We will complete the proof of the pumping lemma for context free languages. Recall the statement of the lemma. Basically, it says that suppose L is a context free language, then there is a constant n which depends only on the language L such that for all strings z in L such that the lengths of these strings are greater than equal to n, you should be able to break up this z in five parts u v w x y such that both v and x cannot be empty. In other words, length of the string v x that is greater than equal to 1, length of v w x all together is less than equal to n where this n is the pumping lemma constant for the language L and then the pumping condition that for all i greater than equal to 0 that u v to the power i that means i copies of v followed by w followed by i copies of x followed by y, this string is also in the same language L. Last time we really completed the main crux of the proof which is showing how this condition 3 we managed to obtain for a certain break up u v w x y. What was left was to show that this condition 2 that is the length of v and x is greater than equal to 1 and v w x together their lengths all I mean the concatenation of v w x the length of that string is less than equal to n. This particular part was left otherwise we had completed the proof. Let us complete the proof by showing that the proof that we gave it is such that that this condition 2 will also hold. Now, very briefly what we did was first of all we started with the assumption of course that is given that L is a context free language and therefore, we said that let G be a Chomsky normal from grammar for L. Then we said that let G has or let G this grammar G let it have m non-terminals. Next what we did was using this value of m which is the number of non-terminals of the context free of the Chomsky normal from grammar G of the language L we defined for us the pumping lemma constant we said let n be 2 to the power n. Then we said consider any string whose in the language Z whose length is greater than this number. So, we said that let and then we considered the derivation tree for such a string Z and Z is greater than equal to n remember n is to power n. Then we said look at the longest path in this derivation tree. Now, we proved a small fact which showed that this path this path longest path length is at least m plus 1. So, once I have the longest path in the tree starting from the root node which is the start symbol S and of course, going to a leaf node which is labeled with a terminal. We know that this path has length at least m plus 1 we proved this fact. Then what we did was we started going up from in this you know we started from here the end of this path and going up till we found a non-terminal which got repeated. And again we argued that this case must happen that is a non-terminal must repeat further more the argument that we gave also clearly showed that by the time you move up m plus 1 edges one non-terminal must repeat. So, this length of this path you cannot be any more than m plus 1. So, is this clear what I am saying is that we started from this point first of all we said look at the longest path. This path of course, has to be of length itself greater than equal to m plus 1, but it could be in general much larger than m plus 1 because you know your z can be very large and then you are considering the longest path. But now you are going up from the bottom of this path till you find the first non-terminal which has occurred earlier in the path as you go from below. And the reason that we gave some kind of pigeonhole principle argument that this repeat must occur by the time this path is of length m plus 1 or less. And then we said that look remember we said that suppose this particular a derives this part of the string and this second a derives this part of the string and this part we identified as w this part we said is v this part is u this part is x and this part was y. So, this is how you would break up the string will it is clear that s of course, derived the whole string z which is u v w x y further a derives this string v w x first of all I can see that a derives this part a derives this w part. So, a derives w and if you if you think in this manner the derivation tree of a is you think of this.  And now it is easy to see and this see this fact is very clear from the diagram itself. And now it is very easy to see suppose this condition is not true that means length of v x is 0 you know it has to be something length cannot be anything other than any anything negative. So, if it is not greater than equal to 1 then this v x length is 0 which means both the strings v and x is empty. So, what it means is if v x length is equal to 0 then this of course, implies both v and x are empty. And in that case this particular derivation would mean that a derives a. But that is not possible because the grammar is a Chomsky normal form grammar remember for this to happen we need to have either epsilon productions or unit productions or both. I mean either some unit productions such that a derives a or you know some epsilon productions such that some non terminals get rewritten as epsilon and starting from a we get only a back. But these cases are not there because our grammar is Chomsky normal form grammar. So, if we assume that both v and x they are empty then we get a contradiction because that cannot happens as the grammar is Chomsky normal form grammar. So, therefore, we say that we can see that this condition therefore, must hold. And the other condition is what we said that length of v w x is less than equal to n. But what is v w x now you what is v w x is derived by a. And this is the derivation tree this part is the derivation tree for v w x in that the longest path is the path from here to this see that is clear is not it because here they cannot be any longer any path which is longer than this. Because then the original path which we which we said is this is the longest path that could not have been the longest path in the big tree. So, this is the as larger path as possible in this derivation tree. And we know that is how we are good that this path length is is no more than m plus 1 see let us not get confused by this statement this was about the overall tree. And then when we what we said was that we are going down from here up and by the time we go up it no more than by the time we get no more than m plus 1 edges one non-terminal must repeat. So, we are waiting till the first non-terminal. So, this path length. So, how shall I write it. So, let us just say this path is theta. So, length of theta is less than equal to m plus 1 and theta is the longest path in the this derivation tree starting from it. That means what we go back to our old fact that suppose I have a derivation tree where no path is greater than m plus 1. Then the string that is generated cannot be of length greater than 2 to the power m plus 1 minus 1 which is equal to 2 to the power m which is of course equal to the pumping lemma constant. So, let me write it. So, that is clear length of theta is m plus 1. So, the string V W X cannot be of length greater than this which is equal to 2 to the power m which is equal to n where n is the pumping lemma constant. So, we have said the length of the string V W X cannot be greater than cannot be of length greater than this strictly greater than this. Therefore, length is less than equal to n and that is the other condition. So, we have proved this also and this and therefore the proof of the lemma is complete. This is something we must appreciate and this kind of thing was there for our pumping lemma for regular languages as well. What we are saying is that this lemma conditions they are necessary but not sufficient to prove a language to be context free. In other words that suppose you find the language L which satisfies all these from there you cannot conclude that the languages context free. In other words what does it mean that it is possible that some non context free languages also to satisfy all these conditions that is what we mean when we see that these conditions are necessary. In other words of course as the lemma states every context free language L they will satisfy these pumping lemma conditions but the other way is not true just because for a language all these conditions hold you cannot conclude the language that language L to be context free. In fact, so let me make this point once more that what it means is that it is not always possible to make use of this lemma to prove a non context free language not to be context free. So, such an example let me give right away is a well known example L 1 is a i p j d L such that either i equal to 0 or j is equal to k is equal to L. So, what it means is that when you know firstly this language L 1 has a string of a is followed by b is followed by c is followed by d is where either there are no a's or if you have a number of a's then it must be the case that the number of b's is equal to the number of c's equal to the number of b's. Now this language is not a context free language but you see that it will satisfy all these conditions. Why see suppose see there are two cases either i equal to 0 then there is no really restriction on j k L right. So, basically we have a consider a string like b j c k d L and let us see the entire v w x part occurs within b and then you pump. So, number of b's go up or 1 b goes down that is ok right this is still in that form because we cannot add any a's in front by pumping up or down right. So, will remain within the language L on the other hand suppose I have some a's followed by b's. So, let us say this is I know R then it must be the case if since I have number of a's C R and D R these number of occurrences of b must be equal to number of occurrences of c's and as well as for d's. Now again it is possible if you take such a string from the language then your v w x can very well be within this right. You can choose your u v w x y is such that that v w x part entirely is within a's. So, when you pump up or down all that happens is that you change the number of a's number of b's c's and d's do not change. And therefore, on pumping the string that you would get will be also in the same language L 1. So, the point I am making is that this is a language L 1 which satisfies the conditions of the pumping lemma and yet L 1 is not a context free language. So, let me write it down L 1 satisfies the conditions of the lemma, but is not a context free and we will be able to prove that this language L 1 is not context free language by some other means, but not by using this form of pumping lemma. There are stronger forms of pumping lemma in particular one stronger form which you can use which is fairly well known and used is