 Also, but not now I will create an exam guidelines later on to tell you which areas you need to focus on or pay attention to and so forth. Usually I do not me. Usually your lecture will give you some guidelines and then we go through them, but I don't think this year your lecture will do that. So this is one of an example of what the lectures used to do. They used to give the guideline to student to say concentrate on these areas because they will be part of your exam. And then they say, God bless you after that, because they know that they said the hardest question papers. So that is one example. I haven't seen anything for STA 1610 and I don't think we also did that because we have a mock exam. You will receive a mock exam from your lecture. And remember also I said I will set one for everybody who is on under my group on my UNISA so that you can practice the questions. But then we also going to come back and discuss those questions after we completed with the revision. So expect that to be loaded this week. I will load it and open it up. You can go through it as many times as you want any time of the day. I will not allow you to go back. So it will be similar to how you wrote your assignment where you don't go back to look at what you answered previously. You just go forward and submit and you can do it as many times as you want. Just to get used to the questions. Okay, so let's start with today's session. What I want to do today is because it's revision. I'm going to give you a brief or remind you of what chapter one is. And then we go into the question. And then when we get to the questions that relates to chapter two, then we deal with chapter two. And then we go into the questions and then like that until we get to the last question. Okay, so when we talk about study unit one just to remind ourselves. And the study unit one. Remember study unit one is where we introduce statistics to you. We talk about how do you describe what statistics is. The method of describing or summarizing information for decision making. That's statistics. We talk about summarizing or describing because describing will be in terms of tables and charts. And summarizing will be in terms of calculations like calculating your mean, your standard deviation or others. Then we also talk about the two branches of statistics. Remember, we have what we call a descriptive statistics and also we have what we call an inferential statistics. And we said descriptive statistics is a method of describing your data in terms of the locality or variability. Or we can also describe it in terms of summarizing it in tables and charts. That inferential statistics is about drawing conclusion about the population using the sample. So we do a descriptive in your chapter one, two, three and a little bit of a four because four is basic probabilities. And then we do inferential statistics in your chapter six, seven, eight, nine, ten, or six, nine and ten and eleven. Those study units. That's why we do inferential statistics where we do confidence intervals and hypothesis testing. That's part of inferential statistics. So you need to know how to differentiate the two. We also talk about because I'm talking about populations and all that you need to know how to define a population that a population of study is all elements of interest that a person will be studying. And if the population is big enough, we cannot study the entire population. We create a subset which we call a sample where we draw a sample out of the population and use that to calculate or make decisions. And then once we do the calculations and making the decision, then we infer back the results back to the population of where we collected that information. So now when we talk about the population and the population and the sample, there are measures that you collect or calculate. Like you mean your standard deviation, those are measures. If you calculate the measures from a population, so let's write them there. If you calculate any measure from the population, we call those paramitas. So those will be your paramitas. And those can be your mean, your standard deviation, your variance, and so forth. And you also need to know the symbols. So that's the mean for the population is mu. The standard deviation is sigma and the variance is sigma squared. That is for the population. If we do it for the sample, you also need to remember the sample. You can calculate all this because you collect them from the population. So we call them statistics. And those statistics also, if we calculate the mean, the standard deviation and the variance, you need to know that the mean of a sample, which is the statistic, we use x bar. For the standard deviation, we use s. And for the variance, we use xs squared. And remember all this, you can use your calculator to calculate by putting your calculator to state mode 0. To state mode 0. That will calculate all these measures, but not yet. When we calculate this statistical parameter, we need to have what we call a variable. Because from a variable, we can have the data and the data will use them to calculate this. So we need to also know how to define what is a variable. And a variable is a characteristic that describe the population or a sample. It's just a characteristic. Like gender, marital status, color, height, type, political formation, all of them, type of school you attend, those are variables. Within those variables, there are values that you get. Like when I talk about marital status, they single, divorce, merits, and so forth. Those will be the values, we call those values data. I don't know whether you guys call it data or data or data or yeah. So people call it many different ways. So I call it data. So you get data and that data you can take it and do the summarization of it or you can do the visualization of that data. That is chapter one in a nutshell. Oh no, not in a nutshell because we still need to understand the type of variable that I'm talking about. So when we talk about the variable, let's delete all this because I don't have space. When we talk about variables, you need to know that there are different types of variables. Variables. So you can get qualitative variables and quantitative variables. When we talk about qualitative variables, we talk about variables that you can put into categories. We call this categorical variables as well. When we talk about quantitative variables, we talk about numerical variables, which are variables that you can measure or count. So if those are the two variables, so we know that these are categories. And in every variable, there are levels of measurement or scales of measurement, not measurement units like your kilometers or centimeters. I'm talking about scales of measurement, which for categorical data, that data, when we talk about the scales of measurement, we talk about nominal and ordinal. And when we talk about nominal data, it is data that does not have an order or there is no preference in terms of order. There is no rank on that data. For example, categorical data can be marital status. I'm going to use that because it got stuck in my head. Marital status, there is no data value that is higher than the other or there is no order in terms of how things can happen. So nominal data, no order or rank. Ordinal data, there is order or rank. There are things that are perceived to be higher than the other in terms of the order. So for example, like I asked you, rate my services. So you had the opportunity to either say I suck or my services are low or they are high or depending on the scale that I use. I think one of the question was would you refer someone or to use my services and there was a scale from zero to one. So there is a rank because zero will mean that not likely and 10 will mean extremely likely. So it means definitely you will refer someone. So that is the rank from nowhere to highway. And that is ordinal data. Then we also have what we call qualitative quantitative. There are also scales of measurement in there. So you get what we call interval data and ratio data. So usually we only work with interval data. But anyway, so ratio data, there is no, I'm also going to, I need to Google this now. Because I also get tricked in terms of defining what the ratio between ratio and interval. One of them does not have, let's use Google quickly before I tell you wrong news. Not that I know statistics by the back of my head. One of them has no definite zero. Zero means another value. Is it ratio? Ratio has no zero. Ratio has no zero. Uncle Google also I think agrees with you. So ratio, there is no true meaning of zero. Yes. So it means with the ratio, the example that we can have, there will be temperature or bank balance. Because there, there is, can you see my slide? This is