 Okay. Welcome to your third session. It's not the fourth session, it's the third session. Where we're going to discuss measures of variation. So today, because measures of variation uses a very complex calculations, I'm going to demo on the calculator, sorry, I'm going to demo on the calculator on how you can use your calculator to answer some of this because instead of using formulas, then you can rely on your statistical calculator or scientific calculator to do some of the calculations as well. So in May, this are the topics that we're going to be discussing. We're going to look at the quartiles, then the basic concepts of probabilities, and then we're going to look at the basic concepts of discrete probabilities, and then we go into doing the binomial discrete probabilities and also the Poisson one. And that will conclude our May sessions. So please don't miss anything. If you're doing 1501, those who are doing 1501, what we do not cover when we do discrete probabilities are the marginal probabilities. But if you need help with those, feel free to ask as well. Okay. So let's start with this week's session. Do you have any question, comment before we even begin with the session for today? Are there any questions? Okay. Please remember also to complete the register. I've posted the link on the chat. So like I said, today we're going to be looking at measures of variation and the requirement is a formula and your calculator. And always remember that we use the Newman's error method or error prompts to analyze the problem that we are given so that we can understand what we are given and then be able to do some calculations as well. Okay. So when we talk about measures of variation, we talk about things like your range of variation, your standard deviation and coefficient of variation. So what does this mean? What is measures of variation? Sometimes it's also referred to measures of dispensation. What it does, it gives you how spread your data is or the variability of your data or how far apart your data is from the mean. So that is your measure of variation. It gives you those type of information in terms of the spread, in terms of the variability, in terms of the structure of your data, whether how far apart your data is from the mean. And we know that the mean is a measure of central location. So when we do some calculation on the measure of variation, we do use the mean so often. That is why the mean is the most commonly used measure of central location, because from now on there, we're going to be referring to the means so often for most of the things that we do. Okay. So how do we then calculate this? So like with measures of variation as well, you can calculate this because these are parameters or statistics. So if you calculate these measures from a sample, remember that those will be your statistic. If you calculate this from your population, this will be your parameters. So what is the range? A range gives you how far apart your data side is. So it is the difference between your largest value and your smallest value. So if I have this data set, where I have the bubbles, those represent my data. So I have one and my highest value is dating. So in order to find the range of this data set, I say 13 minus 1, which is equals to 12, and that gives me the range. And that's how you calculate the range. Use the following information below and to answer the question. So you are given the data and the question is, a range is that score above or below which 50% of the scores fall? Is this correct or is this too or false? Remember what I just said? What is the range? The range is the difference between the highest and the highest value and the lowest value. And what did we learn from the measures of central location the last time we met? We learned that the median splits the data in half. So 50% of the data will fall below and 50% of the data will fall above. So the statement, therefore, it is incorrect because the range is the difference between the highest and the lowest, not the score below and above 50%. That is the media. So the answer here will be false. So if that is type of a question that you would get in the exam or in your assignments. One of the other measure of variation we said is the variance. And also we have the standard deviation. Now, the variance and the standard deviation are similar to one another because the standard deviation is the square root of your variance or the variance is your square of your standard deviation. The variance we do not interpret and we normally don't use it so often, but it is the average of the square deviation of the values of the mean. And we can calculate it for the sample. We can calculate it for the population. For the sample variance, the formula is a square. Remember, for the sample, we always use normal letters, alphabetical letters. For population, we use Greek letters. So the sample variance is given by the sum of your observed value minus the mean or the sample mean squared divided by n minus one. You need to know how to calculate this because what the sum it means, it is a summation. It means adding up. So it means you're going to add your observation minus the mean squared plus another observation minus the mean squared plus another observation minus the mean squared plus like that. It is the sum. It means it's adding together and everything divided by n minus one way n is your sample size. The population variance on the other hand is represented by a sigma squared and it's almost similar to what the sample variance is, but the difference here it is divided by the capital letter n. And that is how you will differentiate between your sample variance and your standard deviation variance. So this population variance, the sum of your observation minus the population mean squared divided by n. So when it comes to the standard deviation, standard deviation, we can interpret because the value we get when we do the calculation we bring it back to the same value or the same unit as the original dataset and therefore it allows us to be able to interpret what that value means in relation to the mean. And it's also one of the most commonly used measure of variation because from now on even when we do the hypothesis testing when we do the confidence interval, we're going to be using the standard deviation, standard deviation, standard deviation and the mean. What standard deviation shows us, it shows the variation about the mean. So it will tell you how far apart your data is from the mean. And it's also like I said in the beginning, it is the square root of your variance. So if you calculated the variance and you're asked to calculate the standard deviation, you don't have to go again and do the same calculation again that takes forever. You just take the square, the square root of the variance and that will give you the standard deviation. So sample standard deviation is denoted by s and s and a population standard deviation will be denoted by a sigma, as you can see. How do we then calculate this? Going to calculate the standard deviation. Calculating the standard deviation, remember the formula for the sample standard deviation is your s is equals to the square root of the sum of your observed value minus the mean squared divided by n minus 1. That is the formula that we need to use. So given the data set that we have which starts from 10 and it is in order anyway from 10 until 24, we can count how many there are that will be our sample size. There are eight of the data values that are here displayed. We can also go and calculate the mean because we will require the mean in the formula. The mean is the sum, remember the mean is the sum of all observations divided by how many there are. So you add all the observations and you divide them by eight and that will give you 16. Now we need to substitute into the formula in order to calculate the standard deviation. Our x is all our x-observation. So we start with 10 minus the mean of 16 squared plus 12 minus the mean of 16 squared plus 14 minus the mean