 Remember that the session will be recorded and the recording will be on my UNISA over the weekend. Do you have any questions before we start with today's session? I know that we have one more minute before we start. Any questions that you want to raise before we start? Nobody wants to say anything. So you are all happy. You are all fine. Yes. Likewise, all sessions are interactive. Therefore, during this session, when we do exercises, I expect everybody to do the exercise and then we come back. We all do the exercise together or somebody answers the exercise. And please make sure that you are able to write on the chat. Those who can speak will stay in an environment where it is not conducive enough for speaking or talking over the video. You can write or you can type on the check. I tried to make sure that everybody is linked onto the group so that the chat capability can be activated for everybody. For those who joined as guests, the possibilities are you have used your Gmail account or your other accounts which are not my UNISA account. If you want to be loaded on the chat, you will have to join the group. I will send the link again on WhatsApp for people to join the group. Okay. So let's start with today's session. It's going to be short and sweet. So today we're only going to be doing Quart House which is study unit 3 and tomorrow we will do the probabilities from 12 until 2 o'clock. And by the end of tomorrow's session, you should be able to do all your assignment questions for assignment 1. So the agenda for today, how I planned it. For 30 minutes, we're going to just do the basic introduction to Quart House, looking at Quartile 1, 2, 3 and Interquartile range. And then from half past 7 until around 10 to 8, we will do the five number summary and some exercises in between. Then we'll take a break so that we can send away from where we are and also those who want to go get water, they can go get water and come back. Then we will do more exercises, not too many, but at least enough for you to be able to know how to answer some of the questions that might be asked regarding the Quart House. Okay. Any questions before I move on? If there are no questions, then we can dip in. No questions for me. Thank you. If in the absence of no questions, then today's session, by the end of today's session, you should have or you should be able to learn how to find the Quartile position and how to find the Quartile value. You should be able to calculate the Interquartile range from the Quart House and you should be able to identify the five number summary values. And you should be able to construct a box plot or read at least a box plot if you are given in the exam or in your assignment as well. So, what are the Quartiles? Quartile is a way you can split your data into four parts. So, say if we know that we have 20 values, we can split them into equal parts of 25% points, that every value will fall within that 25%, 25%. And the first 25% will represent your Quartile 1. So, any value, your Quartile 1 will be the value that is, most of the values are 25% of the values are less than or 75% of the values are more than that value. That is Quartile 1. Quartile 2. I should have switched off the notifications. Quartile 2. It's the same as your median. Remember last week on Saturday, we did the measures of central location. And we said one of the measures of central location was the Quartile. Quartile 2 is the same. Oh, sorry. One of the measures of central location is the median. Quartile 2 is the same as your median. Which represent 50% of the values will be below that value and 50% of the values will be above that value. And Quartile 3 represent 75% of the values will be less than or below that value and 25% of the values will be bigger than that value. And in order for us to find this Quartile, we first have to find the position. But before you can even locate that position, your data needs to be ordered from lowest to highest. Like the same thing we did with the median. So since we first need to find the position and then the data also needs to be sorted from lowest to highest in order for us to identify the position. Then once we have the position, we should be able to locate the Quartile value. How do we do that? How do we locate the Quartile value? Quartile 1, which the position for that Quartile 1, we find it by using the formula n plus 1 divided by 4. Once we have sorted the values and we calculate this Quartile 1, we will find that position there. And we will use that formula to find the position. For Quartile 2, since it's the same as the median, it's n plus 1 divided by 2. In the exam, all these formulas will not be given. So you need to know how to find these positions by heart. You must always remember that for the Quartiles, you will have to know the formulas by heart when you go to the exam. In case your exam is a written one where you have to go to the database. But if you're writing online, you will have access to this formula because you will have your books with you. The third Quartile is 3 multiplied by n plus 1 divided by 4. And that will give you your position where your n value is just the number of observations. So if they gave you 10 values, 10 will be your n. So let's look at an example. But before we look at an example, let's understand the rules. Because when you apply these formulas and we're calculating these formulas, there are values that will be whole numbers. There are values that might appear as fractions. There are values that will appear as a non-fractional value like 0.25 or 0.75. You need to know how to work with