 So please remember to complete the register, I've just shared the link on the chat and I will also share it later on if new people joins this session at the later stage. Okay, so today we're going to deal with Quad Health. We're going to learn how to solve questions when we answer questions relating to the Quad Health. And remember likewise, all sessions are interactive. We also follow Newman's prompt error analysis. We ask ourselves, what is the question asking us to do? What are the important facts that are given in the question? And also we identify what kind of a formula we need to be using. Like I said, also with statistics every week we introduce a new formula. So you just need to make sure that you understand the formula and how to use that formula as well. And after you have identified all the important facts and the formula, then we do the calculation and then we do feedback or we review our solution by redoing it with others and see where we went wrong or we validate our answers. And that is the process that we follow in the session. And the sessions are interactive. I expect you to also do the exercise if there is anything that you are not sure about you can ask. I also need to make a disclaimer at this point. We're only going to use the Quad Health and I'm only going to show you one way of calculating the Quad Health. Sometimes other modules, they use what we call percentile. Quad Health and percentiles are different, but you can calculate them at the same, not the same way, but they can still give you the same answer. And I will always keep on doing those references when I talk about Quad Health and when I talk about percentile, so that you don't get lost, especially if in your module you use percentile instead of Quad Health as well. Okay, so the session plan for May looks like this. So today is the first week of May that we have a session. We're doing Quad Health and then the following three weeks we will be doing. The first one will be the basic concepts of probabilities. We'll learn the skills on how to answer question and tackle question relating to basic probabilities. And then we're going to go into looking at the basic concept of discrete probabilities. And because with discrete probabilities, there are two branches and I'm not touching on, there are four branches actually, but I'm only going to touch on the two after doing the basic concepts of discrete probabilities as well. Remember also during the session, I might not, but I might because it's a two hour session, we might include the marginal probabilities. I just thought about those who are doing 1501. We might include some marginal probabilities by the right at the end. And then the following week, we will do the two concepts of discrete probabilities, which is binomial and Poisson. The first hour will concentrate on binomial. The second hour will concentrate on Poisson, so that then we can cover both. And we're not going to cover exponential or uniform distribution. So those are the two that STA 1501 also uses, but we can find some time, some way during the course of the acolytesis to find where we can do both of those two concepts. But for now, this had the schedule or this is the schedule for May. Do you have any question or comment or query before we start with this week's session? No. If there are no questions, you guys, you don't have questions. You always don't have questions for me. So I like it or I am sad because I thought people could be asking questions and telling me, okay, maybe today I must just back the session different, different than the rest of the other sessions. We are two, four, six, eight in this session, except me. So we are nine, including myself. So I just want to have an understanding. How do you feel so far up to now? Because this is our fourth session that we have been having. I want to have a general understanding in terms of how you're feeling and have these sessions been helpful up to now. Just a general comment from each one of you. Like everyone, I need two, four, six, eight answers because not everyone feels the same. So anyone? Good morning. Morning. I usually like going first then that way. Like I do not have to think hard about what to say because if everyone else has taken up what you wanted to say then it becomes a challenge. Yeah. So I think the sessions have been very good and I did statistics like in high school but the way you are teaching it like takes us a bit further than what we learned earlier on. So I think it's very interesting and it's very informative and I love the format that you have as well. So yeah. It's a very good format and very enjoyable. Thank you. Next. Good morning everyone. Morning. I think the first speaker was Arnold. I somehow agree with what is saying. The way you are teaching the class it's so easy and it looks simple and easy to understand. I did not do stats in high school but I find that it's easy to follow with what you're doing. I just wish you were my tutor. My e-tutor for the 1501. It would have been even awesome. I'm even doing this even though I find that I'm struggling a little with 1502 but I think if I just keep on with the workshops every weekend with you eventually I'll get there. Thank you. Thank you. Next. Morning Miss Boy. Morning. Excuse my voice. I have a part of flu from the past few weeks but yes I concur with everyone. I'm enjoying the sessions. I've attended all of them. I didn't attend last week unfortunately but I did watch the video and now that we've gotten to use the calculators I've obviously watched the videos and the way you explain it as they say it's it's simple. It's my first encounter with any form of statistics and so I'm understanding, I'm following and hopefully the assignments of the exams then bear fruit as to the as to what I am actually feeling like I'm understanding in the subject so I'm enjoying them and I like the format so thank you. Okay thank you. Next. Good morning. Yes. Good morning. Linda was speaking. I don't have much to say but I like to concur with others that it's my first time doing stats and you make it very very simple to understand even the difficult concepts. I don't know that maybe I like you or I like the way you teach it. I don't know. Oh thank you. Even the youtube videos it's like we're interacting so I don't want to miss sometimes I miss because of other circumstances but I feel bad when I don't attend. Thank you. Next. I think I can take two more and then we start with the session. Good morning miss. Hello. Hi. How are you and everybody? We're good justice. Yes I also want to in in cause how we say to who's the way to confirm what others are saying I'm also new in the statistics but at least