called Ogden's lemma is a stronger, but we will not discuss Ogden's lemma here or there are other versions even Ogden's lemma will not be able to prove some languages to be context free. Then in fact, we gave one reference while discussing with discussing for regular languages and that reference that paper contains the most general form of pumping lemma for context free languages. Here are some examples some more examples of languages which are not context free and all these three languages you can prove that they are not context free, but by using the pumping lemma that we have seen. Now, just a little discussion on the form of these kinds of languages and at least intuitively we should be able to appreciate certain things or certain properties which context free language cannot ensure. See here what is happening? There are three strings a, b and c. What you want is first of all that b and c they must be equal in length and length of a is less than equal to length of either of this. Now, if you if you let us remove this then it will be a context free language, but adding this is the problem. See what you will see later when we discuss the machine version that it is easy to ensure this or this, but together it will not be easy for a context. It will not be possible to ensure both these constraints at the same time. These are intuitively I am trying to explain to you and similarly if this is not there this condition of course, we can ensure we can write a context free grammar which will generate this language b and c and such that n is greater than equal to 1 there is no m. But together both these conditions we cannot handle using the context free nature of the grammar that we have. Take another kind of thing similar things you see again there are these two condition business that i is less than equal to j and j is less than equal to k. The problem is the once you ensure this again you see this one of these was not there either a or you know this or either of this letters then again we can ensure that by means of a context free language. In other words supposing a was not there b j c k such that j is less than equal to k this is something we can handle we can we can write a c f g context free grammar to generate such strings, but these two conditions together we cannot handle. Now another version of the same two condition business is now I should say that you should also realize in fact let me let me let me say what I want to say after I discuss this. What is this again I have two conditions right that number of a's must be equal to number of c's and number of b's must be equal to number of b's two conditions. Again we this is something we cannot take care again if you look at pumping lemma y that is the case where is you know you can say pumping lemma constant is let us say k then you take a string a k b k c k d k right. And then what happens is that the window v w x will be either in entirely within one of these you know letters strings of one letter like entirely within a's or b's or c's or d's or can straddle two consecutive ones. So what will happen is it will change the lengths of two consecutive ones at most, but you know here we need to make sure that the lengths of the first and the third they are they match and that is where the problem will happen. The same way that we had proved for you know that language a n b n c n not to be context free language the same kind of proof will idea will go through here too. But you know I am somewhat incorrect by saying that we cannot handle two conditions we can handle two conditions so long they are not kind of intermixed or together. So for example if you if you take another language l 5 let us say I write it slightly differently a m b m c n d n this is context free right how will you do that remember I can separately generate this from some s 1 separately generate this and this these are just the two concatenations in other words what will be that grammar. So we can start with s s goes to s 1 s 2 right. And then s 1 is a s 1 b or a b and s 2 is c s 2 d or c d and you can see that this grammar is going to generate this language right. So we can handle two conditions, but not together is that clear or you know this is really intuitive way with what I am explaining and whenever you see that the conditions have to be kind of there mixing up or all both the conditions you need to ensure together that is where the problem arises right. So you should be able to at least intuitively see that the situation with l 2 l 3 and l 4 is different from l 5 or for that matter l 6 which is a m b n c n d m right. Here I need to keep track of correspondence between a's and d's separately from the correspondence between b's and c's this is something we can handle so long. So what is the difference between this and this as you handle this m is this m is you know number of a's here is equal to number of c's there I am getting some b's inside and you see that is where the problem will happen. We will kind of be able to appreciate this a little more whereas here you know this I can handle you know I have generated some a's and this is taken care of and separate I mean best is you should yourself write the grammar for l 6 this is a context free language. So you will be able to again very simply write a context free grammar which will generate this language. Well now that we have the pumping lemma and we now we know in particular one language you know several languages which are not context free now using this that fact I can come to a very strong conclusion right. So let me show what the conclusion is that the class of context free languages this class is not closed under intersection we will just now little later we will talk about the other closure properties but you know this kind of immediately almost immediately follows from whatever we have been discussing. So recall what does it mean to be for a class to be closed under intersection we are talking about classes of languages each language is a set you know I take two elements so one language and another language l 2 and I create the intersection of these two. We say the class is closed under intersection if whenever you pick up two languages from here in from the from within the class take their intersection the result is also within that class but we will be able to show very easily that this is not the case with context free languages. So let us take two languages l a i b i c j and l dash a i b j c j so claim which we can easily prove that both l and l dash are context free that let me let me quickly give a grammar for l for l you can this let me show you the productions s goes to let us say x y x goes to a x b a b and y goes to c y or so you see basically y can generate any number of c's and x will generate equal number of a's followed by b's right. So x will generate a string of a's and b's where number of a's will be equal to number of b's and y will generate just any number of c's and your string s is the intersect I mean the concatenation of these two so therefore you will generate all strings of the kind which is mentioned here and a very manner similar you know similar manner you can also give a grammar for l dash but what is the intersection of l and l dash so obviously they have to be again of the form a's followed by b's followed by c's since there in l all these strings in the intersection strings are in l so the number of b's must be equal to number of sorry number of a's must be equal to number of b's since the same string is also in l dash that means number of b's also must be equal to number of c's so therefore a's is equal to number of b's equal to number of c's so this is in fact this language a n b n c n n is greater than equal to 1. So as you see a very important result we proved quite easily from the fact that this language is not context free and this particular language is the intersection of two very simple context free languages so the class of context free languages this class is not closed under intersection because you know I could find intersection of two context free languages which is a n b n c n which we proved by pumping lemma which is this language is not context free this situation as you know is very different from the situation of regular languages regular languages are closed under intersection so since we are talking of closure you might as you will see some closure properties of context free languages so first point which is again fairly simple to see that class of CFL's is closed under union why you see what we are saying that you take two languages which are context free languages then take their union l 1 union l 2 and we are claiming that that union language will be context free so this this is this is very simple so let us say so let me give the proof with let l 1 l 2 be context free and generated respectively by by g 1 and g 2 so in particular let us say g 1 is n 1 s 1 and g 2 is now assume that you know we can if need be by rewriting some by renaming some of the non-terminals assume that these two sets v n 1 intersection v n 2 is empty that means we do not have do not use the same name for two non-terminals from the these two grammars right and now you see think of another grammar which is like this g which is a new start symbol s union put it in braces so basically just take the union of this v n 1 and v n 2 add s to that so you know that make it your new set of non-terminals union v n 1 union v n 2 right this is this is the set of non-terminals p of course sigma sigma p and this new non-terminals is your start and basically your p is p 1 union p 2 plus one more and which is that p is p 1 union p 2 union just one more production that is s goes to either s 1 or s 2 so what is happening you start this grammar g with the symbol s and this s can be rewritten as either s 1 or s 2 if you rewrite as s 1 you will generate a string of g o use the grammar g 1 to generate any you can you can generate any string of l 1 similarly you can generate if you first rewrite s by s 2 then you can generate any string of l 2 so therefore together it you know it means that from s you can generate all strings of s 1 as well as sorry all strings of language l 1 as well as all strings of the language l 2 which is precisely what the union language so therefore the class of c f l's this class is closed under union so from these two which we have just proved we can conclude something very important another property closure property that class of c f l's not closed under complementation remember complementation is that language l is there you take the complement and the complement language is sigma star that does alphabet minus language right the set of all strings over sigma which are not in the language l that set is the