those things. And to do that, if the result of your Quartile position is a whole number, since your data is sorted, the value where you are will be your Quartile. So let's say for example, we calculated our Quartile. So let's say our values are 3, 5, 9, 15, 21 and 32 and 33. Let's say this is our Quartile. So we calculate Quartile 1 and we find after we use the formula and we find that Quartile 1 is on position number 3. It's a whole number. So because it's a whole number, so we just start counting 1, 2, 3 and that will be our Quartile value. And that's how we're going to use the Quartile position to locate our Quartile value. So therefore it means our Quartile value will be value number 9. Since my data is sorted in order. So what happens if the value becomes a fractional half? So let's say Quartile 1, we calculated the values and Quartile 1 is equals to 2.5. Let's say for argument sake, the answer we get we end up with is 2.5. So when it's 2.5, we say this value, the position is the fractional position. So therefore it means it will fall between two values. We will locate it between the two values. So 1, 2.5 will be somewhere in between those two values. When it is between the two values, we're going to take an average. What do I mean? It says I'm going to say 5 plus 9 divide by 2 and that will give me my Quartile value and my Quartile value from the position 2.5 will be 9 plus 5 divide by 2, which will give me 7. And that will be my Quartile value. We will find that the value that you get from the Quartile is not a fractional half. Let's say the value, let's say Quartile 1 when you calculate and you find that the value is 2.75. When it's 2.75, we're going to round up this position and say it is closer to 3 because the majority of the values are 0.75 closer to 3 and 0.25 less than 2. So it cannot be 2. So we're going to round this up to 3. Therefore, we're going to count and say 1, 2, 3 and therefore our Quartile 1 position will be positioned. It will be 9. In position 3, it will be 9. What happens as well? If the Quartile position, let me write it right there at the top. I'm going to remove this now again so that everybody can see. So let's say the answer you get is 2.25. When it's 2.25, we can round and estimate that this says the position is on position number 2. So we round down because it's not closer to 3, but it's also 25% closer to 2. So it means we can round down the value and estimate that the position is on position number 2. And therefore we go and say our Quartile value is 5 and that's how we do the Quartile. So let's look at an example in more detail with the real data. Let's say we have this sample data and we can count how many there are. There are nine values that we are given from the sample. If we want to calculate Quartile number 1, we know the formula is n plus 1 divided by 4. Quartile position, we substitute n is 9. So it will be 9 plus 1 divided by 4. It will give us 2.5. And that position, since it's 2.5, it will be located between 12 and 13. Since it's located between two values, we're going to take an average between those two values. So we're going to add 12 and 13 and divide it by 2 and we get the Quartile 1 as 12.5. And we can do the same calculation for Quartile 2 and Quartile 3. Any questions before I move on to the next? If there are no questions, okay, I see there is a question. Sam, your hand is up and your hand is gone. Okay, can you hear me? Yes, I can hear you. Good evening everyone. All right, my question is the Quartile number, can it be the number that is not on the number that we have? We have 11, 12, 13. So if they ask me what is the value for the Quartile 1, then I'll be saying 12.5 whereas we don't have 12.5 there. Yes, it can be a value that is not on there because if the position is located between two values. Let's say this was 14, then the Quartile value will be 13. Even though it was not on there, but it will be the value that is there because of you going to take the average of the two values. Okay, I understand. Thanks. Okay, so let's look at now how to calculate Quartile 2 and Quartile 3. So we already did Quartile 1. So we know that Quartile 1 is 12.5. Calculating Quartile 2, remember the formula for Quartile 2 is n plus 1 divided by 2. So n is 9 plus 1 is 10 divided by 2. It tells us that the position is on position number 5. So it's the fifth position, 1, 2, 3, 4, 5. Therefore 16 will be our Quartile 2. And since 16 is our Quartile 2, it is also called the median. You must also remember that Quartile 2 is the same as the median. And for this dataset, it's 16. To get to Quartile 3, we calculate Quartile 3. Remember the formula is 3 times n plus 1 divided by 4. So it's 3 times 9 plus 1, which is 10 times 3 is 30 divided by 4. The position will be 7.5 and you can count 1, 2, 3, 4, 5. So 7.5 will be located between the two values and we do the same. We take the average of the 2 and the Quartile 3 value is 18 plus 21 divided by 2, which gives us 19.5. Quartile 1 and Quartile 3, these are non-measures of central location and Quartile 2 is a measure of central location. And that's how you find the Quartiles. When you have the Quartiles, you can calculate what we call an interquartile range. The same as what we do with the variation, measures of variation then before, which is the range. Remember the range, your highest value minus your lowest value. So for the Quartiles, your interquartile range uses the values of your Quartiles, not your positions, but the values. So it means we're going to use the 12.5 and the 19.5 because we're going to be using the values, not the position. So let's