 Okay, so welcome to this week's session. We are going to look at how to use your calculator effectively to answer some of the statistics questions. I'm going to be toggling between screens and the calculator's end and the presentation as well. So by the end of the session you should be able to, I don't know why my slides are not moving, you should be able to know how to calculate the mean, the standard deviation, the variance and the coefficient of variation using your scientific calculator, either the sharp calculator or the case your calculator. And these are the type of calculators, they might not look exactly like your actual calculator that you have in front of you, but there are features that look exactly the same. So if you are using a case your calculator, especially the one with a fraction function, this is the thing I'm referring to when I say the fraction function, it makes it easy to do some of the calculations. But today we're not even going to concentrate too much on that, we're going to concentrate on putting it to state mode or what we call the statistical mode. And I think I opened the wrong calculator on this one. Oh no, because this is just a picture, it's fine. And then those who are using the sharp calculator, your sharp calculator might look different, but the look and feel should be the same, especially for those ones who have the green buttons or the green letters. That's what we're going to be using today to calculate the mean, the standard deviation. Okay, so we are still going to continue with the age because we're working with numerical data, so we're going to use our age. As you can see that my dataset has so many numbers, the data values like 20, so it will take us some time to get it. I will be as low as possible so that then everybody is able to follow. So I want everybody who has a calculator to make sure that they follow what I am doing and from now on then you need to practice because you cannot just look at it now and then leave it as it is, you need to practice and practice. So we're still going to look at the measures of central location, we're only going to concentrate on the mean and then under the measures of variation, we're going to concentrate on all three of them, except the range. The reason why we're not concentrating on the mean, the median and the range is because you don't require a scientific calculator to calculate them or you don't require your calculator to be on state mode to be able to calculate them. So when we were doing the measures of central location and the measures of dispersion, we did touch on some of the functions and some of the steps that you need to take when you answer the question and we looked at this at a high level in a rush, we rush, rush, rush because it was part of the session. So today I thought let's put some more effort onto it and do practical thing. So I'm going to show you on either the cashier and also on the sharp calculator. So we're going to first start with the cashier, those who have a cashier calculator, I'm going to open my cashier as well. And if you don't have a calculator, this is my cashier calculator, I'm just going to make it bigger, it will fill up my screen. So I think it's big enough. You need to put our calculator at the moment, my calculator is not ready. So your calculator will normally come in a compute mode or the met mode. We need to put it into state mode in order for us to do the statistical calculations. So the first thing that you do on your calculator, like the steps say, you need to press the mode function. So before we get into the mode function, I just want to tell you about some of the functionalities that we're going to be using. So we're going to be using the mode, we're going to be using the shift, we're going to be using button number one for the state. As you can see that the ST80 is written in orange. Before we press this button one, we first need to press the shift button and then press the state because we want to call the button that is this statistics functionality that is on this button number one. Like the same thing with when you are working on your computer, in order for you to create a capital letter or to create to write up the ad sign and the hashtag, you always have to press the control button first or the shift first and then go and find the letter on top of the number. So we're also going to do the same. So our shift gives us all the letters that all the functions that are written in orange. We are also going to be using the AC and the delete button. So often the other thing is the arrows very important when we navigate going back and forth up and down, we're going to be using the arrows. They are also important in this whole situation under the state button number one. There are more functions when we open it up and we can only see those functions once we put our calculator in a state mode. Okay, so let's start. So first on first everything we first have to put our calculator on or press the mode button. And once you get to the mode button, then the dialog box will pop up on your screen and we need to choose where it says stat. So depending on the type of a calculator you have, you also need to let me know if your calculator is different to what what you see on your calculator is different to what I am presenting. And then you're going to press stat. So every time you see a number and the letters, the number represents the button, the number button. So stat, it means we have to press button number two. So we're going to press two and then we get another menu with a number and another alphabet. So at the moment, because we only concentrating