complement of l so what we are saying is it is possible that you take a c f l context free language l you complement it and you get a language which is not context free or similarly it is possible that you take a not context free language take its complement and it may turn out to be context free so see point I am making is that this three actually follows from 1 and 2 why because I can write intersection of two languages l 1 l 2 as you know take the language l 1 complement it take the language l 2 complement it take the language you their union right and then complement the entire thing this just a set theoretic way of expressing intersection in terms of union and complementation right essentially it is those of you know it is a kind of de Morgan's law so l 1 intersection l 2 is this now suppose the class of c f l's where I mean this class was closed under complementation so now suppose l 1 and l 2 are context free languages if the class was closed under complementation then this will be a context free language l 1 complement l 2 complement is another context free language you are taking their union which is union we know is you know preserves context freeness so then this whole thing will be context free again you are taking a complementation of a context free language which by assumption would be again context free so then what would it mean that l 1 intersection l 2 would be also context free so in other words what I am saying is if complementation if class of a context free languages this class was closed under complementation along with the fact that it this class is closed under union we would get the class is closed under intersection but we know this class is not closed under intersection therefore and we also know it is closed under union so what is the possibility left that it is not closed under complementation so that is how we prove 3 there are other closure properties which we can very easily see you know we talk of two other things often which is concatenation so we will say in fact this we can prove again these two things class of CFLs is closed under concatenation and class of CFLs this class is also closed under CLEANY star remember that what is this is an unary operator whereas this is a binary operation so we take two languages l 1 and l 2 and this is the concatenation language remember that l 1 l 2 is nothing but u v such that concatenation of u and v such that u is in l 1 and v is in l 2 right again this is very easy to see that class of CFLs is closed under concatenation why because you know for l 1 you have a grammar l 2 you have a grammar both are context free grammars and they have two separate you know something what we used for union same idea will do will use that suppose g 1 is the l of g 1 the language language generated by g 1 is l 1 and the language generated by g 2 is l 2 right and let us say g 1 is v n 1 sigma p 1 s 1 g 2 is v n 2 sigma p 2 s 2 and the new grammar for grammar for l 1 and l 2 will be a g which is will obtain by taking the unions of v n 1 and v n 2 assuming that they are disjoint that you can you can understand why I want them to be disjoint because otherwise the derivation of one will interfere with the other and will add a new star start symbol s and they will write it as we will just add this production and rest of the productions will remain g 1 and g 2 right. So, you can easily see that if you start with this s we generate s 1 s 2 s 1 and s 2 are the start symbols of g 1 and g 2. So, through s 1 I can generate any string of l 1 with s 2 I can generate any string of l 2 and therefore, I can generate the concatenation language Cleany star was if you recall we used it extensively in case of regular languages you know there was a language l and Cleany star was that star operation. So, what was it very briefly l star is the set of all strings obtained by taking 0 or any number or concatenation of any number of strings from l that will you will remember what it was now l star. So, basically l star is a c f l if l is a c f l this is the meaning of 5 and again that is not very difficult to see that suppose l is generated by g where where the grammar is v n sigma p s right. So, all we have to do is to just add one more production. So, basically sorry I should not have said this way. So, I should have said g suppose g is this such that l g is l then for l star the grammar is g 1 right which is just you add one more production p union just add this production keep the same start symbol s goes to s s or epsilon right and you can easily see that l g 1 is l star right because you see then now starting from s you can generate any number of copies of s and from each s you can generate a string of l and that is what would generate the language l star.


Hi, this is Debbie from Socan. You're watching Trucker Josh with his friend Diesel. Enjoy the show! Good morning from a familiar sight. The shop. How you guys doing? I'm gonna find a place for these when I get back later. I'm gonna leave these right here front and center so I don't forget. Got this calendar from the guy with the Kenworth cab over. You guys all remember him right from the truck show at Truck World. I'm gonna hang this up. There it is right there. Beautiful, beautiful truck and I also am keeping safe in this calendar a very special picture that someone drew for me. Brought all the way to Truck World to give to me. Cool as that. His name is Dayton. Sorry, I think he is from Drayton. His name is Joel. Sorry, Joel got your name mixed up with your town name there for half a second. Don't worry. We figured it out. His name is Joel. He's from Drayton, Ontario. And he says, hey Josh, I hope you like this. Does it look like your truck? Because it's supposed to. It sure does. It actually looks better than my truck. Look at that hood. Nice long classic Peterbilt hood. It's even got my unit number up at the top there. That is awesome. That's going up on the wall here. It's got a flatbed trailer behind him. I'm gonna find a perfect spot on the wall here somewhere, maybe front and center. So that every day when I come to my shop, I can see it and then you'll see it in my vlogs too in the background, but It'll be right there probably. We're gonna decide after work today. I've got to get going because I got to get trucking, but it's gonna be right in here in this calendar so it's safe. Put that right there. Grab these gloves. I'm off to work. It's back to trucking. We had lots of fun in the truck world, but you know, real life always has to come back around. We have to get back to work. I'm gonna be a van hauler today. We're looking for van trailer 5058. We're gonna pull it down to Thief River Falls USA. It is full in the yard here. I hope I'm not gonna have to dig it out from behind all these trailers. Yikes, what's going on here? 5058. Man, there's just trailers everywhere. 5058. Please don't be in the back corner there. Please don't be in the back corner. Okay, good. I don't have to dig it out. I don't have to move one trailer, but 5058. Do you guys see 5058 anywhere? 5051. That's not even one of ours. Someone else's. 50, here's 5058 right here. We're off officially back on the road after truck world. Well, it's straight to America. Crossed down at Pembina, North Dakota. I'm already cleared to cross there. So they're expecting me. Thief River Falls. They're not sure if they're gonna live offload me. There's a chance that they'll, what that means is they'll unload me when I'm there.  If that's not a possibility today, I'm gonna drop this trailer there in Bobtailback. That's the plan. I don't make the plan. I just execute the plan. That's my job. That's our job as truck drivers, right? We get a plan given to us. We execute the plan professionally, flawlessly, and with style. At least we try to, right? Execute it with pride. Do your job with pride. This is Highway 59 South. I got to find a way to get over to Highway 75. I'm pretty sure our spring road restrictions are still in effect. So I can't take the 210 or whatever this road is here, 206. Whatever that road is there, that goes to Santa Dolph. That is restricted. I'm loaded. I'm pretty sure I'd still be legal because it's 90% restriction, and I'm not very heavy. I've only got about like 10,000 pounds in the box. So I'd probably be legal, but you know, I'm gonna try to avoid getting pulled over and like the mobile scales and stuff just to get let go. Whatever. Avoid that. I'm gonna go down to Highway 23 South of St. Pierre, Jolli. That road doesn't have any restrictions in spring. That'll take me through to Morris, Manitoba on the 75. From Morris, we'll stop at Timmy's. Actually, no. We'll wait for on the way back. I have a coffee here. I forgot. I brought my coffee from home. We're gonna save our money and drive past Timmy's down into the United States of America. And we're gonna go up to the window and promise to be very, very good. I usually don't have a problem crossing there. I cross there often enough that they know me. And plus all of my information pops up on their screen when I get to the window. So before I even get to the window, they already know who I am and what I'm doing, where I'm going. But they're gonna ask me those questions just to corroborate. It's good to be back trucking. I tell you what. This is what makes me most happy. Trucking right here. At Truck World, there's a lot of suits. Suits walking everywhere. You know what? That's good. That's awesome. We need suits to keep things running and stuff in the office, right? But I'm definitely not a suit. I'm a blue collar, boy.  