 You will let me know if you are unable to see my screen, right? Okay, so remember also, as part of your exam, like I said, there will be 25 questions, probably. So it means every study unit will have at least two questions per that study unit, exception of some of the study units where you might get three questions because there are 11 study units. If you go 2222, you'll only get 222, and then there is three more questions that needs to come from somewhere. The format and the structure of your exam paper will always follow the flow of your study unit. So you will have study unit 1, study unit 2, study unit 3, study unit 405 up until you get to 11. However, study unit 1, 2, and 3, sometimes because they overlap. Some of the questions might be also overlapping when you're writing your exam. You need to be able to know your study unit in order for you to identify the questions and link them to the proper study unit so that you are able to know how to answer that question. What are the formulas that you need to use? If there is any tables that needs to be used, what are those tables that you need to go and use? So you need to know the format of your study unit or the content of your study unit. So there is no room for cramming the work, so you can cram this work. You need to literally know that this comes from study unit 1 or study unit 2 or study unit 3. So now in order for us to summarize what study unit 1, 2, and 3 are all about, they are about introduction to your statistics, they are about visualization, and they are about summarization, which is the basic knowledge that you need to know in terms of statistics. In terms of your introduction, you need to know how to define what statistics is all about. You also need to know the terminologies used in statistics, like what are the branches of statistics, whether it's a descriptive statistic or inferential statistics, what do they mean by that. You also need to know how to define what a population is and the measures that come from a population. You also need to know how to define the sample and the measures that come from a sample. Not only that, you need to know how to define some of the terms that are used in statistics, like what is a variable, what is the data, and the types of variables, and the scales of measurement in terms of those types of variables. So you also need to know all that. When you move to study unit 2, you need to be able to know how to summarize your study or your data in terms of tables and charts. Based on whether you have numerical data, what are the charts and tables that you can use to summarize numerical data? And when it comes to categorical data, what are those charts that you need to use to summarize that? But not only know what are those things, know the properties of how you create them. How do you build the frequency table? How do you build a pie chart, a bar chart, and so on. The properties of each and every visualization that you are going to be using, you need to know those ones. Then you move into summary or summarizing your data. And here we're talking about numerical data. You need to know your measures of central tendencies, which are your measures of location. Those three measures, you need to know how to calculate them or how to define them, the mean, the median, and the modes. You also need to know the measures of variation, which are your measures of dispassion. You need to know how to calculate them. You need to know how to interpret your standard deviation. But more specifically, you need to know how to calculate your standard deviation and your variance. But also remember, especially when you get to study unit 3, where you calculate the mean, your standard deviation, and your coefficient of variation, which is the other thing that I didn't mention now, those you can use your calculator to calculate them. That's when you start using your calculator. But not only that, when we talk about the measures, the visualization, especially the numerical measures like your standard leaf plot, you need to be able to know how to decipher the numbers and rewrite the numbers into proper numbers, not in terms of standard leaf plot, but in terms of the data points like 25, 26, 30, 31, and you should be able to use that information and calculate your numerical measures like your standard deviation or your mean. Sometimes, hence I say, you need to know your study units, because sometimes all these study units, one, two, and three, the questions might be linked to one another. They might give you a standard leaf plot and they might ask you to calculate the standard deviation or the mean, or the median, or they might ask you about the properties of a standard leaf plot. You will never know. So you just need to make sure that you know and understand all of them. Now, that is everything that you would have learned in order for you to answer assessment number one. So we're going to go through every questions that are on assessment number one, and once we are done, we're then going to go to assessment number two, and I will also do the summary. So I expect you to also make your contribution in answering these questions, so that it's not only me, because some of them, remember, these are practice exercises. Some of them are straightforward. You should be able to answer them. So don't expect me to give you all the answers. So we're going to go through all of them together. So let's see if you still remember everything that you have done in March or April, which one of the following statement is correct with regards to some key terms in statistics? Which one of these statements is correct? So we're looking for the correct statement, A, B, and C, D, and E. A says a statistic is a summary measure calculated from a sample. B, a sample is a subset of all elements in a particular study. C, a statistic is a property of a population. D, a sample mean is a population parameter. E, a sample standard deviation is a population parameter. Which one of those statements is correct? A. A. And A, it is. Question two, it's cut off, and that's why I don't understand these things. I don't know what question two question was about. It says question two. There are no context in terms of that question. So probably we're looking for... Lizzie, it says which one