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Question 23of 40 Step03.21.57Supposc busincss statistics studcnt must makc frcquency histogram , and that there arc 30 data valucs with maximum valuc of 60 and mini...

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Question 23of 40 Step03.21.57Supposc busincss statistics studcnt must makc frcquency histogram , and that there arc 30 data valucs with maximum valuc of 60 and minimum valuc of 45, Further; supposc that thc student uscs the following proccdurc: Shc usCS quotient of 15/5 = 3 to get the class width. Ncar thc end of her work, shc becomcs concerned about whcther she did thc problem correctly, because the largest data value is not mcmbcr of thc last class_ Why?Answer 10 PointsTablesKeypadShe did not

Question 23 of 40 Step 03.21.57 Supposc busincss statistics studcnt must makc frcquency histogram , and that there arc 30 data valucs with maximum valuc of 60 and minimum valuc of 45, Further; supposc that thc student uscs the following proccdurc: Shc usCS quotient of 15/5 = 3 to get the class width. Ncar thc end of her work, shc becomcs concerned about whcther she did thc problem correctly, because the largest data value is not mcmbcr of thc last class_ Why? Answer 10 Points Tables Keypad She did not use an appropriate number of classes_ There are 5 classes of width 3 for a total width of Therefore, the last class is [47 , 60) , and 60 is not an element of this interval: Shc chosc tOo many classcs to havc adcquatc covcragc for thc data Shc chosc an incorrect proccdurc in gencral.



Answers

The following ogives come from different distributions of 50 whole numbers between 1 and 60. Labels on each point give the cumulative frequency and the cumulative percentage of data. (a) In which distribution does the most data fall below 20.5? (b) In which distribution does the most data fall below 40.5? (c) In which distribution does the amount of data below 20.5 most closely match that above 30.5? (d) Which distribution seems to be skewed right? Skewed left? Mound-shaped?

So the table here gives us a table which essentially gives us a particular number where X here is gonna represent again the number of pairs of sneakers here and the frequency is gonna tell you how much or how many times they occur here. So we know that from our case, here is the question that's given that our sample size is going to be 40 selected students. So for part A here, it wants us to find the means, which is essentially just going to be between four and five, just based on the relative frequencies here. So we can quickly do that by just looking at our numbers here. And based on the sheer numbers, it's going to be around 4.5 here for be here. It wants us to find the sample standard deviation. And of course, the standard deviation is gonna be the variant squared where, um, the variants here is basically gonna show his house spread. The data is so as we're going from 1 to 7 with our mean being around 4.5 here, we can say that our variants. So our value of V here is going to be approximately 3.5 to 3.5. Squared is gonna be about 12.25 here for part C here. It wants us to construct a hist a gram. So let's do the history, Graham. We're just gonna have values. 1234567 Here we have our frequencies. So for number one is about to, so we can say that is to five. To be a bit double than that. It's gonna be much higher than that. Then 12 hit me at the top of the peak. They were gonna have 12, 50 at six and one for seven here. So it's gonna be something like this. Um, for part D here, it's asking us to complete the columns of the chart here. So the chart is going to essentially be that here. So this is going to be the number of pairs, so that should be number of pairs of sneakers, and this is going to be our frequency. Um, so that's gonna be police charts in parts E f N G. Here are gonna basically be part of our box and whisker chart where we want to find the bottom 25% the media and the third court style, which is gonna be the top 25% or the 75th percent title in this particular graph. So we need to find exactly what our relative distributions are. So if we have 40 here, we know that 25% of 40 is going to be 10 here. So this is gonna occur at three. So 25 is going to be at three f here. That's gonna be the median. So that's where 20 is. So this is going to occur at four. Um, Fergie here 75 is gonna be where the 30 occurs. So if we just added up, we're gonna start with one is gonna be 22 is five. So that's gonna be 73 is eight. So we have 15. 4 is 12. That's gonna be 27. So that is gonna be five here, and that is going to be our value. So h can be the boss chart, which is gonna be something like this. Where we have that is a 43 and five here with our minimum that one and maximum that seven here. So that is going to be are answers for this question here