now I have a green light the way we are teaching us really there is a little bit light I maybe I also say like the letters bigger that maybe I think justice call cut off. I think like the same applies to this one. Okay thank you. Thank you very much. No problem thank you. But my participation will be limited because I'm also on the car now going to the meeting. Oh busy people. Thanks. Okay last person. Hi ma'am. Hi Kelly. Oh hi. Yeah just to add on to what everyone was saying I appreciate and love the pace that you're going on. It makes it easier and one doesn't feel overwhelmed because you're not rushing the sessions and it makes it easier after the sessions to go back and go through the chapters because I find it easier to to attend your sessions and then cover whatever you covered in the chapter again. It just puts everything else in perspective so kudos to your teaching method it's honestly brilliant. Thank you so much. Hi thank you. I appreciate all your your your your comments and yeah it really gives me that energy to go on as well because I don't want to do things and people are not learning from them or they are not appreciating them but from what I hear is that you guys the pace that I go with and how I do things so I don't have to change much but I think also as a person I have grown from when I started with the accolades and now I'm trying to also implement new things in my method of how I deliver these things because there are no tutorials there are skills so I'm also leaning in this to also move away from a tutorial teaching method to a facilitation method but I will get there so but I appreciate all your input so let's get on to this week's session where we discuss Qantas so today's session you just need your formula and your calculator as well even though we're not going to use functions and all that from the calculator we're just going to do normal calculations and I think the formulas there are only three or four formulas that you just need to remember and they are easy to remember so yeah and the calculator is just to calculate the the values adding and subtracting so there is not much that you will use the calculator form as well so let's look at what we're going to learn by the end of the session you should be able to find Quartal position and Quartal value those two things are different so the Quartal position we find it using a formula and then the Quartal value you go and identify based on the value that you found from the position to allocate to locate the same way as we did with the median when we were finding the median we would find the position and then go find the value that the median is located at then we also going to identify the five number summary and construct a box whisker plot and here we also include visualization of your Quartals which the visualization will be in a form of a box whisker or a box plot okay so what are Quartals? Quartals are a way of splitting your data into four parts like with the with the percentile a percentile is splitting your data into 200 parts right Quartals will split your data into four parts four equal parts of 25 percentiles within it so the first Quartal which is Quartal one is the value of which 25 percent of the observation are smaller or are larger than 75 percent of the data and that's where the Quartals and also the percentile go hand in hand because if you want to calculate 25 percentile of the data which means calculating Quartal one you can use the percentile to do that but with percentile you can also calculate 13 percent of the data 12 percent of the data whereas with Quartals you can only calculate the three Quartals Quartal two which is the same as your median and that is where 50 percent of the data is allocated above or below that value or they are smaller or larger than that median value and Quartal three is where 25 percent of the data or the observation are larger than that value or they are smaller than that value so that is your Quartal three how do we then calculate or locate the Quartals to locate the Quartals we use the position before we can determine what value that Quartal is at we need to find the position Quartal one position we find it by using Q1 is equals to n plus 1 divide by 4 where n is number of your observations or the number of the data or your sample size and that will give you the position of Quartal one which is n plus 1 divide by 4 Quartal two which is the same as the median it's n plus 1 divide by 2 and Quartal three which on my slides I'm going to quickly fix it on the fly as well because I think I made a mistake there and Quartal three is given by three times Quartal one which is 75 percent of Quartal one value so it's three times one plus one n plus one divide by four which will give us the Quartal position Quartal three position how do we then do this the same way as we have done with the median in order to find the Quartals there are certain things that you need to take into consideration because also Quartals helps us to measure the the distribution of your data and the center alone can be misleading if you use the 50 so you just need to make sure that you also have the other Quartals and how do we do that you first need to arrange your data from lowest to highest like we did with the median we arrange your data in ascending order and once you have done that then you can calculate your first Quartal and locate your third Quartal and your second Quartal and also you are able to calculate what we call the range or the interquartal range which is your Quartal three value not the measure not the position but the value Quartal three value minus Quartal one and we will get to that in in no time when you calculate your Quartals now because you are dividing by four or dividing by two sometimes the answer you will get might be a whole number sometimes it might be a fractional number sometimes it might be a non-fractional number and when i'm referred to a fractional number i'm referring to a value that ends with 8.5 so if the results you get is a whole number then it's easy to locate the value of the of the Quartal so for example if we have one three three four five and six and we say our Quartal one position is on position number is this it's on the second position so that is easy to locate because it's a whole number once we calculate n plus one divide by four and we find that it is equals to two we can locate that Quartal easy you also need to remember that sometimes when you do those calculations Quartal one can be Quartal one you can find the position of Quartal one and it might be 2.5 so when it is 2.5 it means it will be located between two values so you will say one two point five will be between