on a univariate, which means one variable, we only going to use one minus var, which will help us to calculate some of the measures that we are looking for. So one minus var is what we're going to concentrate on. Later on when we do regression, we're going to do a bivariate variable and we're going to use number two, which is the a plus bx, but do not worry about that at the moment. For today, we only concentrating on one minus var. So we're going to press one and we get a table. Now this table, because you can see it says it's x, our x now represent the h data that we have. So it means we're going to enter all these values from 45 up until we get to 35. I'm going to move my calculator to the side so that I have clear view of all the data that we have. So how do we enter the data onto the calculator? We are going to use the number and we are going to press the equal sign, which is the other button. So it is 45. So we're going to say it's 45 and then you press equal sign and you continue entering 36 equal sign, 37 equal sign, 28 equal sign, 26 equal sign, 19 equal sign, 25 equal sign, 40, 43 equal sign, 36 equal sign, 28 equal sign, 28 equal sign, 26 equal sign, 18 equal 27 equal sign, 35 equal sign, 28 equal sign, 26 equal sign, 18 equal sign, 27 equal sign, and 35 equal sign. I can see that when I'm done with all my data set, I know that there were 20 and when it's 20, so the number here at the end, it's counting. It's a counting number, so I'm online number 20, and I can see that I've got big five, and you can also use your arrows moving up with an app arrow to move to the top of the table just to double-check your data that you kept charted correctly, and that is always very important to double-check your information before you continue, because sometimes we are in a hurry without double-checking, it's very important to check, and I can check that I've kept charted all the information I need, 37, 28, 26, 19, 25, 23, 36, 28, 28, 26, 18, 27, 35, 28, 26, 18, 27, and 35. Now, let's say I made a mistake on 18, I put there 19. I put there it was 19, but I know that it is 18, so it's easy. You just go to that number where you are at, you just change it to 18 and you press Enter and it will override that number. So it is on the case you to override the numbers without you starting from scratch. So once you have captured all your data from the table, it is stored on your calculator. The next step is to press the AC button, not the delete, the AC button, and then you just press AC, your data is stored on the back of your calculator, even though you don't see it right now, but it's there. And since, or the other thing I forgot to mention is when you press the mode step one bar, the calculator changes. It used to say met, now it changed to state. So it tells me that my calculator now it is in state mode. Now I'm ready to calculate the mean, the median and the mode and the standard deviation. Now I'm gonna move it back to the site again. So remember, under case you calculate all those things that I've just referred to, they are not visible, but we do have this step function. So if I press the shift and I press state, I then get a menu that tells me number one, it says type. The type will tell me the kind of data that I have. So if I want to see what that is, so I will press one and it will tell me nothing. It doesn't tell me anything. So let me go out again, shift. Oh, sorry, now I cannot go out like that. Okay, now we'll shift state and I press one. And it goes back to the same menu. So number one doesn't give you anything that you need. So you just press the AC button. If I go back, shift, set. And I need to see the data that I kept shut. I can press two and two should take me back to the table that we have kept shut. And once I'm done, I press the AC button and I go back, shift, set. And number three, it says it's some. So this one will say the sum of X, the sum of X squared, that way you get the summation. So when I press three, I get the sum of X squared, the sum of X, so the sum of X is the same as that one that you calculate from the mean. Remember, on the mean, the mean, we say it is the sum of all observation divided by N. So this summation, it is that summation that you see there. They also have the sum of X squared. So the sum of X squared is when you take this 45, you say it's 45 squared plus 36 squared plus 37 squared. When you add all of them, they will give you the sum of X squared. So that is not what we are calculating right now. So that is the summation. What else is there? Oh, we can also even, let's go and get the value of the summation, number three. And the summation is number two. So you press two, remember, where you see the number, that's what the function wants you to call. And then we press the equal sign and the answer is 591591. And we can divide by 20 and we will find the answer to the question. So the answer to the question is 591 divided by 20 gives you 29.55. 