of 16 squared plus until we get to 24 minus the mean of 16 squared. And that gives us 180 if we add them but we need to divide by n minus 1 which is 8 minus 1 which gives us 7. So the top part when you solve that you will get 130 divided by 7. The 130 divided by 7 it is your sample variance. It is your sample variance and it is the same as 18.5714 or 18.57 if I leave it to 2 decimal. If I take the square root of the answer of 18.57 I will get 4.3095 which is my standard deviation which shows me the measure of the average values scattered around the mean which means my data is 4.3 different away from the mean or far apart from the mean and that tells me what the standard deviation is. Any questions before we start with any of the activities and exercises but before we do the activities and exercises because we're talking about the variation and all that so that when we go to do the activities and exercises you are able to do all of them and I don't have to come back to theories and all that. Let's look at another measure of variation which is a coefficient of variation which measures the relative variation and we always represent it in a percentage form and it shows your variation relative to the mean and can be used to compare the variability of two or more data sets and this usually it's used by people who works in the risk department like for example if you work in an investment company you will most likely use the coefficient of variation when you do some analysis to check which of the portfolio you want to suggest your clients to use or to invest in and you can use this measure also to guide you in terms of in terms of highlighting which one has the high risk which one has the low risk in order for to make sure that your your your customers or your clients get to turn on investment on the money that they save with you. Let's look at this example stock A has an average price of last year of 50 rent and the standard deviation of five rents so they would have took the stock A for the whole year and calculated what was the average which is the mean what was the the mean average price for last year which they found that it was 50 rent and they would have calculated what was the standard deviation which they found that was five rent. If we calculate the coefficient of variation which is your standard deviation divide by your sample mean multiply by 100 then we take the five rent divide by 50 rent and multiply by 100 then we get 10 percent. We can also look at stock B which had an average price of 100 rent and the standard deviation of five rent we also substitute your standard deviation of five rent divide by your mean of 100 and multiply that by 100 and we find that the variation is five percent. Looking at the two results of 10 percent and five percent we can deduce that both the stock have the same standard deviation but stock B is less variable relative to its stock relative to its price because if you see your price of 100 it means the the prices last year were almost close to one another of an average of 100 rent the rest of the whole year as compared to stock A where there is a 10 percent and variation in the prices as compared to in the prices of last year as well. So if this was for example an investment portfolio I would invest in stock B because then stock B would have more returns than in stock A where the variability is way high as well because then it means there are a lot of fluctuations that are happening on there but if I have if I'm that person who wants high returns who plays in the risk category like I like to take risks then I will invest in stock A because then it means on some months I might capitalise and make more money on some months I might lose more money so but if you are conservative you will you will only stick with stock B. Okay that is measures of variation. Now I know that the last time we met we discussed the mean and the standard deviation I'm not going to ask you to do this question but we also spoke about the the distribution of the data I'm not going to talk too much about the distribution of the data but just to let you know that your measures of variation can also help in terms of identifying the peak of your data whether is your your your data set a ketosis or elliptochetic or is it a platychetic or is it a mesochetic in terms of using some of the measures of variations but you don't have to know all of this for your module but that is just for interest sake as well and also because this is skills literacy so we just need to make sure that you also have an understanding of some of these skills or some of these knowledges. Okay so now before we go on to doing a lot of exercises like I said I'm going to demo or show you how to calculate the measures of variations using your calculator. On the screen right now we do have 12 monthly sales bicycles sold by a bicycle dealer and we do have all the monthly sales 12 of them and we are asked to calculate the mean the variance the standard deviation and the coefficient of variation. I hope you do have your calculators with you because we're going to use calculators to calculate this. I also have the steps that you see on the red dotted thing. Those are the steps if you have a financial calculator. If you have a financial calculator those are the steps that you can use to calculate the mean the standard deviation and the coefficient of variation. Okay now those who have a cashier or a shop other than the shop financial calculator let's see let me go to yeah let me come here. I want to know what type of calculators do you all have. You can post it on the chat if you don't want to unmute so that I can have an idea because I don't want to also waste time using another calculator then you don't have that calculator. I've got sharp cashier and HP 10B. Okay you have sharp in a cashier. In HP. Okay so the cashier that you have has a fraction let me open the cashier. Does it look not that I will still have to open my cashier calculator just a sec. I closed it by mistake. Can just open it. Does it look like this? Does it have a a fraction thing? Let's open another one just give me a second. Others what type of calculators do you have? Yes. How are you? I'm good thanks. Fine I have a sharp. You have a sharp calculator. And cashier. Okay so you have a cashier so I think I will show both so your cashier calculator does it look like this? Does it have a fraction button? Yes it has. Okay and your sharp calculator does it look like this? Does it have the green things written on it like? Like alpha? Yeah like alpha in green and so forth and the green buttons you see where I'm hovering it's blue it's turning blue you see where on my calculator where I'm clicking the thing it's in blue on top there are weights written in green you see those? Yes so those who are using the sharp we're going to use the sharp calculator those who are using the cashier we're going to use the cashier because I cannot do this at the same time we will have to deal with one set of a calculator and then we will move to the next calculator please bear with me so we're going to start with the cashier cashier calculator so let's open so does the HP work similar to this too? The HP also works similar but HP it's more complex because I'm not going to touch on the HP because you said you have the cashier and the sharp right unless if you don't have those two calculators and you have only HP mostly I'm using HP but at the moment do you have a cashier or a sharp because HP is more complex you have three of them so for example now for statistics you are only going to use either the sharp calculator or the cashier calculator for your financial account then you can use your HP right but I have HP you only have you see the challenge I have with an HP because I don't have an emulator for HP it makes it difficult for me to show you how to use your calculator to do this what I will do those who are who have an HP calculator I will same do a documentation that you can follow on the same exercise that we are doing okay right