What we are going to do today is, I am going to put different ways and means of how the evaluation can occur as such. I am going to also discuss at times what are the problems with one particular type of system as such. And then finally, you are the best judge for your department and your system as such. Everyone has to come out with one's own system as such. I can set a paper for 2 hours, for 3 hours, set it giving the same weightage for the paper as such. 3 hour paper can be 50 marks paper, half an hour paper can be 50 marks paper, 2 hour paper can be also paper. What should I do? That is why finally, Indians will have to come up with their own solutions to their own problems as such. But the idea is to look at these different aspects out here as such and see what are the problems, how we are going to look at. So, we will have if look at these different types of things as such. I am coming to these types of problems and things of that kind as such. I am not restricting anything to any particular field or any such thing as such. But in one way, we will try to put the different aspects before you as such. When we think of problems, we need to categorize their message. And what are the things? Maybe where the method and the solution is known. So, if I am going to give a problem as a test thing, something more complicated, but you know the methodology, you know also the solution maybe. Maybe the method is not known, but this solution is not known. Like if I give 3 into 3, 5, 9, that much most of us will be able to do. 3, 3, 3, 3, 3 into 9, 9, 9, 9, 9, 9. If I put, no one is going to be able to give an immediate response like 3, 3, 9 as such. So, you know the method. Not that you do not know, but the solution, are we able to put it, spell it out immediately? No, it is not going to be possible for such thing as such. This again I have to try to put out here. The simple examples can be basic arithmetic calculations as such. I am not even coming to trigonometric or some such thing. I am looking at only the simplest possible, which is possible to do as such. So, ethnically. The other types, the method is known, but solution is not known. And what are these kinds? I am picking up the examples which I am picking up. Do not look at that set of examples as the only ones as such. These are the simplest ones which I have tried to pick up, so that I can talk a bit about it and there is no problem in looking at that example from anyone of SS. So, solving the quadratic equation, you get two solutions. For any quadratic equation, you get two solutions. Which one is to be picked up? So, again you need a constraint out there as such. Whether positive value is to be taken, a negative value is to be taken or a higher value, both roots are positive that is to be taken. What exactly needs to be done? So, your problem is not going to be complete by just asking him to solve the quadratic equation. That may be possible for a lower level. But if you are going to make use of that as one small step in your calculations, you must give some hint, some idea to the candidate or the student that he has to pick up particular value based on certain criteria as such. And then they are going to be settling like the methods not the solutions are known. So, you ask him to solve some 7 degree polynomial as such. Something is given and now you also do not know what are going to be the values to start with as such. Unless you have taken that effort to solve it yourself first, this kind of thing happens. You know that they are going to lead to some numbers as such. But you have not done the calculations yourself. And then maybe it may happen that 2 of the roots turn out to be same. Out of some 7 roots, 2 roots may turn out to be same. Whether 7 degree polynomial may lead finally, into 2 quadratic equations from which 1 1 root may turn out to be. Now, we have thought about it. So, idea is we have to think about it. This part has to be done before the paper or question is set for a particular part as such. Once we do this setting part as such let us briefly have solution and grading of the solutions as such. We will look at some 2, 3 very very simple problems as such. I do not know whether you are having the write up before you or not. But we will look at it and so I am trying to put very very simple problems before you. But idea is I am not suggesting the methodology to solve it. It is all known to everyone out there. But my thinking is how should we evaluate these kind of things as such. And from that angle I have tried to put out here very simple things as such. Simple multiplication 2 0 5 0 into 3. Only constraint is no one is allowed the use of calculator or loctable or any such thing. No slide rule. Slide rule I do not know how many of you of our faculty members also may not have used this slide rule possibly. So, not even this slide rule. So, none of these things are available. So, you have to go through your basic things and do the problem as such. But method 1 is all simple. There is what we normally follow. Method 2, is it complicated compared to method 1? No. Is it different than method 1? Certainly. Has method 1 been derived from method 2? Yes. Because multiplication we keep on saying that not so many times you add and you will get the product value as such. So, we have done it exactly on the same lines. Only thing is with this simple problem I have tried to put it as one method, another method. And now how do I evaluate this once these things are done? But problem is only this. So, in general I will not be giving them any specific method to be used or something. They can use anything whatever they feel like it has to be correct and two students come up with this. So, they are used the different methods. Now look at it from this angle. I have not taught them the multiplication part at all. I have not taught them at this stage, multiplication at all. I am still at the addition, subtraction, stage only. And if someone comes with this multiplication method, should I give them marks or should I tell them that this was not in the syllabus and you have used some method which is out of syllabus. So, you cannot write anything. What exactly should I do as such? In such cases, the one way such using either the methods you are getting the same solution. So, your unique solution criteria is satisfied. Methodology you have not mentioned anything what are the problem level what you have mentioned is only without the use of calculator. You have not used the calculator. It is very clear from this. Now, how do I grade them as such? Should I put the same marks as this for this method? Because the problem is basically the same. Now, which route I follow that may make the system more complicated or easier as such. And in such cases some hints come into picture as such. Who will tell this to end that this addition 1, calculator only 3 or the multiplier out there. So, you could put the same number and add them as such. What happens if the multiplier also becomes 2050? Can I write down this 2050 that many times and then go on adding it? Is it going to work as such? No one is going to tell this to anything. You also have not put any constraint and on how exactly it should be done as such. But you know for sure that this first method which you are looking at is not the one which has been taught as it. I am still in the preliminary stage of addition and subtraction part. So, addition has been taught. This has not been taught. But we have just started with the multiplication and saying that 2050 into 3 means that you have to put 2050 3 times and add them up as such. So, if it does it in this fashion, do I give him the maths or not? This is something which one has to look at as such. How one has to evaluate now if I am putting certain maths? The difficult layer level at each state has to be looked into. I am giving the examples which are really simple, very trivial. I know that. But the idea is the example should not become a problem as such. That is why I am giving such trivial examples. Look at this now, 123.3 into 21.3. The setup is somewhat similar. There is not too much of difference except that that second method, the addition method is not going to work out here easily as such because the numbers are large too many times. So, one will have to wait and the time is limited. So, one will forget about that particular option of adding up the thing. Look at the various specific features out here. There is a correct solution. Normally what we do? Let us first see what are the steps involved in this simple part as such. Again, keep in mind the problem is trivial one, but trivial problems also have evaluation problems as such. So, I am now looking at this problem as assessment of this how I should be going for. So, first thing which I have come across is I have multiplied this number by these three. Put it as also out here. We will go back to this. Before multiplying and