29.55. So let's see if we can get the same answer. Yes. Yes. After you get 591, before you divide by 20, you must press AC. Okay, sorry. So let's say you went and you said shift stat and then you got number three, right? And then you say number two and you say equal and it gives you the answer. You don't have to press the AC. So you can just go from there and say divide, then it will tell you your answer divide by 20 is equals to 29.55. I just canceled it and then went and calculated manual. But you don't have to, you can just do equal and then divide that answer by 20. But that is also the long way to go. So the shortest way to calculate the mean, we can use that from four bar. So under four bar, let's go there. Under four bar, that's where you will find your sample size, which is n. It will just give you that they are 20. So if we press one, you will see that they were 20. And if you press going back, every time you want to go back to the menu, you have to press shift stat and then it takes you back to the menu. And number two is the mean is the X bar, right? So let's see if we press two, it should give us 29.55, see? That is the easiest way. So you capture your data, you go shift one, four and equal and that gives you the mean. Then we need to calculate the other thing. And the other thing as well, you don't have to play your calculator and press AC. I like to press AC button because it clears everything on my screen, then I start from scratch. But you can still go ahead and say shift stat and then go four. And now you have three and four. You need to remember that we have the population parameter for standard deviation and the sample statistic standard deviation. So, and always remember that Greek letters are for the population because they are complex, they are big. They are huge, difficult to pronounce, difficult to collect. So it's population. Greek letters, simple alphabet, Roman, not Roman, simple alphabet that we know of. I think we can call them Romans alphabet, I think so. Simple alphabet that we know of like S represents statistics and all that. Now the only difference with how you calculate the mean of a population and the mean of the population is how you calculate the mean of a population and the mean of the standard deviation, the formula are the same. So that's why for the population and for the sample statistics, we only have one mean, the X bar, because the population mean is given by the sum of all observations satisfying divided by N, which is the same as for the sample. So we use the same formula for the mean, mean of population and mean of the sample. But when it comes to standard deviation and the variance, we use two different functions. So number three, we'll calculate the population standard deviation, but we're not interested in the population standard deviation because we calculate in the sample. So we're going to use number four. So you're going to press four and you see the reason why I don't like leaving the answers on the screen is because now it's still seeing the mean. Until I press the equal sign, I only saw the mean of the sample data. So this is the sample standard deviation and our sample standard deviation is 7.533. If I round it off to two decimal, it's 7.533. Now, we have the standard deviation. How do we then find the variance? The variance, if you remember, this is your sample, which is S, the variance will be S squared. Then it means we can take this number, multiply it by itself twice to give us the variance. You don't have to, if you have your calculator, it has the X squared button. You just take the answer that we have and then we square the answer and we press equal. Always remember to press the equal sign. And that gives us the variance. The variance is 56.68. 56.68. That's the variance. That's how easy it is. When you have a cashier calculator. In the exam, it will save you a whole lot of time to know how to use a calculator, especially if they have given you the data. Okay, so that is case show. Let's help those with a sharp calculator. So those with a sharp calculator, your sharp calculator might look like this or it might be a financial meds calculator. It doesn't really matter which one is which. Okay, so to calculate, let's bring the data in and then I'm gonna open my sharp calculator which looks totally different to my case show. You can see it has two big screen. It's got a sight cheek as well on the side. The view on the side, I'm gonna hide the view but it's going to be very difficult for me to work with the data. Okay, so now let's understand our calculators. On the sharp calculator, all the stats functionalities are visible on in front of your eyes. They are written in green most of the time. So if you look on button number four, there is X bar written in green. There is SX, remember S for sample standard deviation. There is Sigma X for population standard deviation. Those are the things that we're going to be looking at. At the bottom here, you remember those summations. There is your N, there is your summation and there is your summation X squared. So we're not going to concentrate on those ones because we're not using bivariate. So that line where zero and a dot and a plus or minus four, five and six, that's where we're going to be at. The other thing is the alpha function. So that button is very important because for all the letters written in green, before you press those letters, we need to start by pressing the alpha button first. We also going to use the shift button, but not today. We're going to use the shift button to, if we make a mistake on the data, we need to cancel or we need to clear our calculator. So we're going to use the shift button and the mode button. So the mode button, the CA and the on and off. So there's no AC on this one, but we're just going to press the on and off. Do not press second function and on and off because then you're going to switch off your calculator. We're just going to press the button on and off on its own. If we're clearing the calculator, if we capture the data wrong, we're going to use second function CA, which is the mode. To put our calculator on state mode, we're going to press the mode and we're going to follow the instruction. Also here, the instruction will be there. The other thing that is very important with this is the M plus. This button M plus, it's