 Hey, and welcome to your second session where we do revision. I am going to share my entire screen so that it enables me to navigate between the programs. I just need to close some of the things that are open, things that we're going to be using right now. And so we're going to continue with today's session with study unit. I think we did study unit one and two and a little bit of study unit three. So we just going to finish off with the study unit three content. And remember with study unit three, we stopped at this point where we needed to answer this question. And I said, I'm going to show you how to answer the question on Excel, on your calculator, whether you're using a Casio or a sharp calculator. So let's get down to that. So on, I will start with the calculator. On your calculator, let's start with a Casio or a sharp calculator is the one that popped up. Remember to capture your data. You have one unit or we call it a univariate data set or one variable data set because you only have one sample. You don't have X and Y. You have only the X data. So you need to press the mode and then you need to take your calculator to state mode zero, which you say mode and then you press that, which leads to one. And the state zero is SD or this standard deviation or SD. You can call it SD and then you present and your calculator is ready to capture the data. You can, because it's just one univariate, you can do row by row or you can do column by column. So I'm going to do row by row. So my row is 29. Leslie, can you please share your screen? Am I not sharing my screen? I am so sorry. I apologize for that. I thought I am sharing my screen. Oh, yeah. I'm sorry. I said sharing my entire screen. Are you now able to see my screen? Yes, thank you. Sorry about that. Okay, so we're going to continue with study unit three. And the last question that we ended up with was question number 14. We needed to calculate the value of X web and I said we're going to use Excel and the calculator to calculate the values. So I'm going to start with, with a case, you know, I just want to take it back out. You go mode and you go step and you get state zero. And we are ready to capture the data. So I'm going to go 29 and plus 30 and plus 31 and plus. 1, N plus, 31 N plus, 33 N plus, 34 N plus 33 N plus, plus 38, plus 35, plus 36, and plus 34, and plus. And if you made a mistake, you just did that game, you just did your calculator. Second function CA will clear the values that you have captured. So it says I've captured 15 data sets. So three, six, nine, 12, 15, they are 15. So it means I've captured all of them. And once I'm done, I can just press on and off. Oh, not the on and off, there is a H. You see, because this is not like a normal calculator, you press on the on and off, I did press the second function and it switched off. OK, so now I need to calculate the value of the summation of x squared, which is the summation of all these values squared. And where you get the summations, they are all written in green. You can see there on the plus or minus, the summation of x squared on the dot, it's a full stop. It's a summation of x. On two is summation of y. On three is summation of y squared. On one is summation of x, y. And on four is summation of x bar, which is the mean. And this is the mean for the population or the mean of the sample. And your five is your standard deviation for the sample. And six is your standard deviation for the population. And if you need to calculate the variance, you would press the second function. Oh, sorry. You will press the x squared button for the variance of standard deviation for the sample or for the population. So our question is calculating the summation x squared. So the sum of x squared, we first press the alpha button and then you press the so minus and press equal. And that will give you the answer. And our answer is optionally. And that's how you will use your calculator. You need to practice all this so that then it makes it easy in the exam to use your calculator. So that is if we're using a sharp calculator. If we are using a case your calculator, the steps are almost exactly the same. You need to take the calculator to state mode zero or to state mode. Here you press the mode button and you will press the number that corresponds to the state and you will press the one minus bar, which is button number one. And you can capture the data. I'm also going to use the row. So it's 29 equal, 30 equal, 31 equal, 31 equal, 31 equal, 33 equal, 34 equal, 33 equal, 33 equal, 33 equal, 33 equal, 46 equal, 38 equal, 35 equal, 36 equal, and 34 equal. And I have captured all 15 of them. And I'm happy you press the AC button and your data is stored. The data is stored on your calculator now because the case your, the values of your X and the X square are not visible. You need to press the shift and the state, depending on the type of case your calculator you have, some have the var and the SD or something like that. So you've got the two buttons for state, but look for the one that says STA or var. That's the one that you're going to be using. So you press shift and we press the STA because it's written in orange, we press shift first. And you will have