 Like I said, welcome to your second session. Today, we're going to still continue with question and answers based on study unit 1, 2, and 3. Remember, these sessions are not content-related sessions. We're not going to cover a whole lot of content. We're just going to look at questions and then answer them, and then also look at ways in which you can target questions when you are asked to answer those questions and how do you answer them as well. In terms of theory, please go through the recordings that I have posted on my UNISA. I'm going to call it my UNISA because that is what I'm still in my mind. So please go through my UNISA or my module. Let's call it my module. On your my module or module platform, because there is a whole lot of information we already posted there, a whole lot of information that can help you understand some of the content. Also, please make sure that you are free to ask any question that you have. I am here, and your teammates are here, or your other fellow students are here as well to help you unpack some of this content or concepts if you don't understand them. Please make sure that you use all the platforms. We also have the WhatsApp group. Make sure that I saw that before the session today, you guys were active on there. It's good that you are active on there, but also don't forget to also be active on my module as well. Being active on my module helps you to get the feel and understanding of the platform as well because that's the platform that you're going to use to write your exam as well. So you need to make sure that at least you spend most of the time there practicing and looking at things and seeing how the platform works as well. Okay, so enough with the intro. Are there any questions before we start with today's session? Go in once, go in twice, and we are off. We are now plan B up. So I'm not going to go through the same content. We already discussed this. We did some summary in terms of study unit one. You still need to remember all this. They are still relevant for today's discussion. We're going to continue looking at some of the questions, but there are not a lot of questions that will come from this because I think we covered them enough for one and a half hour last week. We're going to also not cover a lot in terms of study unit two, which is how you visualize or how you put numerical data or categorical data into graphs. However, because study unit two and study unit three, sometimes they are linked. Some of the questions might be asked on the same information, about the same information. So we're going to have a lot of questions that overlaps between study unit two and study unit three. But you still need to remember that study unit two is about visualization and you remember that you need to always remember the properties of each and every one of the visualization or the graph or even if it's a table, you need to remember the properties of those. And then we're going to look at study unit three and in terms of study unit three. Last week we didn't cover almost no question was asked last week in terms in relation to this unit. So that is why this week we're going to concentrate more on central tendency, variation, empirical rule and quotas. So without wasting any time, let's get to it. The first question, and remember as well, this is not about me, it's about us. Let's have the discussions. Some of the question in the beginning because it's just one question, you don't have to do any calculation. We're going to go through the slides as quickly as possible. So I will expect to ask a question and then someone needs to respond. We don't have to wait and think about it. Someone needs to explain and if it's not correct then we can state why that question is not or why that answer is not the one that we are looking for and then someone can give the correct answer and then we move on so that we can go through the slides. I've got about 32 questions that I want us to go through today. But if we don't finish all of them, no problem. You can still go through them on your own time and we can have the discussion on WhatsApp. Remember all these questions are there to help you understand the module better, not only for the assignments, but making sure that even when we get to go and write the exam in November, remember now you're going to be writing in November, you can still remember some of these things because we're also building up as we move along every chapter, every section. Okay, so the first exercise for today is the easy one. The question is asking the two graphical techniques that can be used to represent nominal data are. Do you know what the answer is? Is it number one, number two, number three, number four, number five? Number three? It is number three, it is just only a bar chat and a pie chat that can represent nominal data because nominal data are categorical data. And then exercise two, consider the following score and you are given the score, the outliner or the outlier score is, what is an outlier? Option five. Remember that's very far from everything else. The number that is far from everything else. So what is that number that is far from everything else? Stating. It's stating, so therefore it will be number five. So now by now you should already have realized how I asked you the question and looked at some of the items within the question to identify the meaning of that so that it can help me answer the question. And that is what I want you. Every time we look at the question, you go into read the question and then look at what you are given and then look at the key terms that are given or identify the important facts that are given. If it's something that you need to clarify in your mind for yourself, like for example, an outlier, what is it? Then you clarify it and then you go and answer the question. So I want you to get that into your practice every time you read the question. Don't jump into doing something as well, right? Even if you know the answer, but try and think of ways to figure out what the question is asking and identify key items within that question. Okay, let's look at exercise three. It says, given the following symbol, we have A mu B S C X bar and D sigma. Identify the symbols that represent a parameter as a measure of a population, right? They give us also what a parameter is, it's a measure from the population. So from A, B, C and D, so tell me what is A? Mu. So you answer the A is? Mu. Yeah, it's mu, but what does it stand for? What does mu stand for? The symbol is mu, but it stands for the mean, right? I'm not gonna give it, whether it's a population or a sample, but it stands for the mean and S, what is S? S is standard deviation. S is standard deviation, yes. Standard deviation. Yes, and X bar? It's a, X bar, it's a median. Nope, X bar. No, no, no, no, it's more good, I mean. No, X bar, X bar is? It's a mean, it's the mean. And sigma? It's variance, no, it's variance, it's variance. No, sigma? Standard deviation again. It's a standard deviation. Now we have two means and two standard deviation here. We already know what those symbols stands for, but every symbol stands for the mean or the standard deviation based on whether it's collected from or it's calculated from a sample or it's calculated from a population. So number A, is that calculated from a population or from a sample? Sample. Sample. Nope, A