of the following statements is the correct with regards to variables and descriptive statistics? That's the question. Okay. Thank you. So are you on my UNISA? Are you able to see all the questions? Yes. Thank you. Then you will be able to help us because I'm working through the paper that we got dumped or we got from your lecture. Okay. So there is your statement. Which one? Is it A, B, C, D, or E? A says qualitative variables take on a value with equal units that indicate how much or how many. B, quantitative variables have either a nominal or ordinal scale. C, measuring attributes of an element result is a quantitative discrete variable. D, quantitative variables are also referred to as numerical variable. E, statistical inference refers to a process of summarizing and presenting data in a form that is easy for the reader to understand, such as the table or such as a data, maybe tabula, graphical, or numerical, A, B, C, D, O, E. Sorry. The question is asking for... Sorry, sorry, Liz. The question is... Sorry, sorry, sorry, Liz. The question is which one of the following statements is correct with regards to variables and statistical inference? Yeah, so we're looking for the correct statement. So which one of these statements is correct? E is not correct because E says statistical inference in terms of that. That should be descriptive or if descriptive statistics refers to the process. So which one of those statements is correct? I think D. D, yes. D is the correct statement because D says quantitative variables are also called numerical variables. Number A, B, and C are incorrect because qualitative talks about... It doesn't just talk about how much because how much it means you would have measured the money or the amount or things like that. So that should have been a numeric or quantitative variables and B, it says quantitative variables can be nominal or ordinal. We know that those are qualitative scales of measurement and measuring attributes of an element results in quantitative discrete. Remember, anything that is measured, it will be continuous. Oh, we have question two. So I'll send you this document, don't worry, which has more explanation as well. Question three, so also question three, I can't see what the question was all about. Help us with the heading. Which one of the following statements is correct with regards to variables and the scale of measurements? Correct in terms of variables and scales of measurement. A, a nominal scale of measurement is the strongest form while a ratio is the weakest form of measurement. B, the mean cannot be determined for an ordinal scale of measurement. C, an interval scale of measurement is a higher level of measurement and ratio, scale of measurement. D, a nominal and ordinal scale of measurement share similar properties in addition, order or ranking of the data in a nominal scale is meaningful. E, quantitative discrete variable results from measuring attributes of an element. Which one of these statements is correct? B, indeed, because you cannot calculate the mean of an ordinal scale because an ordinal scale is like a, a, a, agree strongly, sorry, strongly disagree, agree, not applicable, agree, disagree, strongly agree, something like that. So it will be on a scale from one to five. So you cannot calculate the mean of an, a, a, categorical data as well. So B will be the correct statement. Okay, question four. A majority of rural schools in South Africa are in the Eastern Cape, Cozillumetal and the Lumpopa province. The basic, the part of basic education requires assistance in gathering some information to effectively manage their scholar transport system in some of the rural areas. Which one of the following statements is correct with regards to the type of variables? We also looking for the correct statement with regards to the types of variables. Remember, the types of variables are qualitative or quantitative. And when it is qualitative, if it's measured, it's continuous. If it can be counted, it's discrete. Okay, so A, the list of schools requiring learner transport is a qualitative ordinal variable. So what is very important here is the list of schools and they say it's qualitative ordinal, therefore they should be ranked. B, the distance from the learner's home to the school is quantitative discrete is a distance. So it means it should be measured. C, the number of learners at each school is qualitative continuous. The number of learners, it's a counting process where you are counting how many number of learners you have. G, the travel time from the learner's home to school is a quantitative discrete. So travel time also it's something that needs to be measured. E, the level of school whether it's primary, junior and high school requiring learner transport is a qualitative ordinal. So the level of school should be in an order because there is some rank in terms of the types of school. So which one of these statements is correct with regards to the types of data? I think it's E. Yeah, I also think it's E. Yes, definitely E is the correct one because it says level of school from primary, junior and high school. It is an ordinal because there is a rank and it is qualitative ordinal. And we do have a diagram there that explains the variables. So this is another question. Yeah, you were expected to create a bar graph or a pie chart, right? A pie. I'm taking all these values and counting how many there are. I'm going to assume that it starts from that blended there. So you will need to go and count how many there are in total. Did they tell you how many there are? What is the question? The heading? Sample of 70 job seekers. 