all the numbers that corresponds to letters like type, data, it takes you back to the table. The sum is where you're going to find those some summation of X, the sum of X square and then the var is where you calculate the standard deviation, the mean and all that. And then the mean and the max will give you the minimum value and the maximum value. So we're interested in the summation. So we will press button number three and the first one is X square. So which is the one that we are looking for and then we press one and we press equal and the answer is the same. And that is if you are using your case your calculator. So let's forget it when we are using the Excel. So when you're using Excel, I'm just gonna bring the Excel and minimize it because I want to be able to see all the values. I don't need all of the columns and I can just call this the beta column or you can even study it at the beginning. It doesn't really matter where you put your column or you can put it in A or B. Just gonna put it there. So 29, I'm gonna write them as a, in a column, not in the row the way they've written them so that I can use the information from part. 31, 31, 31, 31, 31, 31, 31, 34, 33, 33, 33, 36, 38, 85, 36, and 34 when it is on 16, I know that I've captured all of them because my first rule is my header. So because I need to calculate x squared in order for us to calculate x squared, I need to calculate x squared in order for us to calculate x squared. X squared is the same as, we can take this value and multiply by itself. Multiply by itself and say equals that will be, and you just put, you just drag, so from calculating the first one, you say enter and you just drag from the corner everything and then at the end where we are at the bottom, you can just say this will be your summation of x which is your total, which is the sum of all of the values. So I can do total here total and I can do the summation, summation you will find it at the top so I can expand the excel as well so that you can see all the columns here. So on here you have the summation. If I press the summation, it will add all the values of the data and it will enter. It added all these values that are here in order for us to get these values, you can also just drag, it will calculate all the values. Something didn't work out right. Did I capture the values correctly? That's the question. Yes, I didn't capture the values correctly. The last one is 34. So in the exam as well, you will need to make sure that you pay attention to the details for my last frame is 34. I can chart it as 36 or 35 and the answer is the same. That's what we have there, 173. Okay, so that's how you can use Excel or you can use your calculator, whichever one you feel comfortable with use, especially when they're giving you the data. Any questions? No questions, no comments. Okay, so let's move to the next question, which is question 15. So question 15 says using the same sample data, calculate what is the value of the summation of your X observation minus the mean squared, which is the values on the observation values minus the mean value. So we didn't calculate the mean value, we calculated the sum of X squared. So now on your calculator, because you have stored your values on your calculator, you can just press the on and off button. We calculate the mean because that's what we need. So that's the only thing you can do. So you just calculate the mean and the mean is 33.8. That's the mean of this data set. So that is the mean of this data set. Which is 33.8. So we don't record that. The mean is 33.8. So now what we need to do is we need to take 29 minus the mean and we square the answer. And 30 minus the mean square the answer squared plus 31 minus the mean and so on. So I'm not gonna go and do it on the calculator. I'm gonna do it on Excel. So on the Casio as well, you can calculate the mean press the AC button, shift, start. You go to var, it's four and you press equal. Oh, sorry, you go to two and you press equal. And the answer is 33.8. That's the mean. On your data set, I'm gonna come back to our Excel because it makes it easy for us to work here. We can calculate the mean. The mean of the data set, you remember, the mean is the sum of all the values divided by how many they are. So I can just count how many they are and that is the mean, right? So you just take the total divided by count of all the values that you have. Or if you know that there were 15, you can just say it is 510.7 divided by 15 and it will give you, let's say, 33.8. Now, we need to calculate this whole thing. My apologies for our mean and we supposed to say 15 minus one, so it shouldn't be 14. Nope, remember your mean, whether it's for the population or it's for the sample, the mean of the population is calculated by the sum of X divided by N. The mean of a sample is calculated by the sum, sorry, I'm using the wrong word. Sorry, I wanted to say the X bar, not the mean, our N. Is it not supposed to be 114? Nope, the mean of the sample is the sum divided by N. So the mean formula is the same whether it is for the population or the sample. Your formula is the same. It's just that when we represented mathematically for the population we use a capital letter