is calculated from? Population. Population. So let's remember population uses Greek letters, right? So this one, it's called the population mean. And S, is it calculated from a population or a sample? A sample. It's calculated from a sample. So this S refers to sample standard deviation. And X bar? Sample. It's a sample mean. And sigma? It will be population standard deviation. So always remember that, that the Greek letters, they represent population and the alphabet letters that we know, the standard alphabets represent a sample. Now, we need to identify symbols that represent a parameter as a measure of a population. A, B, C and D. Which one is the correct one? Number one, number two, number three. A is the correct one. Nope. Number two. Number two. Number two, because we said A is the population mean and D is the population standard deviation. So therefore, number two is the correct one, right? That's how you will find the answers. You first need to understand the symbols and then come in and answer the question based on what you have identified. Okay. The following day, do you have, wait, sorry? Yes? We have a question? Send it in, yeah. Please make sure that you are muted if you are not discussing with us. Okay. Let us manage that. Exercise four, the following data give the starting admission price in rent for one day tickets to the theme park and the numbers are 58, 63, 41, 42 and so forth. Which one of the following statement is incorrect? And they gave us, all the statement, they give us the sample mean and the sample standard deviation. So it means we need to go and calculate the sample mean and the sample standard deviation. Have you looked at how we use the calculator on one of the videos that I shared with you? Because questions like this, you can use your scientific calculator. Otherwise, you need to go and calculate the mean x bar, which is the sum of observation divided by how many they are. And you need to go and calculate your standard deviation, which is your standard deviation. It's given by the square root of your variance, which is the sum of your observed values minus the mean squared divided by n minus one because it's the sample standard deviation. So it means the mean, you will add all of them up and divide by how many they are. They are one, two, three, four, five, six, seven, eight, nine, 10, they are 10. So you will add 58 plus 63 up until you get to plus 40 and divide by 10 and that will give you the mean. The standard deviation, because you've already calculated the mean, you're going to take the value of the mean, subtract every observation and sum it, or every observation from the mean and square the answer, sum them, meaning adding them all up and dividing everything by 10 minus one. So you can follow that. Otherwise, you can use your calculator. I'm going to show you on the calculator and I'm going to stop sharing my screen right now so that I can share my entire screen, sorry. Okay, so that we can save time, sorry. We can save time, don't worry, I'll go back. I just want to go back to my, okay. So I'm going to start first by showing you on a cashier calculator. Those who has a cashier calculator, I'm going to hide all of this and only show the values. So in order for you to calculate this information on your calculator, you're going to have to put your calculator to a state mode function. So you press the mode and then you press two for state and then you're going to press one for one minus var. The two for a plus bx, we will use it when we get to later on, when we get to study unit 11. But for today, we're only going to use one variable, which is one var and we're going to press one. And then we're going to capture the data by putting the value as you see it and pressing equal sign. So I'm going to press 58 equal 63 equal 41 equal 42 equal 29 equal 50 equal 62 equal 43 equal 40 equal 40 equal. I hope I put everything correctly and you were watching what I was doing. So now you have all the data in your calculator, then you press AC button because your data is stored on your calculator. Now I can calculate the mean. Calculating the mean, I need to press the shift button and button number one to reach for the state. So I'm going to press shift, state. And if I want to look at the data again, I can press button number two. If I want to look at the type of data that I have, I can press number one. I'm not looking at those. And if I want to find out my sum of X, I can press button number three. So I'm going to go there and there is your sum of X. So it means it's adding up all these values. So if I divide, I press number two because two corresponds to that summation. So I'll press button number two and I press equal. Therefore I will have, the answer here was 468 divided by 10. And that will give us the mode of 546 comma eight. You can do that manually, but you don't have to because on your calculators, you can also calculate the mean. So if I go back, shift, state, and there is a four var, there is where you will find some of the descriptive statistics. So if I press button number four, there I can see my sample size. If I press one, it will tell me that there are 10 values in this data. My number two, it's your X bar, which is your mean. Number three is your sigma X, which is the population standard deviation. If they told us this data set is for the population, then we will calculate using three to get the population. And what we are looking for is number two and number four because number four is your sample standard deviation. So let's go ahead and press two for the mean, and I should get 46 comma eight. And there is your answer. It will be as quick as possible like that. Now I can go and calculate the standard deviation instead of using the long formula, but sometimes you do need the long formula because sometimes they can ask you what is the sum of X minus X squared? You need to be able to calculate those things, whereas you can't do them on the calculator. So in order for us to do that, you go into press shift again and press stat and go back to four. And then now we're going to press four again for the SX. And when I press equal, then I get my answer of 11.10. So my standard deviation is 11.03. So now I can look here and look for the answer. Which one will be the right answer to choose from? Did I copy the answer correctly? Oh, I didn't copy it right. It's 10, 11.1003. It's 10. So which one is the correct answer? It's option number. One, three. No, option number one says 46. Option number one says 11.01. The answer was 11.03. Option three, oh. Please also, when you're answering questions like this, pay attention to the numbers because you see if you're going to look at the first number that you see and choose that as an option, you might not get it right. So with multiple choice questions, it's always good that you evaluate all the statements before you state which one is your final answer. Maybe verify all of them again and see if all of them are incorrect before you finalize your last answer. And this is as you are practicing, as you are doing your assignment, remember your assignment, you get two chances to submit. So the first time you're gonna do all this around one, two, three, four, five and evaluate all of them and then choose the last one. The second time you go, you already know how to calculate some of these things, then you don't have