everything that you had. So there is no true meaning of zero. So no, ratio has a true meaning of zero. So this one interval does not have true meaning of zero. So it's like your temperature and bank balance. Ratio has true meaning of zero. Zero means a fixed point where if you pass zero, it means you don't exist. So zero has meaning in terms of ratio. So you need to remember that. I also get between the two. Because usually on statistical programs, we don't have what we call ratio. We always use intervals. Okay. So going back to our summary note, in a nutshell, that is what you needed to know in terms of study unit one. So let's see if we can answer some of these questions. I've hide out all the answers that your lecture has given. So it means me and you, we won't know if we have the right answer. So let's see if we can get the right answer without copying. Which one of the following statement is incorrect with regards to statistic? Is it A, B, C, D, or E? A says statistic is an estimate of a population parameter. B says statistics represent a property of a population, not a sample. C, a statistic is a summary measure calculated from a sample. D, a sample standard deviation is A statistic. E, a sample mean is a statistic. Remember what statistic is a measure collected from? Is it collected from a sample or a population? Sample. From the sample. So read the questions and choose which one is incorrect. Is A correct? A statistic is an estimate of a population parameter. A is incorrect. Anyone with a different opinion? D is incorrect. Sorry, I got distracted with the noise so I went to switch off the old mute. So A is correct because A says a statistic is an estimate of a population parameter. So it means a statistics can estimate what the population parameter can be. We do this with the confidence interval. Remember we can use your sample statistic to go and find out if your population mean is within the confidence interval. Or your population parameter which is your population proportion is within the interval by using the sample statistic. So number one is correct. You need to know that because it says it's an estimate. And those are the key words that you need to also pay attention to when you write the exam. When you read the question, make sure that you read it and make sure that you understand what that question is saying. Number, I'm going to go down. Number E is E correct? Yes. E is correct? Is D correct? It says a sample standard deviation is a statistic? Yes. That is correct. Number C, it says statistic is a summary measure calculated from a sample. Gosh. We did that in the beginning. Is C correct? Let's go to B. Yes. B says a statistic represents a property of a population, not of a sample. So that would have been the incorrect one. So let's see if we are right and your lecture says it's... Is it correct? I can just remove... Sorry. My bad. Forgot how did I do this? So I used that. So I can just remove this. I'll send you the document if you want as well. You should have this from your lecture. So let's go to number two. Which one of the following statement is incorrect with regards to the variables? Remember what the variables are? Variables are just characteristics that define a population or a sample. And there are two types of variables. We did talk about them earlier. So A, B, C, G or E. A, quantitative variable takes on values with equal units. That is numeric variable that indicates how much or how many. B, variables can be classified as categorical or numerical. C, quantitative continuous variables results from counting attributes of an element. The numerical variables can either be discrete or continuous. Oh, that is one of the things that I didn't discuss with you. Now I remember why. Qualitative variables uses labels or names to describe attributes of elements. Which one is incorrect? Pick and choose your answer. If you grew up at the period like in the 80s, 90s, the incorrect. Which one? B or B? It should be. Are you saying B is incorrect? Yes, it should be qualitative and categorical. Not numerical. Let me also come back here. And in terms of, remember, qualitative can be also called categorical. And data here can be placed in two categories or can be observed. These are observed data. Yeah, can either be counted or measured. I forgot to do this. Counted or measured. And if they are counted, we call this, if you are able to count how many they are, this will be discrete. They take the whole number, like one, two, three, four, zero, one, two, three, four. They are counted. If they are measured, we call them continuous. My handwriting is bad. It's called continuous. Because we measure them. The temperature, you cannot look at a person and say, are you at 37 degrees Celsius? We're not going to get it right. So we need to take a thermometer and measure the temperature. So let's go back to our question. That is this one. Which one of the following statements is incorrect with regards to variables? Quantitative variables such as numeric variables, we can do how much or how many? How much is in terms of measuring how many counting? Variables can be classified as categorical or numeric. They could have just said classified as qualitative or quantitative. Continuous variables results from, I'm not going to say that because we just said it just now. Numerical variable can either be, I've also just added it now to the conversation. Qualitative variable uses labels or names to describe attribute. A, B, C, D or E. I'm going for C. C is the incorrect one. Because continuous variables comes from measuring attributes. So we measure them. Counting is discrete. So this should have said measuring. So that is incorrect. So only C is incorrect. Which one of the following statement is incorrect with regards to variable? Now we're talking about scales of measurement. Without the scales of measurement, let's go back. I will not even go back. We can use the presentation here. Remember that the ratio has a true value of zero. And it's for numerical or quantitative measures or variables. In TAVA, there is no true meaning of zero like the temperature. Also quantitative variable. Nominal, order in terms of rank, qualitative variable or categorical variable. Nominal, no order or rank, categorical variable. Remember that. Which one of the following statement is incorrect with regards to the variable and the scale of measurement? Nominal variable, which are variables that you can put into categories. Nominal variable. Oh, that's the other thing that I forgot to also show you, remind you about. So in terms of the order, because now I see that we're going into the order just to remind you. In terms of the order for the, sorry, qualitative or quantitative variables takes up the highest order. Whereas the categorical variable or the qualitative variables takes up the lowest order. Nominal being the lowest of them all and ratio being the highest. So coming back to the question, I hope you memorized everything that is on this slide. Let's come back and answer this question. A nominal scale of measurement is the weakest form while a ratio is the strongest form of measurement. I don't know that. Okay, we haven't discussed what the mean and the median is, but I hope for now you know what the mean is, is the average is the sum of all the values and the median is the middle value. The mean and the median cannot be determined for a nominal scale of measurement. Quantitative continuous variables results from measuring attributes of an element. Ordinal scale of measurement is the highest level of measurement that is done in cover. That's incorrect. Quantitative discrete results from counting attributes and you say D is incorrect. And that is true. D is incorrect. What do they mean by mean and median cannot be determined on a nominal scale? What they mean is because remember nominal scale is your categorical variable. So you cannot calculate the mean of a categorical variable. It will not make sense. The mean we calculated from quantitative variable. But there are exceptions in terms of the median, which is the middle. But also it will also depend on the type of analysis that you're doing in order for you to say the middle. Probably you will be placing your variables in order of the frequency, but not the order of the variable themselves. If you have, let's say, a meritor status way on your meritor status. Let's say if this is your bars of how the people are represented. And you order your information from highest to lowest or lowest to highest. One, two, three, four, five. And there are five of them. Irregardless, so you can say the middle one, which will have the highest value can be the one in the middle. But that will not make sense. So you cannot say the median of the information is that the only thing