N and for the sample we use a small letter N. But the formula is exactly the same. The only difference is the standard deviation. We're going to get to that just now. After this question, the next question is calculate the variance. The variance or the standard deviation is where the difference between the two formulas are. Okay, so going back, let's calculate what is inside the bracket first. So it's your observation, which is this. I'm going to change my data to X. It is my X divided by my X, sorry, X minus my X bar, which is inside the bracket. So it will be that value minus the mean, which is the value at the bottom. Now, if I want to keep the mean constant for all the values, I need to go to the mean on the red one. I'm going to put a dollar sign in front of B and also a dollar sign in front of 18 to lock the cell. So it means for all the columns on here, the only thing that will change is the X. The mean will stay the same. So I'm going to press Enter and I'm going to drag the whole thing across. And that is, if I click on this one, you will see that the mean stays the same. If I didn't lock the cell, when I drag, it will go on and include the other values like 19, 20, 21 for the mean, because it will be looking at the next column, next column, next row, next row, next row, not next column, next row, next row. So you need to lock the cell for it to work. Okay. So then you have your X bar, which is everything inside the bracket. Remember, that's everything that is inside the bracket there. We still have to do the square because we need, you have two choices. The last time I showed you by saying the square, you can calculate it by taking the same value and multiplying by itself. Now I'm going to change that because I'm going to do it on this side. So I'm going to change this value and I'm going to put the X squared, X minus X bar, and we're going to square the answer. Remember, we need to square the answer. So that's what we're going to do. So the same button that I'm using on button number six, I don't know if on your laptop's way is the Gabby's. The Gabby should be on the letter six. Six on the row. And then if you are using some, calculate the laptops where the numbers, you have a number of functions on the side, you must look where your Gabby is at. So we're going to use the X squared for the power. So let's do that. So we say equal this same value and we just say Gabby to, it will create to the power of, so it's the same. So if I can show you that is the same, let's do on the left side. We take this value, we multiply by itself. It gets you the same value. So you can either take the value multiply by itself or use the Gabby's squared. And we just drag because it's the same till the last and for the summation, I can just go there and do the summation. So it is my summation button and equal and that is the answer. And because our answer is in two decimal, we can just use the decimal point at the top where it's number formatting. We just format by moving the point and this reduces the decimal, this increases the decimals, reduces and decreases. And that's how you will use Excel if you have to use Excel in the exam and that the answer is option E. Otherwise you can calculate this manually the same way as I did. So manually you will take your calculator and say 29 minus 33.8 square on your calculator and then plus and so on. So the next question, unless if there are any questions from you guys, no questions. The next question is asking you to calculate using the same data calculate the sample variance. Like I said, remember, for the population, the variance will be the sum of your X observation minus the population mean squared divided by L. For the sample, the sample variance, it will be the sum of your X observation minus the mean squared divided by N minus L. Those are the things that we need. So now, because this is easy, we already calculated the top part, right? We found that it is 236.4. You can just substitute 236.4 divided by 15 minus one and that will be easy on your calculator. Calculate. I can take back to normal mode. 236.4 divided by 14. Because 15, it's minus one. It's number, 15 minus one is 14. So the answer is 16.885. We round off to two decimal and the answer will be option A. How do we round off? Remember to round off correctly. If the number to the left of way you want to round off to, it's bigger than or equals to five, you add one to the right. Sorry. If the number to the right of way you want to round off to, it's equals to five or bigger than five, you add one to the right. If the number is less than five, you do nothing. That is something wrong. On your... I don't have to use the cashier. So those with the fancy cashiers, I need to take back the calculator to normal mode, which is the med mode. In order for me to use the fraction, 236.40 divided by 15 minus one, which is 14. And you get the answer like that. And you just press the SD, it changes your values to a decimal. And you just round off. And that is it. The next question, unless if there are any other questions, because I'm moving too fast. Sorry, Lizzie. Can you go back to the previous screen? Name, thanks. And if you want to use Excel, you can also answer the