to evaluate all of them. And when you get to the exam as well, you will not have enough time to play around. So you need to make sure that as early as now, you are able to evaluate all the statements and work through all of them and not only take the first one that you see, right? And that will help you a lot. Okay. Exercise five. The ages of a sample of 40 records are shown below on a STEM and LEAF plot. Now, this is a STEM and LEAF plot. We discussed this as part of study unit two. So which one of the following statement is incorrect? The first one, they're asking, what is the smallest age? What is the most age? We're not doing it with the sharp calculator. Oh, sorry. My bad. Okay. You want me to show you with the sharp calculator, sorry. I can show you again with the sharp calculator, my bad. Sorry, I forgot. Thank you for reminding me before I move on. Okay, so let's look at the sharp calculator as well. So if you have a financial calculator or a scientific sharp calculator, on your financial calculator, on this M plus, you have an E and T button, right? So you will use, when I say M plus, you will use E and T, but the steps will follow the same, like on either your financial calculator or the sharp calculator, your calculator will follow the same steps. So first you need to put it to a state mode. So by pressing mode button and then pressing number one for state and number zero for SD. And we're going to, now our calculator is on state mode. Now with a sharp calculator, you will not have a table, but it will tell you that you have captured your data set one, data set two, data set three, up until you get to data set 10. If you capture every one of them and you get to 40 and it says data set eight, it means you skipped something some way. Or if it says data set 11, therefore it means you captured something twice. So you need to be very careful. And then in that case, you will have to start from scratch. And starting from scratch sometimes is just making sure that you just press a second function and CA to clear your calculator from any stored value and then start capturing again. But let's capture this data. So it's 58, M plus ENT for the financial calculator and it says data set one, 63, M plus. You just continue 41, M plus, 42, M plus, 29, M plus, 50, M plus, M plus, 62, M plus, 43, M plus, 40, M plus, 40, M plus. And then it will say, I've got 10 data sets. So with this, I am done capturing the data. It's not on my calculator. I can press the on and off. Now I'm ready to calculate the mean on your shop calculator. It's easy because the mean is on button number four is written in blue or in green. It's X bar on button number five is SX. It's your sample standard deviation on button number six. It's sigma squared. It's your standard deviation for the population and your sum of X, there is your sum of X and your sum of X squared. So if they ask you any questions around those ones. Okay, so now let's calculate the mean. You're going to press alpha first, alpha, and then you press button number four, and then you press the equal sign. And it's 46.8. Same thing, you can calculate your standard deviation, alpha, second number, button number five, and you press equal sign and the 11.10. Now what if they ask you, what is the variance? I forgot to also show you on the cashier, the variance you just press the X squared button, it will give you SX squared, which is your variance, and then you press the equal sign. So that's how you will do it. Also on the cashier, to calculate the variance, you just press the X squared button. It will put the answer squared and you press the equal sign and that will give you the variance. And to get to the standard deviation, you remember, standard deviation is the square root of your variance. So you just press the square root button, the square root of the answer, it will give you back your standard deviation. That is how you use a calculator. But you need to practice these things, you cannot just do them once off and never use them again. You need to find more questions, practice, practice, practice so that you understand the steps and get used to using your calculator. Okay, let's go to question number five. Question number five, estimate leaf plot of 40 workers, we need to find the incorrect question. But first finding the smallest age, the most age, the mode, the range and the median. We're gonna answer all these questions together because then I'm not gonna give you time to go and think about them because then we won't get through all the five slides. So which one of the following statement is incorrect? We're going to evaluate all of them. The smallest age, before we even answer the question, what is the smallest age? First, you need to look at your standard leaf plot and make sure that it is in order. It is an ordered array, it's the median leaf plot, right? Yes, it's in order. Yes, so now let's identify what is the smallest age? 25. The smallest age is 25. The smallest age is 25. Most ages in the sample are greater than 40. True. True. It says most ages in the sample are greater than 40. How do you know that they are greater than 40? I would say it's false. I said true because I calculated the ages of 40, 50, and 60, and this is understanding, yeah. But you don't count the 40. Let's count them, one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 18, 14, 15, 16, 17. Yes. 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. They are 23 below 40. Most ages in the sample are greater than 40. It's false. False. That is false, right? Because we know that most are below 40, right? The mode of the distribution, what is the mode? The mode is the most appearing value. Yes. That's 41. So the most is the most appearing value. Which number appears more than the other values? 41. 41. 41. The range, what is the range? The range is the difference between the largest value minus the smallest value. Okay, so what is our highest value? 61. And what is our smallest value? 25. 25. 25. And what is 61 minus 25? 36. Okay. And the median, they say the median is 38. So we first need to find the position, right? By using n plus one divided by, divided by two. How many are they? They are 40. They told us that they are 40 workers. So it's 40 plus one divided by two. What is 41 divided by two? 20.5. 