very important. If you are using a financial shop calculator, then on your site, this is data, it's ENTA, ENT. In state of M plus, you use ENT, but everything else still looks exactly the same. So now let's start capturing our data. And because I have, I'm going to, let me first remove the, I'm going to keep everything. I want to take this data set that we have. I want to squeeze it, squeeze, squeeze, squeeze. And I want to move it and put it here. Put it there on top so that I can have space. I can have space for my calculator. It's going to be very destructive because I've got this bit of piece of view that pops up on the site. Okay, now we've got the data. So now let's capture the data. So we first need to put our calculator on mode. I actually do not want this because it's distracting. When you press mode, then you get two functions, normal or state. Our calculator is on normal. When you see degree, it means your calculator is on a normal mode. Then we're going to press one for state. So also with this one, every number corresponds to the function. So the function state is on normal mode. In order for us to get to that, we need to press button number one. And then you have SD, line, and quad. For today, we use SD. When we do regression, we're going to use line. You'll never use the quad in your module. So we're only going to concentrate on SD, which is your descriptive statistic. So it corresponds with button zero. So it means we're going to press zero. Then our calculator is on state zero. So when your calculator is on state zero, it means you are ready to capture your data. Now, with a sharp calculator, it's different. You will not see the table because this is how you're going to see your information. The only thing that you're going to see is when after you have captured your data, it will tell you that you've captured data set number one, data set number two, data set number three. So it will say all these data points or data values are data sets. One, two, three, and when you get to 35, it needs to say data set 20. If it doesn't say data set 20, it means you made a mistake and then we're going to go and do second function CA and start capturing again. We will test that. So let's see, 45, and this is how you capture your data. 45, and you're going to press the M plus and it says data set one. And you say 36, and you press M plus and it says data set two. I'm just going to make an example because I don't want to go far ahead and then make a mistake and then come back. So I'm going to make a mistake right here and then I'm going to say 28 and then M plus and I realized, oh, I skipped 37. So I made a mistake. I captured something that is not there. So in order for me to correct this, I can just say second function CA, it clears my calculator and I start from beginning. 45, M plus and it will say data set number one. So your second function CA will clear your calculator from any stored value that you have already and you can start capturing. So now I must pay attention because I don't want to make a mistake. 45, 36, M plus, 37, M plus, 28, M plus, 26, M plus. 19, M plus, 25, M plus, 43, M plus, 36, M plus, 28, M plus, 28, M plus, 26, M plus, 18, M plus, 28, M plus, 26, M plus, 18, M plus, 27, M plus, 35, M plus, 28, M plus, 26, M plus, 18, M plus, 28, N plus 35, N plus, and it says dataset 20. It means I've captured all my data onto the calculator. It's dot, then I can press the on and off, and I know that my data is dot. Now I need to calculate the mean, the standard deviation, and the variance. Now, how do we do that? The mean is on button number four, therefore it means I must first press alpha and press button number four and press equal. And there is your mean, easy. In one, two, three, four steps, you are done. That's the mean. Remember it's the same mean as we have calculated before. The standard deviation, when I press the on and off button and go alpha, oh, that is for the population. I don't need that. I need alpha number five for the sample, and I press equal. I remember we did get 7.53. Now to calculate the variance, we just press the X squared button, and we pressed equal, and that is the mean, the variance and the standard deviation. Now I want to go back, before I go back to the case show, I want to show you from here, how do you calculate the coefficient of variation? So remember your coefficient of variation is your standard deviation divided by your sample size. So if they've given you the actual data, sometimes they don't give you the actual data, they give you the values, like standard deviation is this and the mean is this, and we just calculate. So in case they gave you the actual data, the raw data like we have, to calculate the standard deviation from this is easy. Because we know the formula is S divided by X bar. So we press alpha button number five, we say divide by alpha button number four, and we say equal and they, and to remember what I forgot to mention here is multiplied by a hundred, coefficient of variation is always in a hundred percent. So multiply the answer by a hundred, and that is our coefficient of variation. And if you look back at what we did the previous time, we did get the same answer, 25.48. So now that is, if you are using a sharp calculator. So if you are using a Casio calculator, we're gonna go back to the Casio now, let's go back here. So we know that our mean is there, that our variance, our standard deviation was there, but we want to calculate our, we're gonna press the AC button. I've never tried this before, so it will be the first time. You cannot use the met function or this functionality because it is in state