because I don't have that with I don't have the simulator like the calculator that I'm going to show you right now okay so let's do this just need to make sure that this moves a little bit to the side I'm not going to write on the just give me a second I just want to okay sorry I needed to go close the door okay so let's deal with the calculator thing I hope you are able to see my screen I've tried to make it bigger okay so now those who have a cashier calculator you will have to write the steps as I talk don't don't try and do it we will repeat the same steps again don't try and do it you write while I speak you write the things that I am showing you so the first thing that you need to do is to switch on your calculator right then you need to press on the mode function which is that button that you have there different cashier comes with different views on yeah so you will have to tell me if your cashier is different to my one so that I can guide you to the right uh menu on your calculator as well so don't get left behind on anything so once you click on the mode the menu will pop up we need to go to state stf so depending on your calculator you need to press the number that corresponds to stat to the state function so here on my calculator it's two so I'm going to press two then I have another new menu if you look at this new menu I have one which has one minus var and I have two which is a plus bx now for today's session we're only going to use one one one minus var when we do regression we're going to use two a plus bx so for today we're going to only use one one minus var so you're going to click one as number one corresponds with the first number and you will get a table that looks like this now it means you're going to enter your data into the table so your data are those numbers 10 6 5 10 9 it is very important that you enter your data as you see it on the screen as well so let's enter our data so how do you enter your data on the cashier we're going to type 10 and then you're going to press equal sign it will place the data into the table and then we move on six equal sign five equal sign 10 equal sign nine equal sign seven equal sign 10 equal sign nine equal sign six equal sign eight equal sign six equal sign and six equal sign I know that they said they should be 12 when I look at the table already when I get to six the last six it should say it corresponds to 12 therefore it means I have captured all the data now once you have captured your data you can press ac button okay I hope you have written that down to some extent so that you can always remember remember it's mode two for stand and one for the table then you capture your data 10 equal six equal five equal 10 equal nine equal seven equal 10 equal nine equal six equal eight equal six equal six equal and you have captured your data and once you have captured your data then you can press the ac button your data will be stored on your calculator it's not lost if you want to see your data you can press on this stat button we need in order for us to bring that button up we need to press shift so you're going to press shift first you press the shift button and then you press button number one and it will bring a menu for your statistical analysis the first one will give you the type of the data that you have number two will give us the table that we completed can you see that there is our table I'm going to press ac again go back to shift and then go back to step one now you have number three and number four number three gives you the sum remember on your mean let's hope my pen can write on here remember that the mean is the sum of your observation over n so in order for us to know what the sum is we can use number three to get the sum so if you press button three and there you will have some x squared but we are looking for the sum which is your number two and then we just press two and then you press equal and that will give us our mean 92 divided by 12 and we can calculate that by say 92 divide by 12 which is equals to 7.67 7.67 you don't have to do it that way so shift step remember now I showed you where to find the sum she's just the summation but number four will give you the variations so if I press number four button for var and there I will have my descriptive statistics which includes also the sample size the mean the sample mean so the sample mean and the population mean on the calculator are one and the same thing they use the x bar so population mean sample mean will you use the x bar number three will give you your population standard deviation and number four will give you your sample standard deviation always remember that so let's look at our mean which is number two if I press two and I press equal and as you can see I got the same answer as I had when I calculated things mind why going back every time you want to go and calculate the statistic or a parameter you use shift one and the menu will come and then you will choose whichever value you want to calculate whether you calculate in the the variance the standard deviation and so forth the mean and the next if I click on five it will give me the mean of the data set if I click number one I know that the mean of the the minimum value of my data set is five and if I click on number two and it will be 10 because my highest value is 10 so you can go and get that and you can calculate your your range as well from here so how do we calculate the rest of this other things so to calculate we're going to start with the standard deviation the first one you need is the standard deviation because on the calculator and the the menu that you have on the var you have the standard deviation not the variance this is the standard deviation so we're going to calculate the sample standard deviation because they told us this is a sample of 12 monthly sales so it means we're going to press number four if they would have said consider a population of 12 monthly sales then we will use the population standard deviation okay so number four and equal and that gives us one comma one comma eight eight seven and that is the standard deviation remember our standard deviation is s if we need to calculate the variance our variance is a squared so it means we can take one comma eight seven and square that answer and that will give us if we square the the answer three point five let's see so if we press square button and you press the square button to get the variance and you press equal and it gives us three point five one three point five one and that's how you use your calculator now how do we calculate the coefficient of variation easy to calculate because we do have the standard deviation and the mean so how you will calculate this on your calculator your case your calculator you will go and say shift and you will go and press button number one let's do that uh sorry uh yes so it's shift because we know that this is your standard deviation over the sample mean multiply by hundred that is what coefficient of variation is so we're going to start shift button number one and then we press button number four then you press four and you press four again for the standard deviation and you press division because it's divide by and you press shift so you're going to press divide by and then you go back shift one and four and two and equal and you can see there it says standard deviation divide by x equal and that will give us the answer and multiply that by a hundred and that will be equals to 24.45 and that is on your case your calculator now let's move to those who are using a sharp calculator you can also use the you can use the fraction when you are in the state mode it will not work so and to take back your calculator to normal mode of med mode you just press mode and then press one it will take back your calculator to your normal mode and you can use your your your fractions to remember that it's mode two one for state then you put in the data onto your your table by pressing the value equal the value equal the value equal and then when you are done