20.5. So it means it will be between two values. Let's go and see. We need to count one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 18, 14, 15, 16, 17, 18, 19, 20.5. It's between eight and eight. So it will be between 38 and 38 divided by two, which is the same as 38, right? Because 38 plus 38 divided by two, it will still give you 38. So which one of this question is the incorrect one? Number two, option two. And that's how you will evaluate every statement in order to find that one answer. Before you even come and look at the answers, what I didn't do actually, I should have went through the question and answered every one of them. But because I already can see the answers based on what we wrote in red, corresponds to the answers that they gave. And number two is the only one that would be incorrect. I have a question, ma'am. Yep. In exam situation, will we ever have, in a question like this, where you'll have more than one statement that's incorrect or correct? No, then that will be an error. Then it means you are writing your exam paper in an error and you will notice, you will see as we go along because most of the question I'm using come from past exam papers, come from past tutorial letters. There are lots of errors on those ones. We will notice some of them. Please don't take it too hard. I think nowadays, there is a lot of improvement in terms of quality assurance, in terms of the questions asked in your statistics papers as well. But yeah, it might be in rare cases, but if that is the case, then if it gets picked up, the marks will be adjusted, especially even if when you are doing your assignment and there is those kind of cases, the marks will be adjusted. Can I just say, in my first attempt at assignments, there was a question where more than one was correct and I got less marks for choosing a less correct answer, if that makes sense. Yeah, so the other thing I will talk to you at a later stage is around the marks allocated during your assignment because you don't also get full marks. You can also get a half a mark, a quarter of a mark or two marks, three marks, depending on the closest answer you get to. But we will discuss that at a later stage. I don't want it to dilute our session for now, but we will get there. Okay, question six, given the data for a small sample of respondents on the number of hours per week that they spend using email are given below and these are the numbers. Which one of the following statement is incorrect? We need to find the median, we need to find the mean, we need to find the range, we need to find the mode and the interquartal range. So the median, we need to first sort the data. So in order for us to answer that question and this question and probably this question, we need to sort our data. Let's quickly sort the data. We have two, two, we have three, we have zero, sorry. I didn't see zero. What else do we have? It's two, three, zero, two, three, five, six, seven, 11, 15, 25. Thank you. There we go. It's sorted always. Now let's go find the median by finding the position first. How many are they? One, two, three, four, five, six, seven, eight, nine, 10. So 10 plus one divided by two, 11 divided by two. 5.5. 5.5. 5.5. So one, two, three, four, five, 5.5 is between. 5.6, yeah. 5.6 divided by two. 5.5. 5.5. The mean is the sum of all of them. So add all of them and divide by how many they are, or you can go and use your calculator. 7.6. So you were so... I'm getting late. Why am I getting 7.8? You're also getting 7.6. Yeah, no. I'm gonna go to E equal. 5 equal. 25 equal. Zero equal. 15. Yeah, 7.6. E equal, two equal. Seven equal. Six. 11. Equal. Close, shift stat, four. Mean is two. E equal, 7.6. There we go. Absolutely. Absolutely. So I'm just playing with the calculator so that you get more chance to look at how we do with your calculator. The range, the highest, minus lowest, which is 25 minus zero, which is 25, right? Which is correct. The mode, which one appears more than the others? Two. Two. Two. Interquartile range. Now with interquartile range, there are a couple of things that you need to do. I'm gonna say this thing now because then later on we're gonna be looking at questions relating to quartiles. So we need to first find the quartile one, which is n plus one divided by four, the position, which will be 10 plus one divided by four. 11 divided by four. 2.75. 2.75, and if it's 2.75, we estimate that this is the response is on position three. So position three is on one, two, three. It's two, right? So our Q one is equals to two. We also need to find Q three. And Q three is three times Q one, which is n plus one divided by four. So it's three times 10 plus one divided by four, which is 11 times three, which is 33 divided by four. What is 33? 8.25. 8.25, yeah. 8.25. 8.25, we're going to round it down and we say it's on position eight. And therefore our Q three is? 11. One, two, three, four, five, six. Yo, I'm counting on the wrong one. One, two, three, four, five, six. 11. Eight, it's 11. Yes. Oh yeah, why am I putting 18? 11. So therefore our interquartile range IQR is given by Q three minus Q one, not the position, but the value. So which is? 11 minus two, which is equals to? Nine. Which is correct. So some of the things at the moment while you are practicing, it will take you longer to get to the answer, but we could have stopped the inner exam. You will get number one as your answer and go with that. But now while you are doing your assignment, make sure that you go through all the statements. They help you to learn as well because you learn as you do the activities, some of these things. Okay. Let's go to seven. Seven asked, consider the following data set. There they gave you the data set, not in order. Oh, sorry, before you proceed, can you just go back to the previous question? Just that. So interquartile range, 11 minus two. Why are we doing two? Are we not using? Okay. We use the values, not the positions, right? Yes, okay. I'm sorted. Thank you. Consider the following statements. Which one is incorrect? Incorrect. It says we need to find the median, the first quartile, third quartile, the mean, and we need to state whether is it symmetrical. So the median, we need to first sort the data. Let's sort it. So the smallest bit, yes? Four, three, four, six, seven, nine, 10, 14, 23. There we go. So let's go find the median position. There are one, two, three, four, five, six, seven, eight. There are eight. N plus one, divide by two, eight, plus one, divide by two, which is nine, divide by two. 4.5. 4.5, which means it's between two values. One, two, three, four, 0.5 is between seven. And nine. And nine, divide by two. Eight. Which is eight. So that's correct. The first quartile, we need to go find the position. And plus one, divide by four. Eight, plus one, divide by four. Nine, divide by four. Two, 2.25. 2.25, therefore we can say it's on position two, right? So let's go count one, two. So the first quartile is four, because it's on position two, right? So that one is also correct. It's on the second position. It's on the 4.5 position. The third quartile, it's three times the first quartile, which is eight, plus one, times three, divide by four. Nine times three, divide by four. Six, point five. Is? Six point five. Six point five. Of course we can see. Four is on position seven. Seven, yes. And we go count, one, two, three, four, five, six, seven. It's 14. So that is correct, right? The mean, the sum of all of them, divide by how many they are. You add all of them, divide by how many they are. It's 76, that's the sum, divided by eight. It's, wait, just hold on, please. Look. Nine point five. It's nine point five. Now, in terms of the last question, it says the distribution is symmetric. If it's symmetric, it means the mean should be the same as? The mean. The mean and the median. Yeah, but we can use those two, the mean and the median. So let's check. The mean is nine point nine point five. The median is eight. So the answer is five. Therefore, the distribution is not symmetrical. So, incorrect answer is number? Five. Five. Easy, right? How you do the answers? Sorry, a question, please. When you were calculating the third quartile, didn't you say when it's, then the answer is six point five. It's between two values because I can see that you wrote. Yes, you are right. Then it means we are also here, not right there. We said it's six point five, right? But it'll be between six and seven. It