two values and that is what we say it is when it is a fractional half then we're going to take the average of the two like we did with the median when it's located between two values we take the average of the two values thank you machine Elizabeth yes i think your your presentation is paused we still see where you edited the Quartal three on there you still see this yeah that's what we were seeing but it's in presentation mode now thank you okay so i explained all this so you order your data you can you find your Quartal one you find your Quartal three and we you are able to also find the Quartal three value and minus the Quartal one value i am now at this point where i am explaining that when you do those calculations and find your Quartal as the whole number the value you see on your Quartal so like i'm going to rewrite all that i had was one three three four five and six and i said if Quartal one value you find that it is two which is on the second position which is the position so it's on the second position then you can allocate or you can locate the position easier because it's a whole number it's one two you just count there but if your Quartal one is 2.5 position therefore it means it's located between two values like we did with the median you're going to take the average of the two values so then to say three plus three divided by two which will be the same as three that will be your Quartal one and that is when it is fractional half when the result is not a whole number or is not a fractional half we call it a non-fractional so therefore it means the answer you might get will be point not zero but it might be point two five or it might be point seven five so there are several things that you need to also remember when it's like that so let's say our Quartal one value now it is 2.25 if the position is we located it and it is on 2.25 we can then estimate that Quartal one value is at position two so we round down the position to Quartal two because the values are very far away from three from the third position but closer to the second position if Quartal one value is 2.75 therefore we go into round it up because the values are far away from from the second position but closer to 75 percent closer to position three so we're going to round it up so that is the same as met right with met if the value to the left is less than or equals to two we do nothing oh it's less than or equals to five we do nothing if it's greater than or equals to five we add one to the value on the right that's how we round off so when Quartal one is 2.25 we round down to two if it's 2.75 we round up to three because the values are closer 75 percent closer to position three okay so you always need to remember this how do we then calculate and locate the Quartals let's look at this example given this data set which is audit already so your data set that you will get in the exam or in your assignment might not be audit you just need to always remember when it's Quartals when it's median you need to order your data from lowest to highest so this data set is already audit and I can count how many there are there are nine observations on this data set I can go and find Quartal one position by using my formula and plus one divide by four to find the Quartal one position then it means I must replace n by nine because I know that there are nine observations plus one divide by four and I find that that it's located in position 2.5 so it's somewhere between 12 and 13 so because the value is between the two values then I must take the average and it's just saying 12 plus 18 divide by 2 because to take an average of a number you divide by how many they are and there are only two values so 12 plus 18 divide by 2 gives us 12.5 and that will be our Quartal one value remember position and value position and value we can also take this and calculate our Quartal three Quartal four sorry Quartal two and the interquartal range so first let's calculate the rest of the Quartal so we already calculated Quartal one in our previous example calculating Quartal two we know that Quartal two is given by Quartal two it's given by n plus one divide by two which is the same as the median and is nine plus one it's 10 10 divide by two it's located on the fifth position so we go and count one two three four five position and that will be our median or our Quartal two value which is equals to 16 we can also go and calculate Quartal three and Quartal three value it's given by three times n plus one divide by four three times nine plus one nine plus one is 10 10 times three is 30 30 divide by four it's seven point five position go and count one two three four five six seven point five it's located between two values 18 and 21 and we take the average of those two values and we find that our position is 19.5 Quartal one and Quartal three are measures of non-central location because those are not measure of central location but Quartal two is a measure of central location because it's the same as your median and that's how you find the Quartal any questions before we move on we're gonna get to the exercises just if there are no questions if there are no questions then we move on to the next how do we find interquartal range remember we said we can find the interquartal range which is the range of your Quartals an interquartal range is calculated as like we said before Quartal three value not position value minus Quartal one value and that gives you the spread in terms of the Quartals and the spread 50 range of the Quartals your interquartal range is also called the mid spread because it covers the middle 50 percent of the date only and you will see when we look at the box box whisker you will see how the interquartal range now relates to the statements that I am saying now the interquartal range is a measure of variability that is not influenced by the outliers because the outliers are on the extreme length or on the maximum and the smallest value and here the interquartals only talks to Quartal one and Quartal three measures like Quartal one Quartal three and interquartal range are not influenced by outliers because there are resistant measures and because also we do not consider the extreme outliers because we only looking at the middle box as well how do we then calculate interquartal now remember from our exercise that we did we went and we found that our Quartals we said the first one Quartal one is between 12 and 13 and Quartal three so we said Quartal one is located there and Quartal three is located there and we did go and find the value and we found that it was 12.5 let's go back we can go back if you said it's 12.5 and 19.5 so I don't have to go and