Here in the hum of the tires. That's where I'm happy. The lineup is all the way back here. All the way up there around there. You see that? I guess the fisheye lens sort of distorts everything. US border and customs is way out there. Probably about a mile up. Close to a mile up, yeah. And we've got a long lineup of trucks here. There must be a little bit of a back up there. Maybe I came in the middle of a rush, or maybe sometimes when they're on shift change at the border, they'll shut down everything while the customs border agents change shifts and stuff. And they do it pretty quick. It's not like they take forever. They do it pretty quick. But sometimes in that short amount of time that it takes to switch them out and bring on the next shift, there's a long back up. Long lineup right away. A lot of freight moving back and forth between Canada and the United States. Billions and billions and billions and billions of dollars. The United States is definitely our largest trading partner. Well, because they're right here. And also we're very close. Canada and the US are like BFFs for life. Best friends forever. We're actually not best friends. We're actually brothers and sisters. Or brother nations. Two brothers from the same mother. The only difference is for those of you not from North America. The only difference, political, there's a lot of differences that are small, right? But the two biggest differences between Canada and the United States is the United States gained their independence and fought for their independence in 1775. In Canada, we stayed loyal to the Crown of England, which is what we're called the loyalists. So the Queen of England, Queen Elizabeth II, is our Queen here in Canada. She is Queen of Canada, sovereign of the nation, head of state. And in the US, just over there, their president is the head of state. They don't have a monarch. They have a constitutional republic. Up here in Canada, we have a constitutional monarchy. So we each have our own constitution. They're both very similar. The only big difference between the two is that the United States has the right to bear arms. Whereas in Canada, that's not enshrined into our constitution, unfortunately. So that's the only big difference in our constitution. We still both have freedom of assembly, freedom of speech built into our constitution. Whether or not the government on both sides of the border adheres to that all the time. That's another story for another vlog channel. Not here, but it is in our constitution. In Canada, we have our own, US has their own. You hear about it a lot in the US because they're very proud and protect their constitution very, very diligently. Same thing up here, we just, you just don't hear from us, mind. We're like the quiet neighbor. Like the quiet brother. You know, we're the quiet brother in the US next door. He's the loud brother. You know, everybody knows him. He's the popular guy. He's the school jock, like the football player. You know, he's got big muscles and everybody likes him. Whenever he walks into a room, everybody goes, ooh, America's here. And then we walk in right beside them and they're like, who's that? Oh, there's his little brother. That's nice. America! We're very close. Our militaries are very intertwined. We have combined defense across North America and our Air Force and all other military. Last week, we had military vehicles and troops on our soil in New Brunswick, I believe, training with us, so they come here all the time, train with us. We go there, train with them, and we work sort of as a single unit. Two separate countries, but we work very closely together. Okay, an attack on one is an attack on the other. Sort of like, you know, it's like NATO. Sort of, but this, we're very close. Yes. That's what I'm trying to say. That is going to be a long wait, I think. Ah, bye. Ah, bye. The good people let us in. Here's the sign as evidence. North Dakota. Be legendary. Remember that. I always remind you. If you come to North Dakota, that's the one thing they ask. Be legendary. It's on their sign. Minnesota is right there. Oh yeah, it's out of those trees. That's a river right there. That's the Red River. I'm going to go into Pembina here and go over the Red River into Minnesota, and we're going to head down to Thief River Falls, Minnesota. The port of entry that I have to go through is just on the North Dakota side. That's why we're here. North Dakota is a beautiful state, though. It really is. I bug them about their slogan, be legendary, but you know, it may look boring and flat here on the west side of the state, but you go to the east side and start getting into those hills. It's beautiful. Beautiful. It's a beautiful state. Anyone living here should be proud to be from North Dakota. Okay, and I understand the rest of the states always forget that you exist. I understand because I'm from Manitoba, where I'm from, all of the rest of the provinces in Canada forget that we exist, too. But you and I, Manitoba and North Dakota, we both know each other exist. We got each other's backs. Flyover states unite. Right? We got you. People may not want to come here touring all the time, but that's okay with us, right? That's okay. We like the peace and quiet. We like the open space. Just a bunch of peaceful farmers and truckers leave us alone. We'll leave you alone. Right?  I promised I'd be good. I'm actually going to pull in the gas tracks here real quick. I'm going to use their facilities here for a second. I'm going to go right down that way around town and down Old Highway 75. But first, it's the first truck stop into the United States from Manitoba, and they get quite a bit of business here. It's usually quite busy. Oh, yeah. Oh, yeah, potholes. That's okay. I forgive you because Winnipeg's potholes are worse. Believe me. I just about got thrown into another dimension driving through Winnipeg on the way back from the airport the other day. Couldn't believe it. Couldn't believe it. The state of the roads in Winnipeg right now are... There's no words to describe them. You have to bring a helmet, okay? So I've dropped off my trailer in Thief River Falls, and I'm on my way back, Bob. No trailer behind me. And I finally got the opportunity now to stop in Carlstead, Minnesota. I want to check out these mattress tracks or whatever these track systems that they make here. Remember I always talk about them when we go through here? I make them here. And I want to go and take a look at them. Remember they had that smart car with tracks parked on the side of the road? This is where we're at now. They don't got the smart... Oh, it is there still. Yes. It's awesome. Okay, look at this thing. So this is what they make here. Mattress. I guess they work on any vehicle, right? Even smart cars. Look at this. I want a smart car? No problem. Mattress got you covered. Who needs a snowmobile? Take this thing to work and then take it into the bush right after. Can you go down the highway with these things, I wonder? It's plated. It means it's registered and licensed, right? Is that legal to take it down the highway with the tracks? I wonder, right? You can get the tracks for these side-by-sides too. This is a Kanan. This is a Canadian brand made in Quebec from Bombardier. But those mattresses are all American made. Correct me if I'm wrong. I believe Kanan is Canadian, right? I might be wrong on that, but I'm pretty sure that's Quebec. And then you got a Hummer H1 here. I wonder why the tracks on the bottom come out so far like that. I guess just to go underneath the body, right? That would make sense, yeah. Look at that thing. I wonder how much they want for this? Think it's for sale? $5. It's probably worth a lot more than that. I'm just joking. That's a real H1 Hummer. This thing's worth probably $100,000. Super cool, eh? We're just over the border back into Canada now. And remember how I said it was all Ukrainian settlements as soon as you get over the Canadian border? We're into the first Canadian town, the border town, inside Canada. And this is Tolstoy. And right here is the Tolstoy Ukrainian national home. And you can see on the flag pole up ahead there, there's a Ukrainian flag. The wind has got it all twisted up on the pole there. And over here, the general store, it's got a Ukrainian flag flying up there. Canada flag down below on the bottom right. This is all Ukrainian settlement. So here, the next town up and pretty much all the way up Highway 59 here is all Ukrainian settlement until you get up to, say, Malo where it then turns into French settlements. And you go through the French settlements and you get to Hanover municipality which is where I hail from. The Germans and the Dutch. Together we have built a great land right between the rivers because the French settled along the rivers, right, in the inland part where Steinbeck is and Lakeler, that was the Mennonite reserve, the East reserve that was reserved for us for our exclusive use by the Crown. And later on they took that away from us, but that's a story for a different time. That's a different part of history, we'll talk about it another time. But Steinbeck was the East reserve for the Mennonites and the Germans and Dutch Mennonites, right? And then you come down here, you get our Ukrainian friends. So Manitoba has a deep connection to Ukraine. This is just one of many, this is a small town but Canada, especially Manitoba here, has the largest population of Ukrainians outside of Ukraine. And since the whole conflict out there has started and since the war has started out there and their country got invaded many millions of them have fled as refugees and many many of them have come here to Canada and many have landed at our airport in Winnipeg and when I was traveling to Toronto there was a big sign there with the Ukrainian flag in our airport and said welcome Ukrainians. So personally, here right now I want to welcome Ukrainians here to Manitoba in Canada. If you're here in Manitoba and you've been fleeing the war in your home country first of all, I'm glad you're safe. And I hope all of your loved ones made it out as well and if you have any loved ones back there fighting we pray for them and hope the best for them every day and we hope for victory. But I welcome you here to Canada. There are many of your fellow Ukrainians here already and we're blessed to have you here with us. So enjoy your stay here and have some Tim Hortons. Enjoy the full Canadian experience. Go see a hockey game and go play in the snow because we still have snow and it's April. I'm sure you're itching to get back home and rebuild as soon as you can. So until that day comes, enjoy your stay. I can't imagine having bombs falling down in your home region. Like living here in town I look outside of like, can you imagine just one day you're just living your life and then the next day is like...  You got soldiers coming up to your house here stealing your TV and for some reason they're stealing people's washing machines and stuff and just tying people up and shooting them and can you imagine? So I feel for them. And so if they end up here at our airport, absolutely, I welcome them into our community. I hope they have a nice stay and I know that they're going to want to head back when this is all over and rebuild. So enjoy your stay. Have a cup of Tim Hortons. Don't forget. Okay, go see a Winnipeg Jets game if you're able to. At the very least, I hope you find comfort here because you're safe, you're safe here. This is a very safe area of the world. That's why we're here. Thanks for tagging along with me today, everybody. Tomorrow's another day of truck and I hope you join me. Don't forget to subscribe if you haven't already and don't forget, hit that like button. A lot of you always forget. It does help me a lot with the algorithm. If you want to leave me a nice comment down below, go for it. If not, it's your choice.  I'm still welcoming you back tomorrow.


