 So we have our data and we know that we want to calculate the standard deviation, our SD, which is our standard deviation, and this is our sample standard deviation. How do we do that? So those who are using a sharp calculator, you will have a sharp calculator that looks almost like this, where it has a, on your calculator, the letters might be blue. It's called an alpha, it's blue, and you also have some letters that are written in green that are like the X bars. I cannot make it bigger. So on button number four, there is an X bar there, which then will calculate the mean, which we use it to calculate the mean. We also have the SX, which will calculate the standard deviation. SX calculates the sample standard deviation. So those are the buttons we're going to be using, but I'm also going to introduce this one. This Sigma X on button number six, it calculates the one that looks like this. Sigma X, it calculates the population, the population standard deviation. Then we're going to use, on your calculator, this might be an M plus on some calculator, and on some calculator, this is data change. We use this to store the data. So now what you do on your calculator, is to first put your calculator to state mode, and put in your calculator to state mode, you first press the mode button, which is that, you press the mode button, and you will have a dialogue that tells you one for state, and zero for normal, and two for real. So we're going to use the one for state, you go and press button number one. So you will press one, that relates to state, and you will see that it gives you a new menu at the top. It will say state one, and it will give you some menu as well. So zero for SD, we're going to be using SD for standard descriptive statistics. And those who do MES, they can use it for doing the quite, the logarithm, later on when we do chapter 12, we will use it for doing the linear regression using the line. And so forth. So for today, we're only going to use zero for SD. So you're going to press zero for that SD. So you just say zero, and your calculator will be in state mode zero at the top. It will show you like that. Then now we need to capture this data that we have. Remember, we created, we were given the data set, which is 10, 12, 14, 15, 18, 19, 21 and 20. So to capture that data is easy on your shop calculator. Remember, this is only for the shop students. So shop, you say 12, also return, you press 10, and you press the change. So for cashier, we wait a bit while you show the shop users first. Yes, yes, yes, yes, yes. Let me do one calculator at a time. All right, thanks. Yes, so you will press one and you press the data change or the M plus. So on some calculators, it will be M plus, especially the shop, G-A-L, somebody bought that calculator this morning. So that one, you will press the M plus, and then it will tell you data set one, and then you continue. You say 12, and then you press the M plus, which is the data change. It will say two, until you get all the data set. So you should have data set eight when you get to 24. So we continue and say 14, M plus 15, M plus 17, M plus 18, M plus 18, M plus and 24, M plus. You need to be very careful when you enter the data so that you make sure that you've entered the right information and you didn't type something wrong, otherwise you have to start from scratch again. Okay, now we have our data start, you just press the on and off button. And once you have pressed the on and off button, then you are ready to do the calculation. Remember, if this was the population's information, the mean formula, you remember, the mean formula, which is the X bar, is the same as the mu on the calculator because the formulas are almost the same. So on the calculator, your mean for sample and your mean for the population, they use the same button, which is the X bar. So let's say we want to calculate the mean of this data set. So the mean, oh, sorry, we don't press four. You say alpha first because we want to call that function that is green on button number four. So you first press alpha and then you press button number four. Do you remember the mean from the previous slide? So the mean, if I can make this slide bigger, I will keep on hiding it. We remember that the mean was 16. So if I press the X bar, you always have to come back and press the equal sign and you will see that the mean is 16. Then we do the same. We do the same for the standard deviation. Remember, we calculated the standard deviation, which is this whole master calculation that we did here. And we found that the answer is 4.3095. On your calculator, you go and you say alpha. It doesn't matter whether it's still in the answer mode for the other one. So you say alpha. And remember, it was the sample standard deviation. So therefore we press five and we will press equal sign. And you can see that the answer is the same as the one that we had on the screen. And let's say we want to calculate the standard, the variance, the sample variance. Remember the sample variance is that underneath the square root, which is 130 divided by seven, which gave us 18. On your calculator, there is an X squared button, which is the button there on the calculator. X with a square button. That button will help you to convert your standard deviation that you got from your calculator to a sample variance. So to do that, while we're still in the answer mode for the standard deviation, you just press the X squared button and you will see it converts into the variance and you press the equal sign and it is 18.517. And if we go to our variance, which I calculated manually, I got 18.57 as well. And that's how you use your calculator. To calculate the mean and the standard deviation. So if you are given the population, you will use number six for the population, but that's not what we were calculating now. Those who are using this calculator, please, you can practice the steps. At the later stage, you will come back to the video. It will be the second video. I will post both because I stopped the video and I hope I started the recording on this one. Did I start the recording? Is it recording? Does it show as the meeting is recording? Yes. Yes. Yes, thank you. Okay, so you can come back to the videos to see the steps again and practice and practice. Remember, those who are using the shop, your calculators might look different to this one. You might have the M-plus. This M-plus will be here as a data change for your calculator. And