Okay, so the fortune that we have at 10 is a lengthy one, but a very easy question. Now, over here, we have capital eggs, which is the number off pairs of sneakers owned, Right? We have been given a table, so if I just draw that table here Just a moment. All right? That's right. Great. Okay, so So here. We have aches. And here we have the frequency. And here we have the frequency one to three for Fife, six and seven. Alright, for the frequencies to 58 12, 12, 01 So this is to save eat 12, 12, zero and one. So this is the table that is given to us. Now let us go to the questions. The first one is find the sample mean X. Okay. How do we find the sample mean? It is the addition off all the values that I have and divided by the total number of values. So the formula, for example, mean away. Let's say that this is a formula. The formula for sample mean is going to be addition off. In this case, let f be the frequency an ex be an individual value. Upon addition off all the frequencies. All right, so let us see how this will turn out. This is two into one. What is two into one? It is too. 5 to 10. See, what is happening is I have 25 times. So if I add 25 times or affirmative life I buy, too. Won't make a difference. So this is plus still plus eight three 24. Plus, I have 12 in +24 which is 48. Plus, I have 12 and five, which is 60 plus six and zero is zero plus seven upon What is the addition of all the frequencies? Two plus five with seven plus eighties. 15 plus 12, 27 plus 12, 39 plus 1 40. Okay, so this becomes 40. Now, if I use my calculator to calculate this two plus 10 plus 24 plus 48 plus 60 plus seven divided by 40. Now I get 3.775 This turns out to be 3.775 and this is my mean. All right? We're done with the first one. The second question is find the sample standard deviation. Now, how do we find the sample standard deviation. We're going toe. Take the help of this table aware. Oh, kick. What is the formula for sample? Standard deviation. Okay, Instead of writing the formula, it is just trying to solve this. Now, what is the value that I have over here? The value that I have over here is one All right. And we have X bar as 3.775 So let me do one thing. Let me just fine eggs minus x bar and let me just square this. Okay? So one minus 3.775 square. Alright. So I again go to my calculator. This is going to be two point 775 in 22.775 This is 7.7. Okay, this is 7.7. Then I have tu minus 3.775 squished. Okay, so this should be 1.75 to 1.775 which is 3.15 3.15 Similarly, I would have three minus 3.775 So this should be 0.775 in 2.775 which is 0.6. You get the gist of what I'm doing, right? So I'm not writing the entire thing. I'm just going to write the answers. Then I have four minus 3.775 for minus 3.775 And this will to play by 0.2 to 5. So this is 0.5 This thing is 0.5 Now there's 55 minus 3.775 into 1.2 to 5. So this is 1.5 one point five. Then I have six minus 3.775 What did they ever do? Point to do five. This is 4.95 four point night fight. Okay, then I have seven minus 3.775 This is three going to 500 square. This 3.2 to 5 inches. 10.4. This last value is then point four. All right, so we have the squared deviations. Okay, We have the squared deviations now. Actually, the thing is, I do not require this, so let me just erase testing. Let me just it. Is this okay? Yeah, This I have it now. What do I need now? I need frequency multiplied by the third column multiplied by this valley that I have X minus X bars. Squish. Okay, this is what I see. All right, So one is, what, two times so the CIA to be too. In 27.72 in 27.7, which is 15.4, 15.4. Then I have five. And to 3.15 which is 15 points. So in faith, 15 0.7 life. Then I have eight in 2.68 in 2.6. This is four pointed four point eat then I have 12 and 20.5 12 in 20.5 which is 0.60 point six. Okay, then we have 1234 We have 1234 Did we just make a mistake? Note. So this is 12 1 to 1.5 12 into 1.5. This is 18. Then we have 00 and toe 4.950 Then we have one in 2. 10 point for this is 10 point for. Let me just check this again. Two and two. Yes. This is correct. Five into this is also correct. This is also correct. This one is also correct. 12 and 20 point 18 to 01 success. This 12 in 2015 Is this 12? 1 to 1.5. Is this then we have zero. Okay. All right. Now, what do I need? I need the addition off this column. I need the addition of the fourth column. So let me just add this. If I add all of these values, this is 15.4 plus 15.75 plus four pointed plus zero point six plus 18 plus 10.4. This is 64.95 64.95 Now, what we have to pay attention is we're trying to find the sample standard deviation. So we will divide, not buy in, but by end minus one. Okay, this submission will come in the numerator. So this will be 64.95 Okay, this will be 64.95 And over here will be n minus one. This is very important. What is N. N is 40. So let me just write this. This is going to be 40 minus one, which happens to be Cuddy. Night it was 64.95 divided by 39. 64.95 divided by 39 which is 1.66 five threes, which is 1.6653 Okay, but is this our answer? No. Because what is this? This is s Square, which happens to be the variance. What do we want? We want the standard deviation. Standard division is s. He says what route? Office square. Which means we have to take the square root off this. So if I do that, this is going to be 1.66 Fight three raised, 2.5. This is 1.29 West Standard Division is 1.29046 Let me decide. This is 1.29 This should suffice. All right, so this is my answer or this big. Okay. The C part says, construct a history Graham for the data construct a history Graham for the data. So over here you can see that I have created a history. Graham, this is what instagram for this particular data Looks like. This is part, C. Of course, you can make an even better one. But this will work for us. So this is what the program looks like. Then they say complete the columns of the church, which we have already done. These are the columns over here in order to find the answers. These were the different columns that we have to complete. And then we had to find s square. That is the variance. And then from there we find the standard deviation. Then let's find the first quarter. Now, what exactly is a quartile? This is what part? This is part E. Okay, now moving on the party. There should be black. Let's erase this. Okay, so But now they're saying, find the first quarter first quarter needs 25%. 25%. This is what was squatting, which means the value who's percentile is 25. Okay, so do we know any formula for this? I think we do, right. The formula for this is I is equal toe. Just a moment. Yes, literally. Is this this is going to be 25 by 100 25. 