 60. So this is 60. 20 will be below this. This is 15 in front of 60. Because 20 is above, 15 will be here. So what point is this? 15 in front of 60. This is in front of 30. Look ahead.
It was 32, sorry. Look ahead. Look ahead.
What is in front of 80? 35. So this is 80. 35 will be somewhere in between, 80 to 35, it will be coming from here, 80 to 35, Next, 92 to 60, 90 will be somewhere here, 92 will be somewhere here, 60 will be somewhere here, so see this point is in front of 92 to 60, 100 to 100, so this point of 100 is here, all these are joined, so what is our? Lawrence curve, and this is to make line of equal distribution straight line, so this is the help of our lawrence curve of these percentage, which is made by you as such no formula is to be done in this I hope you got this chapter measure of dispersion in a summarized form now you can read it well formula is super super easy if the concepts are clear now apart from this you want any other chapter which you want in summarized form let me know in the comment section I hope you like this video if you like this video do like share comment and subscribe to my channel which is dreamers thank you so much for watching