calculate them again because I know them we did calculate them so it's 12.5 and 19.5 interquartal range it's Q3-Q1 so Q3 value was 19.5 we put there Q1 value was 12.5 we put there and 19.5 minus 12.5 gives us seven and that's how you calculate interquartal range easy stuff right now let's look at this example we're gonna do this together together together so we are given a table of 20 travel times from 20 travel times for 20 New Yorkers and the data is not sorted as you can see and we can sort the data I'm going to save you a whole lot of time because I want us to get to the exercise so sorting the data I've already color coded some of the things but don't worry about that sorting the data and that is our sorted data now if we need to calculate quartals from here I need to also count how many data set we have we have 1 2 3 4 5 6 7 8 9 10 11 12, 18, 14, 15, 16, 17, 18, 19, 20 so our n is equals to 20 now remember that in the exam they will not give you a huge data set but in the assignment they might give you a huge data set in the exam they will give you 10 or 15 or 5 so a small data sets a manageable data set that you can work quickly through it so here we have 20 data sets or data points or observations now we need to calculate quartal 1 so let's go and find quartal 1 q1 it's given by n plus 1 divide by 4 our n is 20 plus 1 divide by 4 21 divide by 4 it's how much 21 divide by 4 is 5.25 5.25 what do we learn or what did we learn about the quartals we learned that if it's round down we round down so that will be since it's on it's located at position so it's on the fifth value of fifth position so we're going to count one two three four five and that is our fifth value and our q1 is equals to 15 regardless of whether there are two fifteenths so that is our q1 so now let's go find q2 q2 it's n plus 1 divide by 2 which is 20 plus 1 divide by 2 what is 21 divide by 2 it's 10.5 10.5 so 10.5 it means 1 2 3 4 5 6 7 8 9 10.5 it's located between two values so our q2 this is our position our value will be 20 plus 25 right divide by 2 what is 20 plus 25 divide by 2 it's 22.5 22.5 that is our q2 now let's go find our q3 our q3 remember it's 3 times quartal 1 which is 3 times n plus 1 divide by 4 3 times 20 plus 1 divide by 4 21 times 3 divide it's 63 divide by 4 it's 15.75 15.75 what do we know we round it up round up round it up and that will be on position 16 so we go count one two three four five six seven eight nine 10 11 12 13 14 15 16 our q3 it's on position 16 and it is equals to 45 now we can calculate interquartal range which is our IQR I just want to check because I think the IQR so we've got our 15 our 2.25 please ignore this I think it's an error here it used the percentile it's 45 the answer so therefore it means I must also fix the interquartal range so this should be 45 and what is the answer sorry I must I am apologizing for this because I think I made a lot of errors on this slides the answer is 30 let's go fix that so this should be f and this should be 45 and the answer should be just date and the date so the answer will be just 30 and we can conclude by saying the range of the middle value or half of the times for the new yorkers in the sample is 30 minutes so it means they travel almost on average 30 minutes that's how you find the quartals now when you have your quartals like if I look at this data set we have the make the smallest value we have our quartal we have our median we have our quartal 3 and we have our highest value all those values so all this small and highest all these values there are one two three four five of of them they are what we call a five number summary and those five number summary helps us to visualize the quartals the five number summary includes the minimum the maximum values and those alone tell us a little about the distribution as a whole but if we include the median and the quartals they will tell us about the distribution of that data that you are working with and later on we're going to look at how we also interpret the distributions using the quartals whether is it left skewed or right skewed and whether it's symmetric in order for us to get that distribution or to be able to display the distribution a five number summary chart or plot it's helpful because it will display your smallest value which is your minimum value your quartal 1 your median your quartal 3 because your median is quartal 2 your quartal 3 and the maximum value which is your smallest value and you can also use your box plot or your five number summary to identify any outliers so let's look at this dataset that we had previously remember we found that our quartal 1 now i forgot what our quartal 1 was was 15 quartal 2 was 22.5 and quartal 3 was 45 so let's plot the same data we had we have our minimum value is five from the sorted dataset our maximum value from the dataset if you look at the maximum value would have been 65 85 85 85 85 is our maximum and our minimum and we know that our quartal 1 was 15 our quartal 2 which is the median was 22.5 and our quartal 3 was 45 so now we can draw a box so the box is made up of these three values the whiskers that is why it's called a box whisker the whiskers are the lines that will connect the quartal 1 to minimum value and quartal 3 to maximum value so if i have a box you will see that it will look like this and here you will have your quartal 1 and here you will have your quartal 2 and here you will have your quartal 3 and there is your maximum your smallest or minimum and your maximum will be 85 now you can see that 85 is an outlier already because i think most of the data with 65 was somewhere there that will be 65 and something like that so probably my box also should have come to this because my my quartal 3 is 45 and this i drew it with 32 as you can see there is your box whisker plot any questions any question if there are no questions then we can go and do some exercises but before we go then let's look at the distribution of our data by using the five number summary to describe the distribution or the shape of the data whether our data is left screwed right screwed symmetric now you will need to remember all the permutation but because you're writing an online exam you don't have to you just need to make sure that you know where to find this chart the chart says if your median value which is your quartal 2 your median is quartal 2 always remember that if your quartal 2 minus your quartal 1 oh sorry quartal 2 minus your smallest value if it is bigger than your largest value minus your mean then your data is left skewed the other way of also identifying whether your data is left skewed if your quartal 1 minus your smallest value it's greater than