you can do with nominal data. Is not create the median and the mode, but you can. Sorry, not the median and the mean, but for nominal data, you can look at the mode, which is the most appearing number. So it will be the most frequent, but that will be your mode. The only thing that you can do here on nominal is just finding what the model distribution of your data is. And that's it. Nothing else. So let's see the answer. And it's D. Number four. Majority of school rule of the rural schools in South Africa are in the Eastern Cape. The Department of Basic Education requires your assistance in gathering some of the information to effectively manage their scholar transport system in some of the rural areas. Which one of the following statement is incorrect with regards to the types of variable? We're still on the types of variable. Okay, so we need to pick up the pace. I know that we're doing revision, but we're going to run out of time. The types of variables. Number one, the age at which the learner enrolls at the school is a quantitative continuous variable. So yeah, the key thing is look at what they gave you. So look at the age, ignore the rest of the other things as well. So the eight at which the school first and wrong at the school. So just look at the age and look at, is that correct? The travel time of the learner, travel time is the key weight here from the learner's hope to the school is that continuous. Always ask yourself, can I measure this or can I count this? Can I put this into categories? Then you should be able to answer that in terms of the types of variables. The number of schools requiring learner transport is a discrete variable. And also for discrete or continuous, you must ask how many? Sorry, for continuous, you must ask how much? For discrete, you must ask yourself how many? Because then now it forces you to count. So the number of schools is that quantitative discrete, whether or not the school is classified as a need school. So that is your key weight classified as whether or not the school is classified. That is your key weight. Is that a categorical data or a numerical data? Or is that a qualitative data or quantitative data? And if it's a quantitative data, is it discrete or continuous? If it's qualitative data, is there an order or no order? Is it nominal or ordinal? You need to ask yourself those questions. The size of the bus. Now, here is the other thing. Don't just look at the weights. Read the whole sentence first because there might be additional information that converts a number into something else. So yeah, they say the size of the bus that is mini bus, small, medium and large. So now that size is no longer a number like when we say it's 10, 20 or date. So it's a small, medium or large. Ask yourself, can I add them? Can I put them into categories? And that's how you will know what you need to do. So which one is the correct answer? Yeah, we're looking for the incorrect answer. Is age continuous or discrete? Is travel time continuous or discrete? Number of schools are they continuous or discrete? Whether or not a school is classified as special school, is it discrete? Or is it nominal or ordinal or qualitative nominal or ordinal? The size of a bus from small, medium, large. Is that qualitative or quantitative? I think it's E. And the answer is correct. Because age, we cannot count age. So you remember when we also did the content, we talked about age. Age is continuous. Time continuous, because you measure time in minutes, seconds. So it's continuous. The number of schools, because you can count how many schools you have, that is quantitative, discrete. Whether or not the school is classified as special school or an inclusive school or normal school or independent school or whatever school that is. There is no order in that. So those will be nominal. So it's a categorical nominal data. The size of a bus, small, medium, large, there is an order. Because there is rank in terms of that. There is a small one, there is a medium one, and there is a large one. So it cannot just be nominal. It has to be ordinal. And that is E. Oopsie daisy. That is E. You guys are very quiet. I'm very scared now. Because then it seems as if I'm talking to only one person. You see, we're thinking. I think better than this assignment. We're doing big time memory recall here. Okay, so number five. Some personnel and school related information was collected on the learners requiring scholar transport. Variable one to four below are shown. Progress at school as satisfactory or not satisfactory. Sex assigned at birth, whether the person is female, intersex, male, and so forth. List of subject enrolled, whether they do English, math, African, life science, blah, blah, blah. Those are the list of subjects. Number of subjects enrolled, whether I'm doing two subject, three subject, four subject, five subjects. Emotional quotient score or EQ score. That will be in a range of either depending on how the scores are captured. 10.5, 18.5, 6.5 if it ranges in that manner. Intelligent quotient, which will be your IQ scores like 300 and something scores and 345, 365. That is if the scores are kept at that. Which of the following variables is it possible to determine the median? Which one can we calculate the median? Number one, two, three, four, and five. So I will ask, how do you calculate the median? The median is the middle value. You can calculate the median from numerical values. Think five. Is it here? The first one is correct because the levels of satisfactory are for ordinal and we use ordinal to measure the median. We use ordinal to measure, but the levels are satisfactory or not satisfactory. It's like pass or fail. There's no order or rank on that. You failed another category or you passed which is another category. One is not superior than the other. Sex is categorical. List of subjects are categorical. Remember we just finished the question where we looked at to say the meaning the median cannot be calculated for ordinal variables. So if progress at school is ordinal, probably we can find the median because it will be the middle value of the order of the variables. So if there were more variables, let's say satisfactory, not satisfactory and not achieved or not applicable. If they were like that, then we will say which one is the median will be the not satisfactory. I'm not sure if that is applicable in this instance. So for which variable is it possible to determine the median? I know that some material says it is possible to do it for the ordinal. We can do, we actually have to do the median. We can calculate the median for all numerical values. The number of subjects is numerical. Emotional score is also numerical. So four and five should be the right answer for this question. Let's see if four and five is the right answer for the question because I think your lecture had C is also as a correct answer. Because satisfactory not satisfactory can be either one and a zero. Yeah, but one and a zero, they represent a categorical value. They don't represent a numerical value where you can calculate or measure or create a measure of central tendencies. So let's see what five is. It's C. So they say ordinal variable can also be calculated as you can calculate the median of ordinal variables. So they say it's C, but I still have my own reservations around this. Not that I'm disputing what they have. So let's mark that. Sorry, I marked the wrong one. So they say C is the correct one, but I still say E is the correct one. So I don't want you to get zero in the exam because I gave you the wrong information. I will blame you. You didn't because I'm looking at the notes from the first video for Unit 1. So the notes correspond with that question that we just did now. So the note says we can calculate. So let's see the notes. No, the notes from the video that we did with you on YouTube. It said that cannot be used in calculation, but can be compared and ordered. So it's called shoe size levels of satisfaction and education levels. Which what number of slide is that that you're looking at? No, it was from the video on YouTube. The first video that you did, Unit 1. Yeah, I am on Unit 1 thing slide that we used. Oh, there we go. Let's see. Ordinal variables can be used to calculate the medium, not the nominal. Nominal we only do the count and the mode. So I need to get it into my head as well. So medium can be calculated for ordinal. So option number 3 is the correct one. So don't get it wrong in the exam as well. So let's go back to that slide. So for ordinal we can do, we can order, we can count. We can calculate the mode, which is the most appearing the number of value. And we can calculate the median, but not the mean. So I got confused with the mean. So we can calculate the mean, but we