Hi. It's just trying to solve a problem. Number 14 Problem Number 40 is the same givens as Exercise 39 Mrs Whole. Give her class at N question. Multiple choice with exes. A number off on randomly selected correct questions. N. G in the Grade four students in the class where the grade off each citizens is equal to 10 multiplying by the correct answers. Questions. This is a given for the distribution for it's random variable and the question is asking about how can you find the median off G first Mind steeping that, uh, median three x close B This is a property off. The median is equal to a blind by median. Thanks, plus B. If we try to substitute in this equation, we can say that first list the state, the relationship between G and X, where G is equal to then thanks. So here we can find that if we stayed explodes be so a X loss be so here we can find that a is equal to 10 and B is equal to zero. If we substitute here in this equation by a and B, we can find, that's this is the attitude here and with the equation. So Reunion G is equal to 10 withdrawing by regional backs. And here we can find medium. Wilbanks is equal to 8.5. So then Ryan by eight point Frank. So it is 85 this How can we get median on Jake? Ah, question Be which can be, uh it is stating that Ah fine the enter what time or g Until your methods We can't say the same scene here that I q r which in the Inter queer in time. So let's first on calculate the art you are off X friend in bed. You would. So it is student, but pine minus first. What kind? As with so here, early quarter is equal to nine and first floor tile I couldn't giving is equal to eight. So this is equal to one. But why? Using the property's off the core tight. We can say that I like you r a x plus really is equal to a not the blind by like you are X. And by knowing that a is equal to 10 we can say that I like you are off. G is equal to friend Mark O'Brien by i q r x, which is one. So the final answer would be would be that thethirties which is asking about what shape with the probability distribution on jihad. So now we are trying to find this the shape for than your and the very well at G. And first we can ah created the mean off G 20. For this confusion, we can transfer these Ah huh. That space we can use the same property for median to calculate g ah mean for jeering the variable the same property mean off the X plus B is equal to aim at the blind. Why mean of X plus plus B So we can say that a with the blind. Why, I mean off X plus be And we know that e from here we know that is equipped depends to attend Brother Brian by me, Novak. So let's to try to find me no match, which is 76 7.6 plus the road is 76. So let's try to get her mind or find the shame off. Uh, run the variable g by knowing that Ah, sorry about that. This in chi lines. Okay, so food run the very well g mean is equal to 7.6. So let's assume that it is the mean 70 70 76. And the median is equal to 85. So 85 is more than the mean. So here is a median. So his 18 five And by knowing that the median, the mean is never in the median is indicate that the distribution is lift is skewed, since the mean is influenced by the hour lawyers, which have to be very small because I mean, is Lin then? Ah, well, then the median. So the distribution must mean left left, excuse. So here we can say that the distribution is lift. Yeah, it's cute. And this is the shame. And this is the justification for our financing. Thank you.

Been 14 here. We know that. Ah, the median The median of X is equal to 88.5 n g is equal to tell me 10 x So the media and the median off, um as we know that the 1,000,000 of a X A plus B is equal to a I'm not running by the median off X plus B s o ah remediate of ah g is equal to 10 not going The boy, the median people of X So just then we're going by it for crimes. So it is different toe 85 and this is answer for 40 48 for 44 40 bean um and the inter quartile range is a difference between the third and the first a court time. So the inter choir time a range of X is equal took you three minus Q one eso is equal to mine. My minus h is equal to one and edgy is equipped with 10 x where you know that like you are ah g z is equal to like you are our X welcome blamed by boy tends always thin The blame by once was the final answer will be will be there. Ah, for 40 c, we're 40 c o as we know that the immediate the mean the mean G is equal to 76. And the median a ah gene is equal to 85 and the I Q R or the Inter Quint kind. Uh oh. He is equal to 10. We know that the mean is lived in the media. This indicates that the distribution is left skewed, since the mean is influencing by the hour fire, which have to be very small because the mean is live in the medians. That's why we say that it is lift Ah s que And this is answer for 40 if he

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.


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