will be between six point five. One, two, three, four, one, two, three, four, five. Six and seven. Fourteen and twenty-three, am I right? No. I disagree, I disagree. It is six. It's not six point five, it's seven to six point seven five. It's six point seven five, no? Six point seven five. It was six point seven five. Oh, okay. Yes. Okay, all right. Now it makes sense. Thanks. So then it is on position seven. Okay. All right. I have a question. On the calculator, when we change it to stat mode, and we are done with the question that we're working on, how do we clear that data? Because I noticed that if we try to do another question, it keeps adding to that information the first day before. Okay, so if you are still on the state mode, I don't know which calculator you are on, so we can do both. Shop. If you are on the shop, you just go second function CA, it will clear everything you have. You will see if I press alpha, and I press that, it will give me an error because there's no data stored. So you just press second function mode, the CA will cancel because second function calls those orange values at the top, the functions at the top. So it clears your calculator. Once you're done with the state mode, and you want to go back to your normal calculator, you press the mode button, and then you press zero for normal, and then your calculator will go back to normal. The same thing with your CA sure. With CA sure, it's a little bit difficult to clear your calculator. Sometimes the clear button doesn't work. So you press shift, and then you press clear, and it says clear the memory. So then press two, and it says yes, you press equal, and you press AC. Sometimes it works, sometimes it doesn't work. Let's see data two, you see it didn't work. So with the CA sure, you can't clear a memory. What I suggest you do is go back to mode, shift mode to step, and then it will clear your calculator. You will start from scratch again. It always works. Otherwise, you can clear your entire setup. Clear on my pressing three, and yes, and AC, and then it will clear everything. But then you will start from scratch because it goes back to meds. Otherwise, yeah, you just press the mode and then press one for going back to your normal calculator. Okay. And then question on answer number four, the mean. Did we use the calculator? Sorry, I missed that part. No, I didn't use the calculator. They calculated the sum, they added all the values. That's why they have the 76 divided by eight. So you can use your calculator. Remember, use your calculator to practice because it gives you shortcuts. I'm getting 7.5. Did I do something wrong? Yes, it means some way you added one of the values wrong incorrectly. So just double check that you enter your data correct. Okay. I can also demonstrate that just to give you some comfort as well. So number one, number two, because it's gonna be quick, I hope. Okay. Four enter, 14 enter, six enter, nine, 23 enter, three enter, seven enter, and 10 enter. And I see, shift, start, four, two. Yeah, I think I had made a mistake, I did 9.5. 9.5, there we go. Thank you. Right, let's move on to question number eight. Time moves so quickly when you're having fun. Consider the following cumulative frequency distribution of distance from home to school. For example, of 50 grade seven, LENAS on a school transport. Which one of the following statement is incorrect now? They give you, they told you that this is a cumulative distribution table. They have given you the interval, the class intervals. They give you the cumulative frequencies. What they didn't give you here are the frequencies or even the percentages. So they expect you to know how to get to the frequencies. So you should be able to move between. What also they didn't give you are the relative frequencies and also the cumulative relative frequencies, which are your cumulative percentages if you convert them into percentage. Now, I'm not going to go and answer all the questions like complete the whole table. But if you have time, you need to be able to complete the entire table. So the frequency, for example, we know you need to know how this table is constructed in the notes in the videos. We do give you those explanation. You need to go and learn how they construct a cumulative frequency in order for you to be able to answer this question. So a frequency, a cumulative frequency is adding up all the values of your frequencies as you go along. So it's summing up. So in the beginning, it will be the same. Your cumulative frequency will be the same. The cumulative frequency for 9 to 12, 9 to 11 is the value that sits here, which are your frequency from here plus your previous cumulative frequency. So in order for us to find out what this frequency is, we can just say 17 minus 4, which is 13, because 13 plus 4 is 17. We can also do the same here. For the 2 minus 17, we should give us this value here, because 17 plus the value that this year should give us 42. So what is 42 minus 17? I'm just going to... 25. 59. It's 35. It's 30. 25. 42 minus 17, right? Yeah. It's 25. It's 25. Oh my God. 42 minus 17. So you just minus the previous value. So 48 minus 42 should give you this value here, which is 6, right? Yes. And 50 minus 42, 48. So 50 minus 48 is 2. So this was your frequency, and from this frequency, they built the cumulative frequencies. So that's how the table works. The relative frequency adjusts. You need to add all these values together. They should give you the same as 50. So the total year at the bottom should be equal to 50. To calculate the relative frequency, remember relative frequency is a decimal point. It says for this value, it's 4 over 50. That is the relative frequency of 6 to 8 interval, or class interval, and so forth. So what is 4 divided by 50? I'm just going to do 1. 0.08. 0.08. 0.008. And so forth. Then you can also do for the rest of them. So you say 18 divided by 50, that will be your relative frequency. 25 divided by 50, that will be your relative frequency. And percentage wise, it's just this value multiplied by 100, which will be 8%, and so forth. And the relative frequency percentages as well, you can calculate it by saying 4 divided by 50 will give you your relative frequency. And if you multiply that by 100, it gives you a cumulative percentage as well. So now based on this kind of information that we just learned now, let's see if we can answer A, B, C, and A, B, C, D, and E. Because I'm not going to complete the whole table. So let's go. The frequency class of 6 to 8 is 4. Is that correct? Correct. Because we just calculated it now. The relative frequency of class 9 to 11 is 0.26. Where is class 9 to 11 is that one? So you just say 13 divided by 50. Do you get 0.26? Yes. You get 0.26. Is correct 0.26? Yes. The percentage frequency of class 12 to 14, so where is 12 to 14? 