can find the median because with the median we can compare. Yes, you're right. We can compare which one is the middle one. Okay. All right. So you need a lot of reading and studying in order for you to get the questions right. Okay. Which one of the following statement is incorrect with regards to tabulation? Now we're moving into the area that I didn't describe. Quick, quick. Let's do that. Now in study unit, study unit 2, study unit 2 deals with summarization of the information in terms of tables and charts. So we also need to know the two things. Your qualitative variables, qualitative variables and quantitative variables. So when it comes to qualitative variables, there are three visualizations we can do. You can do a summary table or what we call a frequency table, summary table. Or sometimes they call it the frequency table. You can do a pie chart or a bar chart. You also need to know the properties of each. So in terms of summary table, you will summarize your values in terms of categories. So it will just be a summary table where you have your frequencies, which are your count and your different categories. Category one, category two, category three. Or you can also calculate some percentages there. The pie chart. Now that your categories are the slices and so those are represent your categories. The size will represent either the frequency or the percentage. Then you'll have a bar chart. You also need to know the properties of a bar chart. The bus represent categories, category one, category two, category three. The height of the bars represent percentages or frequencies. That is qualitative. Quantitative, we have multiple graphs that we can use. We can use a frequency distribution. Let me write it correctly. Because now my pen slides off my screen right now. It doesn't stick. We have frequency distribution table, which also summarizes your data by putting your data into different class width. So from zero to one, one to two, two to three, those are your class width. And you can calculate your frequencies, your frequency count or your percentages. But you can also calculate what we call the cumulative frequencies. We will deal with that later on. You will see when we do we answer the question. Accumulative frequency is just adding up and creating cumulative summation as you go along. And you can also calculate your cumulative percentages. If it's not a percentage and it's called relative frequency is just in a decimal format. A percentage is multiply that frequency, relative frequency by a hundred will give you a percentage. That is a frequency distribution table different to the frequency table because on the frequency table, you only have frequency and percentages. This one has the frequency and the cumulative frequencies. So that is one way. The other way you can visualize by using a histogram. A histogram is also a form of a bar chart. But with a histogram, because we use the cumulative, we use the class width. When one class ends, the other one starts. So the bars of a histogram represents your class width or your class intervals. Your height will either represent your frequency or your percentages. With a histogram, unlike the bar chart, the bars of a histogram, they touch. There are no spaces in between. The bar on the bar chart, there are spaces. On the bar chart, there are spaces. Histogram, no spaces. That's one form. The other form of visualization, we can use a frequency polygon or we can use an ogive, which is a cumulative polygon, an ogive to create. One will look like that and one will look like that. The same way as this data looks. So one will be accumulative frequency, which will add up and one will. So this will be an ogive, whichever way you want to pronounce it. And this one would look the same way as this data points up because it's a line. Actually, I'm not drawing it right because it starts at the bottom and it goes up. So it starts there, then it goes there, then it comes down, then it comes down. So it will look like this, which is your frequency polygon. So those are the types of charts you can have. You can also get what we call a stem and leaf plot. Remember a stem and leaf plot? A stem and leaf plot, we do it when we do the chapter three. Let me not go into the stem and leaf plot. So let's see if we are able to answer any of these questions. So I will have to remove all this information. Which one of the following statement is incorrect? With regards to tabular method of summarizing the data. A percentage is equals to the relative frequency multiplied by a hundred. I just said it. Accumulative frequency distribution, are you tabular methods suitable for summarizing qualitative data? A frequency distribution, relative frequency distribution and percentage frequency distribution are methods suitable for summarizing qualitative and quantitative data. And we're looking for the incorrect data. And to create a frequency distribution for qualitative data, we first need to define non-overlapping classes by determining the number of classes, the class width and class limits. A cross tabulation are suitable for summarizing the relationship. So this is a cross tab or contingency table. So you just need to remember what we did in chapter ten, or study unit ten when you answer that one. Which one is incorrect? A, B, C, D, O, E. C is incorrect. C is incorrect. C is correct because it talks about the frequency distribution and the relative frequency and the percentage frequency. Remember what the relative frequency is? So in order to calculate a percentage frequency, you multiply your relative frequency by a hundred. So A is correct. So it means on a frequency distribution table, because now when I was explaining it, I didn't include the relative frequency. But you need to know that a relative frequency is the same as a percentage multiplied by a hundred. It's a decimal multiplied by a hundred. That's your relative frequency. So on your summary table, we have a frequency, I said, and we also have a percentage. Now, in order for you to get a percentage, you would have calculated first a frequency, a relative frequency. Why can't I delete now? Let's go back there. I have to remove all of it. So if I have males and females, and I have 10 of them and 20 of them. So in total, so that is my frequency. And this is my gender. So in total, I have 30 of them to calculate relative frequency. I just say 10 divided by 30. That is my relative frequency. And this will be 20 divided by 30. And 10 divided by 30, which is 0,33. 0,33. Therefore, this one will be 0,77. Or is it 7, 7 or 7? 6. 666. 666, yes. So that will be, let me just remove that, that will be 0,666, which is 0,67. Both of them, if I add them, they should give me one. So that will be equals to one. In order to calculate my percentage, then I need to take 0,33 multiplied by 100. 0,33 multiplied by 100. And that will give me 33%. Take 0,67 multiplied by 100. And that will give me 67%. And that is the difference between a relative frequency and a percentage. And you can do the same with your frequency distribution. Because when your frequency distribution, in state of having categories, you will be having 0 to 5, 5 to 11, 11 to 16 or something like that. And then you will calculate your frequencies. And you will calculate your relative frequency. And you will calculate your percentage. You can calculate your cumulative frequencies, your cumulative relative frequency. Or you can calculate your cumulative percentage. So you must know the difference between them. So that is correct. That is correct. Cumulative frequency. I say D, Lizzie. Yes, D is the incorrect one. The reason why I picked up well, why I'm saying D, qualitative data is not married with number of classes, class width and class limits. Yes, because there are your class, number of classes. Yeah, I've created three classes with the class width of 5. And my class limits are from 0 to 5. So D is the incorrect one. Or we can also check your answer from the lecturer. Let's see if I'm telling you the right things. Yes, we are correct. Consider the following cumulative frequency distribution. So now, yeah, it's cumulative frequency distribution. So what do you need to do with this information? I'm not going to read the whole entire question. This intervals. We're not created correctly. I am not sure if, because when one ends, the other one must start. In this instance, there is a gap between 8 and 9. Because what happens if the distance traveled was 8.5 or 8.4? Are we rounding them off to the nearest value? So we need to pay attention to this as well. Because how you will define your class width as well? Because the class width tells me from yet, from 6 to 8, what is the distance? So the distance, you will calculate it by saying the class width. Close this. So your class width, and this are my intervals. So my class interval, there are 1, 2, 3, 4, 5. That's my classes, number of classes. 