For the Marines, the Sailors, the Marine Fighter-Attacks Squadron 242, and the members of USS America Crew, the eyes of the world are on you and your ability to integrate with our key ally. I want you all to remain focused and ensure the successful execution of this critically important capabilities test that you should be very proud to be a part of. For members of the region who will be watching closely, the state will have to recognize that bilateral interoperability demonstrated by this event cannot be accomplished by any other member in the region.


So, the notion of finding the coefficients of a power series through differentiation leads us to this concept of Taylor and McLaren series. So, if the McLaren series came first, given any function f of x with as many derivatives as we need, we can produce the McLaren series through successive differentiation. For example, let's find the first four terms of the McLaren series for y equals 1 over 1 minus x. So, again, our base assumption is that our function has a polynomial approximation which we can differentiate repeatedly. So, we'll assume that 1 over 1 minus x is equal to some polynomial. So, to find these coefficients, we'll substitute in values of x and get a system of equations that we can solve. If we substitute x equals 0 in the left and right hand sides of our equation, we get a0 equals 1. To get the other coefficients, we can differentiate repeatedly. The derivative of the left hand side is, and the derivative of the right hand side is, substituting x equals 0 gives us, and so all of our other terms drop out and we have 1 is equal to a1. We can differentiate again, and substitute in x equals 0 to solve for a2. Differentiating another time, then substituting in x equals 0 gives us an equation that we can solve for a3. And so by evaluating the function and its derivatives at x equals 0, we find the values of the coefficients a0, a1, a2, and a3, and so we can write down the first four terms of the McLaren series for 1 over 1 minus x. Now, the only problem is that our function and its derivatives have to exist at x equals 0, and that might not happen. So it's possible, and sometimes convenient, to generalize this process to form what's known as the Taylor series. Suppose f and all its derivatives exist at x equal to a. The Taylor series is the power series sum from n equals 0 to infinity an x minus a all raised to power n, where the coefficients an are determined through the values of the successive derivatives of f at x equals a. So let's find the first four terms of the Taylor expansion of y equals sine of x at x equals pi over 2. And we assume that sine of x has a Taylor series expansion centered around x equals pi over 2. So the first four terms of such an expansion will look like we'll evaluate the function at x equals pi over 2, where the point of using pi over 2 is all of our higher order terms are going to drop out. This gives us an equation we can solve for a0 and we solve it, which gives us the first term in our expansion. We'll differentiate our function. At x equals pi halves, most of the terms on the right hand side will drop out and will be left with an equation which we can solve for a1. Differentiating again, substituting x equals pi over 2 and solving for a2. Differentiating again, substituting x equals pi over 2 and solving. And so by evaluating the function and its derivatives at x equals pi over 2, we find the first four terms of our Taylor series expansion.


The Abaddon Custello Program, starring Bud Abaddon and Lou Custello, brought to you by Camel, the cigarette of costlier, properly aged tobaccos.  Godly said, he got up coming in here with those overhauls and straw hats. Oh, I'm in close abut, I've been out working in the garden all morning and I plant... Now wait a minute. How can you plant mashed potatoes? I use a hammer. I bet you're some gardener. What else did you plant? Well, I plant a row of onions, put some peas and another row of radishes. And then I got some lettuce and another row of radishes. Some more beans and another row of radishes. Wait a minute, wait a minute, wait a minute. And another row of radishes. Just a minute. Why did you put every other row of radishes? I can't help it, radishes always repeat on me. Forget about it, let's drop the radishes.  