putting it here, I have put one 0 or cross out here as such. That is an important step. If I do not put this 0 or cross here, we will 1, 2, 3, 3, we will fall below 3, 6, 9, 9. Things are going to be important as such. Next part I had to put 2 0 out here and then I done the thing and then simply add them up. There the things do not end. I need to now know how many decimal places I had in this part. Accordingly put the decimal places and put that decimal point after that point. So, these are the split ups if I want to evaluate. Why I am doing all this? Because the incorrect solution if I do not get this final value of 2626.29, should I give straight way 0 to that particular student or does it deserve anything specific? And there the assessment part becomes important as such. And so now I have look at this. Up to this point everything else is done properly. This 1 is to up to e by mistake has written 1. You know for sure that he has done multiplied it the support on even with 3. So, multiplied multiplication by 3 compared to multiplication by 2 is a difficult thing at that level. So, he has been able to do that but he has not been able to do that with a lower level of difficulty. Still he is not in. So, this 1 is wrong out here. Because this 1 is wrong, here again he has made one more mistake. He has not looked at the things properly. Instead of 2 coming here because he has made a mistake. Same mistake is getting transferred here. And finally, the way we will look at the various things. If I am looking at the class 3, class 4 students as such, I will be expecting them that they should write the answer in this form. And then here again he makes one more mistake. Is this part the most important part to which we should give stepwise weightage or where should the stepwise weightage start? Again here the things are again the same as such. So, the steps involved have to be taken into account when you go for the evaluation. So, looking at it this product part which I was looking at, these 2 terms he has calculated very recently. There is no error, nothing of that kind. No mistake out there. This one mistake has laid to 1, 2 and 3 mistakes as such. Out of this, this mistake is the one which is getting carried forward as such. And so, one has to look at again how exactly the thing should be done. Should I split the marks or should I have the total marks? If the correct answer is there, 10 out of 10, otherwise 0 out of 10. Is it really proper? There is something which the paper sitter has to look at. And why this is becoming important is paper sitter's time or the examiner's time. So, evaluate his time. Lot of time is going to be required to see these things and split the marks stepwise. And that is why initially I talked about, if I am putting it in steps, do I mark marks for each step LB, CD, EFG or something? Or I put total marks there and then I have some discussion at this point. Should I have a discussion? I am not questionable if I am using discussion. Today I finish up some 40 papers and sit down tomorrow. I am in a better mood. Maybe the discussion value changes. It happens. I have seen that happening with others, with me. I have gone through the papers second time because I knew that I am not doing something proper as such. How many of us really keep on doing it? That carefully and regularly. Carefully yes. Regularly yes. Both things simultaneously chances are very low. I am not commenting on anyone's capability or capacity. But the way we need to look at the answer books, sometimes 70 answer books, sometimes 100 answer books. Even today we have to finish the job of evaluation. You have to handle the things because the ancient history is coming or some such thing. So, there are different constraints. Why exactly this is happening? I am not looking at that aspect. But the way it should be done, this kind of problem must be evaluated in stepwise pattern. How you give the marks? That is again left to the examiner or rather the paper set. If there are going to be 10 examiners, the paper set is the one who has to give that backup of marks and not the evaluator. He must get it very precisely. If this is completed, this many marks, if this step is wrong, this should be cut. Now, from here, little bit later we will be coming to another aspect about this part. Please. In a question paper, should we have objective type of questions or not exceeding 4 to 5 marks? Or is it not necessary to have 10 marks question? This is the second remaining question right here for us. I will take that also into consideration while moving ahead. So, somewhere halfway through you will get your answers. So, last thing which we have seen was this and we have seen that we need to bring in the stepwise answers at some stage of the other message. We will discuss that later, little bit later again before we come to another simple problem as such again 999 into 999.  But I will put it here so that everything becomes clear to each and every participant whether he is from this branch or that branch should make no difference as far as these kind of problems are discussed. And as you see here, see out here the thing is given in a particular fashion as such and so one can come out with the calculations and do certain things as such. There can be an alternative method and this alternative method might not have been taught by you. Can do something which becomes very difficult for acceptance for a teacher as such. I have not taught him and he has used it. How come? Why should he do that? Why he did not use the method I had taught to him? There are some of the things which are always in the mind of the teacher as such. Because one thing is you are not expecting an alternative answer alternative method rather. But students can come out with they are learning 10 different courses simultaneously. You are not teaching just one. And methodology can be used from one purpose to another and some such things can happen. And so before putting a J-O mark or putting just a cross or a line, cross line or the whole page one should really think whether is there anything in that as such. Does that answer really merit any consideration and win the marks as such. So, if some such thing is put out here 999 into 999 these are the routine anyone can go through. But this is not something which everyone is going to do as such not everyone. Everyone knows this as well. At least this particular specific problem all students from engineering side are aware of these parts as such. There is nothing unknown to them. But once you are asking it in this form most probably almost 1995 percent or even more are going to do it in this fashion. Should this fellow get the equivalent credit or not. If not more and that if not more is something which one has to really think whether it is possible in our system. In our system you cannot exceed 100 percent marks as such. So, any innovative idea any new methodology to give the same unique solution also may not create any additional advantage in terms of marks. What should one do that? We cannot give any more marks. He gets full marks if you agree with the arrangement that yes he has done it with alternative method. But the method is correct there are no mistakes because things can things of this kind also happen. And they happen more frequently that two mistakes cancel each other and you get to correct answer. This also is something which happens quite regularly. You change one answer somewhere again you are putting it as minus again you are adding it at somewhere the whole thing gets cancelled out your final result turns out to be correct. And now if you look at this step by evaluation you cannot give him full marks because he is intermediate steps are not correct. His final value however is matching. Does it mean that he has done these things correctly? No. You must get something deducted for those mistakes. So, if you are looking at the problem evaluation saying that the final answer is correct means everything is correct then you are mistaken. Most likely there is going to be a chance out of 20 at least one or two places there are good chances that the mistakes are getting cancelled out and you are neither noticing the mistake nor the cancellation of that mistake. So, two mistakes you are committing when you are evaluating the answer. One has to be extremely careful about these things and so one has to see whether the step wise things are required or what exactly is to be done. After a moment so one has to look at these aspects now logic and creativity. We use these terms left and right. Time and again we say logically this should be the case. Creativity also we begin to picture at times. Basically these two are the ones which can provide us a new approach as such to get the same solution. It can be possible. You can use logic, you can use creativity and get to that as such. The one which I showed just now this alternative solution is something