learn how to calculate the interquartile range. An interquartile range takes your largest Quartile, which is Quartile 3, minus your smallest Quartile, which is Quartile 1, and it tells you the spread of your values at a range of 50 percent house. An interquartile range is also a measure of variability, and it's also not influenced by the outliers or the extreme values because it doesn't look at those, it looks at where 50 percent of the values of 25 percent and 75 percent of the values are located in. From the data set that we had previously, we know that there were nine of them and we calculated our Quartile 1 and we also found our Quartile 3 to calculate our interquartile range. Remember interquartile range is Q3 minus Q1. So therefore our Q3, Q3 minus Q1. Not the position, but the values. And our Q3 value was 19.5 and our Q1 value was 12.5. So it's 19 minus 12.5 and the interquartile range is 7. And that's it with Quartiles. Later on, we will discuss how we calculate, how we identify the five number summaries using the Quartiles and how do we plot the box plot. For now, there is your exercise. If you look at this data, the data is sorted because it starts from 159, 170, 172 up to 257. It is in order. Applying the same method that we did, you can answer which question is incorrect. But before you go and answer this question, remember, you can, for now, you can go find Quartile 1 position by using n plus 1 divide by 4 and go find Quartile 2 position by using n plus 1 divide by 2 and go find the Quartile 3 position by using 3 times n plus 1 divide by 4. Once you have found the positions, then you can go find the values. So once you have the positions, then you can go and locate your values from there and then we will come back and discuss the answer just now. For now, that's your exercise for 10 minutes or for actually for less than 10 minutes for five minutes. And then we will do the answers just now. Are you still busy or are you done? I am done. Yes, you are busy. Done. You are still busy. You have one minute. We're going to come back to the options. Which one is correct and which one is not correct? For now, I just want to do the positions. Who wants to go with me and do the positions with me? Who's volunteering themselves? Anyone? Any volunteer? Nobody? Sam? Your hand is up. I'm voluntary. Thank you. Yes. For quarter one. For quarter one. Quarter one is four. I got it. Let's help those who didn't know where did you get four from. I got four by counting the number of observations, which is 15. That will be N plus one. That will be 15 plus one is 16. And then 16 divided by four gives me the answer of four. And the position for quarter one. The position for quarter one is four. It's four. Okay. Let's continue to the next one. Quarter two. Quarter two. I have to get N by that 15. 16 over two. Which is. 16 divided by two is eight. So the position is eight. Okay. And quarter three. I said. I used the formula of three into N plus one. Over four. Then I got 16 into three, which is 48. Divide by four. And I got 12. So the position is 12. The position, sorry for my pen. Position for quarter three is 12. Position is 12. Okay. So since we know all the positions, we can go and find the values. So the values for quarter one. The value for quarter one is 173. 173. Quarter two. Because it starts from there, we count from 159, one, two, three, four, since the position was four. And that gives us 173. And for quarter two. It's 201. 201, because if we know that is four, five, six, seven, eight, that will be quarter. Quarter two, which is the same as the million. And quarter three. And quarter three is 217. Starting from eight, nine, 10, and 12. I should have switched off my WhatsApp. Quarter three. So if we're going to look at the answer, we are looking for the incorrect answer. So now you have all the values. You can just come in tick, tick, tick, and say which one is incorrect. So if we look at option number one, position of quarter one is four, and we know that it was four. So that is correct. The position of quarter two is eight. We can see that the answer was eight. That is correct. The position of the million is eight. Do you agree? Yes. Yes, you agree because I already also gave you the answer there. So therefore it's correct. The position of quarter three is 12, and we know that the position was 12, and we can find that answer there. The value of quarter three is 216. The value of quarter three is 217. Therefore this is the incorrect one. That will be the option we were looking for. Whose extent is difficult? Very easy. Wow. Into our next segment. The five number summary. Any questions before we... I can go back to the question. Do you have any questions? Before we move on. Anybody who is still lost and needs some clarity, your hand is still up or is it the historical hand? No, it's not historical. I tried to use the chat there to give the answer on the chat, but it failed to send. Okay, no problem. We can always chat like you've always been doing. Okay. Thank you. Any other questions? Nothing? So it's half past seven. So we sent in half past seven. We're going to look at the five number summary and the box plot. If we know how to calculate the interquartile ranges and the quartiles, we can use the quartiles to find, I think my slides are repeating themselves, to find the five number summary. So if we look at this, it's what we call a box plot. It's a summary of the five number summary of your quartiles. Where it also includes your minimum value and your maximum value. If we look at the blue box starting from there to there, that is the blue