Well, I won't do any glow. Don't let it come right up again. Look, Castella, didn't you plant any tomatoes? I say, didn't you plant any tomatoes? Oh yeah, I planted a row of tomatoes, one at a part. Castella, now that's too close together. It'll squeeze the tomato and into a funny shape. So what, so what? What do you mean, so what? Did you ever see a short fat tomato? Yeah, I danced for one last night at the playground. Oh, talk sense, please. Did you talk sense, Castello? How's the dirt around your place, Lou? I don't know, I haven't heard any lately. No, no, no. I'm talking about the soil. What state is your soil in? State of California, dope. I'm talking about the condition of the ground. How's the dirt? Oh, it's no good, it's full of worms. I'm trying to find out if you have any weed. Huh? I'm trying to find out if you have any weeds on your...  And I pulled and I pulled. And what happened? Finally, this devil came up and said, look, Castello, when I want y'all's son for you. Well, I'd better help you. By the way, what are you putting in those two acres in the back of the barn? Ad libs till I find my place. You know those two new acres you have in the back of the barn? What are you, what are you planning in the back of?  Thank you, thank you, thank you. You realize... Huh? Do you realize what you're doing? What? What are you planning in those acres? Oh, putting a whole thing of Mexican Jumper Beans. And then when they grow up, I'll feed the Mexican Jumper Beans to the cow. It makes the cow easier to milk. Makes the cow easier to milk? Yeah, when the cow is full of Mexican Jumper Beans, I just grab a hole and hang on while the cow jumps up and down. Thanks, will you please? Will you please talk, Saint? Well, I've got to leave now. I've got to go out in the orchard and hang prunes on all the iron streets. Hang prunes on your iron streets? Who told you to do that? My Uncle Artie Stebbins? Uncle Artie Stebbins. He said my orange trees needed pruning.  Your uncle meant... Your uncle meant you should get a ladder and saw the limbs. Did you saw the limbs? Probably I saw the limbs. They were hanging right in front of me. No, no, no. I mean, did you saw the limbs off the tree? No, I saw the limbs on the tree. Look, Castello, I'm trying to tell you that your trees need trimming. You've got to trim it before the sap rises. I've got to trim it before the sap rises? That's right. What time do you get up? No. Please, Castello, now, if you want to have good oranges, you've not only got to trim the tree, but you must put a smudge pot under it. A what? A smudge pot.  Oh, sure. A smudge pot is a tin can that smokes and burns oil, and you can find them on any used car lot in Hollywood. No, no. Tell me, what kind of oranges grow in your trees? Oh, the regular kind, down ones. Look, please, are they Valencian or naval oranges? They're naval oranges. How do you know? I saw a sailor picking some. How can you be so stupid? You can tell the difference between oranges by the color of the juice. Did you ever squeeze one of your oranges? Yeah. Well, what came out? Milk. Milk? How could oranges have milk in them? Now tell me that. I got the tree from the nursery. Oh, come on. Come with me. We're going out in the backyard and look at your orange tree. I'm really after them tonight, ain't I? Come on, now. Hey, what I tell you is we're going out in the backyard and look at your trees. Hey, wait a minute. Hey, look out that window. There's a great big crow sitting up in your tree. Hey, that crow's got a lot of nerve. Abbot, hand me my sore-off shotgun. Okay. Hey, this gun hasn't got any handle. How do you like that? I showed off the wrong hand. You got it? Watch what you're doing. You're pointing that gun right at me. Don't worry, Abbot. Wait a minute. You want to shoot me? I've got my finger over the hole. Keep it there. Was that the crow? Yeah, that's the biggest old crow in this neighborhood. That's Mrs. Niles. That's terrible, Castella. Come on. Let's see what happens. Uh-oh. Here she comes, Castella.  