which he has not been told. Everyone is aware of this kind of thing but not everyone is doing it in that fashion. So, maybe you may not call it as an innovation. It is not something new created but as far as that particular person is concerned it is an innovation for him and you have to look at it as an innovation. A different methodology worked out for getting a particular answer as such and in that case the things have to be given weightage as such. So, if you say that this was not the method by which I wanted the answer that is not a very correct approach on our part as teach as such. You have to accept I have taught it by one method. There can be another two methods available possible but they are not called at this stage. So, I did not expect it. So, on the other hand you should be getting in full marks and in the class till that is he gets a pat on his back because he has used something different when he could have gone for that lengthy approach which was a simpler one. So, certainly they deserve some additional appreciation for that and not only the marks as such. So, there is something which becomes very which is a very rare thing as such. So, one has to keep that in mind and every time is it going to be worthwhile doing it. So, 999 into 999 was fine only 1000 minus one kind of thing. Can I do it for 566 into 566 kind of thing and use the same methodology are we wasting a lot of time in doing that. So, when your student is doing it he does not know when exactly that approach should be used as such. Maybe if you tell him that last time he got a pat. So, next time you put another problem he will also do it on the same line. And what do we need to do it? Maybe a mistake committed out there because the calculations involved are much more and may be no pat and a deduction of marks because of some wrong answers coming in us. So, where exactly the innovation should be brought in every time is it not going to be advantages or disadvantages that something which the student has to think. We are not going to even know whether he has done it or for other the problem also or not.  But this has to be known to that particular person as a and so maybe once you are going for the distribution of answer books and taking the solutions in the class or something that time one can clearly tell that this was the methodology used by one of you. But this is okay for this problem do not try it out when such such such things happen as such and things become more complicated. You may waste more time your innovative method will take much more time than the regular method which we are looking at. So, try to see and work out the balance between the two as such. So, once we look at this name do these things become possible. This innovative approach which that one student has used as such when is it going to be possible. They should get some time. They should get some time to either have a look at the notes which they write within the class or have a look at not just one textbook but additional two, three textbooks to get their ideas clear and influence on what notes they have. It is not improvisation over your teaching. It is improvisation over what notes they have taken down in the class. Everything may not get properly covered in the class and I must accept that. I must accept that whatever I have planned for a particular lecture each and everything may not get covered in each and every class. Some classes a part of it few points we can miss us say it is possible. It is generally possible and generally happens than not happening that possibility of that happening is more than 50 percent rather than saying it is less than 50 percent. Some small points which you at the beginning of the lecture you have in mind that I am going to talk about this, this, this particular and one or two things get left out. If that gets covered in the next lecture fine but if the lecture gap between the two lectures is a lot in that case most probably that will get just skipped of your mind as such and that will not be noticed by you nor by the students as such and so such things can happen and so the students should get some time to go through these particular things and then only if he is in position to get some time that will give him some chance to come out with some new methodologies or small, small changes which can reduce the time required for a given solution or the answers. As I indicated there are studies which have been conducted on problem solving and the implications as such and here the indirect way we already have started with this particular approach as such. I have not brought this particular methodology or anything at the moment as such. We are already working on it as such. The procession of the problem by the student is really an important one as such. How he will look at that problem as such and based on the problem perception the student tries to find the links between various data. Other things normally what I am looking at is the analytical problems as such in the sense the numericals and things of that kind and I am not touching also on the descriptive type of things as such. Descriptive type of things have to be as less as possible. They have to be covered in the class but the questions weightage should be somewhat less on that as such because repetition of the things they write pages after pages if it is a descriptive question. I have gone through that student time as such and I have also written and got the marks also for that. But those questions should not have been given that kind of weightage that is our feeling which I am having now for the questions which I have answered 25-30 years back. Those questions are still feeling that those questions did not deserve that many marks and that kind of detailed write up kind of thing for writing about the boilers and lathe machine sketch and shipping machine, slaughter machine all such things you draw the sketch draw it for 10 minutes you waste in that write about 3 pages of mentioning each and everything does it really deserve that kind of attention as such. Does it really deserve that many marks for that particular part? The same principles can be finished with the five line, four line gap as I said in the question paper if it is a question or answer paper otherwise very specific instructions that this answer should not stretch beyond five lines or six lines. Five lines or six lines then let him write in the smallest possible letter you have to be prepared to write these policies later out there I said. But lines number is fixed so he cannot write an essay on those things I said and that is something which we have to tell that we have to define how the things have to be written I said and that part also will be coming to little bit later I said. Once he comes up with the links within the various problems sometimes the intuition of the student also can give him an advantage that if I do this, this, this the answer all like that. So, let me not proceed in the normal fashion but straight away maybe instead of calculating something let me assume some value and show that it is the same value. So, certain things are there which are all intentional everything will not be occurring every now and then. But these kind of cases we come across time and again I said instead of calculating it through the steps he finds an easier way he takes the final answer assumes that and shows that that matches the things properly. So, uses one or two conditions to satisfy the requirements and he has done the problem now should he get full marks should he get full marks his method is not proper intuition is not acceptable in engineering calculations. Intuition is not acceptable you might have jumped on to the way precise exact number and all that. But you cannot justify that value why that particular value to start with if you have some reasoning that ok my answer is expected to be between 9 and 10 and so I am looking at 9.5 as my first assumption when he can get it but he does not know value at all whether it is 1 to 100 or 1 to 1000 and he is taking that 9.5 he has no way to explain how he has come out with that and such answers even though correct cannot get full marks. Whether to gain 0 or not depends on the actual problem and definition and how the methodology is working out or some such thing. But intuition sometimes can work that is I know that value has to be between root 2 and 1 or some such thing and I am picking up this value as the first value if it does not work I will go for the second iteration change it slightly again try it out and then he gets the things are matching in the first iteration you have to gain the full credit. So there are problems both ways can I give him full marks in certain cases yes can I give him 0 in certain cases yes. So that is no way clear cut answer except for the paper setter to come out with this. There is no way clear cut answer that this cannot be acceptable or