your largest value minus quartal 3 value then your data is left skewed if your median minus your q1 which is your one if it's greater than your q3 minus your median then your data is left skewed so there are three scenarios that you can use to find out whether your data is left skewed how do we identify whether the data is symmetric your median minus the smallest value should be equals to your largest value minus the median so it should be 50 50 they should be equal if your quartal 1 value minus your smallest value should be equals to your largest value minus quartal 3 or your median minus quartal 1 should be the same as your quartal 3 value minus the median and that should tell you that your data is symmetric or it's normally distributed for right skewed you need to remember that if your median which is your quartal 2 value minus the smallest value if it's less than your largest value minus the median then your data is right skewed otherwise if your q1 value minus the smallest value if it's less than your largest value minus your q3 value then your data is the right skewed the last one to determine whether your data is right skewed is if your median which is q2 minus q1 if it's less than your q3 minus the median then your data is skewed and that's how you will identify the distribution of your data using the quartal so you remember now you can use your as measures of central location to locate whether your data is skewed to the left or to the right by using the mean and the median and mode if they are all equal then it is symmetrical and so forth or you can use the five number summary to allocate whether your distribution is left skewed symmetrical or right skewed so you just need to remember that now we're done any questions then we can start with exercises i'm gonna give you some time to do some of these exercises and then we'll come back and reflect so now need to read the question what is it that it's asking you to do and identify the formulas for each one of them and answer the question now because there's a multiple choice questions i would suggest that before you even start with doing everything or answering the question what i will suggest we do because we are practicing the first step because most of the questions will have a data set order your data or read the question first so you must just make sure that you read the question sort your data from lowest to highest in state of answering the question look at the options and answer the key terms that are given on the question and once you have answered those key terms then we can you can then answer the question and choose whichever is incorrect or whatever is correct or whatever the question is asking you to do okay so let's look at question exercise one consider the following data set they have given you the data set which one of the following statement is incorrect so it means we need to be finding the incorrect answer option one states that the median of the sample is eight therefore it means if i count the observation i should get eight observations the second one it says the first quarter is for therefore it means i need to know what the formula of the first quarter is calculate the position of that first quarter and answer the question if they would have said what is the first position or what is the position of the first quarter then you know that you only stop at the position but yeah they're asking you what is the first quarter so you first need to calculate the position and then find the quarter the quarter the third quarter is 14 you do the same find the position then calculate the quarter what is the mean the mean is the average you calculate the mean and find out now you are also asked oh sorry the the first one was the median so therefore it means the median you need to sort and find the median position and then calculate the median which is your quarter two what is the distribution then you can use either the median and the mean to find the distribution or you can use the quarter values to determine what the distribution of this data set is so i'm going to give you five minutes to answer this and then we'll reflect on the question in the meantime those who joined late i'm going to post the register please make sure that you complete the register if it's your first time we always keep the register so that unisa paro can know who attends the session and also for communication papers in case there are certain things that we want to share with people who are in this session remember you can use the chat also to to give your final answer but we're going to work through all the options together are we done are we done let's look at the question so let's sort the data anyone um so i sorted the data by order um sorting them from three versus three then four then six seven nine 10 14 and 23 that is our sorted data the median of the sample is eight how do we find the median position it's n plus one divided by two our median position will be n plus one how many how many are they there are eight eight plus one divided by two which is nine divided by two four point five it's equals two four point five four point five therefore the median okay two will be one two three four point five it's am i counting right one two three four four point five it's yeah right yes yeah it's between seven and nine and then our median so that will be divided by two then i'll make it eight okay and that will be equals two eight so therefore that is correct right the second one our first quartile is that so we need to find the position first so n plus one divided by four which is eight plus one divided by four which will be nine divided by four which is um two point uh two five two point two five therefore we can round it up round it down to to two so it's on the second position one two the second position therefore our quartile one is equals two then we round out yeah so it's on the second position so on the second position the quartile one value will be equals to four therefore that is correct going to the next one going to the next one says quartile the third quartile which is three times n plus one divided by four which is three times eight plus one divided by four nine times three divided by four it's how much twenty seven divided by four which is six point seven five which is six point seven five and we also do the same we round it up and that will be on position seven so we go count one two three four five six seven it is our q three it's on position seven which is equals to 14 and we have that quartile as 14 therefore that is correct right the last one or the second last way we do calculations the mean is nine point five so the mean we know that the mean is