And the law says whatever hangs out. I know. All right. Now don't answer. Castella, I apologize to Mrs. Niles. We're knocking her out of that tree. You want to apologize to me? What did I do? You said I'm not going to get away with this. I'm going to take you to court. I'm going to charge you with assault. I'll charge you with battery. I'll charge you with mayhem. And I'll charge you with attempted manslaughter. And it'll cost you a thousand dollars. What do you think of that? You can charge that, too. There were throat specialists and doctors who concentrate on the nervous system. There were diagnosticians and cardiologists and ophthalmologists. Doctors in each and every branch of medicine among the 113,000 doctors covered in a recent nationwide survey. It was a survey of cigarette preference. What cigarette do you smoke, doctor? Was the gist of the query made by three leading independent research organizations. And the brand most named was Camel. Camel. Rich, full-flavored, cool, and mild. Truly a superb blend of costlier tobaccos. Try Camel then on your own tea zone. That's tea for taste and tea for throat. A most critical laboratory for the testing of any cigarette. You, like so many doctors, may find that Camel suit your tea zone to a tea. According to a recent nationwide survey, more doctors smoke Camel than any other cigarette. For Camel fans everywhere, Carl Hoff and the orchestra play. Let it snow, let it snow, let it snow. Camel is going to press her suit against you. She can't press her suit against me, Abbot. I don't care for the lady. Young man, you can't refuse this, subpoena. I'm an officer of the law. Oh, you're an officer of the law? That's right.  Yes, I am. Give me a glass of water.  Don't get funny with me. See this scar? Yeah? Gunfight, 1941. You see this scar? I don't care for the lady. I don't care for the lady. Young man, you can't refuse this, subpoena. I'm an officer of the law. Oh, you're an officer of the law? That's right.  Yeah? Vaccination, 1946. And boys, you're that pick-out. Young man, you forget that I'm a sheriff. How do I know you're the sheriff? Read what it says on this badge. Donut, I always wear the wrong ones. Well, Castella, the subpoena says that you are to appear in court tomorrow morning at 10 o'clock. To answer, Mrs. Niles is charged.  Abbot, I'm too young to go to jail to say that I am poor boy who has never been away from my mother's apple strings. She'll become a victim of foul circumstances to be incarcerated behind cold-grave walls. Do you feel that way, Castella? No, but Universal Studios, call me to hand it up tonight if I got a chance. All right, luck.  This is serious, Lilith. The first thing you've got to do is get out and get some character witnesses. Everyone's doing no good at it. You mean you have no witnesses? I've got no character. Oh, don't talk to me. I've got to get out and get some character witnesses. Come on. I've got to see my old girlfriend, Tessie Tinfoyle. Fat lover, boy. Everyone tells me I have an hourglass figure. It looks like all the sand stopped at half past four. Filling in those Sunset Bus Slacks. What do you mean, Sunset Bus Slacks? Eventsus reporting. Hope gets nothing with it. I don't expect nothing. Tella, you came here looking for a witness. Remember? Oh, yes. Tessie, could you go to courthouse with me tomorrow morning at 10 o'clock? Oh, I'd love to, Louis. But I'm giving a lecture on biology tomorrow morning. You know, biology is one of my favorite subjects. And I can safely say that I know more about the human body than anybody else. You should. You had one longer than anybody else. Well, you didn't get yourself a witness there. Let's go next door and see Scotty Brown. He'll vouch for me. Punks are hard on the door, laddies. There's a burglar under the bed. Burglar under the bed? Didn't you call the police? No, the burglar's asleep. And when he wakes up, I'm going to charge him for a night's lodging. Hey, Scotty, I have to go to court at 10 o'clock in the morning. I'd like to have you appear as a character witness for me. I'm very sorry, laddie, but I have to go to the doctor's in the morning to have my hand dressed. I've got a terrible burn between my thumb and my index finger.   Scotty, can't we just come in for a minute and talk to you? No, you can't. My wife is in the living room, taking a bath.  Aye, laddie, the people upstairs let their bath to run over and it's licking through our ceiling and my wife is standing under the leak, taking a shower. Well, Castellum, you haven't got a character witness yet. Wait a minute, Abbott. Here's my friend, Fessy Maymucho. She's getting out of the car. Oh, yo-ho, Fessy! Time to talk to you now. I'm on my way to the Santa Fe Railroad depot. Santa Fe depot? Oh, Abbott, you know what that is. That's where you buy your train tickets. Where are you going, Fessy? I'm taking the Santa Fe back to Sin Sin Naughty. Sin Sin Naughty? Yes, you know where Sin Sin Naughty is. Oh, sure, that's back in the state of Ohuhu. It's fair to be toastmaster at a bonquat given by the Chomber of Comers. What could be more thrilling than being surrounded by a bunch of men at a bonquat?  