this is this has to be done because he has got the correct answer no. Both ways one has to think and then take a decision out there. What to do to invite problems? Till now we have looked at only the problems solving part. But we have meaning lot of things which we do and our intention whether known knowingly or unknowingly we are doing it as such like what we ask these students to draw the angles of say 30 degrees 45 degrees 60 degrees 75 degrees 90 degrees all these things with the protector a third or fourth standard may be fifth standard student can easily do it now. But you are asking him to do it with set squares no more use of protector like in the first case I have said no calculator nothing of that kind use your brains and do it. Similarly now use your brains and not the protector with the set squares which is a major drawing instrument setter and come out with the angles of 30 45 60 some of these are directly available some additional subtractions and you have to place the set squares this way that way and you can get different types of angles. It is possible to get it without the protector but then you teach them something additional the bisection of angle and things of that kind so you draw 90 degrees angle and bisect it and you get 45 degrees angle. But now you are not using protector or set square for that purpose or the different ways in which you go for polygons and other things as such. So you are teaching them how to go for problem solving when this is not available that is not available. You are teaching them one by one but they are looking at it as one more input as such and nothing else. It is not taken in by the students also in the same way that they should look at it as such. They are not looking at it as additional method without using protector without using set square they think that there is one more method available. But the constraints or the requirements are different if the protector is available I will never draw 130 degree angle with anything else that is anyway difficult to draw with any other method but I will never try to be here. But these methods have to be looked at in that angle. Similarly the problem solving needs to be forming the part of syllabus or rather teaching part it cannot become a part of the syllabus as such but we have to invite ourselves to teach certain things out there to give them idea of how they should go about solving the problems. Innovation is also one more thing. So how to tackle a new problem as such. So when we look at a new problem the first thing is the knowledge about the subject matter and practice in one particular context. You have used the angle drawing in engineering drawing. Do you restrict that knowledge to only engineering drawing unless you have a sheet and the set squares and other things you will not use it. It has to get used somewhere else wherever that need arises. So one has to be clear that that knowledge which is available with you has to be used and you have that knowledge as such. So when will this start in the field that he is in position to do this as such and when the student will be in position to do that we will see that in a moment as such. So use of knowledge in the given context that he does as such. Can he apply that to a new problem that is something again one has to look at. So these things are some of the things which are causing problems with the students. Some misconceptions I am going to have a look at one or two small examples of them. Some missing links and finally even if all these things are clear he gets into problem where he cannot form the equations as such. And as we all talk about mathematics is very important when one goes for engineering. Whether he goes for mechanical or electrical or civil does not matter. But mathematics has to be strong and that comes where the conversion to equations form becomes the regular features. Each and everything the data has to be converted to equation form whether it is simple algebraic equation, trigonometric equations, differential equations, integration. Somehow or the other you have to bring it to that form then come out with the solution and re-convert that equation form back to your text form or the final values form us. So there he gets stuck as such. And so we need to now look at how to motivate the students to go for these different things as such. He should get that confidence that he can do the things as such on his own. And what is going to do that this motivation part also what also I heard in the morning these slides are prepared much earlier as such. So you have to be in position to motivate him and in that sense he must get confidence that he can do it as such. That is the motivation step. If you are getting how does one get into that as such. You ask him to solve one or two simpler problems in a tutorial sheet to start with. Where what kind of information we have given in the class the same is getting used to start with. Now he gets a feel that yes he can use the information which are been provided by the teacher. Now then you put a slightly tougher problem as such where the complexity is increased but still they are not beyond his reaches. Misconceptions. I am just trying to put one or two simple things. Very recently most of you if not all must have gone through the cricket matches. I just put one small example out here. Cricket ball and bowler's hand move in the same direction. Everyone knows that what is so funny about it. Your Newton's second law says that the action and reaction should be equal. So if the ball is moving in one direction the hand should move in the other direction. Shouldn't it happen that way? It should happen in that way as per the Newton's law. But can Newton's law be looked at as a single thing controlling everything? There are additional things which are coming in. Momentum transfer. These kind of things are everything we will consider and under that Newton's second law or something one has to think about it. You will all be in position to explain to your students that no Newton's law is good but this is not the case where you have to apply the Newton's law. So that is the kind of thing and that happens when the slip filter catches a ball and automatically goes closer to his body. So now the ball has hit and the hand has moved in the opposite. So things are okay in different cases. So one has to see how these kinds of things or these misconceptions are sorted out. One will not know these things unless the students are open to you. And there is something which is very difficult thing in engineering colleges as I have seen because the faculty members in engineering colleges have to teach maybe 6, 7, 8 different subjects for different levels. Not like us that we stick to our specialization maybe taking 4 or 5 courses but of similar type at different levels but never losing the temper out here because we have enough time to spend on that and we do that as such. And there is really something which is not an individual problem as such. The situation those conditions are like that that 6, 7 different courses have to be taken. The faculty member is not in position to concentrate on each one of them. And then I have seen this happening not only as a student but sitting at the back of the class also. The teacher getting irritated if some student asks some questions. And if he shouts back at the student after that the whole year no other student is going to ask you a single question as such. There is something which happens and there is something which has to be avoided altogether. This must be avoided.  At times I heard comments oh that was a really silly question as such. Yes but now he knows that it was a silly question because he got the response and explanation for it. Till that no question is a silly question unless one gets a exact proper response for that particular part as such. So please let your students ask questions. We assure them that they will not have any effect or effect because they have asked questions. They will not get singled out because they have asked questions. You need to do it for each and every batch for each and every course. We do it here. At least I do it here regularly. I tell you also I have put a slide. Please do not hesitate to ask questions. No question is a silly question. Don't think that way. Don't hesitate to ask. If you are going to go without that information throughout if you could not ask me or the colleagues out here you are not going to ask to anyone throughout your life as such. With this group if you cannot be open with whom can you be open as such and you have to say that you don't know the answer without that you will not be in position to ask anyone as such. If you ask the right time is the class or outside you can go and ask the teacher if you are so scared of of the other lot which is there. That is something which one has to avoid. I have just tried to put one or two examples which