70 job seekers. So you are told how many job seekers are there? In the exam, if you get something like this also, sorry. Sorry, where are the questions because my view, I can't see the headings. Yeah, there are no headings here. They are on my UNISA. You should be able to see the actual questions. Which section on my UNISA, sorry? On the assessment. The assessment you wrote. These are the questions from the assessment one that you wrote. Okay. All the questions. All right. Thank you. There might be different types of questions that you got, but they are exactly almost the same. They will be similar. All right. I think the questions are the same. I think the answer is very short. Yeah. Okay. So there are 70 of them. So I was saying in the exam because you don't have all the time to go and create a pie chart and do all of them. I would suggest what you do is you look at or you count how many, either the blended and the four day. Maybe the easiest one is to count the office. So because if these are the only values I see here, so office, they are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So you will take 10 divided by 70. So depending on the data that you got, so this will be office. And you can also do the, let's do the remote 1, 2, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. So remote, they are 20 divided by 70. So you just need to go and calculate that. Maybe we can also do four days. I think four days it will be the same. Oh, sorry. Remote they are. I didn't see this one. Sorry. They are 21. 21 remote. I didn't see the last one there. 3, 4, 6, 8, 10, 12, 14, 16, 18, 20. Four days. 20 divided by 70. So what is 10 divided by 70? It's 0.143. 0.143. I'm just going to keep for two decimals. And the remote. Remote is going to be 0.286. 0.286, which is 29. And four days. No, no, no. Listen, hold on. You said the remote is 21, right? It's 0.3, sorry. 0.3. Yeah. And then a four day, it's 0.286. 0.286, which is 29. So we have office and remote and four day. And the blended one. So we can look at this. So we're looking for office. 14%. So this one says 17%. This one, they didn't have a value there. And wait, I just need to remember that. Remote is 30. That one says 32. So it cannot be 14%, which is what we got. And remote is 30. That's what we got. 14.30 and 29 for four days. And that says 26. Oh, and this one we can't even see the picture. This one we are able to see. 14 is correct. 30 is correct. So now we can go and calculate blended. So if office is 14, four day is 29. And remote is 30. You can just say 1 minus or 100 minus 14 minus 30 minus 29. What do you get? You get 27. Which is probably number D. Because this is the option that is correct. So blended two, four, six, eight, 10, 12, 14, 16, 18, 19. So if you take 19 divided by 71, what do you get? 0.267. 0.277. So we have 14, 80, 29, and 27. So probably this one that is hidden here because blended is 27% 14. So which one was that? Number D would have been the correct one. Because I can't see this is hidden. You can see that this is the graph that is hidden. And the rest of them do not have the values. So we know that this is incorrect. That is incorrect. And that is incorrect. That is incorrect. And that is also incorrect. So the only graph that would have been correct is this one. And it also relates to the answer that we got here, even though they didn't put the one for you, which is 29%. So D is the correct one. So that's how you would have answered this question by just identifying or calculating your percentages and then come and look at the graph. Otherwise, you could have taken these values, put it in Excel spreadsheet and created the pie chart. But it's going to take you forever to do that. You just count the number of office, calculate the total, the percentage. Okay. So moving on to question number six. What was the statement on question six? The data below shows the daily electricity consumption in kilowatt hours for 50 randomly selected households. Use 15 as the lower class limit of the first class to construct a histogram for daily electricity consumption with six classes. So you need to use 15 as your lower your lower class boundary. Is that what they said? Yes. Now, what they expect you is to create an interval. But here the question say what with x as the lower class limit of the fourth, what is the relative frequency of the class x238? Did they give you what is the midpoint or anything like that? What other number did they give you in the statement that will help you to create the class boundaries? Because if 15 is your lower class boundary, there should be another value, the upper class boundary and we need the other ones. We need those two values because this will be x because it says if it's the fourth plus limit x of 38, we need to be able to create a class interval. So did they give you another value? How big is the class width? They don't give you any other information. It only says 50 so it's selected from 50 and then they also say consumption with six classes. That's the only information. Okay, so if it's consumption with six classes, then we need to know what is the range of the data. So is the data sorted? Let's look at it. 16, 18, 20, 25, 23, 24, 24, 25, 25. So it looks like it is in order, ascending order. So in order for us to create, we need to find the range of the data to create the class intervals, right? So we know that we need to create six class intervals. So in order for us to create this class intervals, so we need 46, we need to calculate the range which is 46 minus 16. What is 46 minus 16? 30. It's 30 and we divide that by six. That will tell us how big the class interval will be. So it will give us the width, which is five. So if your lower class interval is 15, so say 15 plus five is 20. And this will be 20 to 25. And because now where does 38 goes in if it's five? 15 plus, so they said the lower boundary should start at 15, right? And if that is five, so 15, or maybe it's 21. So let's see. But 21 minus 15 will give us six. It will not give us, then I won't know how to get there. So this would be 20, 20 to 25, 25, 20 to 30, and 30 to 40, and 40, 30 to 35. But that doesn't get to four. One, two, three, four. Am I calculating right here? Help out with maths. Less for this question. They made a mistake with that 38. So if the class width is five, so 15 plus five will give us the upper limit, which would be 20. Because the difference between the two should give us the class width. And from 20 to 25, 25 to 30, 30 to 35, which doesn't take us to the fourth class limit, with x as the lower class limit of the fourth. Because then if the fourth class limit is 38, and that is 38, they're asking what will be the relative frequency of that class. So it means we now need to count how many falls within each and every one of them. So if this is between 30 and 38, then it would make sense to count from 30 to 38. But it cannot be 30, because 30 will end at 35. Unless for this question, there was an error on this one. I'm not convinced. So let's just see. Let's assume that they start from 30 to 38. So then it means it will include everything except 38. So they are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. There will be 23 divided by how many there are. 