those who are using the financial calculator, which is also, it's relevant to those who are using the financial calculator, the shop financial calculator somebody posted, that orange one with the cover, the cover is Merun, yes. The Merun cover on your one, instead of the data change, that M-plus that I'm talking about, the data change, yours will press the ENT button. The steps are the same. Your ENT button will be there. It will be the last button on your functions before the delete button. After, yeah, before the delete button. So you press ENT at the steps, you follow the same. And your values and the screen looks exactly the same as this. Okay, so that is the measures of variation and the measures of central tendency for this. At the later stage, when we do the covariance, we will use the same because the covariance is your standard deviation, which is button number five divided by button number four, but we will get to that at the later stage. So now let me do, or help those who are using the other calculator. So I'm going to remove all these notes that we have here so I can create space for them one. Okay, so now those who are using a shop calculator, this one I can make it bigger a little bit. Helps. Okay, those who are using the case shop. So your case shop will look like that. I am assuming it has the fraction thingy, some that they don't have the fraction thingy and you have the STA button on button number one, some have some some and some var something like that on button number one and button number two. If you have those kind of button where it splits the some some and some var, please after the session contact me on WhatsApp on the group so that I can help you with your calculator. But the rest of the calculators that you showed me yesterday when I asked, you are using this kind of a calculator. So also we're going to create the same thing that we did. So we first need to understand our calculator as well a little bit. So there is the mode button. We're going to be using button number one and shift. So yours, you don't have the values displayed here at the hidden under button number one under the state. So we're going to press shift and press set to reach the other things as well. So how do we get there? So the first step you do is to press the mode button. So you go and press the mode button and you will see that it has so many menus unlike the previous one. So our one that we are interested in is number three. So you're going to press three or this set. So you press number three, the value number three and you get this menu. So going forward as well, when we do chapter 12 for you as well, you will use number two. For today, we only want to use number one and that is what we are interested in for today. So you're going to press one for that one minus var and that gives us the descriptive statistics. So you're going to press button number one and it will give you a table. Some calculator, it will give you two tables. Some calculator just gives you one but others it gives you two tables. So you must just check which one is yours. So it will give you a table and now we need to capture that value, those values. So we know the values are 10, 12, 15, 17, 18, 18 and 24. To capture them, you just say 10 and you press equal sign, it will store the value there. Then you go 12 equal sign. You say 14 equal sign, 15 equal sign, 17 equal sign, 18 equal sign, 18 equal sign, 17 equal sign, 18 equal sign, 18 equal sign, and 24 equal sign. And you will see that the last value will correspond to number eight, which then tells me all the values are stored on your calculator. And we can go cancel AC, you press the AC button, your values are stored, they are not lost, they are still there. Now we need to calculate the standard deviation and the moon. So we're going to press the shift button. So you press the shift button and then you will press button number one. So you go shift and you press one. And it will give you this menu where it says one and two sum var sum and fours and distribution and all that. We are interested in the var, not in the sum, the sum will just give us the summation of the values and the sum squared and all that. We don't want that, we want the var. So we're going to press four for var. So you just press the button number four and it will give you this menu. As you can see, it tells you that if you want n, you will press one. If you want the mean, you will press two. So if we want to calculate the mean, remember also the same happens with this calculator for the standard deviation, sorry, for the mean for the sample and the mean for the population is the same. We'll use number two. But if we calculate the standard deviation or the variance, we're going to use that sigma. So let's first calculate the mean because this one is for the sample standard deviation. So to calculate the mean, we're going to press two and if we press two, remember, we always have to press the equals sign and you can see that the mean is the same. You can see that the mean is 16. I'm not going to show the slider again because we have shown, we know now that the mean is 16 and to get to the standard deviation, here is the thing, you will have to go back and repeat that step and this step. So you will have to go back and say shift one and it gives you this and you press four again and then you press four again for the standard deviation and you will press four again for the standard deviation and you will press equals sign so that you get the standard deviation and if we remember very well, the standard deviation was 4,0309 and that's what we have calculated. Similar, if we want to calculate the variance, if we want to calculate the variance, we'll have to use the x squared button, which is this button here. We will have to use that button. So to calculate the square of the standard deviation, to calculate the variance, we just press x squared and it will square the answer and say equal and it will give us the same as what we had, 18.514, 18.514. Okay, and that is how you use your calculator to calculate the mean and the standard deviation. So on the screen right now, I have the method for the sub-sharp calculator. So remember, it's the same calculator that I just used. So where there is an M plus, those who are using financial calculator, you use ENT and those who are using the other calculators like the sharp right, use data change. You will use data change and it will give you the same answer. Okay, so