we looked at. Looking at this taxonomic scheme taxonomy is basically the practice and science of classification. It is a Greek words being put together and I have tried to include out there. These are basically used for classifying living organisms to start with. But then this term is getting used more and more often for different applications and systems of process. The term is now used in a wider more general sense and can be put for anything. So our classification for problem solving scheme we are going to have it in this problem part as such. There are certain things which we are going to define which are sort of expected things in the system as such. And one of them is what we call as the routines. Most of you, almost everyone of you must be aware what are the subroutines in programming. One way of programming one language or the other you are all aware of subroutines. There is nothing but exactly the same thing put out here. There are very simple steps which do the calculations in a normal way as such or decision making in a normal fashion without coming out with a decision on its own as such. So it is finally going to give you some value. If it is in the form of yes no kind of thing it will say yes or no kind. But no decisions are available from this as such. And what you are doing now going to use them regularly like I am going to use quadratic equation solution a small subroutine for that. That I am calling out here in this methodology as a routine which in our computer programming we call as a subroutine as such. Small small programs we write and we incorporate them at any place we want and we get the answer that exact problem part of the subroutine part stays outside the main program in a way. We call that subroutine or routine and do the same. Exactly the same thing here except that here also we do not get any decision from that as such. We only get the values from it. So what are the things which we have out here? The scheme is basically adopted from Wankert and however is and it consists of 4 different steps as such. The diagnosis the strategy, the interpretation and then the generation. Let us look at briefly at each one of them. It is a selection of the correct way to use a routine. If I want to solve a quadratic equation, which routine should I use? I may not have only one main method or routine available. I may be having 2, 3, 4 different routines. Is that just not for the quadratic equation or anything as such. So integration differentiation, area calculations, these are all these things are coming under these routines part. So having appropriate knowledge of these routines, the diagnosis is getting completed. In the sense I have no chosen problem what method or what split procedure I need to go for. Strategy is the choice of routines. So we will need to look at the, so we will be going through this strategy part. We will be hiding the choice of routines considered out there as such. Interpretation is a real world problem solving as such. Let us see the real world problem to representation of one so that it can be solved. As I said converting things to equation forms and things of that kind. That is the interpretation and finally we end up with certain conditions as such. If you get for example, negative values of mass, length, pressure. Are these the realistic values? No you cannot have negative mass. You cannot have negative length or some such thing. Negative current you cannot have that kind of thing as such. So those are the things which are wrong. So those should give you some clear cut idea where the things are going wrong as such. Finally the generation is the development of routines which can be used for a new user as such. And this way again involve stringing them together. You can have whole five routines brought together and form a new routine as such. So that is something which should be hand. Let us have a brief look at the designing and grading problems as such. The problem is considered as good if it gives the serves or fits the objectives for which you have said that particular thing as such and allows for propagating as well. The scheme which we have to follow for doing this is going to be little bit different than what we normally do as such. How to use the taxonomic scheme? In this when you are setting a question paper of five or six things, questions as such but on a very limited area of the syllabus. You have to start with the simpler questions to get started. The idea is to test them that is one part. To help them is another part. These two things are normally not going together. Either you test them or you help them and people look at it as if you do one the other is not possible. Not true. You have to ensure that they get the help by way of the evaluation process or in the process the feedback they should get help from this. So try to put the questions in increasing order of difficulty. Do not put the toughest question right in the first instance. It is going to have look at our intention is always to go from top to bottom question one to the page end and change the page and go for the next. No one is going to have look at the last question first kind of thing as such. So do not sort of disturb the candidate or start in the way first instance by keeping the toughest problem in the beginning. Let him go through the things as the difficulty level builds up. His confidence level also is building up. He gave the simplest question. You need not put equal marks for all questions. That is one criteria through which you can always be in position to do this. Put 7 questions. 8 questions. The first 5 questions may be giving you a weightage of maybe 40%. Last 3 questions may be having a weightage of 60%. But then you are not killing the interest of the student is getting something possible to be done to start with and then go by that. Getting a evaluation part. It is an unavoidable feature as such. No one wants to do this. There is no process which any teacher generally likes as such. And specially getting a batch of something like 60, 80 or 120. It is more problematic. It takes a lot of time and so one has to think what exactly is to be done. So ranking of students is anyway required. That is an essential feature of our system as such. And the students who can put their abilities into problem solving should be getting higher marks or something. So things have to be done in that fashion as well. So if we start with the earlier problems as such, now let us look at what are the common problems which we have got as such. I have indicated that with the examples which I have put in the beginning, the multiplication problems as such. Very simple Should the student get zero marks for that kind of thing or should he get some credit? Now here there is a difference. Some people have their methodologies which have been put in the literature as well that you go where addition or deletion. Addition in the says you start looking from the beginning of the answer how many correct steps you have done. So if you have gone up to step 3, stop at that. Whatever the marks you have allotted for those three steps, give them that and that is done. There is a deletion step where you go through all the steps and see where the marks should be deducted. Like in our case what we had seen one of the features which is possible is you know that this particular step onwards all values are wrong. But values and steps they are not the same. Keep that in mind that value and steps are not the same. Values are numbers, steps are the procedures as such. So step as procedure may be still correct but with wrong value you have started. So beyond a particular point it does not get anything. There are people who talk of this thing that if you go for three wrong steps after that you need not look at the remaining part of the problem at all. After that you do not normally expect anything to fall in line such or anything turning out to be correct. So you allow for three errors to occur till that time you must check. Beyond that you can just say that anything beyond that is not going to be correct or expected to be correct. So opinions are going to be different out here. Everyone is going to have a different opinion. Whether one should go for a particular value of marks to be given to a particular step or not is not very clear. And that is what I have said positive and negative marking schemes either you keep on adding the correct thing or you go on deleting for negative parts. Possibility of multiple solutions and method there is something which you should never neglect as such. Never cause the answer just because your value expected is not coming. Something which is really wrong also you will have to go through as such. And then tackle that particular part and see whether there is any alternate method available. You may be knowing about one alternate method. But keep in mind you are not the only ones who have learnt the