box. That's what we call the box. And the whiskers are those 25% length that goes out. At the beginning of the box at this point, that's where we identify our quartile one value because 25% of the values are less than that value and 75% of the values are more than. In the middle of the box, it will tell you your median. If there is a 25, 25 spread between the two values, then your data is symmetric. We will deal with that later on. It's closer to quartile three. We say it's due to the left. If it's closer to quartile one, I mean, I'm referring to the median. Then we say it's due to the left. And at the end of the block, at the end of the box, you will have quartile three value defined, which tells you 75% of the values are more than that quartile three value and 25% of the values are less than that value and 25% of the values are less than that value. And at the end of the whisker will be your maximum date. Sometimes on your box plot, you might find that there is an outlier lying somewhere there or lying somewhere there. If it's outside of the range of your data, we always ignore the outliers and only report on the minimum values and the maximum. So your fact number summary is made up of your minimum value, your quartile one, your median, your quartile three and your maximum date. There are five numbers. If, for example, these are our values, we are also able to take the box whisker plot and calculate what we call the interquartile range. Remember at the beginning, we used quartile one and quartile three. Yes, we still use the values because we know that quartile one is 57. So this value should have been there. It's a little bit, but that 57 should be somewhere there. So 57 is our quartile three value and 30 is our quartile one value. So we take 57 minus 30 gives us 27. So that 70 should be here. And that gives you the interquartile range. And this is your box plot or box whisker plot and your fact number summary. It gives you the spread, the center by the mean of, by looking at the median and it also tells you the shape of your data by looking at how far your values are from one another. So let's look at the spread in more detail. How do I know if my data is skewed or not skewed? So using the measures or the five number summary to find the distribution or the shape of your data. It's a little bit challenging. But it's also easy to look at it. I will advise you to always remember this. The lowest, the bottom part, the bottom one where it looks at only the quartile. So if the distance between the median which is quartile two, the distance between quartile two and quartile one is greater than the distance between quartile three and quartile two. Then we know that your data is left skewed because we're looking at that distance, the difference. If the median, which is your quartile two if the difference between it and quartile one is less than the difference between quartile three and the median is left skewed. If they are the same, if the distance are the same then it's symmetric. If the distance is less than for the median and quartile one is less than the distance between quartile three and the median then we say it is right skewed. How do I present this on a data, on a box plot? Let's start with the left skewed. So let's say our box plot looks like this. I'm going to draw it here. So this will be our box. I'm going to draw our box first. If this is our box and this is our whisker and that is our whisker, I'm not interested in the whiskers because at the beginning this is quartile one and this is quartile three. It says if the value of the median which is quartile three if the distance of the median and quartile one if it's bigger than the distance between quartile three and the median it is left skewed. What does that mean? So it means it looks like this. So there is your quartile two. So the distance, if you look at this this is bigger than that distance. The distance is smaller than the side and it means this data is left skewed. For symmetric, if this is our box and this is our whisker and this is our whisker and this is quartile one and this is quartile three therefore it will be just in the middle. The median will be in the middle. For the right skewed it says if the distance between quartile one and the median is less than the distance between quartile three and the median then it is right skewed. So this is our box and that is our whisker and that is our whisker. Remember that the beginning is quartile one and then this is quartile three or I keep on saying quartile two this should be quartile three. If the distance between the median which is quartile two and quartile one if it's smaller so let's say that distance is smaller between those two since this is quartile two the distance is smaller than that distance therefore it will be right skewed and that's how you identify the shape using the quartile. The easy one as well if they are giving you the mean and the median in your question because if for example let's say we go back to one of the examples let's say we take this you are able to calculate as well the mean of this data set you know how to calculate the mean you store the values you calculate or you sum all of the values and divide by how many there are and that will give you your mean of this sample because it's just the sum of your observation divide by how many there are and then you will look at the distribution by saying if the mean and the median are the same then it is symmetric if the mean is less than the median if the mean is less than the median we say it is left skewed we did this on Saturday if the mean is