500 into end plus one. What is N. N. Is 14 plus one. So this is going to be one. This is four. So this is 41 divided by four. What? Even divided by four. Which happens to be 10.25 So the value of that is in 10.25 Position is going to be our first quarter, but what is 10.25 Can you have a 10.25 position? The answer is no. So what do we do? We find the average. We find the average off the 10th. Sure. And the 11th position values. So now what are the values in the 10th and 11th position? Let us look at this table. This is already arranged, right? What? Well is going to be in the 10th position? If I see this is to this is five. This is eight. So one is two times two is five times 38 times. So I can say that in my 10th and 11th positions, I'll have three. So what is going to be my every for this? Obviously it is going to be three, right? So what is my first quarter? I'm first quarter and the value over here or I can see the value of 20 percentile is going to be three. Okay, Yeah. Moving on. Find the median. How do I find the media again? I used the same formula. Okay, this was part E. Now, how work part. If part f say's find the median for them again, ID is going to be 50. Median means half rates of 50. 500. What was the formula? What do you mean? Yeah, into n plus one, which is 40 plus once. This is too. Okay, let's start this data, kids one by two, this is one by two. So what is 40 one? Developer to it is going to be 20 point fight 20.5. But what exactly is 20.5? Nothing. So 25 20.5 cannot be a position. So we're going to take the average off the 20th and the 21st values. Okay. So again, if I look at the table that I had the table that I have told me If I go back here, where is the table? Okay, here is the table. I have 12 times. All right. I have 25 times. So there are seven values gone. I have 38 times, which means 15 values are gone. And then I have 4 12 times. So which means my 20th and 21st values are going to be four. So the average is four. So I can say that my medium happens to be there. Is this? Yes, my mediums, My medium happens to be four. And this is going to be my answer for this big for but F Okay, let us look at the next one. They're saying find the core portal. This is part G. Now what exactly is meant by third quarter and 75th percentile rate? So this is going to be I is equal to 75 by 100 in 2. 40 plus one, which is 41. So this is three. This is four. So if I use my calculator for this, although this is easy, but let's use a calculator. We don't want to make any mistakes. 0.75 into 41 which is 30.75 This is 30.75 again. We know the drill. If this is not an anti, sir, we take the average in this case, we're going to take the average. Uh huh. 30th and 31st values. Okay, the value that are on the 30th and 31st position again. Let's go to our frequency table. Oh, yeah. So one is two times two is five times three years, Eight times. So 15 values are gone. Four is 12 times 2027 values are gone. And the next year values are going to be five, which means 30th and 31st values are five. So my average is five. So my evidence is five. Okay, That are you, Mr G? Okay, So my evidence is fight so I can say that my answer for this case, the third quarter, the value over here is going to be right. This is my answer. Over here. Okay. Jeez. Also done E f g h. 1% of students owned at least five pairs. We know that total is 40. Okay, we know that total is 40. Alright. Total waas 40. So let's just go back over here. Total was 40. At least five pairs means I can count. The students are the Children who have five pairs or they have six pairs or they have seven per so I can see that. That total turns out to be 12 plus 1. 12 last one. Okay, which means 13. So this answer is going to be 13 by 40 e f g s. So this is going to be how do I find percentage? It is going to be No. It is going to be values off interest, values of interest upon total values, right upon total values upon total values. All right, so this is going to be, what, 13 by 40 which happens to me. Okay. If I use my calculator again, this is 13 divided by 40 which is 0.3 to 5. You don't 0.325 Which means, what, 32.5%? Okay, this is my answer for part h. All right. These many students that it's a little 0.5% of students own at least five pairs. Alright, then I have find 40th percentile. Find the 90th percentile. Okay, let's go ahead and find these values. E f g h. Let me find space to do. I Let me just do Iowa. So this is I I want 48% rate. So again I is going to be 40 of 100 in 2. 41 Or I can say 40 plus one. Let's write this according to the formula. So using the calculator, this is 40 divided, 100 in 2 41 which is 16.4, which is 16.4. So what do we do again? We take the average, the average off 16 and 17th values. All right, So what are going to be my 16th and 17th values? Let's come away. I can see from the table in the 16th and 17th. Values are going to be four. Okay, so what is my 48% type? My 40th person time? He's four. Okay, so this was part I. What's part? Say I would find the 90th percentile. I shake. Okay. 90th percentile is what I'll say that the value is going to be 9500 into 40 plus one. Okay, so if I use my calculator 90 divided by 100 into 41 which is 36.9 36.9, which means the average off 36 this is going to be the average off 36th and 37th values. Okay, so let us just go back over here. What is going to be my 36 37th values? Okay, I can see that. My last values seven and then I have Zito 46 and I have 12 values that are going to be five, Which means, let's say from around 28 to 39 I'm going to have fight so I can see that 36 37 both values are five. So that everything's going to be five. Right? So where I come, I say that this evidence is going to be fired. So my answer for this part is fight. Okay, we are done with Jay. Now what escape? Construct a line graph. Now, these are the things that you can do by yourself. I have done these for you, but of course, the scales may vary and you can make even better graphs. But roughly this is the idea. This is the answer for Part K. You can see where I have already drawn this graph and then l part ls constructive stem plot. And this is what the stem plot actually looks like Over here. This is part else. Okay, this is what the stem plot looks like. So we have done with the question. This was actually an easy question, but a very lengthy one just required all the basics off statistics that we have learned. Okay, this was the entire question. So this is how we go about doing this question? Very simple, very easy and conception.