the sum of all observation divided by how many there are so adding three plus four plus six plus seven plus nine plus ten plus fourteen plus twenty three you get seventy six right divide by eight because three plus four plus until twenty three will give you seventy six seventy six divide by eight that is if i my calculations are right it's nine point five seventy six yes okay it's nine point five now we need to come to the distribution they say our distribution is symmetric if it's symmetric it means if we use the measures of central location it means the mean and the median should be the same for it to be symmetric or we can use the quartiles and i'm going to choose the other one so if it's symmetric it means the medium which is q2 minus q1 value which is the easy one should be the same as q3 minus q2 so if both of this can be equal so let's look at the median the mean is nine point five and eight so they are not equal so it's not symmetrical so this statement cannot be true let's look at the second one q2 which is eight so if we use the second statement if we use that so q2 is eight minus q1 is four we say it should be equal to q3 which is fourteen minus q2 which is the median which is eight yeah we get four and here we get seven no we get six right fourteen minus eight that's six it's six yes it's six so they are not equal so they cannot be symmetric so that is the incorrect one and we can also say this the data set instead of saying not equal we can also say because um they are not equal there but four uh is less than six six is greater than four so therefore the data set is actually right skewed the data set will be right skewed and if the data set is right skewed let's look at it in terms of the box whisker we said our quartile one is four so our box will start there our quartile three our box will end there our median is eight our line will be there and if i join both of this and there is our line and i can extend my whiskers to the side and that's how the the data will look on a box whisker plot but in a way if we if we do this properly this will look like this in a way so 14 will be somewhere there and 23 will be somewhere there and you can see that the box will direct to 14 where 14 is here and you can see that this box this side the box this side is bigger than the box on this side so this side and the side are not the same not equal so the right is bigger than the left and that is right skewed and if we do draw a thing it will look somehow like this if we draw a normal bell kefir shape shape to show where your averages are and you can see that your distribution is left skewed anyway okay so that's how you will identify whether your data is how the data is distributed either by using the bell shape kefir or by using the box plot it can also help right let's go to exercise two you also have five minutes to do exercise two pay attention to the keyword asked in the question in order for you to follow in the trap as well and remember interquartal range which is IQR is your Q1 value also Q3 value minus Q1 value are we winning still calculating almost are we winning yes anyone still calculating is it 5.5 or 5.5 yeah so let's do the x let's do some feedback in terms of that so consider a simple data set one two three four five six which one of the following statement is correct so the question is asking us to find the correct statement our data we identify things given here our data is already sorted so there is no need for us to sort this data question number one the position of the first quartile is 2.5 so they're asking you to find the position which is for quartile one n plus one divide by four how many are they six points divide by four so it's seven divide by four 1.75 it is 1.75 so therefore this position is not correct because they say the position is 2.5 number two it says find the value not the position but the value but before we can find the value it means we need to find the position so n plus one divide by two because it's quartile two so it's six six plus one divide by two seven divide by two 3.5 3.5 and there our quartile two will be located between two values right one two 3.5 it's between three and four three plus four divide by two seven divide by two three point five it's three point five and yeah it says the quartile value or the second quartile value is three therefore it is not correct the median is four and the median is the same as quartile two so here it says the median is four we know that the median is 3.5 not four therefore also this is not correct because we can use the same information we got from the first the second question number four it says the value of the third quartile is five point two so they're asking you to find three times n plus one divide by four which is three times six plus one divide by four seven times three divide by four it's how much five point two five five point two five because we're looking for the value therefore we're going to round down because it's point two five and that will be five right yes yes and our quartile three value going to count one two three four five which is equals to five and the eight says the quartile value is five point two five that is the position not the value so therefore that is not correct so the last one interquartile range is equals to three let's verify that we know that quartile three value we did go and find that it's five minus part one value we did go and find quartile one value no we didn't find quartile one value so quartile one value we're going to estimate round up round up to two so our quartile one value will be equals to two two two five minus two is three easy right yeah consider only the number of people living with ASD given in the table table one point one c has the number of people 108 44 206 85 and 57 which of the following statement is correct the median is 85 and is equals to the mean number two the value of quartile one is 57 but the position of quartile two is two the value of quartile three is one 157 the distribution of the number of people living with ASD is symmetric so we need to find the correct question sort your data find what is the median find what is the mean find the value of quartile one find the position of quartile two find the value of quartile three which quartile two is the same as the median so if you have found the position it will answer the two and then determine whether it is symmetric remember the symmetric means mean is equals to the median or q q two which is the median minus q one should be the same as q three minus q q two so you can use those two to determine whether is it symmetric or not but first sort your data i can help with sorting the data as well it's 44 