You're too long now. The hustle of this is to you.  Castello, what are you going to do now? Well, hey, you know what I think, Abbott? What? I'm getting tired of asking my friends to be character with this old. You can always get more out of a stranger. I'm going to ask that new man to just move in next door. Come on, I'll tell him we're Abbott and Castello, and I'll bet he'll do anything for us. Go ahead. You're not in very good mood this morning. Who would be? I've been listening to the radio. These lousy, corny comedians and their bum jokes, tying prunes and an orange tree. Our glass figure with a fan stuck in one end.  Thousands of dollars a week for spale jokes. I'd just like to get my hands on one radio comedian. I'd throttle him. I'd tear him to bits. I'd break every bone in his body. I'd ram every one of those corny jokes down his throat. This month of April marks the birthday of a great man of medicine, and this, in a humble and respectful way, is a salute to him. His name, Dr. William Henry Welsh, pioneer in pathology, preventive medicine, public health, and sanitation. His researches are famous. His teaching and writings influence the entire medical thought of the country. So, this salute in his honor, and to every doctor before him and after him, whose lives and works are basic threads in the very fabric of civilization. The makers of camels cannot help but be proud of the standing of this cigarette in the medical profession. The query, what cigarette do you smoke, doctor, was put to 113,000 doctors by three leading independent research organizations. The brand named most was Camel. According to a recent nationwide survey, more doctors smoke camels than any other cigarette. And here is Camel's lovely Amy Arnell to bring you her celebrated personality. When Madame Pompadour was on a ballroom floor, said all the gentlemen, obviously. The Madame had the cutest personality. And think of all the books about the bearish look, or was it made her the toaster fairy? She had a well-developed personality. And what did Romeo that she knew how to, and what did Harry Jay see in Betty G or Garcin G? Oh, I wish I didn't. I wouldn't harm anybody because I am a boy scout.  What are those two stripes on your arm? I belong to the stunt patrol. Castello, you're not going to talk to me out of pressing my suit. Bayless, I demand that you swear in this defendant. Very well. The defendant, Lou Castello, raise your right hand and swear on this bar of soap. Swire in a bar of soap before. We want you to come clean. Don't worry, Castello. I've got you the greatest lawyer in town. Yes, and here I am, your old friend, Mellonhead. Ah, Castello, I'm a lawyer of the old school. Truth. Look, don't you make remarks about my bald head, Castello? After all, I'm a good egg. Why not? I'd rather have my other uncle jail. Where did he study law? He went to Vassar for four years.  Vassar happens to be a girl's school. Well, that takes a smart guy to get away with that, don't it? Well, he comes to judge. Hey, let's bring in the hip. Bring in the hip. Bring in the hip. Bring in the case. You forget to put the seats in the jury bar. The defense ready.  Now, how do you like that? Paper. No wonder he rustles when he walks. The tenant will kindly address the bench. Hiya, Ben. Castello, let your lawyer do the talking. Your honor, I am representing this defendant, Mr. Castello. It seems that my client, with malicious intent, took her shot at a poor defenseless woman while she was picking oranges out of a tree. He knocked her to the ground. He ruined her bucket, and he did her. He did her. Your honor, he did this woman great bodily injury. The defense read. Wait a minute, Mellonhead. Who's Friday you are? Castello kindly sit down in front. But Judge. I said sit down in front. I don't bend that way. Castello. Wait a minute, Castello. You can't talk that way to the judge. That's the most contemptible thing I've heard in all my years at the bar. Well, a little less time at the bar, you wouldn't be so