Numerical Questions Kollowing 4re the expenditure of ten families in rupees 1s given Alon . Famh 500 250 Ezenditure Cakculate - the mean and interpret the result: w...

The mean weight of a group of 9 students is $19 \mathrm{~kg}$. If a boy of weight $29 \mathrm{~kg}$ is joined in the group, then find the mean weight of 10 students. The following are the steps involved in solving the above problem. Arrange them in sequential order. (a) The mean weight of 10 students $=\frac{200}{10} \mathrm{~kg}$ (b) The total weight of 9 students $=9 \times 19 \mathrm{~kg}=171 \mathrm{~kg}$ (c) The total weight of 10 students $=(171+29) \mathrm{kg}=200 \mathrm{~kg}$ (d) $\therefore$ The mean weight $=20 \mathrm{~kg}$ (1) bcad (2) bdac (3) bdca (4) bcda

For this question, we're told that scores for an exam are normally distributed and have a mean score of 525 and a standard deviation of 80. For Part A were asked what percentage of of testers score less than 350 on the exam. We're looking for the probability that X is less than 350 and to convert his head scores were using that is equal to X minus mu over Sigma. So this is equal to the probability that said is less than 350 minus 525 over 80 just equal to the probability that said it is less than minus 2.188 equals 0.144 So the probability of scoring less than 350 is 0.1 for four or, in other words, 0.144 of the students to take this exam score less than 350 for Part B, whereas what score is needed to make the top 12%. So we're looking for a score K, such that scoring higher than it is equal to 12% or a 0.12 probability of scoring higher than K is equal to 0.12 Another way to state this is to say the probability of Zed being less than K minus 525 over 80 is equal to 0.12 So you can look in the standard normal table or use a calculator or software to find the said value that has a cumulative area of 0.12 And that gives us value a zed score of 1.175 So we can say that K minus 525 over 80 is equal to 1.175 and therefore K is equal to 619 So you must score higher than 619 in order to be in the top. 12% of testers report see, were asked what the inter quartile range is. So the inter courthouse range is the range from the first quartile to the third, so the range is the difference of these court tiles. I remember the probability that of scoring less than the first quartile is equal to 0.25 So we can say that the probability of Zed being less than Q one minus 525 over 80 is equity 0.25 So we have Q one minus 525 over 80 is equal to 1.175 So this 1.175 is this ed score that has a cumulative area of 0.25 So therefore, yes is equal to you. This which were showing in this equation here. So then isolating Q one we get Q one is equal to 471 0.8 and then we can do the same thing for the beard quartile. But the probability that said is less than here three minus 525 over 80 is equal to 0.75 which tells us that Q three minus 525 over 80 is equal to zero point 67 four and then isolating que gives us 578 0.92 So those were the bounds on our intercourse. How range so to find the size of the range, we just subtract those two values where we subtract Q one from Q three and we get 107 0.84 So this is the answer now for Part D. Were asked, What grade do you need so that only one out of 500 score above it? The one out of 500 is equal to 0.2 So we want to find the probability of scoring greater than a value K being only equal to 0.2 So what value of K such that the probability of scoring higher than K is equal to 0.2 So we can say the probability of Zed being less than K minus 525 over 80 is equal to 0.2 This should be three zeros in here. Well, sorry. No, it's it's 200.0 to Okay, we're good to go. So we can say that K minus 525 over 80 is equal to you. 2.878 And that gives us K is equal to you. 755.2. So you must score higher than 755.2, such that only one out of 500 score that high