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 25, 25, 25, 25, 25, 25, divide by 50. What do you get? Sorry, as you said, 23 divided by 50. Yes. 0,46. 0,46. You see, it's not going to be any of those. So unless we can use this to our advantage. Let's take, yes. You said the data is 50. Isn't it not 40? 5, 10, 15, 25, 25, 25, 40, 45, 50. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1, 2, 3, 4, 5 in each. You see, because if you're looking on your site, it might be different. Your data from your site might be different to this one, right? Your data might be different from this one that I'm using. So everyone would have received the different, almost different data sets. I want to go back. Instead of starting from 15, I want to use the 38 and add or subtract 5 so that we can get, because if our class width is 5, we can just say our x will start from 38 minus 5. What do you get? You can use that. So, with our range of 46 minus 16, our width will be 30 divided by 6 plus width, which is 5. Therefore, it means in order for us to find this class width, what is the lower limit of 5? Sorry, lower limit for x, it means we're going to have to use that 5. So, we just say it will be from 33 to 33 to 38. So, it should not include, either it does not include 38 or it does not include 33. Let's assume that it does not include 38. So, if it doesn't include 38, then it will be all those values. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. So, it will be 13 divided by 50. What do you get? 0.26. 0.26. That is, if it starts from 33, but does not include 38, and that answer is not one of them. If it starts from 34 and includes 38, then we start from 34 counting 1, 2, 3, 4, 5, 6, 7, 8, 9. So, we need to include 38, which they are 9. So, it will be 9 divided by 9 divided by 50. What do you get? 0.18. 0.18. 0.18. Which also is not any of these questions or any of these answers. The last hope, which is not the correct way of doing the frequency distribution, included from 33 up until 38. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 14. 14 divided by 50. 0.28. Which is actually incorrect, right? Because when we talk about class interval, because when one class starts, the other one should finish. When the other one finish, the other one immediately starts. So, it should be an open and a close or a close and an open. So, if it does not include that number, which is what we did here, it does not include 33. So, that will be 33 to 38, because it has to include 38. This one includes 33, but it doesn't include 38. On this one, which we just calculated now, then it's a square bracket. It says it is from 33 up to 38. Therefore, it means the next interval cannot start at 38. It will have to start at 39. Then there are missing gaps. The 0.5 missing gaps between those two values. It should always start and end with the previous interval as well. So, the answer here, they have it as option C. That's them, but it's incorrect. Very incorrect. Lizzie? Yes. Lizzie? Yes. Okay. So, I don't remember the class I just have the answers where I was writing for my assignment, right? And then it was the same data set. I don't remember what then I had in my class, and then I had it from 33 to 39. So, then if you're doing 33 as the fourth class, it will be that 14 divided by 50, and then it will be 0, come up to 8. Yeah. So, unless on this one that they gave a preview on, yeah, the answer was 6. Yeah. Yeah. Lizzie, I was also confused because the way you teach us this. I calculated my relative frequency, and the answer was different. So, that's why I was wondering about this question. I was always asking myself which one is the correct one, because I got a different answer, but anyways. Yeah. So, you can go with 0.28. Yeah. In terms of this question, probably I am 100% sure that there is an error on this question. It might have worked with other questions, but in terms of this one, it doesn't work, because if your class width is 38, sub-direct 5, it will end up with 33. So, it cannot be any big, and also you can see in terms of the brackets that they used, they should be using the correct brackets, like open brackets and closed brackets, so that it reflects in terms of where you need to start and where you need to end as well, and because it is intervals plus intervals. The next class interval needs to start where the previous one ended. They should always overlap, because it's not a pie chart or a pie chart. Okay. So, question 7. Consider a sample size of N17 in an ordered area of observation. Which one of the following statement best describes how to determine the quartiles of the sample? How to determine the quartiles of a sample? Okay. Number A, the first quartile is given by observation 5. B, the third quartile is given by observation 13. C, the first quartile is calculated as an average between observation 5 and 6. D, the third quartile is calculated as an average between observation 13 and 14. E, the second quartile is given by observation 8. Now, you might think that, oh no, I don't know how to answer this. All what they want to see is, do you know your quartiles? So, you need to know they've given you your N. You need to know that quartile 1, you calculated using N plus 1 divided by 4. Do you get 5? It's 4.5. So, which means you're going to say 718 plus 1 divided by 4, which gives you 4.5. You also need to know that it's 3 times N plus 1 divided by 4, which is 17 plus 1. Right. What is quartile 3? 13.5. 13.5. 13.5. And, okay, let's jump the others. Let's go to E. E says quartile 2 is given by N plus 1 divided by 2. So, it's 17 plus 1 divided by 2. 