bigger than the median or we can say if the median if the median is smaller than the mean which is the same as the mean is bigger than the median which is mean the same thing the mean will be bigger than the median in this instance then we will say this is positive or right skewed whereas this is negatively skewed negative or left skewed and if the mean and the median are the same if the mean is the same as the median we say it is symmetric symmetric cut symmetric cut and that's how you are also going to identify the range so you don't have to go and think of the quad house how do I say see all this and you can use the mean and the median if you have the data set if you are not given the data set that will give you the mean that will give you the mean, the quad house and all the values and you can find the distribution any other questions going back to our slide any questions if there are no questions there are not so many questions when it comes to the distribution but I have found one where we can end the box plot so there is one question look at it in one minute I'm going to ask one of you to give an answer the following measures can be obtained from a box plot except look at the options you don't have to answer now just now I'm going to ask okay have you found the one that is not a value of the box plot yes which one it should be number three that's the mode that's the mode the mode is the one that is not part of the box plot remember your box plot is your smallest value your box which has the quad house one quad house two and quad house three and the maximum value and from there you can calculate the IQR which is your interquartile range and we know that quad house two is also called the media the media and this is also called the lower quarter is also called the lower quarter and this is also called the upper quarter next exercise we have ten more minutes so there will be one more last exercise and then we take a ten minutes break we'll see each other at eight remember you will need to sort your data from lowest to highest first that is something I forgot totally hello should be answer I think are we done I think so not yet no no I think I'm not let's do it this way I'm going to give those who are still busy extra more time when we come back from the break because anyway we're going to do more exercises there is nothing more to do so it's just exercises after exercise so take your time and let's meet again do you want to come back at five two or at eight o'clock eight o'clock eight so those who are busy take your time do continue working at eight o'clock we will come back going to leave the screen up please make sure that you switch off your videos Tabile please turn off your video thank you one more minute I hope everybody is back while we wait for the rest to come back anyone with a question or you can just tell me how is today how are the sessions are you still alright so far so good so far so good yes like I said remember after today's session you should be able to answer some of the questions from your assignment and then tomorrow we will finish off with the probabilities and you should be able to answer all the questions for assignment one if you need help please don't hesitate to ask we're here to help welcome back it's eight o'clock we can now everybody has had a chance to do the exercise so someone volunteering who is volunteering nobody serious was it that difficult ah Sam are you going to answer all the questions today so go ahead Sam unmute I started by arranging the observation from lowest to the highest it should be three four six seven nine ten fourteen yes and twenty three so after that I counted how many that will be my N which is my number of observations they are eight alright then I started by finding the positions of quarter one two and three okay Q1 is N plus one over four which will be eight plus one over four that will be nine over four the answer is two point two five and I rounded it off to two and then Q2 N plus one over two which is called to nine over two is called to four point five so I left it there and I went to Q3 I'm sorry wait for me Q3 I said three into N plus one all over four which is called to three into nine over four that will be twenty seven over four oh sorry sorry sorry okay I'm writing it step by step okay okay I'm not going to assume that everybody knows math okay so that will be twenty seven over four yes and then the answer six point seven five then I rounded it off to seven okay then I got Q1, two and three so I know Q2 is my media so I wanted the mean the mean I added all the numbers and then divided them by eight and I got my sorry I was still busy changing the color you you were talking about the mean or the median I took about the median first okay so the median so the median value since I got four point five then I went to my observation the one that is in an ordered form then I counted four point five it landed between seven and nine so I said seven plus nine divided by two then I got eight the median which is Q2 you it's between seven and nine so you said seven plus nine divided by two sixteen divided by two sixteen divided by two which is equals to eight yes so then that's eight right then I went to the mean I added all the values and then divided them by eight and then the answer was eight the mean is the sum of all the values divided by n and the answer you get is eight yes right no I'm sorry the answer I got is nine point five the answer you got is nine point five is not eight not eight so you're adding four plus four plus fourteen plus six and divide them by eight and you