1, 2, 3, 4, 5 are my number of classes. My class width, I will say it's 8 minus 6. Because it says the distance between the lowest and the highest. That will be true. And I can count for all of them. I will find that they are only 2. So if this one ended with 9, then the distance would have been 3. But it ends with 2. So let's see if we can answer the question. The other thing here is cumulative. So in order to answer some of these questions, you will need to calculate what your actual frequency is. Because you are not given the frequency. And you should be able to calculate your relative frequency. I've shown you how to calculate the relative frequency. And if they give you a percentage, you should be able to calculate the percentage if you want. Remember, relative frequency is decimals. So let's see if we can answer this question. The percentage frequency of class 9 to 11 is 34. In order for you to answer that question, because they are asking you what is the frequency. So they are asking you for this value here. So in order to get the value there, you need to make sure that you know what the frequency is. So at the beginning of the table for cumulative frequency, the value will always be the same. How did they get 17? They would have added the value of 9 to 11 plus the value of 6 to 8 to find 17. So in order for you to find the value or the frequency there, you will have to say 17 minus 4. It should give you the answer that you are looking for. 17 minus 4, how much? 13. 13. Because we're looking for the percentage frequency. So it means we're looking for percent. So we're going to take our 13, divide by how many there are at the end of the table. When you do cumulative frequency, the last row will always correspond to the total. Because if you do all your frequencies when you add here at the bottom should be total. And also they also told you how many there are. So it should also be equal to 50. So that will be divided by 50 because we take that value divided by the total. And you're going to multiply that by 100. And what do you get? 26%. You get 26%. So therefore this is the incorrect one. So I must come back to this one. This is part 7. I think part 7 had an issue. There are multiple incorrect answers here. So we're looking for the incorrect answer. Just give me a second. Okay, so we continue. What will be the midpoint between 6 to 7? So what they're asking you is add 6 plus 8 divided by 2. It will give you the midpoint. That is B. What is the answer? 6 plus 8 divided by 2. 7. That is correct. And the relative frequency for plus 18 to 20. We don't have 18 to 20, but we can calculate 18 to 20 because we don't have to complete the whole table. Because if they're asking, they gave you the cumulative frequency to get the 18 to 20, which is the value here. We can just say 50 minus 48. 50 minus the previous value should give us the value here, which is 2. And we are asked to calculate the relative frequency. So we are asked to calculate the decimal. So we need to just say 2 divided by 50. What do you get? 0.04. 0.04. And that is correct. The width of the class is 3. We calculated that there. And it is 2. So that is incorrect. So we already have two incorrect answers. The frequency class of 15 to 17, which means we're looking for the frequency class of 15 to 17. The same thing that we did with 50 to 48, you can calculate it by saying 48 minus 52 will give you the frequency. So 48 minus 42. 6. Which is 6. So we need to find the frequency for that, which will be 42 minus 17, which would be 35. So if I add 4 plus 18 plus 35 plus 6 plus 2 should give me 50. But anyway, let's answer the question. The frequency class of 15 to 17 is 6. So on this question, we had two incorrect answers. Can you maybe explain why is the width for each class is 3 is wrong? I will tell you why I'm asking. If I look at, so maybe I must ask, what is the width of the class include? Does it include the beginning and the end numbers or is it something just in the middle? Remember, that's why I started here to say in terms of this, they didn't represent it correctly. Because when one class, the other one needs to start. So let's do it this way. I just want to go back. So let's do it this way. So if I have to draw a histogram of this information, this is what's going to happen. I will have the first one, which starts at 6 and ends at 8. Then the next one, it says it starts at 9 and it ends at 11. So I'll have another one there. Can you see that now I'm not longer drawing a histogram? A histogram for numerical data. When one stop, the other one needs to start. And that is why I'm saying this value should have been 9. So that this is 6, this is 9, this is let's say probably this will have been 12 and so forth. Because when one start, the other one should end and one start, the other one should end like that. That is the proper way of representing the numerical values. Now, the other thing in terms of how you represent, I'm going to remove all my notes now because I need to use this. The other thing is you can use the open bracket and the closed bracket to show which one, where do you start and where do you end. Because it should say it needs to include that value and not include the last one. Because you don't want to double count them. So that won't be included. So you will have a closed bracket and an open bracket. Or you can represent it as it must not include the first one where you open the bracket, meaning and it must only include that. And then you do the same. So that and that and that will represent because this is the beginning, it will close for both of them anyway. Because there is no other value that it will go out to. So if it's in this case, therefore it means it started 6 and ends at 8 and it starts from 9 and ends at 11 something like that. But this doesn't work because it needs to end at 9 and then starts at 9 does not include. So this will mean does not include 9, but this one includes 11. So this one will include 9. So this when we calculate it, it will be 9 minus 6, which will be 3. And that will be your width. Because on this table, they didn't include 9, then you cannot calculate it like that because the width is your difference between your lowest and your highest. That's the width. Okay, thank you. I think also you did receive an errata or something and you got an extra mug. If you either chose D or you chose A, you would have gotten a mug for it, which it's formats. Okay. So we left with so many. We are on 8. Consider the following data set. Now we're moving away from the charts. We're going into the measurements. So into study unit three. So study unit three has three parts to it. So we have measures of central location or locality or measure of central tendency, which is the mean. The median and the mode. Remember the mean, the average is the sum of all observation divided by how many there are for the sample mean or for the population mean. We say the sum of all observation divided by how many there are with a capital letter n. The median is the middle, the middle value, and we can find the position by using n plus one divided by two. And if the value falls, if the answer is 0.5, we take the average of the two values. If the value is a whole number, we take the value that we see. You need to remember all that the mode is the most frequent. Value that appears. So you order your data from lowest to highest and then you choose the one that appears. Sorry, actually the median you order your data from lowest to highest and then you find your position. The mode you look for the number that appears more than the rest of the other numbers. That measures of central location. Then you have your measures of variation. Your measures of variation like your range, which says it's your highest value minus your lowest value. Your standard deviation, which is for the population in Sigma, which is the square root of your variance. I'm going to get to the variance. Then you get your variance, which is Sigma squared, which is the sum of your observation minus the mean squared divided by n. That is your variance when it comes to population and your standard deviation for the sample will be the square root of your variance. And we know that our variance and squared is your sum of your observation minus the mean squared divided by n minus one. So we just take the square root of that. All of this you can use your calculator to calculate them when you put your calculator to state mode one. Then we also have your quotas, which tells you, oh sorry, the variance tells you there how sparse or how diverse or disperse your data. The variance tells you how variable is your data. How far away are