things as such. The students also have learnt the things not from the same teachers as ours but from different teachers who are going to be your colleagues. And they can give different ideas out there. Anyway the other few solutions are the easiest to check. No error averaging tick tick tick tick tick ten marks. The whole thing gets done within no time as such. Ever in the first step everything later you have to check as such. So error free things are always easy. And when this error occurs only in the solution one should strictly speaking track the error through. Why that error has occurred? The feedback part which I was talking about comes at this stage out here as such. You have to say that this value you have taken is wrong. You cannot say that this is wrong. Very pinpointedly you must point out that this is what is wrong and you should have taken instead of this that would have turned out to be correct. This takes long time. This takes long time and so what you should do is these errors are occurring because of these three different types as such. Some lapses, some knowledge errors, there is something misconception or things of that time or the real errors which are basically the multiplication division or numbers. And distinctions are not always easy. Distincting one thing from the other is not easy. When it brings the paper to you saying that you have given less marks you start asking your questions and you may finally feel that I had deducted the marks for this purpose. For that you should have got it but for this you should not get it again. So even that kind of thing happens also perception as far as that part is one. Finally well presented solutions are always easier to evaluate and they never get neglected as such. You will find in your class students in our solution which is given there will be one step here side by side there is a third step given here and the whole thing hodgepodge you are not in position to link the thing. And you also behind the students who are writing it in very neat form neat in the sense I am not talking about good handwriting, good sketches no handwriting may be bad that he cannot help. Sketches drawing may be bad but his arrows and such things he will be showing your current or flow direction it will be there. In other students case the whole thing will be neatly nicely done with the scale but there will not be any direction indicators out there. In such cases which is the one which is to be looked at as a good the one which is not looking good but is no correct has to be given that kind of pity. So marks at times people try to train the students that I am going to do this this time for this test. But this solution is not well presented you are going to get marks deducted answers may be correct. So I may add some two marks basically for that and do that. So that is something which one has to look at. Finally after all these process and evaluation and all that the feedback has to go to the students as such and they most realize where and why the errors have occurred and marks have been deducted or given. So that part is something very important and here a small note may be a word or two at each point where you are going to put a mark cross mark you know what is wrong at that stage. Only thing is a slight laziness from the teacher's side forgive me if I am using the wrong word but from my I look at it a slight laziness not too much of laziness instead of putting a mark you provide this particular parameter then when the student comes back to you you do not have to look at that part again you know what what was wrong with that and you can immediately within no time you can send the student back you have not used this parameter correct and so the mark has been deducted. Otherwise you have to really scratch your head and see what why did I put that cross that time. And at times if it is the the students are also clever do not look at them as always a fools as such. That will not come immediately when you are checked the answer you will come after 15 days by the time you have forgotten what solutions you had marked us and then it really becomes tough to do that. So similar thing one has to do for a tutorial sheet as such to start with a basic repetition of knowledge and then little bit more difficulty level has to be brought in as such. And problem solving strategies as we looked at there is something which has to be done as such. Whether one can change the solution or not that is led to an individual. Here comes the quirks of the thing as such. You have the alternative forms of assessment someone was asking as to can we do this can we do that. Yes you can do all different things as such but all with the information to the students to start with. That is something which you cannot put. We do have something different. We have what we call as a surprise test. We tell them that next month any time there will be a surprise test. And without telling them what particular part of course we give them the quantum of course part which is going to be there but other than that they do not have. So we have the open book examination. When you give the open book examination you are not going to give any descriptive type of questions out there. Concept checking or concept evaluation is something for which you will have to really put in some more time to set those papers as such. Incomplete solutions are tried in them. Give them incomplete solutions. Give the problem give some three four steps and ask them to proceed further as such. And they will get stuck somewhere because they are not looked at those four steps which have been solved and given them in a proper correct way. So they you can ask for the self marked assignments like when we have a small number that time we do this thing also. You exchange the answer sheets. You are allowed for him you are allowed for him. We give the carbon copy made out of this and give those things. If I feel somewhere something is wrong I can check that as such. No problems on that. So even within that when they are doing it they cannot cheat the teacher as such. Teacher teaches or they cheat. That is what people normally think. Not all the time it may be possible as such. You can have the checks out there. Finally coming to this innovations and patents part as people are looking at it. How does one come up with any of these as such? This is something which one has to look at more carefully as such. And how does one confirm that he has really got something worth calling innovation. So what to call innovation? Just changing one instead of using a metallic rod if I put a wooden pencil instead of that and if the pencil do not pick can I call it innovation? No everything cannot be called you can modify this things. You can modify the objects modify the things as such. Innovation is something different as such. You have come up with a totally new idea to do something which is desired as such. It may not be a new object and totally new things as such. And so what leads to patents is this gets checked by the patent examiner as such. Whether anything is available already or not and so from that I will be in position to get to the other things as such.


This paper presents a new technique for creating helically decorated microcylinders, which can be used to create microspheres with helically patterned compartments. This technique involves twisting microfibers while they are being ejected through a nozzle, resulting in helically decorated microcylinders. These cylinders can then be used to form microspheres by interfacial shape-shifting. This article was authored by Manje Gil, Siangjin Moon, J1 Yoon, and others.


I am Dr. Gautam Kumar. I am the surgical gastroenterologist and liver transplant surgeon at Manipal Group of Hospitals at Old Airport Road. I would like to bring in your attention that we have restarted all the elective and emergency cases in Manipal Group of Hospitals. We have taken all the necessary precautions. Namely, we have separated COVID zone to the non-COVID zone and completely isolated the procedure so that people who are COVID positive will never come in contact with patients who need other than non-COVID care. So it's important right now that the patients who have other diseases be able to come here and get all the treatment needed because what we are seeing is that there is a delay in people getting appropriate treatment because of this COVID fear. So at Manipal we have sanitized all the areas which are non-COVID and we have made sure that COVID treatment goes through a particular channel and we have isolated and completely sanitized that area. And the non-COVID patients will get appropriate treatment without the fear of then contracting COVID. So I would like to tell you that this is a good time and at Manipal we can take care of you. Please visit our website at ManipalHospitals.org or call helpline number given below for any further assistance.