12 to 14 is 25 divided by 50, multiplied by 100. It's correct, 50. It's 50%. Yes. The midpoint, now the midpoint of the class interval, so you're going to take the two values. So at the two values divided by two, midpoint of the class of 15 and 17 is 16. Is that correct? So if I take... Correct. ...class 17 divided by 2, should give me 16, right? That is correct. Yes. So you just add both of them for the midpoint. I didn't get that. Because I'm looking for the value that is in between. I get that one, sorry. Okay. And then the width is the distance. That is the difference. So the midpoint is the average between the two. The width is the difference, which means you're going to subtract. So to calculate the width, we subtract. So 20, subtract 18. It's 2. It's 2. So this value should be equals to 2. So therefore that is the incorrect. Sorry, I didn't get D, the midpoint. The midpoint is the average of the two class, the lower limit and the upper limit. So you just say 15 plus 17 divided by 2 will give you the midpoint, because we're looking for the middle between the lower limit and the upper limit. 16. Okay. Thank you. Okay. And then the width we calculate by doing the difference. Okay. Let's see if we get more interesting questions. Okay. The daily consumption in kilowatt by a sample of 10 household is give us the 10 households consumption. Which one of the following statement is incorrect? So we need to go and calculate the positions. Now you need to read the question correctly so that you can do the right thing. Position medium, which is the value, value of quartile two, which is the same as the median. Remember that the range is minus lowest and the value of quartile three. So first let's go calculate the position of Q1, which means we're going to use N plus one divided by four. They are 10 plus one divided by four, which is 11 divided by four. Oh, you know it's one single. 2.75. Sorry. I'm sorry. You're saying it's 2.75. 2.75. Therefore we say, oh no, because we're not going to look for the value. So we're looking for the position. So that is the position. Don't do anything to it. That's the position. And that is the correct statement. We're looking for the incorrect one. The median. So we need to find the position first. N plus one divided by two. 10 plus one divided by two, which is 11 divided by two. 5.5. 5.5. We need to order the data. We didn't order the data. I don't know why we didn't start there. So let's order it. 33. 37. 33, 37, 41, 43, 44. 47. Wait, wait, wait, wait. Do I click? 47. 47, 35, 31. My pen is something else. 47. 50. 50. 51. 51. 55. And 61. 55 and 61.р. and 61 there we go okay so we need to go find the median which is on position 5.5 let's go one two three four five point five it's between 44 plus 47 44 plus 47 divide by two it's 45.5 45.5 therefore this one is the incorrect one Quartal 2 it says the value we don't have to go and calculate it because we did calculate it which we use the same Quartal 2 and median are one and the same thing so this is correct the range your highest minus the lowest so 61 minus 3 should give us 28 and you do the same with Quartal 3 value and plus 1 divide by 4 which is times 3 which is 3 times 11 divide by 4 33 divide by 4 8.25 8.25 therefore it is on position 8 one two three four five six seven eight it's 51 so that is correct that is correct the only question that is not correct is option two okay there human resource collected data on starting salaries of data analysts in Mira group the data below shows the starting salaries in thousands of rents for 16 randomly selected data analyst employees and that is their information which one of the following statement about their empirical rule or about the empirical rule or the distribution of the data analyst starting salary is correct number one the distribution of data analysts starting salary is positively skewed the data analyst salary is symmetric we're looking for the correct one right the according to the empirical rule assuming the starting salary distribution is symmetric approximately 68% of them which is what there are one standard deviation of them is between that those two values and 95% they are between those values and the rest all of them they are between those values so we need to first calculate our mean and the mode if possible so that we sorry mean and the median so that we are able to find out any of those statements are correct so the screen x bar the sum of all of them divide by n and we need to also go and calculate the position and plus one let's see if the data is sorted the data is from smallest to highest it's sorted so there's no need for us to worry a lot so and plus divide by two how many they are they said 16 right so it's 16 plus one divide by two which is seven eleven point five so one two three four five six seven eight nine ten eleven point five two fifty nine plus two sixty three divide by two I get eight points off I'm getting what I'm getting two yes I think so it cannot do six I didn't even check so seventeen divide by two is eleven point five eight point five eight point five eight point five so one two three four five six seven eight point five is between forty seven two forty seven and two forty nine and two forty nine makes it two forty eight which is two forty eight now let's calculate the mean whoever has calculated the mean I get three point two five yeah two three three point two five yeah just give me a second I want to capture all the values to the calculator as well because we need to also calculate the standard deviation two ninety two ninety three fifty two should have six values right okay so shift that one for the mean is equals to do you also get the same two three three yes five yes okay so our mean is two three three point two five so if you also calculate the standard deviation for now because we're gonna use it just now so let's do that shift step for standard deviation is four seventy one point seventy two seventy one sixty one sixty one point seventy six six one as is equals to six one point seventy two so now let's go and answer the question we need to find out if the data is positively skewed so let's see the mean and the median so the mean is two three three point two five and two four eight so the mean is less than the median so therefore it is supposed to be negatively skewed so yeah it says it's positively skewed so that should not be the right one and yeah it says it's symmetric but we know that they are not equal so it's not symmetrical are we saying it right when the mean is less than the median is it positive or negatively skewed it is skewed to the left so if it's skewed to the left it means the tail is to the left therefore it means it is negative so that will be incorrect okay so now we need to and see if either three four and five are correct so number one with 68 percent it is one standard deviation so it means we need to find x bar plus or minus the value of your standard deviation so our mean our mean is two three three point two five minus six one point seven two and the other site we're going to find two three three point two five plus six one point seven two if you can subtract what values do you get one seven one point five three and two nine four point nine seven one seven one point five three one seven one point five three and on the other side you can just change that to a plus you get the same two nine point nine seven yes two nine four point nine seven right then we need to do the same with a 95 which is two standard deviation so two standard deviation we just okay I need to write this values here one seven one point five three and two nine four point nine seven don't worry about my three digit numbers we're gonna fix it just now I just want to do all of them now so if we're going to do two standard deviation so we use the same formula just gonna use the same values here just gonna change it around to standard deviation so it's two times