your data points from the mean? That's what the standard deviation tells you. Your quotas divides your data into four parts and you can find your first quota by using the position n plus one divided by four. Or find the quota two, which is the same as the median, which is your median. Which you can find by using n plus one divided by two. Or you can find quota three position, which we find by using three times n plus one divided by four. Also similar, if you get the value of your quotas, if it's a fractional, which is half, we take the average where the two values. So you need to sort your data from lowest to highest. You take the average if it's fractional. If it's non-fractional and it's 0.25, then we round down. If it's 0.75, then you're going to round up the value in order for you to find the position. Once you have your quota values, then you can calculate what we call the interquartal range. And with your interquartal range, we say quota three minus quota one. Now, once we have our interquartal range and the quotas, you can also find what we call a box whisker plot. A box whisker. I don't have space, so I'm going to remove some of this information there because then I ran out of space. So a box whisker tells you that it's a box whisker. You get your smallest value and your highest, highest value. Then the box, that's where your quotas are. This will be your 25% of your data lies below quota one. 50% of the data is split, 50-50 halfway through. And quota three says 75% of your data lies below that quota or 25% lies above that quota. Anything outside of the whiskers, it's called an outlier. We use quota one and quota three to calculate our interquartal range. And that will tell you the distance, whereas you can also look at the distance between highest and lowest. So sorry, this is low, smallest is low and highest. So you can also make a difference between which one is bigger between the range or the interquartal range. So you will see that the range will always tell you the range of your data and the interquartal range will just tell you the range of your quotas. Also what you need to also remember when we look at the interquartal range as well, we can look at the distribution of the data. If it's skewed to the left to the right, depending on where this value is. So if your mean or your quota three is closer to quota two, then we say this is. So if this will be how the distribution will look, quota two, we say this is skewed to the right. If quota two is somewhere here, we say skewed to the left so it can tell you the distribution. And you can also use this to compare different categories or different groups of data or measures. Because if your average of the other one is bigger than the other or the distribution of one is higher than the other, you are able to tell. So let's see if we can answer the questions. So given this data, so our table is big, it's got 52, we've got 50 data values. In the exam, they will not give you this big data. They will give you a small manageable size so that you can complete your exam. So because this was assignment, the table was big. So here we have the distance from home to school. The first question is calculate the first quota. So it means because they say calculate the position. We know position of the first quota, we find it by using n plus one divided by four. So n represent how many they are. So they are 50 because they have given you the positions. So they have ordered the data. You also need to pay attention. Look at the data before you make your decision if the data is ordered from lowest to highest. So I can see that this data is ordered. So I can just go ahead and calculate. So how many they are? They are 50 plus one divided by four. Calculate and tell me what the answer is. 12.75. 12.75. Remember we're looking for the position. So the position should always be the position that you find. And remember we also did if it's 0.75 we round up. If it only when we go look for the value on the table. Oh, sorry. When we look for the actual quota number, then we round up. Number B says we need to find the position of the second quota. Finding the position of the second quota, quota two. We use n plus one divided by two. 50 plus one divided by two. What do you get? 25.5. 25.5. And this says 12.5. So that is incorrect. Number C says the second quota, which is the position that we have now. The second quota is calculated. The average between the 25th and the 26th observation. So if I need to go find the quota value for quota two. Since I have the average. Oh, sorry. 25.5. Remember it says if I have 25.5 I have a fractional so I must do the average. So since it's on 25, I must take 25 and 26 because it's halfway. I must take an average. So C says the second quartile is calculated by using the average between 25 and 26. Observation. Is that correct? I just want to see what statement that we're looking for. The incorrect statement and then we have so many. Because this one they rounded it off to 18. That's why probably you see in that way. The one that's very wrong is B. So the one that is very wrong will be B. Also I also have my reservation with that because this will be the actual position when we go get the. Quartile value, but the answer to the Quartile position is 12.75 is not 18. So this is correct and the range of the data. Remember range you take your highest minus your lowest. So your highest is 20. Your lowest is 6.2. So that we will say 20.2 minus 6.2. 14. Which is correct. Then the third Quartile. Quartile number three. We use three times n plus one divided by four, which is three times 50 plus one divided by four. So you can say 51 times three equals divide by four. What do you get? And also yeah it says position and they rounded it off. 38.25. And it says when it is 0.25 we run down. So the answer here is 38.25. So therefore it's 38. And that would have been correct. Let's see B is the only one that is incorrect. Number nine. Number nine they give us they say consider the actual distance from the school. The sum of all observations. So it means they have given you the sum of all observations. They say it's 626.6. And they want you to find which one of the following statement is incorrect with regards to measures of location. And interquartile range. So if you look at the information that we use, this is the information that we had, which is similar to what we have. Yeah, so I'm not going to ask you to recalculate some of this because we have them. We can come back and refer to the question that we had previously. So now number one says calculate the interquartile range. We know that interquartile range is your Q3 value, not the position. Q3 value for Q3 value minus Q1 value. So we can go and find our Q3 value. So Q3 value. We need to go to position 38, which is 14. Keep that in mind. And we need to go to the Q1 value. We said it's on position 18. So we go to position 18. That is the value that we're taking. 11. So it's 14 and 11. Come to your question and you say Q3 is 14 minus 11. What is your interquartile range? It will be 3. That means that is correct. There is no mode on this. So remember the mode is the number that appears more than the others. So if you look at the values, already I can see that 9.1 and 9.1 appears more than the others. But it might not be the mode value. So I must look for other values that appears more than the others. 12.5. And 12.1 and 12.1 and 12.5 and 12.5 appears more than the others. Because these are 2. These are 3. 14. 