variance question, because you already have your total there. You can just add another column here and say, I want to calculate the variance. And you can just say the variance is that value divided by, and you can also go back and say, count the values. Come on, sorry. Let's not use count the values. We can say open bracket 15 minus one. It would still work out the same. And you can reduce the number of decimals. Go back to home and you go back to the number formatting to reduce the number of decimals. And that will give you your variance. If you want the standard deviation, if you want to calculate the standard deviation, you just take this square root, you just press square root of the answer you got, and that will give you your standard deviation. On your calculators, you didn't even have to do it manually like that, because I cleared my calculator now. Oh, gosh. In the case you, I cleared my calculator on the shop. On the shop, I cleared my calculator. On the case you, I didn't clear my calculator. Did I? I did because I went out of the state mode. I went out of the state mode. Yes. So if you didn't clear your calculator from state mode, you just go back and say shift, and then you will find on the bar, you will find your standard deviation, the variance and all that. Now, because what takes me? Sorry. I need to go to the next question, which is question 17, which asked about the coefficient of variation. So I need to go back and capture the data again. 29 equals 30 equals 31 equals 33 equals 34 equals 33 equals 34 equals 34 equals Okay. In order for you to calculate the coefficient of variation. So you also need to know the formula. Coefficient of variation CV given by your standard deviation divided by the sample mean. So on your case, you easy man off. Are you standard deviation shift stat? You will find it under the four bar. Your standard deviation. Remember it is the sample standard deviation is sx. So you're going to use four and you're going to divide that by going back shift go back to four. And we need the mean, which is true. And you have s divided by the mean and say equal and that will give you all the other thing as well. Multiply by a hundred. Do the same when you calculate. Just multiply the answer you get by a hundred and that will give you the coefficient of variation. So there are twelve point sixteen percent. So which is option a that is on the case. You're I'm going to go to the excel on your excel. Your coefficient of variation CV you have the mean you have the standard deviation. So it's easy equals your standard deviation divided by your mean equals and we need to multiply by you can also say multiply by one on there. You will see that it will change. Okay, doesn't change. Multiply by a hundred will change to twelve point six and you just point sixteen the same on your I don't know how many of you are using a cashier calculator. I need to go back and capture the data again. Zero and it's twenty nine and plus thirty and plus eighty one plus thirty one and plus thirty one and plus thirty three and plus 34 and plus thirty three and plus thirty three and plus three and less forty-six plus eighty eight and bless 35 N plus 36, N plus 34, N plus. And then we have all the data set captured. We can just go on and off. We need to calculate your standard deviation. Also pay attention. It's button number five, which is SX, and button number four, which is the main. So just press alpha, button number five, divided by alpha, button number four. And then we'll press equal and you multiply that by a little bit. And that is 12.16. Showed you Excel, Casio calculator, and a SHAP calculator. In order for you to practice this, you need to stop the video and try and practice on your own as well. And make sure that you are familiar with your calculator. The more you do exercises like this on your calculator or using Excel, the more you will get it right in the exam as well. Because you cannot practice and hope for the best in the exam. You cannot do that to yourself. You need to practice so that then the steps comes easier. And seamlessly, you don't have to always go and make reference of some sort. You just know what you need to press after you have done something as well. It means practice, practice, practice. Okay, so that is measures of variation and measures of central tendency. I think the next questions are more about other things. So yeah, we're talking about the empirical rules. With the empirical rule, it also uses the measures of central tendency and the measures of variation. So you also need to be able to know how to use your calculator if you are using your calculator. Because you need to calculate the mean, you need to calculate the standard deviation. As we know that other for you to specify whether things are symmetrical or not symmetrical, we use the mean and the mode. So if the mean is equals to the median, we say things are symmetrical. If the mean is less or it's greater than the median, we say it is skewed. In order for you to know which one is which, if it is negatively skewed or positively skewed, you will need to go and find out which one is which now, based on the sign. So those are the things that you need to be aware of. We do