putting in the value you go ac and you go shift state to call the statistics analysis functions and you can select whichever the value you want to do let's say you are doing some calculation and you realize that there is no answer when you are calculating probably maybe you you you input the values wrong you want to go back to the table you can go to the table and you can look at your values on the table and if let's say for example number five is the one that is wrong you just use your error to go to number five and you change number five and you put the correct value for number five and you press equal and it will replace that old value with the new value and if you notice that you have done the whole table wrong you can also go and stand using your error at the beginning of your table and start capturing all your values two equal four equal six equal seven equal and it will replace all the values and if you make a mistake on the value you just use your error to go up and delete and that will be gone so it works like your computer the same way so you use the error to navigate there are delete functions you can recapture you can replace because also remember on your on your computer when you want to change a value you can highlight it and replace that value by typing a new value that's what you do so on the calculator you do the same by going through that value you are highlighting that value and somebody's now we're going to help you manesta who's using a a case your calculator now for those who are using a let's go there for those who are using a this calculator which is the hp you can see also you do have this value here can you see them like your your sum sum y sum of x and your n and there is the mean there is the mean it's written in orange and the standard deviation is written the sample standard deviation and the the population standard deviation so those who are the values written in or in in blue you're going to use the upper arrow to reach for them the button those that are written in orange you're going to use the the orange button to get to them now in order for you to to start working with this you need to store your data and that is where the complexity comes in with this calculator because i am not 100 percent sure and i don't want to do it right now on here because you need to use some input and some c steps or something like that and then capture the data onto your calculator and then use this button to navigate to call the values but i will send you your your document at the end of the session when we are almost done or before well well people are doing some activities i will go and find documentation for you to send to give you so that you can do your activities now those who are using the cash not the cash where the sharp financial calculator those are the steps because on your calculator you have the m plus those are the steps but the steps are almost similar to the one that i'm going to show you which is this this sharp then this sharp calculator so you'll have to follow me using your sharp calculators whether it's financial calculator or it is a cashier calculator so let's put this on the side and i must bring back the same so with this one it's going to be a mission and a half to work between the two screens because when i think it will hide my presentation so let's minimize the presentation so we already have the the values we already know what the values are okay please make sure that you are always muted please make sure that you are always muted okay so those who are using the sharp calculator yours it's easy because all the values are visibility are here that's the mean that's the standard deviation for the sample that's the population standard deviation those are your summations your sum x like i showed you the sum x every value that is written in orange we use the alpha to reach for those values any value that is written in yellow or orange we use the orange the second function green we use the alpha button but we need to get your calculator also to state mode so for you you will press the mode button so you must look for the mode button on your calculators get my calculator because sometimes the emulator is different to way it is different to the normal calculator so look for the mode button and you will have the menu which says zero and one for normal for state you're going to press one for state and you will have sd line and quad for today we use sd because we're using only one unit variable next time we do linear regression we'll use line for two variables and two numerical variables so for today we're going to press sd which corresponds to zero we're going to press zero and your calculator will be on state mode zero now with your calculator you will not have the table but it will tell you every time you put in the value it will say dataset one like the one on the financial calculator you would have followed the same steps so you press the mode button you press one for state you press zero for descriptive statistics which is the sd and your calculator will say state zero so depending on which calculator you are looking at whether it's the financial calculator or is the normal shop calculator you will have state zero in front of you now in order for us to capture the data onto our calculators so those actually these are the steps for a normal shop calculator because it has an m plus so these are for the normal shop calculator those with a financial calculator in state of m plus you go into press e and t the enter button there is an e and t button there that's what you're going to be pressing the enter button so how do we press store the data we do the same you press the value 10 and then you press the m plus with the financial calculator you will press the e and t button it's on the m plus then you continue it will say dataset one you will continue capturing all the datasets until all the data points until it says dataset 12 and then you know that you have captured everything so let's continue six m plus five m plus you can see that the m plus is there not the m plus that i'm talking about the plus five sorry it's losing yes we started by entering 10 or six 10 and then six yes okay thank you then five then ten and plus and then nine and plus seven and plus ten and plus nine and plus six and plus eight and plus six and plus six and plus then i have 12 dataset now the challenge with the shop calculator because you are unable to go back and look at your dataset you won't know if you you enter your data and you see that you are on date you know 14 then it means there is something that you did wrong you can clear your calculator by pressing second function and ca it will clear your store data and you can start again ten and plus six and plus five and plus ten and plus nine and plus seven and plus ten and plus nine and plus six and plus eight and plus six and plus and six and plus so also those who are using the financial one when you you capture and you see that you are way out or the values they are not getting to 12 you are on number six then it means there is something wrong that you did you just need to do second function ca and second function in the mode so that you clear your calculator so once you have captured all your 12 dataset you can press the on and off button your data is stored in the memory of the calculator now you are ready to calculate the mean standard deviation and so forth so now since everything is here in front I'm going to start also by calculating the sum of x sum of x is written in in green and it's on the dot button so I'm going to press alpha and dot and press equal and you can see that I get the same answer as we did when we were using the case show which is 92 and I can divide 92 by 12 and that is 6.677 that is the mean or you can go and find the mean by pressing alpha for equal and there is the mean the beauty of using a shop for financial for statistics calculations is that there is no shift 4 4 1 like the whole step that we do when we use the the cashier calculator the downfall