Item Number – SCP-431 Object Class – Euclid Special Containment Procedures – Backup copies of all Foundation documents are to be kept at site – Any documents and or photographs SCP-431 is found in are to be stored in said site's local database and replaced with their backup copy. Any personnel who report recalling SCP-431 are to be immediately questioned. Office 25 is to be inspected daily for any new objects. Foundation archives are to be monitored for any changes or new documents regarding SCP-431. Description – SCP-431 is the designation given to Dr. Gideon, a man who appears to have been a Foundation researcher. Due to the condition of records at present, it is not known if Gideon is his real name. The existence of SCP-431 was first discovered during what appeared to be an attempt to hack the Foundation database. A number of documents were altered to state that a scientist referred to as Dr. Gideon was involved in researching several SCP objects. However, it was determined that the documents in question were not being accessed at the time that they were modified. Since the initial event, references to a Dr. Gideon have appeared in many additional documents. Every time a document has been altered, it has been shown that it was not in use at the time of modification. Several new documents also appeared, a number of which are SCP documentation of items that the Foundation does not currently possess, including a data expunged and one-time item, a data expunged, which is known to currently be in the possession of Marshall Carter and Dark LTD. A number of objects have also been discovered in Office 25, which is currently vacant. It is not known when items begin to appear inside it, as the office was only investigated when a Dr. Gideon name-placker appeared on the door. Documents have been recovered from the office, including a photograph, Document 431, which is believed to depict Dr. Gideon alongside three known Foundation personnel. Security camera tapes dated expunged show a man who is believed to be Dr. Gideon, conversing with a number of researchers. None of the researchers report ever working with anyone named Gideon, and none show signs consistent with the administration of amnestics. No information concerning Dr. Gideon's hiring by the Foundation exists, nor does any documentation indicating that Dr. Gideon was either fired, terminated, or quit. One document recovered from Office 25 appears to have his fingerprints on it, as the fingerprints have no match within the Foundation's or any government's fingerprint database. No government documentation regarding anyone named Gideon matching the description of the individual in Document 431 exists, including birth, death, census, or tax information. By date, the last documents available presently state that Dr. Gideon was scheduled to oversee the neutralization of an SCP object. However, the document refers to the object being neutralized as SCP a designation not currently in use. No documentation has appeared describing SCP- Lesson complete. If you missed the previous orientation, go watch SCP-430, a peasant's punishment, right now. Or for the complete course, watch this playlist.


Hello and welcome to this session. This is Professor Farhad and this session will look at disposal of assets. This topic is covered in a financial accounting introductory course, as well as the CPA FAR section. As always, I would like to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1,600 plus accounting, auditing, finance and tax lectures. This is a list of all the courses that I cover, including CPA questions. If you like my recording, please click on the like button, share them, put them in playlists, subscribe. If they benefit you, it means they might benefit other people, so share the wealth, especially these days with the coronavirus out there. And please connect with me on Instagram. On my website, you will find additional resources to supplement your accounting education, as well as your CPA preparation. I strongly suggest you check out my website. In this session, we're going to get to the last part of having a plant issue, the last part of its life. And what are the life of a plant asset? First, we acquire the plant asset and we have to worry about computing the cost.  Check the playlist. Then we have to determine the depreciation, which is allocating the cost to period benefit. We already covered this topic. We also have to account for subsequent expenditure. We looked at that topic. And the last thing, once we are done with the asset, we dispose of it. And in this session, we're going to see how we can sell it. So we're going to dispose of the asset by selling it. Now, selling it is not the only option. We could also exchange it. Now, in this recording, we're going to focus on selling the asset. So what are the steps and how when we sell an asset, what are the procedures? So the first thing we have to understand is, and you're going to see why that's important, is we have to update. We have to update our depreciation to the date of the disposal. This is important. Now, why? Why this is important? Because when you sell the asset, you have to find the book value. And if you don't know what the book value is, we talked about the book value in prior recording. The book value is the cost of the asset minus accumulated depreciation, gives us the book value. So we have to have the proper book value. Now, why do we have to have the proper book value? Because once we have the proper book value, we determine whether we had a gain slash loss on the asset. So that's why the book value is important. And to get to the book value, you want to make sure your depreciation is up to date. What does that mean? It means you might have the asset. This is year five. You might have the asset depreciated as of year five. Then you sold the asset sometime in year six, sometime in year six. Guess what? Then you have to make sure you book the depreciation all the way until the date of the disposal, which is the X is the date of the disposal. So the first thing you have to do is to make sure your depreciation is up to date. And you will see why that in a moment. But I want to emphasize this point because that's the first thing you need to do when you are selling an asset. Is your depreciation up to date? This means your book value is up to date. This means your gain and losses are correct. Then you journalize the entry after you book the depreciation. First, if you receive cash, you debit cash. When you sell something, you would receive cash. Sometime the asset is so bad, you have to pay cash to get rid of it. You credit cash. So sometime we might pay cash, we might receive cash, sometime we might have to pay cash. You need to get rid of the asset. So basically, what are we looking at here? You have to remove the asset. And by removing the asset, remember the asset, if you have an asset, client asset, it has a debit balance. So to remove the asset, you have to credit the balance. So removing the asset by crediting the asset. So this is why the asset goes down to zero. And remember what comes with the asset is an account called accumulated depreciation. Remember accumulated depreciation is a contra asset account. It has a credit balance. So it has a credit balance. So to get rid of it, we have to debit the balance to make it go down to zero. So if we paid cash, we credit cash. If we receive cash, we debit cash. Then we remove the asset, remove its accumulated depreciation. Then we have to determine whether we had a gain or a loss. We have to record either a gain or a loss. Again, the balance of a gain is credit. Gain are like revenues. They increase your asset. They enhance your asset. Losses are like expenses. They take a debit balance. So those are their balances. Now, how do we determine whether we have a gain or a loss? And this is what trip students a lot. So now on the next slide, I'm going to tell you how do we determine whether we have a gain or a loss. So please listen to the rules carefully because you want to get them right the first time. And once you get them right, you're good to go. How do we determine whether we have a gain or a loss? Here are the rules. If the cash received, if we received cash more greater than the book value, the book value is what? Again, the book value, sometimes it's giving, sometimes you have to compute the book value. If it's giving, it's easy. Otherwise, its cost minus accumulated depreciation will give you the book value of the app. If the cash that you received is less or if you had to pay cash than the book value, you have a loss. So this is how you determine the gain or the loss. Did you receive cash more than the book value? Or did you receive cash less than the book value? If you received cash exactly equal to the book value, you have no gain and no loss. Once again, you would record the cash, whether you received cash or paid cash, you remove the asset, remove the asset, remove its accumulated depreciation. Basically, those steps, they go hand in hand because