mode. So it means you also go into calculate it the same way as we did with the sharp calculator, right? But because you're doing, you're going into shift one and you need to always be mindful of those things. So let's first, based on the formula, we know what the formula is, our coefficient of variation is s divided by the mean, multiply by a hundred, that's what we know, so. Let's calculate that. So we go shift, start, for, for var, and we go into the variable, set, for, for var, and we're going to press button number four for the standard deviation. We're going to divide that by shift, set, for, and number two for the mean. As you can see, it has written s divided by x bar, and we can say equals, multiply that by a hundred, and that is equals to 25.48. As you can see that it works out exactly the same. So it works out exactly the same. So I have one last activity that we can do together. Let's see if we can answer this question. So now with the partial calculator, let's see if we can quickly answer this question. So if I press the AC button, it doesn't clear my calculator from all those values that I stored previously. Alternatively, I can go and say shift, and number nine foot clear, and I say clear memory. If I press number two, and I say yes by pressing the equal sign, and I must press the AC, I'm expecting that when I go back to the table to set data to, not to find anything, but you will find something on there. So with the partial calculator, it's not as easy as pressing the clear button to delete. So the other way of clearing, shift, clear, you can either clear the setup. So if I clear the setup also, you will see what happens. It goes back to the original way that the calculator was. It goes back to the meds functionality because now I can do the meds calculation, but I don't want that. So it means with occasion, you either go into clear, so because there are three types of clearing. So there is shift, clear. The other one way it says all, it does the same as clearing the setup. When you clear all, it clears everything, and it takes your calculator back to the normal. So you will have to always clear your calculator. So you go shift, clear, and then you press the setup, or you can press the clear on. It will take back your calculator to meds mode, and then you go back mode to first step, one for var, and you start capturing your data. One, five, nine equal, one, seven, zero equal, one, seven, one, seven, two equal, one, seven, three equal, one, nine, two equal, one, nine, three equal, one, nine, nine equal. Two, oh, one equal, two, oh, one equal, two, oh, one equal, two, one, six equal, two, one, seven equal, two, three, zero equal, two, three, five equal. Two, five, six equal, and I can just double check how many numbers we have? One, two, four, six, eight, 10, 12, 14, 15. So they are 15. I can also check if I have got three digit numbers. They are all three digits. And then I can also double check 159, 170, 172, 173, 192, 193, 199, 201, 201, 201, 216, 217, 230, 235, 256. And I've got all the values and I can press the AC button. The mean, shift, stat, four, two, equal. The mean is 201. Next, standard deviation, shift, stat, four, four, equal. 26.73. 26.73. Depending on how many digits they have, the variance x squared equal 714.43. 714.43, coefficient of variation. Shift, stat, four, four, divide by shift, divide by shift, stat, four, two. Equals, multiply by 100. Equal, 13.30, 13.30%. Easy. Within five minutes, I am done with my question number, whatever in the exam or whatever in the assignment, then I move to the next one. Already I've got the answers. Within five minutes saved a whole lot of time. So let's see with a sharp calculator if we can get the same answers. So I'm going to clear my calculator, shift, C8. It needs to clear everything from the stored values, 159, M plus, 170 M plus, 172 M plus. 173 M plus, 192 M plus. 193 M plus, 199 M plus. 201 M plus, 201 M plus, 201 M plus. 216 M plus, 217 M plus, 230 M plus, 235 M plus, 256. I made a mistake. I can just delete, two, five, six, M plus and they are 15. I cannot check whether I've captured all of them correctly. As you saw with 256, I nearly made a mistake. You won't be able to know that you've captured them correctly or wrong, all right? Until you answer the question and you don't find the correct answer, you need to just recapture them again. Okay, so we are done. Let's calculate the mean, alpha four equals 201. Let's calculate the standard deviation, alpha five equal. 26.73. Let's calculate the variance. Oh, I shouldn't have moved out. Calculating the variance is x squared equals 714.43, done. Coefficient of variation, alpha five divided by alpha four equals, multiplied by a hundred equals, 13.30. Easy. And that is how you can save time in the exam, calculating measures of central location and measures of covariance. Oh, measures of coefficient, what am I talking about? Measures of deviation or dispassion or measures of variation. And that is it for me for today. See you on Saturday. Before we leave, we are pambillion analytics. Sorry, you're sorry, Lizzie. Yes. If you don't have a calculator or if you're battling to use a calculator and you get to see the exam, then what do you do? Do you do it the manual way? You do the manual way, yes. But then it will take you time. So that's why I'm giving you all these skills so that you can go and practice before you get to the exam. You already know how to answer the questions, all right? So you're allowed to see the calculator in the exam. You are allowed to use your calculator in the exam. Yes. And if you don't have the actual calculator, oh, I left my