get I got nine point five nine point five then I got Q1 the position of Q1 is true I went through my observations and I counted through the two as on four so therefore Q1 is equals to four the value of Q1 okay then I went through Q3 since I got since I got seven then I went to my observation and counted seven it landed on fourteen so the value for Q3 is fourteen okay so now you are able to answer the questions that are asked yes we're looking for the incorrect one number one the median you got it is right it's correct okay so that is correct the first quarter not the position but they want the first quarter they say it's four you got it as four yes the third quarter not the position but the quarter but it's fourteen which we got it as fourteen the mean which is the sum of all the values divide by how many they are you got it as nine point five which is the correct answer from there is the distribution symmetric no the distribution is not symmetric you should say is not symmetric because the value of your mean is not the value of your median because we calculated what the mean is and what the median is the mean is nine point five and the median is eight so therefore the data is good any question there are no questions then we can do more exercises the next exercise and next time can I have somebody else who is not same or whose name does not start with same or doesn't rhyme with same are we done are we done somebody still busy talk to me are you still busy I'm so busy when you are done let me know I'm done I'm done yes since you are done let's do the answer while you're still un-mute let's go okay so the data is already arranged in order being one to six so I worked out what q one is so it's n plus one divided by four which will equal to six plus one because n is equal to six because there is six values that gave me seven divided by four which equals to 1.75 and then rounding it up I said it equals to two so then I went up to the data set and then number two I put as q one already then I worked out q two which is n plus one divided by two which will equal my seven so I already added it there seven divided by two which equals to three and a half and then rounding that up I got four which the value four was my q two up in the data set anybody around when is the fractional because it's 0.5 what do you do you take the average I'm trying to tell you where you're going wrong because it's a fractional half it's located between the two values you're going to take the average of the two values so you're going to say three plus four divided by two which is seven divided by two and your answer will be 3.5 not four we don't round it up when it's 50 percent because it's 0.5 which is 50 percent it's 50 percent closer to three and 50 percent closer to four so you cannot decide that it's going to be four or it's going to be three so it has to be in the middle okay you are on the right track okay quarter three I went three three sorry three times n plus one divided by four which is seven times three divided by four which came out to 21 divided by four and that gave me an answer of 5.25 I made the same then mistake where I then rounded it up where I was then supposed to take the value of the two no because we round down so it remains as five we don't round it up okay five there and then my inter-quarter range but you didn't go find the values so we found one so we found that one is quarter that's quarter three we do find and then quarter two, quarter three you go to position five so that will be you know quarter three there okay okay and then my inter-quarter range is Q3 minus Q1 which is five minus three also minus two which gave me three if we answer the questions given to us okay I used the data that I previously had I said number two was are you highlighting to give me hey I said number two was wrong so number two is asking the value of quarter two is three so what was the value of quarter two the value is 3.5 yeah so this number two will be wrong the position we did find was 1.75 which is correct and the median we did find it's 3.5 because it's the same as quarter two which is correct the value of the third quarter we said it's five which is correct the inter-quarter inter-quarter is three any questions anybody who still unsure see it helps to speak out so that we are able to see where you going wrong we can correct you immediately and now you know you won't make that same mistake again yes thank you no problem you are welcome your next question I'm going to skip this one for now I'm going to go to the next one I'm going to skip that one I'm going to this one we've done this previously but I just want to highlight something here as you can see on this question it's related to what we did today but it's related to everything that we did the previous time you should be able to calculate the range of your data which is your highest value minus your lowest you should be able to calculate your inter-quarter range which is quarter one quarter three value minus quarter one you should be able to calculate the coefficient of variation remember it is coefficient of variation is your standard deviation divided by the mean we did this on the calculator the last time multiplied by a hundred which is what we did on Saturday the other thing that they are asking you here is the range and the inter-quarter range are measures of variations what we are doing today is the inter-quarter it's also part it is part of the measures of variation as well it's a continuation of what we started last week and yet they are also asking coefficient of variation is the measures of