it's the same thing. When you remove the asset, the accumulated depreciation is part of the asset. Then you record the gain or the loss based on these formula. Now, the best way to illustrate this is to work a few examples. Let's look at a machine that has a cost of 9,000. An accumulated depreciation of 9,000 is of December 31st of the prior year. So if I stop right here and usually I will ask you, what is the book value of this asset? Here's what you should be thinking. We have an asset, a machine. The machine has a cost, which is historical cost of 9,000, and it has an accumulated depreciation of 9,000. So if I ask you right now, what's the book value? Well, the book value equal to zero. Why 9,000 of the cost, which is the cost of the machine, minus 9,000 of accumulated depreciation of accumulated depreciation will give us a book value of zero. So the book value of this asset equal to zero was discarded on June 5th of the current year. So it was fully depreciated. So we don't have to worry about updating the depreciation because it's fully depreciated. There's nothing to depreciate anymore. And the book value equal to zero. It doesn't say we received cash. It doesn't say we paid cash. Good. And it says the company is depreciating the equipment using the straight line method over eight years with zero salvage value. So they already told us it has been depreciated. Did we receive any cash? Do we debit cash, credit cash, no cash? Now, do we have a gain? Do we have a loss? Well, if you did not receive cash and the book value equal to zero, so cash zero equal to book value of zero, there's no gain, no loss, no cash. What's left with is we have to get rid of the machine. We have to credit the machine 9,000, make it go down to zero, and debit the accumulated depreciation to get rid of this to bring it down to zero. Okay. So notice now there's no gain, no loss, and we get rid of the machine. That's pretty straightforward. No cash involved, no gain, no loss. Doesn't get any simpler or easier than this. Now, bear in mind on the balance sheet, on the balance sheet, the machine is worth zero. Why? Because the book value is zero. So on the balance sheet it's zero, but we need to remove it. Let's take a look at another example. Equipment costing 8,000. So start with 8,000. We had a cost of equipment. It has a cost of 8,000 debit balance with accumulated depreciation of 6, and we have accumulated depreciation of 6. If I stop right here, as of December 31st of the prior year, of the prior year, let's stop right here, of the previous year, if I ask you right now, what is the book value of this asset as of December 31st, and hopefully you know the book value of this asset equal to 2,000. Okay. It was discarded, sorry, let's go back. It was discarded on July 1st. It was not discarded December 31st. So before we get rid of it, we have to update the depreciation as of July 1st. Well, January, February, March, April, May, and June. We have to depreciate the asset for six months before. So this amount, that's going to go up. The company is using the straight line method over eight years with zero salvage value. That's easy. If they have an asset of 8,000 with a cost, it's being depreciated over eight years. So every year, you depreciate the asset by 1,000. Now we only have to depreciate it for half a year times half. So we have to update depreciation by 500. So the first thing we do is we debit depreciation expense by 500, credit accumulated depreciation by 500. Now we have an additional 500 as of the disposal date. Therefore, the accumulated depreciation is 6,500. Now if I ask you, what is the book value, the book value equal to 1,500. 1,500 because 8,000, 8,000 of the cost, 8,000 minus 6,500 equal to 1,500. So that's my book value. Now we get root of the asset and we did not receive anything. We did not receive cash. So what happened? What's the cash? The cash equal to zero. So basically, I received nothing and I get root of an asset that's worth 1,500. Guess what? I have a loss of 1,500. So I remove the asset. I credit the equipment. I remove the asset. That's part of my part of the entry. The asset is gone. Then I have to remove its accumulated depreciation. I have to debit this account, 6,500. Let's go down to zero. And so I remove the asset. I remove its accumulated depreciation. Well, I did not receive any money. I lost. I have a loss of 1,500. Why is a loss? Because zero cash compared to 1,500. Guess what? I have a loss of 1,500. I received no cash. Let's take a look at another example. March 31st, BTO sells equipment with an original cost of 16 and accumulated depreciation of 12,000 as of 1231 of the prior year. So if I ask you, what is the book value as of 1231? The book value as of 1231 is 16,000 minus 12,000. So the book value is 4,000, but I did not get rid of it on 1231. I get rid of it on March 31st. It means I have to book an additional three months of depreciation. Let me show you the T-account. So I have the equipment of 16,000. I have accumulated depreciation for that equipment of 4,000, but this was as of 1231. BTO uses the straight line at 4,000 per year. So they're given us 4,000 per year. All what I have to do now is book the depreciation for three additional months. So if it's 4,000 per year, well, I have four quarters. I sold it at the end of the quarter. I have to add 1,000 of depreciation. Now, when I'm selling the asset, sorry, the accumulated depreciation is 12,000, not 4,000. I apologize. 12,000. The book value is 4,000. I have to add an additional 1,000 of accumulated depreciation. Therefore, my accumulated depreciation as of 331, as of the disposal date is 13,000. It means my book value equal to 3,000, which is 16,000 minus 13,000. And the equipment was sold, guess what, for 3,000 exactly. So the book value is 3,000. It was sold for 3,000. So what's my gain or the loss? Nothing. So first, I update depreciation. I have to book this $1,000. I debit depreciation expense, credit accumulated depreciation. As a result, my depreciation is up to date because that's always step one. Step two is compute the gain or the loss. And I already told you there is no gain or no loss because we sold it for 3. And the book value equal to 3, we have no gain and no loss. But we received cash. So we debit cash, 3,000. We have to credit the asset to bring it down to zero, bring it down to zero. We have to credit the asset. Now, the balance for the asset is zero. So this asset is gone. And we have to debit this account 13,000 to get rid of accumulated depreciation. So no loss, no gain. And we receive cash. Let's assume we're looking at the same exact example here, the same exact example, except that we sold the asset for 7,000. So same thing, same example, except we sold it for 7,000. Now, cash equal to 7,000, greater than the book value, which is 3,000. Now we have a $4,000 gain. Well, everything else is going to stay the same. So we're going to update the asset. Now, we're going to receive the cash. The cash is 7,000. So not 3,000 anymore. So if we receive more than 3,000, every dollar more than 3,000, for every dollar in addition to the 3,000, we're going to have a dollar in gain. How many dollars do we have more than 3,000? We have 4,000. Therefore, we have a gain of 4,000. Therefore, we debit cash. That's easy. We get rid of the asset, get rid of accumulated depreciation. The only difference now is we have a gain of 4,000. We have a gain of 4,000. Let's assume the same exact example. Now we sold the asset for 2,500. What does that mean if we sold it for 2,500? If we sold it for 2,500, we have a loss of 500. Why? Because the book value of this asset is 3,000. Therefore, the first entry is the same. Now we receive cash of 2,500. We have to get rid of the equipment, get rid of the accumulated depreciation. Notice this entry is the same. Notice this entry is the same. We get rid of the equipment, get rid of the accumulated depreciation. It's the same. Whether we have a gain, we have a loss or we don't have anything. Notice it's the same. This entry does not change because we need to get rid of the asset. That's the same. In this scenario, we have a cash of 2,500 and we have a loss of 500. Simply put, for every one dollar below 3,000, we have to book a loss. Now we have 500 dollars below 3,000. Therefore, it's going to be a loss, a loss of 500 dollars. That is basically selling the asset at either break even, break even, which is no gain, no loss, a gain and a loss. Make sure you know the rules. Those are pretty powerful concepts you need to be familiar with. In the next session, we would look at natural resources. Once again, if you like this recording, please click on the like button, share them, and if you're looking for additional resources, please visit my website. Subscribe if you haven't subscribed to my YouTube. Visit my website for additional resources. If you'd like to supplement your education or get those 7 to 10 extra points on your CPA exam so you can pass and move on. Stay safe, especially these two coronavirus days.