9. So, we can see that A, B, and E are not the right one. So, now, if we have 17 observations, right, and looking at the answers that we have, we'll see, be correct, because C says it lies between observation 5 and 6. Will it lie between observation 5 and 6? It lies between observation 4 and 5, right? Not 5 and 6. It should be 4 and 5. And D, it says it lies between observation 13 and 14. It is correct. Somebody makes me echo myself. Thank you. I'll play it there. Okay. Probably you would have been given a table I don't have. Can you see? So, I would know how to calculate this. Oh, which is very awkward now. Calculate the three measures of location and choose the best answer for the list of options provided. So, I don't have that question on here. Okay. Can I call the values? Or maybe I was skipping. Okay. You can talk. How many values are there? It's one, two, three, four, five, six, seven, eight, nine. Nine? I see nine values. There are nine. Yes. Okay. So, call out the values. It might be that they are not here, but let's call out the values. 33, 34, 33, 33, 32. No, they are actually 10. They are 10. Oh, that means my laptop can't open everything. Okay. 32 again. 32, 34. That's what I see on my screen. One, two, three, four, five, six, seven, eight, nine. But then now, if you all have 33, 33, then the answer won't be any of my ones. So, someone who had like something, the data set with 20 something would be able to see the data, but nevertheless, let's use the data that we have. We won't find the answer, but just for demonstration purpose in terms of how you answer the question. So, the first question. Yes. We have 33 again after 34. Okay. Like I was explaining, you can clearly see that this data set that they provided me now does not correspond to the answers that we have. Yes. So, I won't get the same answer. So, you will have to give us the answers. For demonstration purpose, the first point is to calculate the mean. So, the mean, you can use your calculator or... I was listening. Yes. So, I was listening. Yes. I wonder where those 32 numbers are coming from, but from what I have, it is actually numbers. Wait. Remember, every student had different data sets. So, the data set that another student has might be different to the data set that you got. So, everyone would have had a different data set. So, 10 of you might have the same data set. I would have had the different data set to you and that other people might also have different data set. Understood. Yes. Okay. Under my data set, Lizzie, I've calculated using the state mode, and then I put all the data on my calculator and then my mean is 32.888, when I round it off, it's going to be 32.9. Yes. Okay. Just hold on to that. So, the mean is the sum of all observations divided by how many they are. So, those who don't know how to use the state mode, you will have to go and calculate these things manually. And manually, I mean, you will go and say 33 plus 34 plus 33. So, someone can continue and do that. And until you get to 33 and divide by how many they are, you count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And you will get the answer. 32.9. 32.9. Oh, alternatively, you can go and use your calculator and put your calculator to state mode. And once you have your calculator to state mode, use capture the data and then you calculate your mean, depending on whether you're using a case or you're using a sharp calculator. But you need to go and practice how to use your calculator to do that. So, that is how you will find the mean. What is the median? To find the median, you first need to order your data, sort your data first. So, it means you need to rewrite all these data sets. 1, 2, 3, 4, 5. 1, 2, 3, 4, 5. Actually, there is 32, 32, 32, there is 32. 32. And 32. 1, 2, 3, 4, 5, 6, 7, 8. 1, 2, 1, 2, 3, 4, 5, 6, 7, 8. And then there is 34, 34. 34, 34. Then you need to go and find the position. There are 10 plus 1 divided by 2, which is 11 divided by 2. What is 11 divided by 2? It's 5.5, right? Yes. So, then you go and count. 5.5 will be located between two values. 1, 2, 3, 4, 5.5 is between 33 and 33. 33 and 33 are the same as 33 plus 33 divided by 2, which will give you 33 as your median. So, the last one. And the mode is? Yes. So, from the data set that we have, the mode would have been? 33. 33. And that's how you would have answered the question. So, you will have to look at your data set and do the same, apply the same concept or the same process to your data set in order to find which one is the correct answer. So, I can answer that question. And the next one, also my data is cut off, so I can see anything. This is so useless because we can't do revision like this. I hope the other exam papers are different. Nope, they are not. This is not going to work in a way. Okay, some of them. Sorry, Liz. Can you not go on to the my UNICEF and see from the assessment, you won't be able to access that? Let's see. If I'm able to access it, remember I don't have the same, because I don't write the assignment. So, I might not be able to see the assignment. Just to give me a second. Oh, Liz, if you can see your data, even though it's different from us, I think it's best if we can discuss it, work it out, so that we can have a view of what we got wrong, things like that, even though the data won't correspond. I think it's best to do it. To do it that way. Let me see if I'm able to access my UNICEF. Sometimes I get locked out of my UNICEF, so it might take a little bit of time. I should have checked the questions before, the questions, but we're trying to find in. If you are not trying to find in, press zero and pound. Can't find you in at this time. Please try again later. What? Unfortunately, I cannot see the questions. You are able to see the questions because you took the exit. Liz, if you can just go back to the question, and then maybe we can see from the multiple choice answers, which is the data sets. Maybe that can help as well. Lizzie? Or somebody can share their screen and show the assessment questions from all end. Yeah, but all the questions are not the same. My assignment opens. I have my assignment open. I can quickly take a picture and send it on the WhatsApp group. If that will help, it will be different, but same question. Let's see. Are you able to share your screen? The challenge is when someone else is sharing their screen, I cannot demonstrate. I cannot write. That's the only problem we have right now with these questions that we have here. Because we can't see the full questions, which makes it difficult to respond to this. We can always, if the data is not too many, someone can always