answer this question. And then there, the next ones, which are A, B, D and C, it's asking you for a 68%, you need to go and calculate the mean and calculate it's A plus or minus one standard deviation. So it means let's do it this way. You will start with the minus and the mean plus the standard deviation. And that will give you between, because it will be between those two values. For A95%, you will calculate, you will have your mean minus two standard deviations. So you will say two times the standard deviation that you have. And you will do the same, the mean plus two standard deviation of the values. And for the last one, let's say, it's the mean minus three standard deviation. And the mean plus three standard deviation, and that will give you the answer. So if you are able to calculate all of them and find that they are between each one of them, we're looking for, which one of the statement about the empirical rule or the distribution of graduates, that's in salary is correct. We're looking for the correct. So the first thing that you need to do is make sure that your data is sorted from lowest to highest because in a way, the median, you will need to find the position first. So the data, looking at it in this query about that, I was able to hear me. Ease, you can hear you. Thank you. And you're ready. So let's start with the median. It's easy with the median and then the rest, because there are more of us using our calculators. So to calculate the median, we need to find the position. So the data is sorted in order from lowest to highest. So to calculate the median, we need to find the position. We need to count how many they are because they told us that they are 16. So I'm going to assume that they are 16. You can also double check, open five. 16 plus one divided by two, which is 17 divided by two. It is how much? 17 divided by two, it's 8.5, right? So therefore it means it's located between two values. So let's go and find the two values. One, two, three, four, five, six, seven, eight. When five, it's between 191 and 191. Therefore the median is 191. That is our median. To calculate the median, oh, the mean, sorry. To calculate the mean, you can use our calculator. I'm just going to use the Casio calculator only for now because it fits. I lost my Casio calculator. I just need a second. I need to stop sharing so I can go grab my Casio calculator again. My machine stopped. Everything stopped. Otherwise, we can just click to you and use the shop at Excel. If this takes long, it must have gone into the service now. OK, so let's go back. We found that the median, our median was 191, right? So because 191 plus 191 is 192, 382 divided by 2, it's 191. So it will be the same. Now let's calculate the mean. To calculate the mean, we're going to use to capture all the values. 05 equal, oh, I need to put the calculator to state mode. State mode 2, 1, we're still using one variable, 2, 05 equal. 105 equal, 121 equal, 136 equal, 144 equal, 159 equal, 179 equal, 191 equal, 191 equal, 191 equal, 201 equal, 217 equal, 229 equal, 252 equal, 261 equal, and 374 equal. I've got all 16 values. Off, shift, set, 4, and 2 equal, and my mean is 177.25. Actually, you need to multiply all the values that you get by 1000. So for example, the mean there is 191,000. So it means the median is 191. The mean is, we found that it was 197 times 1000 will be 250, 197,000. So our mean is not the same as our median. So it means it's not symmetrical. And then now we can calculate the standard deviation. OK, so we should be able to answer, before we even go to calculate the standard deviation, we can answer the two questions based on those two. So because the mean, number one, this will be correct if the mean is the same as the mean here. So we can see that they are not the same. So this is incorrect. The number B, it says that the distribution is positively skewed. How do we know that? Therefore, it means the mean is greater than the median. So if the mean is greater than the median, then your data is positively skewed. So is it greater than the median? It is because the mean is 197,000, whereas the median is 191. So the mean is greater than the median. So number B is correct. How do we calculate the empirical rules? We need to find the standard deviation. So let's calculate the standard deviation. So to calculate the standard deviation, we just say shift, set, go back to four, you press four, OK. And press equal and multiply that by 8,000. I'm just going to, for now, I'm just going to leave the mean as, so that then the calculations are easy to follow and calculate. I'm just going to use the mean of 197.25 plus 60. I'm just going to use 10-0 and 6-0. We're just going to use those two. So it will be plus or minus. So we start with the minus first. So let's calculate the minus first. I'm going to use this one. So let's take it back to normal mode. It's 197.25 minus 64.60 equals 832 multiplied by 8,000. And that is 182,650. And it's between the next one would be. And then I'm going to ask you to do the DNE anyway. So the next one is 197.25 plus 64.60. Multiply by 8,000. That is 261,850. Then calculate the next one. So this one will be 197.25 plus or minus 2 times 64.60. So in order for you, you need to start with the minus first and give me the answer. So it will be 127.25 minus 2 times 64.60. And multiply the answer by 1,000. And what is the answer? Anywhat, are you guys working out or are you just watching me do the work? Are you guys still here? Or am I alone? Oh, you're still here. It's 68,050. 