14. They are 3 only and these are 2. These are 2. Okay. There is a mode. So this is not the mode. That's not the mode. I was just using it to check if there are more than one mode. So all of them are not the mode. The mode is the one that is having more than the rest of the numbers appearing. So this statement is incorrect because there is the mode. The mode is 12.5. The question asks you to calculate the mean. We can calculate the mean because they gave us the sum of X. So we can just divide by 50. And if you calculate that, 626.6 divided by 50. That's 12.5. That will be 12.5. The median is your Q2 value. So if we go to the question we answered, there was the position of Q2. We said we take the average of the two values. So we need to go to 26 and 25. So if you take 12.5 plus 12.5 and divide it by 2, you still get 12.5. So the median is correct. And then it says the distribution is symmetric. So the distribution will be symmetric if your mean is equals to your median. And sometimes even when it's equals to the mode. And if we look at our mode is also 12.5. So it should be B is the incorrect one. Okay. Once again on this one they also gave us the sum of the squared deviation around the mean has been calculated. And this you'll get less of whichever one if we're using a sample. So I'm going to assume that this is the mean minus the mean bar squared because that's what they say. The sum of squared deviation around the mean is calculated. We found that this is equals to 406,369. It means this is very important. We're going to use it to answer some of the question because the question says which one of the following statement is incorrect with regards to the variance and the standard deviation. And we know that the standard deviation is the square root of your variance. Oh, sorry. I must use s because we're talking about the sample. So this should be an s squared. And we know that s squared is our variance, which is the sum of your observed minus the mean squared divided by n minus one. So you can see that that information should be very valuable. Instead of using your calculator to capture all the information, you can use that. So the first one says the population variance for this question is 7.17. So I'm going to assume that they want you to calculate the population standard deviation of this question. But we also know that we are given the sample. So I don't know why we would have to have two populations standard deviation, but you can use your calculator to calculate the values. All what you do is capture all this information. I'm not going to ask you to calculate now because it's going to take you forever to do that. So, and if you watch, I think one of the videos that we did, I think we did do this exercise. But if we don't get to it, we will do it. The first thing we do on Saturday, we can come back to this and look at how we calculate the mean and the standard deviation on your calculator. We'll go through that. So you need to calculate the population variance. I'm going to answer the questions that we should be able, we can answer. But we can also answer this question. It's very easy because we know that the population standard deviation is the square root of your variance. And your population variance is the sum of your observed value minus the mean squared divided by n. Now, the difference between the two is that the mean bar and the mean are the same. The sum of your observation and or capital letter n. You can use the same formula to calculate both of them. So we can calculate for the population because for the population, all what we need to do here is to calculate 4.60369 divided by 50. And for this, we're going to say 406.369 divided by 50 minus 1. So do both calculations and tell me which one is which. I will put the values. First one is 8.127. For example, this one, this site is 8.127. No, since it's the other way around, that one is 8.293. The one on the left. The one where you divided by 50 minus one. Okay. Is 8. Yeah, I got 8.293 for the one on the left. Yeah, I wanted the answer for that. 8.1. No. Lizzie, I'm going to check again. Sorry. Let me maybe I'm messing it all up. I've got the answer for the right one. The one on the right. Okay. The answer for the right. 8.127. For the one on the right, it's 8.293. I'm getting different answers. I'm sorry for the one on the left. For the one on the left is 8.293. Okay. So remember, this is the variance. In order to calculate the standard deviation of the same, we're going to say the square root of 8.127. That should give us the standard deviation of the population. And yeah, we're going to say the square root of 8.293. So the square root of 8.127 is 2.85. Okay. Hold on to your answers just now. Let's look for the variance. The population variance, we know that this is incorrect. It's 8.127. So 8.127. And the sample variance, which is 8.293 is correct. Now I asked you to calculate the standard deviation, which is the square root. So for the population is the square root of 8.127. And what do you get? 2.85. So that is correct. Okay. And the sample standard deviation. So it means yeah, you need to calculate 8. The square root of 8.293. 2.879 or 2.88. Yeah. So that is correct. So the only incorrect answer here is number A. On Saturday, I'll show you how to calculate the mean and the standard deviation of the whole table. Okay. So where are we now? We are on 11. So we left with two more questions than we done. So you will bear with me. Consider the sample data values, 100, 104, 110, 111, and 112. Calculate the coefficient of variation. Now here is where I will rely on the calculator now. Because also it's going to be very difficult to do this because your coefficient of variation, which we didn't talk about as well. So coefficient of variation is your standard deviation and divide by the mean. So it means you need to calculate the standard deviation and then calculate the mean. And is it in decimal? I'm going to assume that you multiply by 100. Usually we multiply by 100. And if they didn't multiply by 100, you can remove the 100 from the equation. So it means if we need to calculate the mean, so I'm going to ask you to calculate the sum of all the observations divide by N. So N of all of them, 33. 537. 7. Divide by 1, 2, 3, 4, 5. There are 5 of them. What do you get? 107.4. 107.4. That is not the answer, Ne. Don't be excited. I got the answer. No, we still need to calculate the standard deviation. Now this is where it gets a little bit tricky because then now you need to work it out quickly. So yeah, we're going to say 100. Because we say the formula for the standard deviation, if I write the formula first, so that I don't do the shortcuts, let's do that. Is the sum of your observed minus your mean squared divide by N minus 1. Remember that. So now we're going to say 100. 100 minus the mean of 107.4. You need to square the answer. Edge 104 minus 107.4 Squat plus 110 minus 107.4 Squat plus 111 minus 104.107 Squat plus 112. So this square root must go all the way plus 112 minus 107.4 Squat divide everything by how many they are? They were 5. 5 minus 1. So it might take us forever. My calculator expired. So I can use my calculator online. I got 26.8. When you take this square root as well now. So the answer you get for S is 26.8. Yeah. Am I right? And that's what do you get? So calculate that very quickly and see if we get the answer. Don't leave me alone. 26.8. So your whether the answer is right or wrong. It depends on you guys because I didn't calculate. So I'm expecting you to give me the answer. And that is not the right. So someone should have the correct answer. Yeah. My mistake. Five points. Five points. One, seven, six, eight. Five points. Just hold on. Let me remove that. So the answer on this whole monster thing. Five points. Five points. One, seven, six, eight. One, seven, six, eight. Which is the same as that is not the answer. But we're going to use that. So five point one, seven, six, eight. So five point one, seven, six, eight. Divide by 107. Did you calculate that? Five point one, seven, six, eight. Divide by 107.4. It's zero point. Zero four. Zero zero. Zero point zero four eight. So you need to multiply that by a hundred. And the answer is four comma eight to zero. I'm sorry. I'm going to multiply by a hundred. And that is four comma eight to zero. Which is action B. I will also show you on your calculator on Saturday, how to calculate that before we start the session. On the other chapters. So let's see what the lecture's answer was. It's B. The last second question. Because I think 13 is the last question. So let's see. Oh, yeah. So we should, we are right on time. Two minutes should be able to answer the questions. Which one of the following summary measure is not used in a five number summary? Oh, we did that. We did that. Which one is not measured in the five number summary? The five number summary is your box. The five number summary is your box with kaplot. So maximum value is your highest value. First quarter, third quarter coefficient of variation CV is your standard deviation divided by the mean multiplied by a hundred. Minimum value is that. And we know that this is your Q. Your Q2. And here you can calculate interquartile range. So the only option that is not supposed to be there is the last question. This is different data. Oh, gosh. So given this information, which of the box plot we can represent in this data set? That's what they are asking. So if I look at their box plot, let's make it smaller so that we can see all of them. So if this is our box plot, A, B, C, E, or D, or F, that is represented on this data set. So in order for you to know that, I would suggest that you calculate only one thing. And that one thing will tell you because we know that this is your minimum, your Quartal 1, your Quartal 2, your Quartal 3, and your maximum for all of them. Maximum, Quartal 2, Quartal 3. It will be for this one, they have the same Quartal 3 value, but they have different Quartal 2 values. So all of them have different Quartal 2. So I will accept that one in this. The pink one and the green one have the same Quartal 3. And B and D have the same Quartal 1. So there's no way to hide. So I'll calculate two things. So choose one. Whether you calculate Quartal 1 or Quartal 2. So remember Quartal 1, Q1, it's N plus 1, divide by 4. So there are 1, 2, 3, 4, 5. So there are five values. Plus 1, divide by 4. What is the answer that you get? 5 plus 1 is 6, divide by 4. 