because this is very small number 85 108 206 are we winning yes we are winning i think uh lindy way are you still not seeing the slides i think you're the only person now i do oh you do went out sorry i will share them again are we done or we're still calculating remember we're looking for the correct answer happiness are we there are we good or are we great can we answer the question okay so the first one says the median is 85 and is equals to the mean so can we find the median we'll have to find the position first so the position of the median is n plus one divided by two there are how many there are there are five right plus one divided by two which is six divided by two is equals to three which is the position what will be the median which is the same as q2 the median will be on position three one two three which is 85 right but the question says it is equals to the mean so it means we need to go find the sum of all observation divided by how many they are if we add all these values how much do you get 500 that's 500 divide by five which is equals to 100 so if the mean is 100 therefore it means they are not they are not equal so this is not the correct answer that we are looking for we move on to the next one the next question asks oh why did i delete that it's fine we know what the we did find our median position was three i'm just gonna write it there so that we can remember that the second one says quattal one is 57 so we need to find the quattal one value but we first need to find the position n plus one divide by four so it will be five plus one divide by four six divide by four it's how much 1.25 1.5 sorry 1.5 it's 1.5 so it means it's between two values if it's 1.5 so it's between so our quattal one will be between two values it's between 44 and 57 right so we'll say 44 plus 57 divide by two and that gives us how much 50.5 50.5 so yeah the answer will be 50.5 which is not 57 so that will not be the right answer as well the third one says the position of q2 is two so it means we need to go find the position of q2 we're not going to do that because when we found the median value to be 85 we went and found the position so this is the same as the position for q2 right because q2 and the median are the same so we found that it was three it's not equals to two right the value of q3 is 157 so it means we need to go find three times n plus one find the position first which is three times five plus one divide by four six times three divide by four it's equals 0.5 4.5 and q3 will be between two values it will be between 1 2 3 4 5 so it will be between 108 plus 206 so 108 plus 206 divide by two gives us q3 value of this is 157 157 therefore this is the correct answer in the exam you stop right there but because this is not an exam we can also go and find the answer for option four remember for option four we just need to prove any of the two because it says it's symmetric so it means the mean should be equals to the median or q2 minus q1 should be equals to q3 minus q2 we know that the median is 85 and the mean is 100 so the first one cannot be proven so it's not symmetric you can go and do the same with q2 because with q2 minus q1 q2 the position is two so therefore it means it's 57 minus and sorry the position is three not that q2 is 85 so it's q2 minus q1 should be the same as q3 minus q2 that's what we want to prove so q2 is 85 minus q1 we found that it was 50.5 and q3 157 minus q2 of 85 so we want to prove if those sites are equal so 85 minus 50.5 is 35.434.5 that will be 34.5 equals 57 minus 85 72 72 they are not equal so we are able to prove that it's not symmetric so that would be also not correct so the only answer that is correct is number four we left with 15 minutes and i've got 10 questions or 11 questions so if i go slowly we've got question number four question number five question number six and question number seven eight nine and ten so you can do all of them at your own leisure the notes will be posted as well you can use this to practice so you can use the same data set to calculate the mean the median the mode calculate the range the standard deviation calculate the part one quarter two quarter three quarter interquartal range and calculate and draw up the box risk a plot so this is just for practice papers so let's go back to our exercises and see if we can answer a couple of them consider only the number of people living with ASD so this is almost the same question as the previous one so we have all the answers here remember what quarter three is it's 157 and remember what quarter one is it's 50.5 so you just need to calculate your interquartal range so they say the interquartal range is is equals to the range always less than the range 149 51 and zero so one of these questions should fill up that blank so since we know that IQR not we're not sure whether the answer that we're going to get here will be the answer that we are looking for we just need to calculate we know that it's Q3 minus Q1 Q3 was 157 remember not the position but the value minus 50.5 157 minus 50.5 it's 106.5 106.5 there we go so therefore it means that cannot be the answer that we are looking for so we can move on to the next question I'm going to start from bottom going up as well so that I can eliminate all the values so we know when we do the calculation your interquartal range is not zero it's not 51 and it's not 149 that's what we got from the calculation that we did so it leaves us with only those two questions now let's draw a box whisker plot because I think with a box whisker plot it will help us answer this question I'm just going to draw a generic box box whisker where we have the smallest value and the highest value we have quartal 1, quartal 2 and quartal 3 what do we know about this we know that we can find our IQR from there but what do we also know about the range we can find the range of the data by taking your highest value minus your lowest value whereas with interquartal is Q3 minus Q1 so now let's see which option yeah replaces the question like the blank space the interquartal range is equals to the range is that true the interquartal range is always less than the range which one will you choose number two I think number two number two will be the correct answer because we know that the interquartal range will always be smaller than the range because the range is your highest value minus your lowest value and that's how you will answer the questions you should be able to answer this question with ease but I'm not going to ask you to answer it right now because it's almost similar to what we have been doing all along so given the data sort the data from lowest to highest and looking at this data