68,050 or 60. Am I writing it right? Yes. OK. And in the plus sign, 127.25 plus. Sorry, Liz. I used 197. Sorry about that. Oh, yes, we need to use 197. What did I use? I wrote it wrong. It's 197. I'm kind of confused. Where did we get the 64.60? It's the standard deviation. We calculated the standard deviation. Standard deviation, it's 64.60. All right, thanks. And the second one. 26,450. So small. 326. 320, yes. 326. Yes. OK, and then the last one is three standard deviations. So it will be 197.25 plus or minus 3 times 64.60. You first start with the minus. It's 197.25 minus 3 times 64.60 equals multiply by 1,000. It's 3,450. 3,000 is a 3,000 or 3. Yeah, wait. It's 3,450. Things are not working out for me. You'll have to read the digit. Oh, it's 3,450. 3,450. Zero. Yes. Hi. It's way too little. Are you sure? 3,450. Because if you multiply 64.60 times 193. OK. All right. And then there. And then on the plus side. It's 3,91050. 3,1391. 050. Am I right? Me right. OK. Yes. So therefore it means C, D, and E are also incorrect because they do not tie to the same values as they are here. So I'm going to give you a chance to do this one on your own because I have a number eight. 19 is the same as that one. So let's see if you can get it right. The data is different. But it's asking almost the similar question. OK. So you will apply the same method that we went through. So let's see if you are able to do this one on your own. I'm going to give you five minutes when you are done. If you are able to write in the chat, you can write which option. I know that the notes you have already, but I don't want you to just write the option A, option B. I want you to write what is the mean, what is the median. You must write those answers on the chat if you have the answers for that. You must write the standard deviation. So I want the answer for the mean, the median, and the standard deviation. You can write them on the chat, and then you can also start answering the questions. Are we winning? You must talk to us if you are lost. Sorry, Lizzie. Yeah, well. On the Casio calculator once I've added all my numbers. What do I do after that? I'm stuck. I can't go further. On the Casio. So once you've added your number, you just press the AC button. And then you press Shift. And then you press the stat. And you follow the instructions as it says. You press off of that. And then you will press 2. And that will give you the mean. You follow the same. I got it. Thanks. Yes, I got it. Thank you. Yeah. Let me just also capture the date. You must be very careful with this data set next. It's not all sorted. There is a number there, 222. Are we winning? Let's check. There's nothing on the chat as well. I cannot access the chat. OK. Well, if you answer, then we will be discussing that. Are we done? We still need more time. Or can we? One more minute, please. All right. Thanks, Lizzie. OK. So let's start with the median. What is the position would be the same as the previous one? Because the median position would be n plus 1 divided by 2. There are 16 plus 1 divided by 2. It will be on position 8.5. And remember, there is this value. You just need to locate it and put it right there. Otherwise, then everything is sorted. And start counting to 8.5. It will be 1, 2, 3, 4, 5, 6, 7, 8.5. It's between 2, 3, 2, and 2, 3, 3. So we're going to say the median is between 2, 3, 2, plus 2, 3, 3 divided by 2, which is going to be 2, 3, 2.5. Multiply that by 1,000 because the values are in 1,000. Multiply it by 1,000. And our median is 2, 3, 5, 0, 0. That's the median. What is the mean? Did you calculate the mean? The sum of all of them, given how many they are. What is the mean of the data set? Anyone? Shift that 1 since you're refusing to talk to me. I will calculate it myself. It's 242. That's the mean, 242. I'm just going to write it down here. Multiply by, since I don't have a lot of space there, multiply the answer by 1,000. So really, where do we get the 1,000 again? The salaries are in 1,000 of rents. So this values you are seeing here, 1, 3, 7, it's 117,000. So the mean is 2, 242, 7, 5. So you can come and answer A and B. Is the mean and the median the same? So there is the median and there is the mean. If they are the same, then they are symmetric. If they are not, so we know that if the mean is greater than the median, we know that it is positively skewed. And if the mean is less than the median, we say it is negatively skewed. This one, we can also say it is right. And this is left skewed or right skewed. So A and B, which one is the correct one? It is positively skewed. You know what you want to know? Take it off. So it is positively skewed. And you should be able to calculate this. You can do it on your own as well. So you have your mean and your standard deviation. Let's go back. Our mean, but the mean is, I can also go back. If we don't want to use the big numbers, we just use