So, to address the issue of the key benefits of dairy products and bone health, we should remind that a well-balanced diet is mandatory, including both calcium protein as well as phosphorus and different trace elements and vitamins. In other words, there is no magic bullet, so it's unlikely that just dairy product could replace all the needs. However, since calcium and proteins are needed for ensuring bone health, this means that the source of calcium and protein, like dairy products, are very useful since the dairy products are covering nowadays approximately two-thirds of the needs per day and between 14-50 percent of the needs of protein. And this is both easy because everything is within the same nutrient and relatively cheaper as compared with other sources of calcium and proteins. During the adolescence, the bone capital is doubling, so this means that it's an accelerated bone growth during which we need to mineralize the bone which has been newly formed. And the mineralization is obtained through calcium and phosphate. And then we need also some well-balanced diet including proteins, since the proteins are also the regulator of the hormone IGF-1 which promotes the growth of both in the longitudinal and radial way of the bone. First of all, in the middle age, between the age of 50 and let's say 16, the women where the menopause is associated with a marked increase in bone turnover and accelerated bone loss, well-balanced diet is certainly important but could not replace the lack of hormones. On the other hand, in the more advanced age, when there is a high prevalence of malnutrition, in this case, calcium proteins are the first for some mandatory. And instead of using supplements, when these components are included in the diet, it's much more physiological, and in terms of absorption, it's probably better. The different issue which should still be solved in terms of via goat and ballhands is the amount of via goat we should have to ensure enough control of bone turnover particularly in the elderly. Second of all, what we should also look at is the relationship with the muscle, how much yoghurt we need to have enough strength in the muscle, and finally, there is a major interest to see how the yoghurt could modify or not the flow of large intestine to improve the absorption of calcium.


In this presentation we will discuss budget options first. We're going to go through the components of the master budget We took a look at this in a prior course in prior presentations in detail in terms of going through each component of the master budget want to take a look and review those Components of the master budget we did so last time in terms of a static type of budget We're going to be focusing here on other options including a flexible budget So we have the sales budget That's the first component that will start out when we're creating basically the master budget type process Remember the end line the end level the bottom line that we're going to be getting to Will be the buzzed budgeted financial statements the balance sheet the income statement also important to have the budgeted cash Statement so all the cash flow budget the budgeted income statement the budgeted balance sheet the income statement and the cash Flower kind of the activity the performance type things we're considering usually the things we


Statistics and Excel. Standard deviation versus average deviation. Get ready, taking a deep breath, holding it in for 10 seconds, looking forward to a smooth, soothing Excel. First, a word from our sponsor. Yeah, actually we're sponsoring ourselves on this one because apparently the merchandisers, they don't want to be seen with us.  Like our, trust me, I'm an accountant product line. It's paramount that you let people know that you're an accountant because apparently we're among the only ones equipped with the number crunching skills to answer society's current deep complex and nuanced questions. If you would like a commercial free experience, consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com. Here we are in Excel. If you don't have access to this workbook, that's okay because we basically built this from a blank worksheet, however, starting in a prior presentation. If you do have access to this workbook, three tabs down below. Example, practice blank. Example, in essence, answer key. Practice tab having pre-formatted cells so you can get right to the heart of the practice problem. The blank tab, we started with just a blank sheet so that we can practice formatting the cells within Excel as we work through the practice problem. Let's do a quick recap of what we have done in prior presentations as we have been calculating the average deviation and the standard deviation where we will now be thinking about the comparison between the two and why we might be using or its standard to use the standard deviation as opposed to the average deviation even though the average deviation is a little bit more simple and it's a little bit more intuitive in some ways. In other words, we kind of thought about the process of what if we wanted to come up with a number and we didn't know about the standard deviation and we're trying to just intuit and think from scratch how we would do it to represent the spread of the data, the dispersion of the data around the center point, the mean. The first thing we would probably do is start to think of something like the average deviation. We would say if this is our data set, we only have four data points, the average of this data set is zero for this particular data set, summing them up dividing by four. If I take each of those data points minus the mean, this is the distance from the mean. However, I have negative numbers here so what I would do then is just simply take the absolute value giving us the distance from the mean 20 and then just dividing by that. So we've got the average deviation, right? We took the average of the distance from the mean to give us an idea, a number to give us that dispersion, that spread kind of idea. Here's the histogram of our simple data set, the mean at zero. We've got data points on the negative and on the positive side of that zero. We compare that to the standard deviation, which you could break out to that everything under the square root sign being the variance and then this is the standard deviation. So now what we are doing, we're going to do the same starting point, we'll take a comparison to the mean, but instead of taking the square root, instead of taking the absolute value that is, we square it. So we have that same kind of characteristic of removing that negative number, which is important, but now we've squared it so we of course come up to a bigger number, the 104 versus the 20 when we sum it up. So, and then we can divide by the count, which is four, and that would give us the variance, this number, and then if we take the square root, that gets us to the standard deviation. This is for a population calculation as opposed to a sample. Notice it's similar, but it's typically higher than what we have when we did our average deviation. But you get a similar kind of calculation, a similar concept, and then you could of course do the same calculations with Excel formulas with the variance for the population and the standard deviation for the population. So now the question is, well, why would I use this one instead of this one if this one is actually a little bit more intuitive, a little bit more simple, because we would typically want to have things more simplified if possible in math usually unless there's a reason. Well, we can see that this calculation gives us the same kind of idea and it removes the negative numbers, which is nice, and it also gives us basically like a unique number. And so let me drill down on that a little bit more. So let's compare and contrast this as though we're comparing every point to something other than the mean for the average deviation. So here's what I mean. I'm going to make a skinny AA. I'm going to put my cursor on the data over here. I'm going to copy the data and I'll paste it on AB. I'm going to make it into a table again. It looks like a table, but it's not a table because it's just looking at the format of the data. Insert tab up top, tables. Let's put a table around it. And so there we have it. And then I'm going to compare it instead of to the mean. I'm going to compare it to a point one, which is not the mean. That's the key. We're not comparing it to the mean. We're just going to compare it to one instead of the mean. So let's compare each one equals the one above it to one. I'm going to copy that down. So instead of comparing to zero, we're comparing to one. We're going to take the difference. And so this is going to be equal to the negative six minus the one instead of the mean. And that gives us our differences from the point of one. So then we're going to take the absolute value because we're looking at the average. So we're using this format. Taking the absolute value. So I'm going to say absolute value absolute value is going to be equal to ABS. That's the function for it. Double clicking on the ABS. And that's going to give us just flipping the sign to all positive numbers in essence. So there we have it. Let's add a total column down below and go to our table and table style options. Adding the total. And then on the data, let's make this one the average. So that came out to zero. So we're not picking the average. We just picked a random point of one instead of the average to be comparing to. And this is the count. Let's do a count here just counting one, two, three, four. And this one, let's do the sum. So I'm going to sum these up. And we don't come out to, you'll note, zero as we typically would if we're using the point of the mean. Because the mean is the middle point by definition. We