call out the data and then or post it on the charge. If you go to question 10, it says once again, consider, so I just want to see maybe that also the question papers that you have. Maybe it says once again again as well, because in question 10, it says once again, consider the sample and then it's given there. So just check. Yeah, but you see on my question nine, which is where we are at, the data is cut off. I can't see whether was the table had 10 other rules or is this okay? Yeah, I can go to question 10. It gives you the data set again, the same thing. Lizzie, can you hear me? Okay, so I see. Yes, okay, this helps. So nine and 10 are like the same data set according to what I'm seeing on my side as well. But I know the questions will be different, but the data set is the same. I'm also going to assume that. So let's use this data set to answer question nine. So question nine says what is the value of the sum of your Xi squared? So you can use, actually, let me stop my and start sharing again. I'd share my entire screen because I want to use the calculators. So we need to find the sum of our Xi. So the short way to use your calculator is to capture the data in your state mode, right? So you go mode, if you have a casual mode, step one, because it's only one var, and then you capture all the data set by say 29 equal 30 equal 31 equal, 33 equal, 34 equal, 33 equal, 33 equal, 33 equal, That's too many, thirty-three. Forty-six. Equal, thirty-eight. Equal, thirty-five. Equal, thirty-six. Equal, and thirty-four. Equal, and they should be fifteen, thirty-six, nine, twelve, fifteen. So once you have captured your data to answer the question, it just needs the sum of your x squared. That's what the question was asking. Even though they give you the summation of where i starts from n to i to n, it's just asking you to find the sum of the x squared. So to do that, once you have captured your data, you can go on and off your calculator and go back to that and you're going to use the summation three. And there is your sum of x squared. If I press one, I should get the answer of seventeen, three, three, seventeen, three, seven, three. If you don't want to use your calculator in state mode to answer this question, all you need to do is square all the values. You will square all the values and add all of them up. That's all what you do, and then you add all of them, and that will give you your answer. It will be the same. Those who are using the k-sure, we can do the same, because this is the same as twenty-nine squared plus thirty squared plus thirty-one squared plus up until you get to thirty-four squared. And that should give you the same answer. If you are using a k-sure calculator or a sharp calculator or a financial math calculator or financial calculator, you will follow the same mode. You put your calculator to state mode by pressing one, and we use the first one, the SD for zero, because we want it to state zero. And then you start capturing your data. Twenty-nine, and you will press enter or M plus. In this instance, thirty M plus, thirty-one M plus, thirty-one M plus, thirty-one M plus, or enter, thirty-three M plus, thirty-four M plus, thirty-three M plus, thirty-three M plus. Forty-six M plus, thirty-eight M plus, thirty-five M plus, thirty-six M plus, and thirty-four M plus. And there will be fifteen data sets. With a k-sure, sorry, with a sharp calculator, it's easy. You press the on and off. The summations are just written in green, and we're going to use this plus or minus. The plus or minus, that's where the x squared is at. So you're going to press the alpha button and press the plus or minus and press the equal side. As you can see that we get the same answer, so you will see that the correct answer is option A. That is easy as it is. Now, answering question ten, you need to know how to calculate the coefficient of variation. Coefficient of variation is your standard deviation over the sample size. So since it uses the same data set, those who are using the sharp calculator easy, your sample standard deviation is five divided by four. So you just say alpha five divided by alpha four. You can see that it is your standard deviation divided by the mean, and you press equal. And that will be equals to 0.12, but remember the coefficient of variation. What I forgot to do here is multiply by a hundred. It's always multiplied by a hundred. And it is 12.6, 12.16, which is option A. Those who are using the casio, the same thing, shift, start. We're going to use var, which is on button number four. We're going to also use four, and you're going to say divide by, and we go back shift. But for var, and the mean is two, and you can see they send and you press the equal side. And also remember multiply that by a hundred. And that is 12.16, which is option A. You need to practice using your calculator because it will save you time as you can see. Even in the exam, it will save you a whole lot of time. But you need to practice. You cannot practice a day before you go write the exam and expect to know how to use your calculator. And when you capture the data, you must also pay attention to the details. Okay, so that is question 10. And so it's 12 points. When I sent the document, let me see. Do you want me to keep all the notes so that I don't delete them? Otherwise I'll post the original. So question 11. I also don't see the data set. Let's see if the bottom one has the data. No data. Okay, someone must help us with the data then. So that some people were able to post. So can someone just post it on the chat? We will use that data set. For question, question 11. Don't post it on WhatsApp because I'm not going to go onto WhatsApp because I'm sharing my entire script. Just post it on the chat. Oh, thank you. Someone already did. Just give me some chance because then I need to be able to write on it. So we know that we are given the data set. She's this data set and we need to find which one of the following statement about the empirical rule or the distribution of the education graduates that in salaries is correct. He calculated the three measures of location to comment on the distribution. So remember the three measures of location that they're talking about is the mean, the median and the mode. So we need to also