set is already sorted but you can write it out so that you are able to sort it so you're looking for the incorrect answer you need to find the position not the value the position of Q1 the position of Q2 the position of Q2 or the median so you can see that those two questions are almost exactly the same and the position of Q3 and they're asking you to find the value of Q3 you just need to make sure that you are able to identify what is given in the question this question is the same as the one that I am giving you we are not different it's one one in the same yes so it's just the repeat exercise six and exercise five are the repeat in I just want to bring to your attention as well so because you write multiple choice questions sometimes your questions might not come straightforward as only the quartiles only the standard deviation so it can look like this this is one of the questions from a previous tutorial letter or a past exam paper so they give you the data and they ask you multiple things on there from different areas or different sections using the data find the range find the interquartile range find the coefficient of variation find the range interquartile range and the coefficient of variation is just repeating themselves so you can see that they can ask you questions relating to measures of central tendencies measures of variation and the quartiles in one question as well so you need to be able to identify the formula that you need to use so for example here the range is high value minus low value interquartile range it means you need to go find the position of quartile three minus the position not the position you need to go find the position and go find the value of quartile three and also go find the value of quartile one so here you will use n plus one divide by four to find the quartile one position and then find the value and here you will use three times n plus one divide by four to find the position and then go find the value. Coefficient of variation remember you can use your calculator to calculate the coefficient of variation otherwise you can use the formula cv is equals to your standard deviation divided by the sample mean therefore it means you need to calculate your s which is the square root of your sum of your observed value minus the mean or the sample mean squared divided by n minus one and the mean you will need to find the sum of all your observation divided by n otherwise use your calculator to calculate store the data and calculate the coefficient of variation and then the other questions will just be general theory questions that they can ask you in the exam or in your assignment you need to know both but remember that also the sessions we only concentrate on the skills in terms of calculations and all that but we do give you some of this theory but you need to go and learn some of the theory um maybe probably your Twitter will give you more in-depth theory than my because I only concentrate on calculations mostly so you need to know like we did previously the range and interquartile range and those measures of variation or not you need to know that coefficient of variation is a measure of central tendency is that correct therefore it means you need to go and learn what are measures of central tendency which are only three measures of central tendency that you need to know about so is that one of them coefficient of variation if so then that will be the correct answer or the incorrect answer but you just need to make sure that you know and understand how to answer the questions this is also same you need to find the interquartile range therefore it means you need to first find the position of the quartile three so interquartile range which is your i q r you need to find q r value minus q one value where we know that q three value is three times n plus one divide by four and q one value is n plus one opposition it's n plus one divide by four and then the value you find you substitute but first you need to search like from lowest to highest before you do anything else other type of questions let's see if there is another variation nothing variation about this because it's almost similar to what we have been doing calculating the position of quartile one finding the median finding the value finding the range remember the range highest minus lowest i just want to remember remind you because we didn't cover the range today it was part of the measures of variation and find the quartile three value always remember to find the position then the value first and always remember that median is the same as q two always always remember that and i think we covered this one i don't have to say it a lot so you can do some of these activities you can share them on whatsapp if you want you can email me you have my email address other than that i think we can conclude today's session what we have learned up to now we've learned how to calculate interquart oh sorry quartiles by first finding the position of the quartiles then finding the value of the quartiles but before you do that you need to order your data from lowest to highest or in an ascending order and once you have your quartile values you are able to calculate your interquartile range and you can also display your quartiles on a five number summary to check the distribution of your data by using a box whisker plot which gives you the smallest value or the minimum value quartile three value sorry quartile one value quartile two value which is the same as the median and quartile three value and the highest value or the maximum value and with a box whisker plot it can also help you to identify if your data has any outliers and you can also see the distribution of your data if it is left skewed there are three statements that you can use but the one that is most clearly remembered is if your data if the mean or q2 minus q1 if it's greater than q2 minus median oh i'm talking right now if your q2 minus q1 is greater than q3 minus q2 then your data is left skewed if your median which is q2 minus q1 if it's the same as q3 minus q2 then your data is symmetrical if it's right skewed therefore it means the q2 minus q1 should be less than q3 minus q2 then your data is right skewed or positively skewed otherwise you can use the median and the the mode to find out whether the data is symmetric or skewed and that is it from me to you any question any comments before we say goodbye going once going twice and in the absence of any question or comment please make sure that you complete the register i've just posted it again in the chat otherwise enjoy the rest of your weekend see you next saturday when we deal with probabilities bye thank you thank you