that is the standard deviation and I'm not going to ask you to do any calculation for now because we only have 30 minutes but I will give you a chance to do the same when we calculate the coefficient of variation. Let's move on to the coefficient of variation and I gave you some of the things as well when you do the exercises there. Okay, so the coefficient of variation is another measure that we use for measuring the variation or the variability of your data and it measures the variation relative to your mean and it's always represented by a percentage and we can use it to compare the variability of two or more things or groups of things. And this is the formula that you will use which is your standard deviation divided by the mean and we have to multiply it by 100. So let's look at an example. Let's say I need to calculate this. So now if you look at this example, I am not using any data so they already calculated the values and they give me the standard deviation and they give you the mean. In the exam they might not give you the mean and the standard deviation but they give you the data set like we had the data set like this and they might ask you to calculate the coefficient of variation. So you just need to know how to calculate the standard deviation and how to calculate the variance which is what we did when we were using the calculator to calculate this, we calculated the mean and we calculated the standard deviation so you can use those methods to calculate. But in this instance because they already calculated the values of the mean and the standard deviation we just need to substitute into the formula and our S is our standard deviation which is 5 prime and our mean which is our X bar which is the average last year which is 50 multiplied by 100 which is five divided by 50 gives us 0 comma 1 and multiply that by 100 it gives us 10%. And we can calculate it for the another stock type which is stock B, we have the average which is the mean of 100 and the standard deviation of five therefore the standard deviation is five friends and the mean is 100 multiplied by 100, we get 5%. Both the stocks have the same standard deviation but they have different means and as you can see stock B is less variable than stock A. So in this type of measures, most of the time the people who use it most often are those who work in the risk department especially those who work with portfolios in the finance area and all that they like using the coefficient of variation because it gives them the indication of how the market is changing in which portfolio they need to invest the money of their clients and if that thing happens almost on a quarterly basis or a monthly basis then they have to change and look for other opportunities and they use this kind of measures to make decision about where they need to invest in. So let's do the exercise. You have 10 minutes to do the exercise calculate the coefficient of variation and then I will do the exercise but I will use the calculator to calculate the coefficient of variation. So you will have to come and do the coefficient of variation CV is equals to S divided by X bar multiplied by a hundred and it should give you the answer. You don't even have to put down the brackets and that is the formula you use. So calculate and then we will check the answer just now in 10 minutes. So let's see it is 13.4 so by 13 foot, let's say 13.41 I will come back and do the exercise on the calculator. Are we winning? Yes. So let's use the sharp calculator. What I haven't told you now is after you have if those who followed me on the calculator you haven't cleared your calculator from the store maybe you will be airing on top of the values that you have. So what do you need to do? Once you have done your exercises and you completed one question and you move to the next one you must always remember to clear your calculator and to clear your calculator from these third values you just press second function and you press the mode button. It will clear your calculator. You will see when I press alpha and I press four it should not give me any value and I press equal the calculator should give me an error because there is no data that is stored. So it means now I am ready to enter my new data so that we can calculate the coefficient of variation. So now I hope I'm able to write on this one. So remember the formula is I need to open 10s then the formula is coefficient of variation is your standard deviation divided by the mean multiply by 100%. Remember that. So now on your calculator, this is a sharp calculator. Let me also write it there. On your sharp calculator, you're going to press mode then you're going to press oh sorry I didn't get it. You can press the on and off. Then you press mode and you press one for STAT and then you go back and press zero for SD for the descriptive statistics and we are ready to capture the data now. To capture this data you will say so here is the sharp right. So you will say 10 and you will press the M plus. This is one alternative. The other alternative or you will say 10 so these are other calculators. You will press the change, the data change that change button. So which is like that. It's a written change. For other calculators, you will press 10 you will press E and T button next to is next to the delete on your financial calculators. So let's say it. So this is your sharp sharp right view or the dial sharp. Those who bought the dial sharp the DAL sharp calculator. So let's write it here is the DAL calculator the sharp DAL calculator. And the next one, this one is the sharp. The old sharp right view calculator which looks almost the same as the DAL calculator but is the sharp right view. It's written right view at the top and then the last bit, which is the last one here. This is your sharp financial calculator so that everybody is aware of how to press on their calculators. So all the sharp calculators are different. So then you continue to enter the values which is six and you press the M plus or you press the 10, the six change, six E and T depending on your calculator which looks so I'll just continue without writing anything on the document. So we say 10 and we press the M plus and then six M plus or data change. I'm going to keep on saying M plus because I'm used to using my sharp. M plus, five M plus, 10 M plus. And when you capture the data, it will also tell you what to type three and it tells you 10 is your data and it's in data set four, it's 13 data set four. Nine M plus, seven M plus, 10 M plus, nine M plus, six M plus, eight M plus, six M plus and six M plus. How many they are? They should be 12. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. Therefore I've captured all my data. I can go on and off the calculator. So once you have captured all your data, you press the on and off on your calculator. Now, the next step that follows is to press the alpha button. Remember the formula, I'm going to write it back here. CV is S divided by the mean multiplied by 100. Now on your calculator, this is what you're going to do. You're going to press alpha and then you're going to press button number five and then you're going to press the division sign from the basic operator side. Then you go back and press alpha and then you go press button number four for the mean and then you go in and press equal sign to get the answer for these first parts. When you have the answer, you're going to multiply that answer. You press the multiplication sign and you press 100 and you press equal sign. Let's do that. You go alpha five divided by alpha four. As you can see there, it is X, S divided by the X bar and we can say equal. So then we don't press the multiplication, then it multiplies by 100. It doesn't really matter because division and multiplication was the same. But to be safe, press the equal sign, press multiply by 100 and press equal and that is your coefficient of variation. And our coefficient of variation is 24.5. So 45% and that's how you do the calculation. Okay, so on the case you're one, we will do the same. Remember when you are done, to answer the next question, you just press second function C A to J or calculator from any store menu. Okay, so let's look at the shop, the case you're one. So case you're, we do the same. I need to go up to get the values. Funny enough on the wet document, I cannot press the equal when I write on it. Okay, so also similar to this, you will have to also do your calculator from any store values and to play your calculator. On this one. Oh yeah, you will use the nine, the calculator. So you will go shift and you press nine and it will say, do you want to get the setup or the memory or all? So I just want to get the memory. So I just press two and it says yes for the memories, then we'll press the equal sign and it says the memory is done. So if I press shift, set and I go to, let's say I go to the table, I go to two, they are still there. So it didn't get my memory. So I will have to get my memory. So shift, yeah. And I think in this instance, I can just go and get all of them. So equal. And AC and then if I go shift, set, nothing happens. Shift, set, that should happen. So they shouldn't be anything because then the data is gone. Now we need to take the calculator back to set mode. By first pressing the mode, you will press the mode button you will press. Now it's different, my bad. Then we can press the four, button number four, for set is T-A-T. Oh, this is just for the setup. So we don't want the setup. So I did press the shift first. That is why it went to the setup. So you can just press the AC button. We don't want the frequency button. So remember, because I press the shift button, I press the setup. So any value that is written in orange when you press the shift button, it will call that function. So I don't want the function. So you must make sure that on your calculator, on the screen, there is no shift written. If you look there, that tells me that my shift button is clicked. So I can just unclick it. So mode and there is our state. It should be state three, not state four. So it should be state three on our calculator. And we need one for one minus var. You press one and we can capture our data. Yours is easy. Remember it's 10 equal, six equal, like that. So 10 equal. Six equal. Five equal. Ten equal. Nine equal. Seven equal. Ten equal. Nine equal. Six equal. Eight equal. Six equal. Six equal. And it should be up until rule number 12. Then it means I've captured all the values. Now I am ready to calculate. So you can just press the AC button. Just press the AC button. The values are stopped. You don't have to worry that, oh, but where did it happen that my values are not showing anymore? So they just thought somewhere in the memory of the calculator. Now we can do the state. So you're going to press. Remember I need to write the formula. Cv is equals to s divided by the mean multiplied by 100. So on your calculator, this is what you're going to be doing because your calculator reach the s and the mean they are underneath in there. So you're going to press shift. This is going to be very long. Shift and you press one. Let's do it while we doing it so that I don't write the wrong thing. And then you press four. And then you press four. And then you press four again. For sx, you will press four again. And that gives you xx. And you say divide by. So we're going to press the division sign and we repeat the step. Shift, one, so we go shift. We press one and we press four again. Four and we press two. So the next one will be two. And equal. So maybe probably I can just put the equal sign there and then say multiply by a hundred and then say equal. And multiply by a hundred and then equal. And that gives us 24.45. Oh, actually it's four, four, six if I run off correct because I just used the closest value. And that's how you do coefficient of variation. Any question, we only have three minutes then it's end of the session but any who I am done with the session. Any question, if there are no questions then we can recap on what we did today. So today we looked at, I know this is very complex but we looked at the measures of the measures of central location. Probably I should not use that. So we use the measures of central location which is the mean, the median and the mode. And then we looked also at the the measures of variation which are your standard deviation and your your standard deviation, your variance, your range and the coefficient of variation. And we looked at how we use the calculator to simplify this complex calculations that we are given. What else? And that's it that we did today. And the final comment from me, we can continue the discussion on my UNISA. Like I showed you the screen yesterday on my UNISA, I'm not going to show you today. We can continue the conversations there. We can also continue the conversation on the WhatsApp group. And likewise, thank you for joining the session.