do the same. So what is the mean? What is the median? And what is the mode? But also not, oh, sorry, on this one. So the questions are actually different because on this one, it says, oh, they are the same. Calculate the measures of the location and comment on the distribution and the standard deviation. And the standard deviation on the empirical rule. So we need to do all that. The mean, the median and then the standard deviation. So it means once you have calculated the standard deviation, then we can do one standard deviation, which is the mean plus or minus. So actually we can do the plus, but it's fine. One standard deviation or two standard deviation, which we're going to use the S instead of minus. Then once two standard deviation in plus or minus, three standard deviation. So this is two standard deviation and this is three standard deviation. So capture the data and calculate the mean. I'm not sure how relevant the median and the mode would be in answering the question. The median and the mean will help us determine whether are they skewed positively or negatively skewed. But it's fine. Have you captured the data set? I'm going to capture it. 29, 235, 135, 250, 135, 250, 140, 250, 145, 266. Move it to the other side. 192, 281, 197 and 301, 235 and 303. 246, 812, 1416, 16 records are recorded. Let's calculate the mean. The mean shift set for the mean is two equals 213.35. I can multiply that by 1000. And that would give us, multiply that by 1000. We'll give us the mean of 200 and we should just put 75. So this is the same as 213.375. And the median, we need to order the data in ascending order. And I can see that it is in ascending order. We need to find the position. So there are 16 plus 1 divided by 2, which is 17 divided by 2, which is 8.5 position. 12345678.5 will be between 235 and 235, which means the median is 235,000. The mode is the number that appears more than the other numbers. Is there a number that appears more than the other numbers? 250 looks like it's 250. It's 250,000 because the data set is in 1000, right? The standard deviation, we go back to our calculator and calculate our standard deviation, which is 1, 4. And our standard deviation is 4, is 65, and we need to multiply that by 1000. That's 1,065403.24. Now calculating the one standard deviation. I just want to go. So you can calculate it manually or you can calculate it using your calculator. So I already have the data on the calculator so we can do this. So the first one we can say is your mean, which is shift step bar 4, your mean, which is 2, minus. We're going to start first with the minus 1, right? Times the standard deviation of 1, so minus, the standard deviation will be shift step 4, 4. And that is, and we can multiply the answer with 1000 for 127. Can you mute someone? The child is screaming in the background. Can you please mute yourself? Are you able to hear me now? Yes. So the first one is 147, 971, 1, 4, 7, 971. And it is between, and then we go into this second one, which is the mean plus the one standard deviation would be equals and multiply the answer by... As if we can't see the screen. 1000. Are you sure you can't see my screen? No, we can just see your profile picture. Maybe his phone has a problem because I can see your screen. Me too. And you can see when I move the calculator around, right? Yes, as if you can see that. Okay. 278, 7, 7, 8, 278, 7, 7, 8. And then we do the same with the two standard deviations. So it will be shift step 4, 2, minus 2 times. I'm going to put it in the bracket. Shift step 4, 4. Close bracket because I'm multiplying with two standard deviation equals. Multiply that by 100. It's 1000, which is 8, 5, 8, 2, 5, 6, 8. 8, 2, 5, 6, 8. And then we're going to do the plus sign, which is 2, plus 2 times the standard deviation. Shift step 4, and 4, and close bracket. Multiply that by 1000. 3, 3, 3, 4, 4, 1, 8, 1. So we don't have the answer as yet, but you get the, you understand what I'm trying to get, right? So we don't have the answer as yet. Oh, because my, my data set is different to this one that I'm using. So I should not expect to find the answer yet. I should not expect to find the answer exactly the answer on the, on this exercise that we're doing because the data set that we are using is different to the one that was given to me. Okay, so we calculate the three standard deviation. You do the same. You will calculate. You don't have to go through this. You can use the mean and the standard deviation. We have them, right? You can calculate them manually. Okay. I find, yeah. I find 17165. Three standard deviation will be. I found 17165. 17165. 17165. 17165. And the plus sign thousand. 409584. And 409584. So once you have calculated all these values. Then you can then go and answer your questions. Oh, come on. This thing. The one I minimize. So once you have. Oh, come on. It happens when you work with multiple things on your screen. Okay. But, but this is the third one. I got it. If you can hear me. Yeah. I can hear you. So depending. Yes. Depending on. The data set that you have. So this is how you would have answered this question. You would have went and calculated your mean, your median and the mode so that you are able to find out because the data set that we are using. Doesn't answer this question that we have right now in front of us. Because we have in different data sets. So the mean and the mode will help you find out if your distribution is symmetric or is positively skewed. Remember that symmetric means the mean and the median are equal in the, in terms of this, the mean and the median are not equal. So it cannot be symmetric. Positive will mean that your mean is bigger than your median. So in this instance, your mean is less than your median. So it is negatively skewed. So it's also not correct. And then you go and find your empirical route, which one standard deviation accounts for 68%. Okay. Because yeah, I used one standard deviation to standard deviation, but you also need to remember that one standard deviation accounts for 68%. Standard deviations accounts for 95% and three standard deviation accounts for 99% of your data set. So based on that, you should be able to answer the question. So come on. So one of those statements should be applicable to any of those