Welcome to this continuation of our lecture about descriptive statistics. In this part of the descriptive statistics module, we're going to be looking at ways to work with data that is in frequencies, group to data, categorical data, getting summary measures, and looking at graphical approaches. Let's start by taking a quick look at a problem we've seen before at the beginning of our lecture on descriptive statistics when we were still focused on measures of location. We looked at this example of reading level. A random sample of 16 eighth graders in a particular school were tested and they showed reading levels from five, meaning fifth grade through ninth grade and 10th grade. So some of some of them were above some of them were below their grade level and the solution we found then is listed for you here. I'm not going to belabor it. We did it already. You order the data and you get the location statistics, the measures of central location and the measures of non-central location. Now the previous problem actually can be set up somewhat differently and you're going to like it better this way as a frequency distribution. Notice you have a five, a six, a seven, a eight, a nine and a ten and now we show the frequencies. Five showed up twice. The six showed up three times. The seven showed up three times. The eight showed up twice. The nine showed up five times and the ten showed up once. You can see why we call it a frequency distribution. It's also called group data. We're grouping it. We're grouping the data to make it a lot easier to work with, especially when you have a huge data set. Here we only have 16 observations. That's why you can ungroup it. It's only 16 separate numbers. But again, with a big data set, you want to group it. Now let's see it. We've grouped it now. We're only looking at six different values. We're looking at reading levels from five all the way up to ten. Notice the important thing to recognize is the sum of the frequencies. Add up all the frequencies. You've got the n. So we sum them. Two plus three plus three plus two plus five plus one. 16. That's n. We have 16 numbers. So n is the sum of the frequencies. Now the mode, you can see it immediately. Mode is the one that occurred most often. Which value came most often? Notice that the highest frequency for the nine is five. The nine showed up five times. That's your mode. Now you know nine is the mode. And again, remember all your values, all your measures actually, the x's, you call them the x's of measurements, they're basically the values of five, six, seven, eight, nine and ten. So your mean has to be between the five and the ten. Same thing. The median will also be between five and ten. Your mode will be one of those values. Now we figured out the mode is nine. We can see it. That had the highest frequency. Now the median has to be somewhere in the middle. Since n is 16, it's going to be kind of right, think of the eighth value. It's already grouped and ordered. It's ordered for you. So we have 16 values. It's got to be the eighth number. Think of the number that cuts the, you have eight above and eight below. Count down eight numbers. Using the frequencies. Two, three, three. Notice the eighth value, the last of the eighth value is the seventh.  You have eight above and eight below, and you go right in the middle between seven and eight. So we know the median is observed just by looking at it. It's right between the seven and the eight, which is seven and a half. So your median is going to be 7.5. Okay. That makes things a lot easier when you set it up this way. Okay, let's compute the mean for group data. Okay, the formula is right there on the bottom. The sample mean is the sum of the xi times its frequency divided by n. Okay. So in other words, what you have to do now is have a new column called xi fi. All right. So we have five times two, which essentially the same as saying, I had two fives. I'm adding them up. Five plus five. Instead of doing five plus five, I say two fives is five times two is 10. There were three sixes, which is another way of saying six plus six plus six, that's 18. Seven times three, the three sevens, that adds up to 21. Seven plus seven plus seven. Eight times two is 16. Five nines, nine plus nine plus nine plus nine or 45. And 10 times one is 10. You add up that last column, the sum of the xi fi, you get 120. That's the same as you would get if you ungroup the data and add up the 16 numbers you started with. But again, you don't have to do this that way. Get the column of sum of xi fi, which is 120, divided by the sum of the frequencies n, which is 16. 120 over 16 is 7.5. And 7.5 now is the sample mean. That's your average reading level. Okay. Let's look at this problem. Okay. Now here we have a thousand values. Right. The sum of the frequencies are thousand. That means n is a thousand. Again, you're not going to want to write this ungrouped, which means you have to write out a thousand numbers. Okay. So now, first of all, you know n is a thousand. The first thing you note, then you do the third column, the xi fi column. Zero times 10 is zero. One times 20 is 20. Two times 30 is 60. Three times 40 is 120. And eventually you'll get to 10 times 100 is a thousand. You add up the last column, which is 5,960 absences. And that's the total number of absences for the thousand people working in the company. All right. So if you want to get the mean, all you got to do is divide 5,960 over a thousand. And the mean is going to be 5.96. Okay. Now let's get the median. And then we'll do q1 and q3. Now the median is kind of the middle value when you order the data. The data is already ordered for us. It goes from lowest to zero to the highest. 10. Okay. We have a thousand observations. So it's going to be the middle value by the 500 mark. All right. So think about going down 500 in frequency. Okay. So we have 10. That's our first frequency for the zero. Plus 20 is 30. We're not yet at 500. Another 30 is 60. By the time we finish the last three, we've had 100 values. We've used up 100 values. We go to the four now. We have another 50. So it's 150. 150 values have been used up. Okay. Now the fives can't go past that. That's 400. 401. 50 is 550. We want to get to the 500th value. So somewhere in the fives, somewhere in one of those fives. Okay. That's going to be the median. So the median is five absences. And as a check, you can go in the other direction. Go backwards. Go up 500. 100 plus 100 is 200. Plus 60 and 40 is 300. Plus 150. So now we have 450 values. Going up, we have to go up 50 now. And guess what? We're again in the fives. So that's two ways of getting the median.  Now the mode, you can just look at it and you find the mode. The mode is a five. That has the highest frequency. 400. So I've shown you how to get the median. I've shown you how to get the mode. We did the mean already. Now let's try to get Q1 and Q3. You do the same thing, but now you're counting down. For Q1, you count down 250 observations. Again, only using the frequency column. Count down 250. 10 plus 20. That's 30. 30 and 30 is 60. 60 and 40 is 100. 50 is 150. Now you want 250. You're going to be somewhere in those fives. One of those fives will be your Q1. So Q1 is five absences. You want to get to Q3. Do the same thing. A quarter of a thousand is 250. Count. Go backwards. Go from the other direction. From the starting and the bottom. 10. You get 100 and 100 is 200. If you go past the eights, you'll have 60. So somewhere in those eights. One of those eights is going to be Q3. So now you found that Q1 is five absences. Q3 is eight absences. Again, to get a median, you just take your end to some of the frequencies, cut it in half. Half of it, like in this case it was 500. And then you can go up and down the frequency table, and you'll get the median. So you want to get Q1. You take a quarter of M, which is 250. Starting from the lowest number, count 250, you get to Q1.  And again, the interquartile range is the difference between Q3 and Q1, which we're going to learn about. And that's just eight absences, minus five absences or three absences. Here's another problem with group data. We're looking at defects and the frequency of these defects. So we're an automobile manufacturer, and we see that 10 cars had one defect. 