central tendency so you will have to go and check where did we discuss coefficient of variation as a measure of central tendency or as a measure of variation I cannot give you all the answers for your assignment as well but I can just point you to the right direction so this is one of your assignment question I think I just wanted to highlight those only option one is what we are doing today and option three option four that's what we are doing today okay going back to our question and I think this will take us to the end we have one minute actually to wrap up are we done? the absence of nobody saying anything we are done okay I am just going to give you the answer and you can compare my answers to your answers so we know what the quarter one position is our quarter one position we find it by using n plus one divide by four and we find the n plus one comma five because there are six it's six divide by four which it gives one comma five therefore the quarter one value will lie between two values one in position one and position two which is 44 plus 57 so therefore if we take the average of the two we get 57 we get divide by two we get 50 point five agree? yes and for quarter two we use n plus one divide by two there are six five it's six divide by two which then it is equals to three that is the position and if we count one two three it's 85 85 is our quarter three value sorry our quarter two value and quarter three three times n plus one divide by two six times three divide by two gives us oh divide by four sorry my bad divide by four gives us four point five and it means it lies between position number four and position number five so if we add 108 plus 206 divide by two we get 157 we can also check the distribution of the data because I can see the other question here says the distribution of the data by checking if for example the median minus Q1 value and Q3 minus the median the sign is less than therefore it is positive alright skewed if it's equal then it is symmetric greater than then it is left negative skewed so you're going to find the value is there and check the position answer there so if you take median value which is 85 and the quarter three value is 157 if you take 157 minus 85 you will find that the answer there you will get is 72 coming in the median which is 85 if you take 85 minus total one which is 15 point five the answer you will get here will be date so it's 85 minus what is what is the answer 85 minus 30 point five 80.5 85 minus 50.5 it's 34.5 34.5 so 34 if I change the color now let me do that 34 and 72 what sign will that be 34 is less than 72 sorry are we having connectivity issues I'm also battling to here I think it's frozen or something it is 108 plus 44 plus 206 plus 85 plus 57 equals to 500 divide by 5 which tells us the mean is equals to 100 so option one is incorrect the value of q1 not the position but the value it should be 50.5 yeah it says is 57 so therefore it's incorrect the position should be for q2 should be equals q2 the position of q2 is 3 and this says is 2 therefore it's incorrect the value of q3 q3 value is 157 so that is the correct answer and we know that because the sign there was less than which is positively skewed therefore that was incorrect should be able to answer the same question and do the interquartal range which is just the q3 minus q1 value and find what the value is if we go back to our question our q3 was 157 and our q1 was 50.5 7 minus 50.5 and therefore we get the answer of 157 minus 50.5 which is 106.5 but I guess that's not what they were asking us they were asking the question the interquartal range is equals to the range less than the range the interquartal will always be less than the range smallest value remember when we throw the box in between remember that is the smallest value that's q1 q3 that's the highest the highest value that's the highest value what the question was asking interquartal is the same as the range we know what the range is range is the highest value minus the lowest value so if I look at this the highest value is there and the smallest value is there so it cannot be equals to the interquartal range so the range cannot be equals to the interquartal range because the range interquartal range we calculated from year to year so this is IQ interquartal range whereas from there to there we calculate the range the interquartal range is always going to be smaller because it only looks at the quartals and when we calculated the values of your interquartals we can see that it was 106 and none of these values are correct so the only correct answer here is option number 2 in conclusion oh there's another exercise but this comes from your wake book so if you look at this they give you the quartals they give you the median they give you the mean you can also apply the same logic as this to answer the question oh you can use the measure of center location so if we go back you are giving the median and you are giving the mean so you can also find the distribution of your data okay in conclusion since I took your 15 more minutes what you have learned today is to find the quartal condition and the value of your data to calculate the interquartal range to identify the five number summaries and to also construct a box plot to know how the box plot is constructed and that concludes today session thank you for joining and thank you for coming if you have any other questions you can find me on my Unisa or you can find me on WhatsApp see you tomorrow between 12 and 2 when we do basic probabilities enjoy the rest of your night good night thank you thank you thank you