options based on the data that you have. And you should be able to say which one is the correct one. Okay. So that is question 11 question 12. So in this question, based on the data that they had, the answer would have been option. But because we don't have this data set, I cannot check it. And also the bottom one, I will need the data for this. If I was a magician, I would be able to read and make out all these numbers. Because this looks like 300, 310, 380, 332. I'm not sure whether this one can be 301 or 310. Yeah, it looks like 301, 330, 300. This looks like an eight. I don't know. I can't make out these numbers. And this looks like four. And this looks like 300, 310, 380, 312, 351, and 358, 381. Okay. So it was easy to do. So yeah, they asked you. Are there data as well on top? Yes, there's data on the top as well. The first row is missing. This is the bottom row that you read out now. Okay, so give me the top row of the same data that we have here. The one who was helping me read out this. Okay, it's 180. 196, 257, 264, 266. 275, 283, and 300. Thank you. Thank you. So it's because the data is already sorted. So we don't have to do anything. And yeah, it says we need to find the lower limit of the box plot. Remember, a box plot looks like this way. You have your minimum, your maximum, and you have your quarter one, which is your lower limit, and your quarter three, which is your upper limit, and your quarter two in the middle. So if they are looking for the lower limit, they are asking you to find quarter one. So we need to find the position of quarter one, which is n plus one divided by four. How many are there? Two, four, six, eight, 10, 12, 14, 16. They are 16. So it's 16 plus one divided by four. What is the answer? 4.25. 4.25. Therefore, it means we're going to estimate it and say it is on position four. So we just count one, two, three, four. And the answer will be F. But there they have the answer is 1.33. Are you sure this answer is this data set? Okay. Maybe I'm going to assume that the data set as well. Hi, Lizzie. It's different. Yes. It's safe. The answer. Pardon? You are muted. Hello, Lizzie. Yes. The data set, even on my assignment, even on the assignment, I answered F and I got it wrong. And then now when I check the feedback says the answer, it's 1.33.5. So I don't know where I got it wrong or how it happened. But the data set is... I guess probably these options, and the option that you are given was using a different data set than the one that we have. So I know that there were some issues with some of the questions, especially with assignment one. A lot of students were also complaining. Because how can you get the lower limit of 1.33 if your data set starts at 180? So we just need to check that the data set is the same for that. Anyway, the lower limit would have been 264 in terms of this question. So you will notice that this correct answer there would not be applicable. But it will also depend on the data set that you are using. Okay. So moving on to, I think, almost the last question. And I can also see what the question was all about. Question they did. Which measure of dispersion is not affected by the outlier? So here we're talking about measures of dispersion. Remember, it's your measures of variation, which is the range, the standard deviation, the variance, the interquartals, and so on. Is it A? The thing because I can't see what the other things are with that. So I will choose A as well because even if you have the outliers, your interquartal range won't change. You won't be affected by those outliers because it looks at quartile one value and quartile three value. It doesn't look at your range of your data set. Only concentrate on the box on this, not on the extent of your box. So A will be the correct answer. But based on, because I can't see other options that we have. So if I have only two options, A and B. A, B is the measure of locality or location. Okay, so that is your study unit. One, two, and three. I'm going to stop there. Sorry, Lizzie. Before you stop, can we go back to question 12 and switch it to upper limit, please, if it's possible. Question, is this the question 12? The one about the lower limit, can we switch it to upper limit? Upper limit is quartile three. So you will use the position n plus one, three times n plus one, divide by four, which will be three times 16 plus one, divide by four. What do you get? 12.75. Yeah, 12.75. So it will be 12.75. And we're going to estimate this to say it falls on position 13. And then you're just going to count. One, two, three, four, five, six, seven, eight, nine, 30, seven, 12, 13. Then your answer will be 351. For upper limit. So Lizzie, this question, we round off. So we don't take the 12. We say it becomes, because it says 12.75, we say it's recounted as 13. Yeah, so when we look at the quartiles, if it is 0.25, you round down. When it is 0.75, you round up. When it is 0.5, you take the average. Yes. Hi, Lizzie. Yes. Yeah, on my assignment, they were looking for the upper limit for the box plot. And I calculated the quartile tree. I got the positions. And then after that, I wrote the answer down. But they wronged me. Thank you. Like I said, this question has some errors there. We can always pick it up. Because if this was the data search, and you can see that the answer is 1.33 in terms of what they gave. But the answer is B. 264. That is 4. If this data set was the same. So yeah. I saw we can say that the exams are a little bit wrong. That's because we thought it was a problem. I hope so as well. OK, so let's stop this one. Let's stop the unit 4. We're not going to get all the study units in one day. Because it's half past five. I'm even. OK, maybe we should stop today's session here. And then we will have next week to do the other assessments. OK, Lizzie. Lizzie, question. Would it be possible if we can do something maybe. You can see how long it takes just to finish one assessment. If it will be possible for us maybe during the week to make time to actually do maybe the second one. And then it's just a suggestion. I'm not sure. Yeah, let's close off this session. And then we will have that discussion. Because anyway, we booked the session up until 6. So we can have that discussion. Let's stop there, Connie.