sixty one point seven two and two times sixty one point seven two which then it means going back to my calculator I can just go back I'll start with the site to open bracket with bracket and equal three five six point six nine because I started with the plus side I'm gonna write it first three five six three five actually I don't even have to write it here let me write it on there so that I can have space to write the other things here so three five six point six nine and on the minus side we get as most with the arrow to minus check to a minus and say equal one oh nine point eight one nine point eight one okay let's do the last one which is there three standard deviation so instead of having two we just change the two to eighty three yeah do the same on the calculator just change two to three say equal 48 from a zero nine 48 comma zero nine and we do the same and change a minus to a plus and that gives us 41 comma 40 48041818 point four one four one so one of them I need to multiply them by a thousand because these are thousands and these are thousands yeah so if I multiply this by a thousand the first one and convert it to a thousands of rent probably they rounded them up if I round them up in state of only using three decimals so if I round this one up it will be 172 probably so this will be 172 times a thousand will be 172 thousand 294 rounded up it will be 295 multiplied by 295 multiplied by a thousand will be 295 thousand this one if I round it up it will be 110 110 multiplied by a thousand it will be 110 thousand and the next one if I multiply this or rounded up it will be three and three hundred and fifty seven three fifty seven multiplied by a thousand will be that and the same yeah it will be rounding up is 48 48 multiplied by a thousand which will be 48 thousand and the next one 418 418 multiplied by a thousand will give us that so which one of the following statement is correct the only one that is correct is the one standard deviation three it's option three and that's how you will calculate them so once you have the answers you just need to convert them into a thousand because they say the salaries are in thousands and they rounded them up to the nearest thousand as well and that's one and we left with nine minutes let's see other questions consider the following variables your height is either a tall or a short so if these are variables what is the question they're going to ask you which one of the volume following variable above are quantitative so we need to identify whether this variable is quantitative or qualitative right height as tall or short is that qualitative or quantitative anyone qualitative I think it's quantitative no 20 no it's not quantity it's qualitative it's qualitative because they told you that the height in this instance is not numeric it's either you are tall or you are short so it's a categorical variable so this is qualitative your status is either full-time or part-time qualitative qualitative as well conditions either poor fair good excellent qualitative so the answer is five a size of a ring medium medium big qualitative so which one is the correct answer one two three it's number three it's number three only he is the correct answer yeah okay okay which one of the following statement is incorrect age if the researcher EO the age if the researcher probably is age of the researcher the age of the researcher is quantitative continuous is that correct or incorrect correct it's correct salary of the researcher is quantitative continuous oh true incorrect true true it is true it's true it's true it's true it's true it's quite it's correct as well yes because there's no order there's no rank or order or preference in terms of that or rank the position junior mid-level and senior of a researcher is qualitative nominal incorrect that is incorrect because they should say yes and order or they know then the last statement we can leave that out it's automatic I'm not gonna ask you to calculate the standard deviation now but you can take the same question and calculate the standard deviation using your calculator and find out which one of those values are correct I'm gonna skip that one the other questions that you might get might be in this instance yeah they give you a frequency distribution table with the frequency but they didn't give you the relative frequency or cumulative frequency and other and other measures the question here is asking you what is the percentage of the show pass between who spent between 800 and 1600 so it means they go between two categories or two intervals so it means yeah we need to add 14 and divide by the total and divide it by the total and your total is that and then times 100 multiply that by a hundred and what is the answer 63 point three 63 point three what is the percentage of of shoppers who spent more than 1600 it means we need those two so what do we do because it's more we take three plus one divide by how many they are and multiply that by a hundred I'm gonna ask you also to do the quotas because it will take us forever but you also get the understanding we did the quarter you need to arrange the data first find the quartile position before you calculate the veil or you find the values so this one says that we need to calculate the quarter position the quarter value second quarter remember that second quarter is the same as quarter two is the median the median give you the already gave you the answer there and and you need to calculate the position of quarter three and the quarter into a quartile range how do we calculate interquartile range it's quattal three minus quattro one not position don't use these positions you must find the things themselves hey let's look at another question consider graphical method a2d and they give you all this and they're asking you which graphical methods are the most appropriate for quantitative data for numerical data is the bar chat good for numerical data no no no no bar chat the the chat the bar chat for numerical data is called a histogram right by chat is for categorical this is for categorical remember categorical data you can only summarize using three graphs bar chat pie chat and a summary table histogram high chat is for categorical data data plots they mainly plot quantitative data and then you need to choose which one is the correct answer here three only bd bd and e are the only correct answers so I actually included in this the notes this same questions that we have here are also loaded on your my mode my my units are my my module on module I've loaded the same I will go and show you just now where to find all the information you need to be able to answer questions relating to a frequency distribution table you can see that this one has lots of gaps in between so the easy way of doing this is to calculate all your frequency your relative frequencies easy to calculate you you can also complete the whole table because we know that the last total of the last class interval is the same as the grand total so you should be able to calculate when complete the whole table and answer the questions and there are about 35 questions that I have posted here that you can go through as practice exercises as you can see there are more than enough to prepare you before you do your second assignment and your last set assignment remember the third assignment don't rush to go and do