phone. I will show you on Saturday my phone. I have a cashier calculator. I will send the link on the WhatsApp. Then everybody can download it. The calculator looks exactly the same as this. But the functionalities are different. And I can take you through that calculator as well in another session maybe on how to use that calculator, especially for those who don't have a cashier calculator or a sharp calculator and they're just using a normal, not a scientific calculator but just a normal calculator. Then I can show you how to use your phone. It's easy. With a calculator, I'm telling you, you're going to save a whole lot of time. With a cashier calculator like this, later on when we do calculations for hypothesis testing or the coefficient of the confidence intervals where the calculations are very complex, easy to use this calculator because it's got this fraction button. So I need to take it back to meds. So when you're done with that mode, then to take it back to another med mode, to med mode, you just press mode again and then you press comp, which is one. Then it will take it back to the normal calculator and then you can use your functions there. And with that function, you can also just go down and apply any function you need under that. You will see that it's something like that that you will work with some, some, some self. And this will just create the function for you. So let's say, for example, I'm going to go up. Let's say we calculating a hundred... Just deleted everything now. We say a hundred, what am I doing? A hundred minus 89 and divide by this square. This is one of the test statistics that you will calculate at some point. The square root of your, maybe probably let's not do the square root of, let's do 20 divided by the square root. So this is one of the, the Z test statistic. And that will be one of the functions that you can use. So there will be some way where you calculate like this. So with the Casio calculator, it makes it easy for you to, to do the calculation. Imagine if you are going to calculate this manually, you'll have to calculate the top part, put the answer down, calculate the square root, have the answer, take the answer of the square root, divide the 20 by it, then take the answer of the 20 divide by the square root, divide the top part. Otherwise you'll have to use the brackets and using the bracket. This is a bracket, then there is a big bracket. This is another value divided by the square root of that. So if I can give you the answer for this one, is 33 point and then on the Casio calculator, those who didn't know, you have this SD change to decimal. If you change it, then it will give you 3.3. So let's say I'm calculating this manually. I'm going to calculate the same thing manually. So you need to use the brackets. So you will say a hundred minus. I'm going to do the whole answer in one, divide by and I need to put it in bracket as well on this side and go back in because I'm doing 20 divide by the square root of 20. So, but then now I'm going to show you again on the other calculator. So if I press this, you can see the, it is doing something wrong. It's not giving me 3.3, right? Or because I used the wrong, the wrong number there. I should be using 36, okay? It's 33.3. So you need to use the brackets. If you're going to be using the same of calculating the same equation. So let's say you are using a sharp calculator way, doesn't have a fraction calculator. So I'm going to also take it back to normal. So with this one, you press mode normal and then it takes back your calculator. So remember we had hundred. Our question was hundred minus 89 divide by 20 divide by the square root of 36. That was our question. So because you're using a sharp which doesn't have those fractions. And if I say hundred minus 89 and I say equal, I get the answer. And I take that answer and I say divide by, I cannot say divide by 20 divide by that because then I'm going to take 20 will divide the answer. I need to put it into brackets and say 20 divide by and then I can put the square root of 36 and I'm going to close my bracket and then I'm going to say equal and then I get the answer. So when you are going to work with your calculators, try and use brackets as often as possible. Remember always to apply both must because both must says both must most of the cases says brackets first, exponents or expressions because at this point we're not going to use the off and all that. The exponents and operation we refer to this. So it means before you do the multiplication, the division and all that, clear out all this. If you have a value that has two squared or three squared, you first clear those ones first. The radicals first, the radicals are your roots or you clear the powers first before you do anything and then you can then do your division and multiplication addition or subtraction because if you go on your calculator and you just say 100 minus 89 divide by 20 divide by, it will take 100 minus 89 divide by 20. It will take 20 and divide 189. That's what it's gonna do. And then after that, because both must says division before addition and subtraction. So this is a subtraction. If you put 100 minus 89 divide by 20, divide by the square root of 36. What it will do is because it works from left to right, it will study and apply the division and then go there and apply the division and then only do that, which you will get it. It will be a wrong answer. So the reason why we show you how to use shortcuts is also to save you from all this trouble because then it's time consuming. Hey, we are done for the day. 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