1.5. 1.5. So it falls between two values. Also, your data is sorted because it's 115, 120, and 125. So 1.5 is located between two values. So my Quartal 1 value will be 1.5 because it's 1.5 plus 1.5. So my Q1 is not 1.5, it's 115. So this cannot be because this is below 100. So it cannot be that. So it can either be those points. If I draw, so it cannot be that. It cannot be that. It cannot be that. So I'm left with the two. The three, the pink one, or is the pink, what color is it? The green and the blue. So let's calculate Quartal, let's do Quartal 3. Let's do Quartal 3 because they all have the same Quartal 2. If I calculate Quartal 2, I'm still back to square 1. So let's calculate Quartal 3, which is 3 times n plus 1 divided by 4. So they are 3 times 5 plus 1 divided by 4. 6 times 3 divided by 4. It's 18 divided by 4 is 4.5. So it's 4.5. So it means 1, 2, 3, 4.5, it's between 125 and 130. So you take the average of the two. So 125 plus 130 divided by 2. It's 127.5. 127.5. So if this is 120, so anything below that will be out. So this will be out and I'll be left with, this is very tricky. So which one? This says the maximum value is on 130. So is that the correct one or not? That won't be. So let's see. I would go for, I would pick the one on the left. Which one of these? Simplifies the values. So I will also go with A because this looks odd because it doesn't have also, it doesn't extend to 115. It doesn't have the, the whisker. So I'm going to assume that A is the correct one. So let's see what your answer is for this one. C is the correct one. How did they get to see? Let's see. How did they get to see? It's just to agree they are wrong. Because if, if I have to draw a box whisker from the information that we have. So Q, Q1, Q3 will be there and because these are the same and that will be. So the maximum value should be one third. Also I don't even think that A should be the right one because it says the maximum value there will be 140. So that should be because it will not have a, a whisker because 115, they are the same. So that's Q, Q1 so that there's no whisker. So E should be the correct answer here. If you look at E, let me remove all these things. If you look at E, it says Q, Q1 is 115. If I go there, that is 115. That's my Q1. And we could calculate the median because the median will be the middle value, which will be that because it is 5 plus 1 divided by 2, which is 6, which is on position 3. Position 3 is 120 and that is on 120. And then we have our Q3, which is at this point which is 127, it cannot be 120. So it should be somewhere above 127 if this is 180. Let's leave 180 there. So this is 130 and that is 130 and this will be 127. And that will be 180. So the correct answer here should be E, not B. Possibly, copy and paste issues. It might be that for this version of part 13, only for this question of the part 13. So we ever got a different data set. It might have been the answer would have been C, which is the correct one. So in order for you to know which one is correct, you need to either calculate Q1 or Q3 or Q2 to see which one is different from the other. You also need to take into consideration your maximums because this is a box risker. The five number summaries are very important when you checking the box riskers. So the answer is E. So four marks. I'm not sure if you guys got three marks for this one as well. Or maybe it's only for those who got this question with this data set. Okay. So that concludes our session. So we already have done studying it one, two, three revision. On Saturday, we'll see. I think we will start with study unit four, five. I also want to do study unit six, depending on the time that we have. Because I want on Saturday, Saturday is there fourth. I want us to do four, five and six study unit. And then on Wednesday, which is the eighth of September, I want to do seven, eight and nine study unit. And then on Saturday, because we don't have to Saturday the 11th of September, we will do study unit 10 and 11. And study unit 10 and 11 should be fresh in your mind because those are the study units that we used last. So we did them last. So after this, this is part of the revision because it's going to take us longer. It took us two hours to do dating questions. All this study unit four and five has, I think also 18 questions or 12 questions. Study unit six and seven had 18 questions. Study unit eight and nine also I think similar. So probably it will take us roughly the same amount. But because those study units we do a lot of calculation might take us longer than this one today because today was mostly theory. So we'll see how it goes because I want to start with the exam question papers on the 15th. So the 15th of September, you will start with your exam prep. So depending on when does your lecture give you your mock exam paper. If he releases the mock exam paper around the 15th of September, then you would have already had the chance to look at the practice exam paper that I would have posted on our site, on my UNISA site. And then on the 15th and the 18th, we will do that exam prep and then after that, then we will do the lectures one because you also had had the chance. So on the 22nd and the 25th, 22nd and 25th, we will do the mock exam. So probably this is your, this is your plan for September. So 15 and 18, September 15 and 18th, Wednesday and Friday, we do the exam prep practice. I'm going to call it the practice exam paper. And then you will do the mock from your lecture. And then that would have been the 22nd and 25th. Why do I have 25, 225? And then I will give you an exam paper, not exam exam, but the final prep exam, which is timed on the 29th. On the 29th, we will do the timed exam paper. So that is two hours, remember? So we will sit here and you do your exam online, timed. So you will go to your My Unisa and you do your exam. And after two hours done, then we are done with the session. And then you will get automatic response with your answers. Then that will be the timed one on the 29th so that you can't prepare. I want people who are prepared to take an exam. You don't have to show me your camera or anything like that. You just sit here and pity. It will only be those who have My Unisa who can use that. But what I will do, I will also print. I will also save the paper as a PDF and email and post it here on the system or on the WhatsApp. I'll give it to you on WhatsApp. But I will only give it to you before you write the exam because I want you to feel the pressure of the exam. And then on Saturday, we'll discuss your experiences and all that and issues that you had and the time and where you spent most of your time. Because then it will be end of September. And then after that, I don't know what else you would want from me because then you should be preparing to write other modules, exams as well. But I will still be available for any assistance in October. So we'll decide after that what next before you go write your exams. So that is the plan of me helping you, preparing you or getting you ready to write the exam. You can embrace the experience or you can just watch. And then we'll have a discussion when the results comes out. And with that, I see that I took forever with MK. Or Sandile, do you want to say something? Yes, ma'am. I just wanted to ask on the previous question. Is it normal to get an option that would have a box without a whisker and it would be correct? Because I would have just ignored it. It would have been normal because if my Q1 values are my last values, then I won't have a whisker because I don't have a minimum value. Like we have, yeah. So the same way, if this was 125, we wouldn't have the whisker. The box would just be the box without the whiskers. So that would have just been a box with the Q2 line. Because if the value was 115 and this one was 125, because we got 4.5. So it would have added 125 plus 125, which would be 125. So then it means there is no mix and there is no mean value. So it is possible. Okay. Any other questions? If there are no questions, enjoy the rest of your evening. I will let you know when the recording has been uploaded. Otherwise, if you have subscribed to my channel, you will get a notification when I upload or when it's ready on the YouTube. Those who watch it via my Unisa, you will have to wait a little bit longer. Enjoy the rest of your evening. Bye. Bye-bye. Thank you. Bye. Thank you. Bye.