is you can see the dataset cashier visualizes your dataset and it makes it easy for you to see what you are doing as well so there are pros and cons so choose whichever when what I will say to those who don't have a cashier or a shop calculator I will advise you to go and buy a cashier calculator for the fact that if you're doing any mathematical calculations you do have this fraction which makes things easier whereas with a shop calculator we don't have you don't have this functionality unless if you're right you use the shop right and you can use those functionality please okay so enough with that let's go to the standard deviation because that's the next thing that we need to calculate you press the on and off and we press the standard deviation is alpha and because it's the sample sorry please press button five and yes I was left somewhere after entering the data we press on and off yes and then after that you press alpha alpha and whatever you want to calculate so now we calculate in the standard deviation so press alpha and button number five and press equal and see if you get the same answer if you don't get 1.87 it means you did something wrong when you captured the data you need to go back and capture the data again by pressing second function mode play your calculator justice are you getting 1.87 let me try to press alpha and button number five no I'm getting it wrong okay so it means you captured your data wrong so you need to press second function and then press the mode button so second function mode and then capture the data again and see if you can get you get it right the steps are easy with a with um inside a new slide and blank one so with a with a sharp calculator the steps are easy so it is mode and mode one and then zero for sd sd zero for sd and your calculator will be ready and then you just press the values 10 and then you press the m plus or you press 10 and then press the e and t button and then you continue doing that you can continue capturing all the values once you are done then you press on on and off your calculator to calculate the mean you just press so for the mean you will press alpha and then you will press button number four for the standard deviation you will press alpha and button number five so now how do we calculate the coefficient of variation which is coefficient of variation which is s divided by the mean multiplied by a hundred so you will say alpha five divided by alpha four equals and multiplied by a by a hundred you just do that so let's calculate the coefficient of variation so i'm going to go back there we know that we got 24.5 oh sorry before we calculate the coefficient of variation we need to calculate the variance we know that the variance is the square you just press the square button which is the x squared and it will change to s squared and then press the equal sign and you can see that we get 3.51 so that's how easy it is so in order to get the variance you calculate first the standard deviation by pressing the standard deviation and then you press the square now let's calculate the coefficient of variation which is the standard deviation divided by the mean and we know from our next one we said it is alpha five for standard deviation divide by alpha four so the mean equals multiply that by a hundred equals 24.45 you can also put it in the bracket you can say alpha sorry alpha five divided by alpha four close bracket multiply by a hundred equals you will still get the same answer which is 24.45 or even when you don't close it because it's a multiplication but must say division and multiplication have the same priority you work from left to right so it will not even make any difference so alpha five divided by alpha four multiply by a hundred it will still give you 24.45 because of what muscle room okay and that is how you find the mean standard deviation and the coefficient of variation so let's go back to our presentation which one of the following descriptive statistics is not a measure of central location let's see if you still remember what have we used today you can just unmute and tell me which one is not a measure of central location anyone think is the range it is the range because that's what we were discussing today the others we discussed the last time we met and the other one says all of the above measures describe central tendency no only the range is not a measure of central tendency given the following symbols identify the symbol that represent a parameter as a measure of a population we have number a number b number c and number d we have the mean the standard deviation the mean the standard deviation so which one a b c and d which one represent a parameter or a population a measure of a population which symbol a and d it is a and d which is option two because for population parameter because it's huge we use the greek letters you must always remember that use greek letters that is a greek letter that is a greek letter the others are just normal as letters of alphabets that we know i'm not going to ask you about this and i think i don't have to ask you about this but i can ask you to calculate the range of this data set so the other thing when you calculate the range you can sort your data or you can look at your data and say which one is the smallest value and which one is the highest value it's always advisable to sort your data from lowest to highest and if you look at this data set it looks like it's almost sorted so calculate the range of this data set 97 and how did you calculate the range um 256 minus 159 256 minus 159 which is equals to 97 and that's how you will calculate the range i'm not going to ask you to what that the number of observation i'm going to assume that some of these things because we did them last time you know how to answer them but anyway which one of the following statement is correct with regards to the coefficient of variation so we've just learned about coefficient of variation today in a right and we said it is a relative variation to the mean and it gives you the variations what else did we talk about and we you know the formula for the coefficient of variation you know that it is your standard deviation i'm going to write sd now standard deviation over the sample mean multiplied by okay so which one of the following statement is correct with regards to the coefficient of variation you tell me whether it's one two three four or five is it a measure of location is it the difference between the largest and the smallest value is it the sample standard deviation squared is it the sample standard deviation expressed as a percentage of the mean or is it the mean squared one two three and four which one is the correct one four four is the correct one because i gave you the answer right there is the standard deviation expressed as the percentage of the mean because regardless because if i multiply 100 by the mean is the same as 100 percent a percentage of the mean divide standard deviation divided by x bar multiplied by 100 is it the location no it's a variation so this coefficient of variation it is a measure of variation or measure of dispassion is it the difference between the large and the smallest this is the range definition is it the standard deviation squared this is the variation sample variation some or sample variance why am i calling it variation sample variance this is a sample variant and is it mean squared no it's not it is not mean squared okay consider the following consider only the number of the people living with autumn syndromes asd and the table is given below so the number of people are 108 for the four 206 85 and 57 which one of the following statement is incorrect now this is what we did last week so it means you need to find the mean the median and answer the question and also find out whether the mode is correct or not so let's we're going to do this one together and then the next one you bring it on your own so which one of the following statement is incorrect before I can come and answer this because I can see that