All right. So we have these two, uh, free Mr Tables part I asked us to find the and I've labeled these x and y just for simplicity. So for a bus was find the mean of X. Well, I'm just gonna be one times two plus two terms, three plus three times. One, That's four times 13 five times three, this whole thing, although by by the total frequency, which is 3689 20. And that will give us a value of 3.545 Starting to be Asian, where that is going to be the square root, some of want and of X, I minus X bar squared by end minus one. Was that me? In terms of our situation, that's gonna be some spurted some from one to 22 of thanks. I minus the mean, which was 3.545 squared, divided by 21. We would actually needed to do this formally correctly. We need to write out this frequency table as actual list. Somewhere in the streak. Unstable is actually a two. Then two threes, then three ones. How I did this all backwards, say to it would be to one so 11 three twos and 13 and then 13 fours than 35 It's produced the innovation of the trialist. You end up with a syndication equal to 1.184 That's a bunch calculator work. So your brother writing it out, it's just do you have to figure out the some part first, then divided by 21 that's were routed and thats much calculated work. So let's restore irrigation. And then, uh, since the two scales differed by a difference of plus one because I could make adding +10 would make it one and this one, the one would make it too, and so forth. They decided to add one toe both and then see what the result was. So the idea behind it would be like we added plus one. But then both rating systems would be could be viewed as being a 1 to 5 system, like adding plus one studies. Have you had plus wonder we could theoretically compare the distributions well, adding plus one to the ratings of why so that would change. Um, change these ratings here that's gonna result in the mean I was gonna ship the mean up to for point to one rez. As it says the problem before it was 3.21 So adding plus one changes the mean. However, before the syringe, aviation was point 568 and adding plus one does not change the Syrian deviation because it would sell the same spread. Just the values themselves have changed, but the spread doesn't change. So the the Post Star innovation would still be point by 68 and you could go ahead and calculate these using the same method I have done here in a and verify these results. It's the idea behind doing this. So like, well, we have a plus one that we could compare. The two tables are the two results. That big question. Could we, with the suggestion allow of adding plus one allow for two sample t test? And that seems like a good idea at first when you're thinking about it. Um, just from like a kind of naive stand standpoint, it seems like a good idea. But the problem is that the distance wishes color the distance between 0 to 1 and 3 to 4 might not be the same in people's minds. So, uh, is adding plus one, and using a to sample T test assumes this to be the case. Also, a T Tests is gonna measure quantitative, not quality, of qualitative donna. And again, it's the numbers words there are 125 So you would think that aQuantive That's certainly the case because of the fact that people treat these numbers as different. Here's a treat deserves is different. We there's like there's no, um it is not a 1 to 1 ratio in the scale of these two differences, even though they're both one. There's some type of potential difference on how people see the difference. These numbers, and that makes it more of a qualitative situation. Even it seems quantitative, so we can't just add one, because that's gonna assume the rating scale doesn't actually matter. And let's kind of also, the whole thing we're trying to prove is whether or not the rating scale does matter so we can be making these type assumptions when we're using a number system that's actually based upon the qualitative data of how people will see these numbers

Those Children's in this question? We are given that the mean of the Mean of the wage of the nine students? Mean of the wage of nine syringe Is given to be 25. Okay. And it is given that if we add one more student To the data then it doesn't affect that mean. Okay, so what will be the weight of 10? Stupid? Now if we know that mean is the some of the data divided by the total number of terms in the data? Okay. So if we have to find the some of the data, it comes out to be a number of terms multiplied by the mean of the data. Okay. Now, if we find the sum, if we find the sum of nine students with okay, it comes out to be Total number of students at nine and the mean is 25. Okay, so it comes out to be to fight right now, one more student is added. Okay, so there's some oh we're of 10 students because I have added the most worried. So it comes out to be or 20 2-5 less leg debater, 10 Syringes X. Okay, now, it is given that if this if we find the mean of the data, that is 2 to 5 plus X, divided by 10, Okay, It comes out of the 25 because the mean has not changed at all. Okay, So if we check, It comes out to be 2-5 Plus X, which becomes equal to to speak, okay, so that means X comes out over 50 cages. Right So sorry, Iraq's comes out over 25 stages So the weight of fifth student attends, student comes out of the 25. We can also done uh we can also have been another way, which is that if the weight of the student is not altering the mean, that means the uh student weight will be equal to me. Okay, because That can only be the way in which he cannot have changed the meaning of the data. OK, so it's comes out to be 25. And that way also thank you.

Looking for 60 screen. We can see that the meaning in some of the products off the rating and the frequencies they wanted. Brother. Some of the quick the frequency so we can see that X for Moammar. Fine. It's equal to, uh, one. Uh, nothing like to us to get my three que en roc roi warm. Plus for not the bright 13 was right on. Why three? We're cool. No. Three. That's one. Not that The well, this is a Quito pretty point forthright fight. We can also say that the summer beeping Asian bathroom uh, medical flying, uh, is equipped room that is square roots off. The difference between the value and the mean two is equal to one mind. With that people in. Fine, fine. It's coming. Cool. Plus two minus fire. Fire. What you mean square? Uh, boy? Free. Yes. Being run with people. And for all right, I for 55 by morning. Well, more environment City went right. Lifeline where it times. Ah, fair theme. Wells, Right? Right now it won't work. Like what it's weren't three on. This is over. This is We're oh, for three was one of 33 Ah, minus work is equal to 1.1 83 It's for a question. A question. Be, uh, we know that Rex bar from zero. The floor is equal to three going toe and send individual from big for two four point front six A. As who, uh, ending one toe. Every value will make the mean also increase by one so we can see events. Thanks for absolutely. I feel most is equal toe transport people that some of the region is not affected in the same valley is added to each lane. So we can see that at the center of the gauge from being before, uh, most warm Do you want to? And being Asian, we're running from six c, but for questions, he, uh we can't see that balconies? No, because it to his handle. Do you test? It's really to be on you was on the American values. Oh, ah, you're American. Very wrong. And, uh, being given Berryville, it's our categorical ready. It is an answer. Your questions