the small numbers. The mean is 2, 4, 2.8, 7, 5. And I keep this 2, 4, 2.8, 7, 5. And then your standard deviation is, you can just calculate the standard deviation by shift, stat, 4, and 4 again, equal. And that gives you your standard deviation, 8, 6, 5, 6, 8, 0. We can say 8, 0, 1, 8, 0, 8. If we can, the regressions. And then you use that to calculate. The first question, which is the first one, is to find one standard deviation. It's plus or minus your standard deviation. And the second one is plus or minus 2 standard deviations. And the last one will be plus or minus 3 standard deviations. And you follow the same calculations we did. The mean and the standard deviation. And then the answer is always to multiply by 1,000. And that should be able to get you to the empirical rules. And that's how you do the calculations for that. You can do this. And if you are struggling, you can always contact us on the WhatsApp. Moving on to the next question. Because we left with only 15 minutes for today. And now I want to finish all of this study unit 1, 2, 3, today as well, so that tomorrow we can do study unit 4 and 5. Now, consider the study salary for bachelor's signs graduate given below. Construct a box plot. So with this one, we need to calculate the quartiles. In the exam, pay attention to the question. Don't spend your time doing all the quartiles. Because in the exam, they will tell you which one you need to calculate. For example, like this one, they just want you to calculate the upper quartile. So remember, your box plot has five numbers summary. The smallest value, quartile 1, quartile 2, which is the same as the median, and quartile 3, which is the upper. So this is the lower limit. And this is the upper limit with the highest value. And from here to here, we can calculate the inter-quartile range. And from here to here, we calculate the range, which is your highest minus your lowest value. Inter-quartile range is your quartile 3 minus quartile 1 value. Those are the things you need to remember when you do answer questions on quartiles as well. And what you also need to remember is for calculating the quartiles, you need to find the positions. Quartile 1 and writing is what was even the last time. Quartile 1, you find the position by using n plus 1 divided by 2, not by 2 by 4. And quartile 2 is the same as your median, which is n plus 1 divided by 2. And then quartile 3 is 3 times n plus 1 divided by 4. You can use that. Otherwise, I'm not sure from which Twitter you're from. Some Twitter, they might prefer to use percentages. So if you use percentages to find the position, the percentiles to find the position, quartile 1 will be 25% of n plus 1. And quartile 2 will be 50% of n plus 1. And quartile 3 will be 75% of n plus 1. So they will give you, all of them, they give you the same answer. Yes, 25% of the entire data set and 4% of the equivalent. And all that. So you can either use either one of the formulas. OK, so let's find upper limit. So upper limit is quartile 3. Therefore, we say 3 times n plus 1 divided by 4, which is 3 times 2, 4, 6, 8, 10, 12, 14, 16. 16 plus 1 divided by 4. Then you just go and calculate and say, 17 times 3 equals divided by 4 equals 12.75. Quartile 3 is located in position 12.75. Now, the question here says, the value not the position. So this is 12.75 position. You need to also remember the rules. If it's 0.25, we round down. If it's 0.75, we round up. So therefore, it means on this one, the position is actually on position 13. So we need to go and count from 1 up until 13. That's where we will find the value of your quartile 3, not the position, the value. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Also, you need to make sure that your data is sorted from lowest to highest. So I'm going to start again because I disturbed myself. So the data is sorted by looking at it. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. It's 200 and 8. And it's none of the answers on there. I think the options on here are incorrect. But this is your quartile 3. I think this corresponds to another maybe another type of data set that they had. Because I think these questions had some errors as well. Any questions? If there are no questions, I'm going to ask you to do this one. Find the lower limit. Remember, the lower limit is your quartile 1. So finding quartile 1, we use the formula Q1, Q1. It's n plus 1 divided by 4. Or you can use the formula Q1. 25 percentile is 0 comma 25. 0 comma 25 times n plus 1. It will give you the same answer. 2, 4, 6, 8, 10, 12, 14, 16. 