they're asking questions about the mean the mode so I can just go and calculate the mean the sum of all the values or you can take your calculator and capture all the information on your calculator and I'm going to go do it as I'm going to do it with the case here to capture the data sorry because I'm writing all the information two and one and I have 108 44 206 85 and 57 AC and then shift stent and four and two and equal and I have my mean is 100 I can also double check with my other calculators so I can function CA to clear my calculator from any stored value 108 and plus 44 and plus 206 and plus 85 and plus 57 and plus and on and off alpha four equal I get 100 so it means my mean is 100 I found that finding the median I must first find the median position remember and plus one divided by two there are one two three four five so it's five plus one divided by two which is equals to three because it's six divided by two is three I need to sort my data from lowest to highest 44 57 85 108 and 203 so 123 85 so my median is 85 now my mode looking at the data set there is no mode right because I can't see any number that repeats itself come and answer the question number one two three four and five the mean and the median are equal is that true is that correct no that's false that is not correct the mean is less than the median that is false that is also in which one of the following statement is incorrect are we looking for the incorrect one probably the statement here was supposed to say what is the the information that is correct sorry I don't think that is what they intended with this question okay so the mode is zero is that true or false it's false that is also incorrect there is no mode that's correct that is correct none of the above that is another option that they like it needs to include for just confusing everyone to say if I can find any of this until let me just choose option five that's my backup okay I hope you already captured your data onto your calculator because the next one is says what is your standard deviation I have already my data because I quickly included the data on my calculator I can calculate my standard deviation but I want to see if you can get it as well then let's see anyone who already has the answer option one it's the 4.24 ah so we do have those who already are on the roll so you go shift one and then you go four for var and then I'm going to use because that is sample standard deviation as they asked so we're going to press button number four and press equal that's 64.25 and also on the sharp calculator we can do the same we go alpha and we press the five button and then press equal 64.25 see easy it is to use your calculator instead of using the formula because at the moment if you are going to rely on your formula remember that your standard deviation is s is equals to the square root of the sum of your observations which is your observation minus the mean squared divide by n minus one so you would have went and set the square root of 108 minus what did we say the mean is 100 right 100 squared plus 44 minus 100 squared plus until you get to 57 minus 100 squared divide by how many there are one two three four five divide by five minus one and you would have found that the answer after doing the whole calculation you will get you will get that so you can see that using your calculator will save you a lot of time but you need to practice not one of that you see this now in in the session and then you you stop using your calculator or you stop practicing you need to practice practice practice okay the next one calculate the coefficient of variation for the same data set so you already have the data start all you just need to do is calculate the coefficient of variation those who don't have the data start remember we calculated the mean we found that it was 100 calculated the standard deviation and we found that it was 64.25 so what they are asking you now is to calculate cv which is s divide by the mean multiply by 100 percent you have the answer yes that is easy option one in 64 64.25 that we have been i'm going to show you on the calculator as well 64.25 divide by 100 multiply by 100 100 and 100 will cancel and the answer will be 64.25 percent so which is the same i have my standard deviation divide by shift that's 14 of two and multiply that by 100 equals 64.25 you still get the same answer same thing i have my standard deviation divide by alpha 4 multiply by 100 and i still get the same answer so that's how easy it is to use your calculator to calculate or find the measures of variation and remember these questions are like you get one question in the exam paper which weighs about four marks so why not save the time for more complex calculations at the later stage as well okay now you have a big data set calculate the standard deviation so those who are going to use manual calculations because they don't know how to still know how to use their calculator so your standard deviation formula is the square root of the sum of your observed value minus the mean square divide by n minus one so you can use that formula if you're using a casio calculator you're going to press you're going to press the mode two one two and one and your calculator will be ready to put in the data and then you can just put in your data 154 170 154 159 equal and you continue capturing your data so you're going to say 159 equal 170 equal 172 equal until you capture all the data until you get to 256 equal so once you have captured your data then you're going to press shift I'm going to press button number one then you're going to press button number four and then you're going to press button number four and that will give you your standard deviation those who are using a shop you press mode and you press one and you press zero and you say 159 then you capture your data 159 and you will press m plus or those who are using the financial one you say 159 and you press ENT and you continue 170 m plus 170 ENT and you capture all of the data set until you get to 256 m plus ENT and once you have captured your data easy stuff you're going to press alpha and then press button number five that will give you your standard deviation and once you are done you let me know what is the answer I'm just going to go on top of this number two says option two is the answer so let's let me quickly do that I'm going to use I'm going to use a cashier calculator quickly so that will be 170 equal 172 73 equal 192 equal 193 equal 199 equal 201 equal and I think the next one is 170 or 201 there are 201s 2201s 201 equal 201 equal 216 equal 217 equal 230 equal 235 equal 192 are they 15 yes okay now you can calculate I'm going to put it here yeah since it's the cashier we've entered all the data sets and we just hi Lizzy yes hello Lizzy yes can you please move the calculator from the data set I'm still trying to calculate to enter the data I'm still trying to see how to to move it it got stuck there and I've got a thingy yeah that is there you go thank you okay thank you no problem okay so we use the step it's shift oh we can press the on and off button sorry I bet ac I forgot the ac button in between days step press the ac button and then you press shift one four and then four again and then equal that's the other stick that I forgot so the equal patch and the ac ac patch also yeah you need to press the ac yeah you press the on and off button yeah you will go and press the on and off button what they'll see okay so let's when I open the case you want the the shop one it will hide the data so bear with me I'm gonna move it a little bit down but I will use my laptop to capture the information don't worry so let's second function CA the calculator 159 see now I cannot I need to start first year it doesn't allow me to use my number button on my laptop so I will have to do this way so 159 and plus 170 and plus 172 and plus 173 and plus 192 and plus 193 and plus 199 and plus 201 and plus 201 and plus how many 201 1 2 3 4 5 6 7 8 9 8 another one 201 and plus 216 and plus 217 and