didn't choose the middle point. So now we come up with differences that in this case add up to a negative four. But the absolute value of them still adds up to 20, which is the same thing when we did it this way, right? So if I was then to do my calculation down here and say that we're going to say this is the sum of distance from point instead of the mean from the point one is going to be equal to the 20. We're going to divide that by the count. So we'll divide by the count, which is n, the number, which we have as four, that's the same. And I'll underline that font group and underline, and that's going to that's going to give us our result. I'll just say this is going to be equal to the 20 over four. And let's add some decimals home tab number add some decimals we get to the exact same number of five. Even though we took we took the count from one instead of instead of from zero. So we're not getting like a distinct number as as by by by using the mean versus any other point, right? We could do it for another point like if I let's go ahead and put some brackets around this and make this blue. Let's do it again. I'm going to copy the whole thing putting my cursor on the skinny column. So we'll copy the skinny all the way to AE right click and copy. And then I'm going to put that on AF right click and paste. So there we have this. And now let's say let's just do the same thing, but we're going to say point number two. Right. So now we and you can see that I just changed that one number and we get the same the same result. The sum of the different distances is now eight. If I take the absolute value from point two instead of zero, the mean or point one, I still get to 20 and I get the same number. Right. And let's just do it one more time. If I copy from the skinny to AJ right click and paste, then I'm going to make this one a three. Right. And we get to that same number five. Now if I instead do the same kind of test, but but I use my my standard deviation calculation. Let's do the same thing. Let's copy this over. Let's just copy this part of it over. I'm going to or let's I'm going to right click and copy. And then paste that here. Right click and paste. So notice this is not a table anymore because I only copied part of the table and I don't need this bottom bit. Let's delete. Well, let's I'll just delete what's in it. And then let's enter a table in here.  So let's actually delete this. I'll just say delete and let's go home tab format. I'm just going to format the cells like that. All right. So I'm going to go to the insert to tables and insert a table. So there we have it. Let's make this a little bit smaller. All right. So now instead of now we have the difference. Now we're going to take the squared. We're going to take those amounts and square them. That was the differences between the absolute versus they're going to be squared. Let's say squared. Hopefully that's spelled right. This is going to be equal to one above it. The one next to a carrot. That's how we represent to the power of with a carrot to which is squared. Enter. So there we have it. Let's put our totals back in table design. We're going to go to our totals. So let's say this one is going to be the sum. So it comes out to zero. But I'm going to go back to point number one again. So let's go to point number one. Let's change my headers. This should be point number three. This should be point number two. So now we're using one instead of zero. So if I add those up, if I count these, we're going to say give me a count. That's going to be four. If I look at the sum of the differences, it comes out to 12 instead of zero. If I use the mean here, zero, and I look at the sum of the differences, it's not picking up this calculation properly. This equals this minus this. There we have it. It would be zero. Okay, so then I'm going to change this to one. And now I come out to four. That looks correct. And then over here, squared, if I sum up the squared items, then it comes to 108 instead of what we had when we did this with zero, which it was 104. So now let's do the bottom bit here. I'll go ahead and maybe I'll try to make this easier. I'll copy what we did over here. So we've got the square difference, this whole bottom bit. I'm going to copy that and I'll put it over here. Right-click and paste. So now as we copy that over, however, notice that this is no longer the variance as we have defined it or the standard deviation because we're not using the mean, but rather this point number one. This is pulling from the wrong table. So I'm going to say this should be coming from this table. This should be coming from this table dividing them out. That looks correct. And the point is that we now come out to the 5.2 instead of what we had before, which was 5.1. So you can see the point is by using the standard deviation, we come up to basically a unique value when we use the mean as opposed to any other point and we did the same kind of variation from a different point, which is we don't have that same characteristic when we take the average. So if I did that again, if I copy this again, I know I did this kind of quickly, but if I go from A, the skinny to AT, right-click and copy and I paste that in AU and paste and make this a number two, number two. So now if I look at my total, it comes out to 120 and so that's coming from the right table. So now we come up with a value of 5.48. So notice that's another kind of reason why it might be more beneficial to use the standard deviation to use this formula, standard deviation, rather than possibly a more intuitive formula of the average deviation because the standard deviation gives you that kind of unique value if you're calculating around the mean rather than any other point. I'm also just going to remove here the variance and the standard deviation because these aren't the variance and standard deviations as defined by the formula because here we've changed the mean, which was zero to point number one in this case and point number two in this case just for our demonstration and comparative purposes.


In addition to my role as founder of Clean Al Gambia, I sit in the United Nations Secretary-General's Advisory Group on Climate Change, which is the YAG. So we have obviously heard from the different panelists about the innovative approaches that they're using to address the sustainable development goal problems that we're facing. But if you look around the room, you will see that there are so many young people sitting here. This shows that youth obviously are very much interested and eager to learn and also collaborate in addressing the problems that we're facing. I come from a continent, Africa, in which majority of our population obviously includes young people. So over 50% of our population constitute of youth. And in our communities, youth have been leading and driving innovative solutions in addressing the problems that we're facing by using digital tools to support communities that are impacted by climate change. For instance, we see small-scale farmers as well as other vulnerable groups that are affected by climate change having young people in the front line providing tools that will also not only provide early warning systems for them, but also supporting them in just their activities in general. But the sad reality is with the innovative work that young people are doing around the world, there are obviously gaps in how well young people's skills and experiences have been utilized. So what our advice or my takeaway from here and a takeaway to everyone present here is, first of all, we need to build more partnerships with young people that are in the front line addressing the climate problems that we are facing. As I always say in my conversations, the government can't do it alone, the private sector can't do it alone, and young people can't do it alone. So we need collaboration and partnership in advancing the sustainable development goals that we're facing, especially climate-related issues. So when I'm talking about partnerships here, I'm talking about long-term partnerships that will include financing youth projects that are addressing climate problems that we're facing. Because I've observed that most of the partnerships and the funding that young people have been receiving have been shut down. So for us to ensure that we find effective and sustainable solutions to the problems that we face, there needs to be a long-term partnership with these young people at the local level where it matters the most, where at the grassroot level where it matters the most. In addition to that, we need to ensure that more platforms are provided for young people, platforms like these, where young people will share the solutions and the problems in their communities, as well as what they have been doing in supporting communities to build their resilience and address and climate-related problems. And finally, obviously, as I always say, with the work that we continue to do, with the knowledge that we continue to have and the skills that we continue to build along the way, it's also important to have platforms where we will continue to build the capacities of young people and also increase their level of awareness. Because some of us are in this space, we have been able to build our experiences, but there are thousands and millions of young people around the world who still need opportunities for them to be able to learn as well as grow, to be able to lead sustainable solutions in their communities and beyond. So to private sectors around here, to the government around here, we need solid partnerships with young people. We need to build strategic collaborations with these young people at the local level, at the grassroot level, supporting their projects, supporting their initiatives that are advancing climate solutions. Thank you so much.