your third assignment if you already did your two assignment without understanding the work so use this to prepare yourself so there are lots and lots of questions that I posted here that can help you and remember we've got the what's up group that can also you can use to discuss and also you can use my module my module my module can I say my unisa I'm gonna stick to say my unisa and on my unisa until I get to the grips with my mode my module or module okay so sorry about that man please have the details to the what's up group okay I will post it on the chat just now don't worry okay so these are all the questions you can see I've got the different questions on yeah most of them have never been touched in any of the recording so you might find that there are new questions please use them to practice but also as part of your learning okay so to recap we've done everything you need actually to help you write your assignment I'm gonna I need to capture this moment actually as well let me stop sharing my screen stop presenting and then please stay online I know that we are almost almost done for some reason I cannot access my screen my PC is frozen can you guys hear me yes yes all right as long as you are able to hear me and just hold on I want to go on to my my module my is it my but it's still written my unisa my unisa I guess we can just call it the class section so do we need to stay online it requested that we stay online cause you wanted to show us something if you are able to see my entire screen are you able to see yes right this is where I want us to be so if I click on and I go to the site my Twitter site and just I need to switch to your view so that you can see from your side okay so when you when you come to the Twitter site for those of you who haven't come through this site and it's for the first time you seeing the site so I have included in the announcement there is the weekly session so you will see which topic we're going to be discussing there we go today is the 15th of May we were discussing that we finished with everything you need to to learn about your assignment one right you done with your assignment one we should be but you need we still need to practice so what I mean is we're not coming back to address any questions online in terms of assignment one next Sunday we're going to start working towards assignment two so that you are also prepared before you start your assignment two you need to know some of these things and then we'll do more activities and then you will do your second submission so the sessions as they are you can see what we're going to be discussing when and what are we discussing then and then the last Sunday it will be a Sunday a week before Sunday a week before you submit your assignment we will do more question collaborated questions more questions and answers based on everything you need for this will be just additional for you to submit your second assignment your second submission or maybe your third submission if your lecturer gives you the set the third submission we will still cover that session the session and you will notice that we do I will cover some question and answers in between but then we will have a question and answer again where we just run through the question so the others will have a bit of a summary before and then we do the exercises there might not be enough and then we will do lots and lots of activities on the last session they are all loaded the only thing that is not loaded here is the exam preparation sessions because then they will be different because with exam preparation then we'll start with the revision and then we do the mock exams papers and we do the practice exam papers that I will set for you and you will do the mock exam papers that your lecturer has set for you then we come and do all those discussions here and we will also do assignment we'll use the assignment as part of the revision so we'll go through all the assignment questions as part of the revision and so forth and so forth so I will have a proper exam preparations like a timetable for us to follow but it will be closer to the exam for now don't worry about the exams worry about the assignment so this is what I wanted to show you the other thing I want to show you if you go back to the beginning and you scroll to additional resources you will notice that there are three folders one is the summary notes folder the summary notes folder is to help you with some of the videos that we have on the lesson plans this are just for all the sessions so you will have all this summary for all the study unit so you can download them and have them and go through them as you watch the videos you can follow with the notes then I do have the templates we'll use them at a later stage don't worry about them every week for every session that we have the questions that we go through I will post them here so here for today's one is here it's got the date stamp of today so this is the session for today so you will find all the questions we went through here plus the additional one that we didn't go through you can access them from there access them yes and then going back to the homepage the other thing I want to bring to your attention as well for those who didn't know so for content every week go through this I've already loaded the basic probabilities for those who want to just go through basic probabilities this is just the session that we had over the weekend on Saturday yesterday I uploaded that session on here so you should be able to go through it it's about two hours long so pace yourself it deals with the basic probabilities use this to build up to Sunday session because on Sunday we're going to just go through the activities so my understanding will be you would have gone through your study unit you've learned through the study guide you went through your prescribed books your wake books and this video and then we go through the questions the practice questions and so forth but I will do a summary first so you just need to make sure that you go through this video and as the week goes by I will post the there is also discrete probability one but it's hidden for you you will get access to it as when I want you to get access to it at the moment it's only those three for now for assignment one you can go through all the content that is in those three lessons right the session for today it's a record it it will be loaded on here under the online session recording I'm separating the two because I mean I don't want to put this day then you won't find the recordings for this sessions so for this session this is last week's session the recording it is on here let's see there is the recording for the first session that we had I don't know why this one is not showing there is there are two sessions actually here there is the orientation one so you can use the venue to the first session for those who are not part of the session you can go through this video and then you can also go through what we went through last week with session one and today's session will also be included on the list so you will be able to also access it from here right that is all what I wanted to share with you in terms of my model don't go anywhere I'm going to stop the recording right now because I also wanted those who are not part of the session to be able to hear what I needed to tell you