plus 283 and plus 235 and plus and the last one is 256 and plus and I have 15 of them and then you just need to press alpha 5 so alpha button number 5 and then equal 26.7 did we also get 26.7 happiness are you good or are you great um easy so we don't have to round it off 273 because on the shop it gives me seven three I'm on the yeah it also gives you can round it off 273 but as I look at the options that we have here number two is the only option that we have which is 26.7 so and this comes from tutorial past tutorial letters so whoever wrote this tutorial letters they just decided to use only is 2.67 you know 2.67 but anyway even if you round it off two to one decimal you still get 2.67 because the number to the right is less than five so it's still not gonna make any difference all right all right all right all right all right I think this is one or two more last three questions this is just a general question anyway but I just want to also test to see if you still remember what you did the last time and what we did today consider the data set one two three four five six seven eight and 99 which measure of central tendency is affected by the outline do you still remember which measure will be affected by outliers I'm thinking the mean it will be the mean yes definitely that it will be the mean calculate the standard deviation you still have two more questions the daily electricity consumption in kilowatt by a sample of 10 households in Bolupani is a recollect as follows the standard deviation is so you just need to find the standard deviation and answer oh should I wait a little bit you can wait a little bit while others are still calculating okay you are so quick all right I'm enjoying navigating around the calculator now it's easy it's easy even though I think the the cashier because now you can see how you're working I'd like to see what of input okay someone might ask why am I always when I use the cashier to and not use the clear you can use the clear button there isn't a clear button let me see if I can because I still have the data start so in order for me to clear that data set I can use shift and then go nine and then it will clear all probably it will it will clear everything I am not sure but let's see oh no it doesn't clear all and that is why the other thing I prefer not to use the the cashier let's see shift start data is true you see it didn't clear the data set so this doesn't work as well as I would have hoped it will do and that is why I always start from from the beginning and that way it clears the calculator from any stored value and then I can capture again 51 enter 47 enter 48 enter 61 enter 55 enter 44 enter 35 didn't do enter 44 which is equal you will see that my equal when I press enter because I'm navigating on my laptop and it presses the equal sign 35 equal okay and then on and off I will also do the same with the cashier I can have second over the shop um 51 and plus 47 and plus 14 and plus 37 and plus 43 and plus 48 and plus 61 and plus 55 and plus 44 and plus and 35 and plus do you have your answers let's see what is the answer number two number two does anyone get a different answer to number two those who came in late please remember to complete the register I'm just going to repost it on the link because I can see we almost almost almost today okay so on the cashier I've stopped my data then I can go find we calculate in the standard deviation right shift set four one four and four again and equal and the answer is 8.07 53 on the shop calculators same alpha five equal and you get the same answer okay I hope by now you are comfortable with your calculators to do to answer any of these questions now this is new data set it's not the same as that one so this one is for 10 households in Rustinbeck you need to calculate the coefficient of variation the coefficient of variation cv is equals to your standard deviation divided by mean times 100 so going to store the data while you also are storing your data remember those who still don't know how to use your calculator the mean is the sum of observation divided by n and the standard deviation is the square root of your observations the sum of your observation the sum of observation minus the mean what divide by n minus 1 you can use those two formulas to find the values and we can finish early today because this is the last this is the last question do we have an answer I'm going to calculate them manually now plus ac shift state for for equal then I have 8.718 divide by shift state for to 100 equal the answer is 18.28 sorry 18.28 let's look at the sharp alpha five divide by alpha for multiply by 100 and answer is 18.28 those who are using an hp calculator I just want to 10 h hb once is it once see 100 h let's call it 8 I mean shall calculate 10 b1 that's what I wanted these are the things that I want hp 10 i by and you can say standard deviation there we go so you can look at there is the video you can go and look at how they calculate it let me just play it anyway okay so that then clears up those who are using the the hp calculator so remember the orange button which has the arrow facing down and I'm just want to go back to to your calculator remember the arrow facing down and c state that will clear your calculator from your memory so you press the orange and then the c state and to capture the data so you're going to use the sub so you are going to put the value so let's say we are using there this question which is 41 47 40 and so forth so on your calculator what you will do is you will say now I forgot the values now 51 47 51 47 so on your calculator you will say 51 and then you will press the sum plus and it will say one and then 47 and some plus and then it will say two so it will do the count like when we were using the the sharp calculator it was doing the data set one data set two so yours will count one two three until you get to the number so there were 10 so until you get to 10 you will know that we've captured all the values now in order to calculate the mean the mean is on button number seven you will press the orange button and press button number seven it will give you the mean of that data set and if you want the standard deviation which is the sample standard deviation you will press the orange button and you get the the the um the you will get the the standard deviation now when we're going to do the regression because there are two of them on yeah so you will use the swap for the mean of x and the mean of y you use the swap button and that is why I said I will send you also some manual but I think you can also go to to youtube and just put in the type of a calculator that you have and say uh mean or standard deviation or regression and they will give you all the steps that you need and that's it from me for today so let's go back to our presentation and we are right at the end of our session do you have any question any comment please remember to complete the register okay one thing oh yes you can yes yeah I just have one question just for clarity the only thing that wouldn't be calculated on a calculator is the median that is something that's still a manual yes calculation okay yes um so um there are calculators that can calculate the next time I see you will be doing I'm not sure is it the courthouse I think we'll be doing the courthouse yeah there are case your calculators these days or or shop calculators these days that can calculate the courthouse um you need to be very careful with those type of calculators because they don't usually are slightly the same logic as they are required in your in your prescribed books as well so yeah but the median is the in terms of that calculator if you get that calculator they are the most expensive calculators you are able to calculate the median but for these calculators that I just showed you today and all that you can calculate the median and the and the mode using that you will need to do that manual okay thanks all right so let's recap what we've learned today we've learned how to calculate the