10 cars had two defects. All the way up to 20 cars had 10 defects. So essentially, if you look at the sum of the frequencies, you'll note right away that the sample size was 350 cars. Just add up the frequencies, 10 plus 10 plus 20 plus 20, all the way up to the last 20, and that's 350. So the sum of the frequencies, N, is 350. The total number of defects is 2,290. That's the total number of defects. Just adding the last column, sum of the XIFI, 10 times 1 is 10, 10 times 2 is 20, 20 times 3 is 60, 20 times 4 is 80, 40 times 5 is 200. Until you get to the last one, 20 times 10 is 200, and now we know that the total number of defects was 2290. The mean, that's just 2290 over 350. So the average number of defects is 6.54, if you want to go to 2 decimal places. Always remember that the sum of the frequencies is N, not just sample size. Now the median, remember we're looking at N of 350, those 350 cars. So we have to basically for our median take half of 350. It's already ordered, so we've got to go down essentially half of 350 which is 175. So let's go down 175 using only the frequencies column.  Now in the 7 somewhere we've got to go down to 175. So we know somewhere in the 7s, that's 7 defects, somewhere in 7 defects is going to be our median. If you want to check your answer, go backwards 175. Starting now with the bottom, 20 plus 50 is 70, plus 60 is 130. Again, we just go up a little bit and somewhere in those 7s is our median. So the median is 7 defects. You want to get Q1 and Q3? Well, you've got to take a quarter of 350. So you need a quarter of 350 and that's as you know is roughly, it's 87.5. Alright, so around 88, 87.5. Let's go down 87.5 and that will get us to Q1. And then we'll go the other direction, going upwards, we'll do the same thing to get Q3. We've got to go down 87.5, so 10 plus 10 is 20, 20 and 20 is 40, then we have 60 and notice in the 5 somewhere we're going to have the 87.5 observation. So Q1 is 5 defects. Do the same thing going backwards. Let's start from the bottom. We want to go up 87.5. Now 20 plus 50 is 70, it's in the 8's. I can see right away, you can't go beyond that because then you'll have 130. So somewhere in the 8's is Q3. So Q1 is 5 defects, Q3 is 8 defects and into quartile range is Q3 minus Q1 is 3 defects. So far we have seen discrete group data that has been organized and collected into a frequency distribution where you have the number of observations that fell into each class. What can we use this for? Well, we've already seen using frequency distribution for numerical data with repeated observations which is another way of saying discrete group data. We could also use it for any quantitative data that has been grouped even if the groups didn't come naturally like collecting income data and organizing it by tens of thousands let's say. And it could also obviously for the same reason be used for categorical data. In fact, we don't really have very many other options for categorical data besides frequencies and percentages where you can have a frequency distribution, we'll see about that soon. Here's a quick example to show what we can do with frequency distributions other than just get the summary statistics like we got before. In this problem, a sample was taken of 200 professors and we asked each for take-home weekly salary. The responses ranged from $520 a week to $590 a week and remember the sample size was 200. In this case, we have numeric data, quantitative data. We did not need to use a classification technique but sometimes you do because it gives you more insight into your data. In this case, we had to collapse it by creating intervals that didn't really come naturally to the data. We just had to decide. I guess we decided here that we wanted seven categories. The range was $520 to $590 that's $70 divided by $7 $10 per category. You can see the categories $520 and under and under $530 there were six of those so we don't have individual values but we don't need them in this case. Six out of 200 is three so that's 3% of the total. That goes all the way through the seven categories. You have the intervals, the frequency and the percentage. That's the frequency and the percentage distribution and the top chart. Then we took this and created a cumulative distribution from it. You've seen this before you know what these look like. Basically what this is as you go along you don't look at individual categories you keep adding to the category that came before. If the first category that we used the classification was $520 and under $530 and there were six of them that's $520 to $530 so under $530 less than or equal to $530 there were six observations. Less than $520 there were zero observations. Less than $540 how many were there? Well the six from the under $530 and the $30 from $530 to $540 so all together $36 and for each of those there's a percentage too. It's the cumulative percentage distribution and when you get all the way to the bottom the final category since you're accumulating everything up has to be equal to the sample size so all 200 observations were below $590 which we knew to start out and that's 100% of the distribution. Over the next few slides we're going to look at some graphical approaches to grouped data taking frequency data or percentage data and seeing what the graph would look like the chart, a graph chart, a bar chart there are other ways of doing it we're just looking at a selection here. You can create a histogram kind of a bar chart from the frequency distribution in this case it's a vertical bar chart across the X axis are the categories, the intervals and they're discrete intervals they're non-overlapping and that's why it looks like bars we do not have regular quantitative data this data has been collapsed into intervals so you don't see a smooth continuous curve. The height, the Y axis is the frequency and you see that sometimes the individual frequency for each interval is written on the top of each bar for clarity. A frequency polygon is another way of portraying the frequency histogram it's not a curve although it looks like a curve it's actually the frequency histogram imagine it overlaid on a histogram the way it's constructed is simply by putting a point at the top center of each bar and then connecting the dots so you could see how that was done. Here's a graph of the cumulative frequency distribution with this data you saw the cumulative frequency distribution on a previous slide and this does look like a smoother curve even though it's not based on purely quantitative data but on categorical data that was in categories in classification the interesting thing about this and you'll see this more later in this course and in other courses is the S shaped curve which is typical of continuous distributions that are based on distributions of their mass in the center and are more or less symmetric and then on either side going down towards zero at the extremes you can see how it's at the left side it starts out slow where the smaller frequencies were and then in the middle with the mass of the distribution is it jumps because that's where the higher frequencies are and then it peters out again at the end at the right again where the smaller frequencies are so it's a typical S shaped curve for certain very very frequently used cumulative distributions including one that we're going to study very very much we're very involved in most of the semester and that's the normal distribution this descriptive topic even though it's at the beginning of the course and relatively easy it ended up being a bit longer all together than what you might expect there's a lot in there it's descriptive statistics and it's a large part of what we do is descriptive statistics don't forget a little bit of shameless reminder here you must do your homework if you're in this course to learn or if you're in this course to do well on your exams the answer is the same you have to find as many problems as you possibly can and practice practice practice and what comes out is a happy smiling student