16 plus 1 divided by 4. And here you can do the same in 0.25 times 16 plus 1. Find the same answer. So what is quartile 1 position? Superposition 4, because it's 4.25. Yes, I'm looking for that one. So it's 4.25. Therefore, we round off to position 4. So it's on the fourth position. And the same thing on this site, you can do the same equals 0.25 times 17 equals 4.25. So you can use either one. You can see that they are the same. I just wanted to demonstrate that. So you go, is the data so attacked? That's the first thing that you need to establish. But the data is indeed so attacked from lowest to highest. And position 4 is 1, 2, 3, 4. You will, I just also want to double check something on this side, this side. I'm sorry, whether they didn't swap the data. OK, no, they didn't. OK, all right. And that's how you do quartiles. Do we have another question? Yes, we do. You have question 22 and 23. And that will take us to the end of the session. Question 22, and this is for you, not me. So you can just say it out loud. Which measures or which measure of central tendency is the most affected by outlier? I think it's a mean, number A. It is indeed number A. The measures of central tendencies are the mean, the median, and the mode. This is not the measure of central tendency. This is not the measure of central tendency. The mode is the number that appears more than the other numbers. So whether there is an outlier or not, it will not affect how you find the mode. The median is the middle number. Whether the number is higher there, it's out there or not, the number in the middle, or its small number out there on its own, as long as you are able to find the middle number, that's it. The mean is the only one that gets affected because the mean is the star of all. If you have a bigger number that is far apart from the rest of the number, your mean will be dragged closer to that. Imagine if in your company you are paying employees 3,500, 3,800, 4,000, and then you have an employee who gets paid 50,000. Let's say this is the CEO, he gives themselves all the money in the business. When you calculate the mode, let's say there is another person who ends 3,500. When you calculate the mode, you just say it's 3,500 because that's the number that appears more. So it means at least more than two employees in these companies are paid 3,500. So they are almost similar or the same salary, the majority of the people in this company. The median is what is the middle salary that you are paying in this company? So the middle will be 3,800 because the salary that is in the middle of all the employees is 3,800. The mean, you will have to add all of them and divide by how many they are. So you will add and divide by how many they are. And you will say that you are paying your employees 12,000 or something like that. You are paying your employees 12,960, which will be wrong because your employees are even any less than that. Because the mean will have your one employee would have skewed your data. So the mean is the only one. So I hope this, even if it comes out in the exam, you will remember it for days to come. Which measure of dispersion is not affected by our clients? Now, yeah, we're talking about the measures of dispersion are your measures of variability? So we already established that the mean and the median are not measures of dispersion because they are measures of centrality. I think the answer here is range, my sister, number E. Number? Number E, a range. Why is it? Why are you saying it's the range? Because from what I learned, what do you call outliers like sensitive to the range? So anyone who wants to try another explanation? OK, so the only one, yeah, remember, the range is your highest value minus your lowest value. So it's not going to affect your range because I thought maybe you would use this diagram that I drew now to identify or say things like that. The only measure that is not affected by outlier in terms of measures of dispersion is your interquartal range. Resid being is that it only looks at your quartals. Remember, quartal three and quartal two. This regards what is happening outside of the quartals, right? Whereas with the range, if you have an outlier, it would affect, especially if your outlier is your highest value. It would affect how the range of your data looks like. But your interquartal range, let's go back there to the blog. It will not because we're only looking at this and you won't have any outliers that affect that block. The only ones that will get affected will be the smaller value and the highest value, which you use to calculate your range. Your standard deviation as well will not be affected because it uses all the values as well, but it normalizes. So the only measure here is interquartal range. That is not, I might say, not affected by outliers. OK. And that concludes this week's, whatever we are supposed to do today, I was hoping that we can also do study unit four because of the lot of calculations that we needed to do, so it was not possible. So tomorrow we're going to look at study unit four and five. And I hope we're going to be able to finish all the questions from study unit four and five. And on that note, thank you for coming. Those who are looking for the link to the WhatsApp group, right? If I can still remember, I think it will be included in the recording if I'm not mistaken, but I don't think so because it's not part of the recording. I'm going to shut down and I'm going to stop the recording unless if there is any question related to what we have discussed today and what we have done today. Are there any questions? I was busy. My sister, please assist me. How can I get the notes because I've tried to check on your stuff, but they couldn't find the notes. All right, we'll sort that one out now. OK, so there are no content related questions, so we can stop the recording. Thank you.