measures of variation the which are the range the variance standard deviation and coefficient of variation and we also learned how to use a calculator to calculate those measures of variation and practice practice practice because from now on you will be introduced to new formulas every now and then every week if you don't practice and learn some of these things don't memorize know them and that way because when you are practicing you will know them and go through your your workbooks your activities find past the exam papers work through them on the concept that you just learned today as well and practice the activities and all that from those questions and that will improve how you answer your questions in your statistics exams and your assignment as well on that note I hope for more detailed content relating to measures of variation your either your your two tasks or the workbooks that get gives you more information because I know that most of you have e-treat us you are linked to an e-treat us so please make use of that space as well because I just concentrated on the skill I didn't concentrate more as you can see that I didn't even use the formula more often I just wanted to show you how to use your calculator as a peoples of today's session while I introduce the measures of variation but in terms of the content related to your module please make sure that you attend your e-tutorials you look at your workbooks because I didn't I only scratch the surface so please do that so that you don't disadvantage yourself when you find questions in the exam that don't look exactly the same as what I have asked you and and also remember with statistics as well they do ask questions and around theory like we did some of the activities just to highlight and show you that you will not always get calculations that some things that you need to calculate but you will be asked about some theory of some sort to a certain extent it might not be too many questions but you need to know your theory as well and don't just rely on this sessions and then say oh after I've attended the academic literacies I don't have to do tutorials other than that all the videos are on my youtube as well that are tutorial videos that we go into detail we explain things we do lots more than what we do in the skills training so you can also follow me on youtube if you haven't already you know a way to find the schedule on my unis on my unisa and the notes are also uploaded on on there and I think what else you need to know that's it so if there are no other questions so it's lazy yes justice where do we get the attendance register today oh I did didn't I post it on the chat sorry I'm gonna put repost it again um I just posted it right there so this each of us you are talking about we get them in my unisa I think so and didn't you receive an email saying you are linked to an e-treater no I didn't receive it most of the first year modules are linked to e-treaters so you can just check usually they are the e-treater modules um let me see if I can get to my site let's see my unisa right let's see I don't even think I've started because I've been linked to a class and there's nothing happening there it's not quiet which module are you are you in remember the e-treaters are not doing like face-to-face tutoring like I do like now they communicate with you via the the platform that unisa has a so it's set up but nothing's happening in there yet which which module are you are you 16 10 15 or 16 16 16 uh what is the code for your module for your e-treater class because my e-treaters maybe you are in my maybe you are in my and I am in statistics 15 oh one yeah so you can see there is my this is this is my e-treater site as you can see that the students in my my tutorial site they should have already because I already started with them last week I have already posted the announcement which they should have already received which gives them all the information that they need to know about tutorials so that is why I'm saying you need to check who is your e-treater um and mostly your e-treater site will have a groups a group you can see that my the lecture site is it ends with a y but my e-treater site is that within one e so if you are in 2e 3e 4e you will know which twitter you are or which twitter site you are in and then if your tweeters are not communicating with you you need to send your lecture as an email to say but I'm linked to this twitter but they're not saying anything so but in terms of my sessions like for example I've already created the content for them so they already they should have already started going through the information as as always um Leslie yes I actually checked I'm in your class I'm sorry then I'm very disappointed in you because yes everything's there I check I just now now you are killing me because I could I go all out for my students so apologies apologies um and I am still waiting for you guys to also respond to my messages because in there it says you need to complete some if I go there when can we have a session because I rely on you responding and telling me and telling me when can we have a session so they we will have a one hour session on a Saturday or Sunday but I need to know when so you guys are not responding to me so how am I supposed to you if I give you all this and yeah so but I'm all I'm all I wanted to to to to say with regards to this is you need to check your e-treater because your e-treater will do things different to what I do and you need to make sure that you attend your classes that your e-treater is offering I will yeah definitely those who are in my class I will have e-tutorial classes but this year I'm not going to have tutorial tutorial it's going to be discussions because the content is already there so I'm linking my videos 30 minutes videos on online so you need to go and watch those 30 minutes videos and then we can have discussions and I'm going to do things differently this year so if there are no questions I need to leave I need to stop the recording as well so just one question yes do you also have like you were saying you've got like a detailed explanation of the HP like calculator calculators do you have the same for the casio ones or the sharp ones you mean they okay so which module are you doing because one of the module which I think it's 1610 they do give you a I did share this the information there is a how to use how to use a calculator content that I shared with the lecturers to include in the tutorial letters so I know that one module they have included that information in one of the stacks so if you scroll through there is a way it explains the casio and the sharp calculator it gives you all that information do you have that do you know I have something like that it it does but it's very very basic it's the 16 that 16 does it yeah yeah so 15 10 16 30 16 30 yeah so I will I will check the documentation and then I will also load it where you will find your schedules if you go to the schedules let me also it's one of the other things that people don't know where to find the thing so if you go to your schedules you will see that they they have a note and recordings there might not be any recordings oh they are but it starts on session one they are nothing after that so but anyway that's not the purpose of this there is a link here for open class notes so yours it will be different the view will be different to my one because I'm I'm an editor on this folder but you will be able to see all oh I didn't load today's notes I will load today's notes yeah so I will also load on here the document on how to use your calculator for HP and for the other the other one I will need to go in such way did I store that it somewhere um but I will include it in here on the note so always the notes will be here if you miss the class and you need notes they will always be loaded onto here you get them via the schedule and the space button notes and recordings other than that thank you very much for being part of today's session and this is Lizzie