contemptible. Castello, I told you to let your lawyer do the talking. That's right. Have it, Castello. You promise tell the truth, the whole truth, and nothing but the truth? I don't. Your honor, we plead insanity. What's that for me? This is a farce. I demand that you find Castello guilty. But Mrs. Niles, I can't do that. I haven't heard the evidence. Oh, please, Judge. Do I appeal to you as a man? You don't even appeal to me as a woman. You object. What for? I haven't had a line of contention. Well, stick around. Stick around, and I'll give you a sentence. Just give it. I need to keep quiet. You're only making things worse. Look, your honor, I'd like to plead my own case. I couldn't do anything wrong, really. I couldn't because I've always been very bashful and shy. I remember on my 12th birthday, my mother and my father was giving me a nice little dresser for my bedroom. I was so bashful, I kept the dresser turned to the wall. You kept the dresser turned to the wall? Why? I didn't want the drawers to show. Castello, I'll listen to your plea if you can produce a character with us. Okay. I'd like to present as a character with us a young girlfriend of mine, Miss Pee-Pee Leblanc. Here I am, Monsieur Castello.  Present this court. Are you kidding?  Oh, let her sit up here on the bench with me. I'm lonesome. Now, uh, Miss Leblanc, kindly tell the court your full name. Meme is El Pee-Pee H Leblanc. What does the H stand for? Hillside 2183. I object! You object? Yeah, she gave me Hillside 2184. Oh, what are you doing tonight, Pee-Pee? Oh, I'm sorry, Judge, but I'm going steady with Monsieur Castello. I will be true to him as long as he lives. Castello, I sent you to be hanged at dawn. Get out of here. You can't do this. My friend Castello is an honest man. An innocent man. He didn't mean to shoot at Mrs. Niles. I don't care about that part. He has no business wasting the time of a beautiful girl like Pee-Pee Leblanc.  In fact, Castello, you are entirely lacking in personal job. I wouldn't say that. Just put a razor in my hand and you couldn't tell me from Gregory Peck. Gregory Peck. While you were, there isn't a woman in town that would take a second look at you. Mrs. Niles is right, Castello, but I'll tell you what I'll do.  Are you kidding? Oh, thank you very much, Judge. I'll show you how you appeal to women. Ladies, this is your chance to kiss me. The line forms on the right.  I have no child. You're going to jail. Oh, wait a minute, Judge. Somebody is pushing you to crowd now. Look at them pushing. Kiss me, honey. And now tonight's salute to the men in the armed forces who won through to victory. Tonight we hail the 106th Infantry Golden Lion Division, heroes of San Viz in the Battle of the Bulge. Since the beginning of the war, the makers of camels have sent more than 150 million free camels to our fighting men overseas. But now, with demobilization and progress, free camels are sent to servicemen's hospitals instead. This week, the camels go to U.S. Army, A.A.F. Regional Hospital, Hamilton Field, California, U.S. Naval Hospital, Bremeter, Washington, U.S. Marine Hospital, Sheepshead Bay, Brooklyn, New York, Veterans Hospital, Perry Point, Maryland, Veterans Hospital, Chili Coffey, Ohio. In your honor, men of the Golden Lion Division. Our broadcasts go out to the United States twice a week. Our rebroadcasts to practically every area in the world were our ministation and to our good neighbors in Central and South America. And I'll hear about Abbott and Lou Costello the final word. Well, Costello, you kept yourself out of jail by kissing your car, didn't you? I knew I wouldn't go to jail, Abbott. I've never done anything wrong. Nothing at all. In fact, if the audience will just stay for an hour after the show, I'd like to tell you the story of my life. No, no! Not to be very interesting. Good night, folks. Good night, everybody. Good night. Good night, everybody. For another great Abbott and Costello show, brought to you by Camel Cigarette. And remember, try camels in your T-zone. See if they don't suit your taste, your throat, to a T. Why smoke a pipe? For pleasure, of course. So why not get the most pipe pleasure? How? With Prince Albert's tobacco. Why? Because it's choice tobacco, crimp cut to burn slow, cool. Because it's specially treated to take out tongue bites. Does that make a difference? You bet. Why more pipes spoke Prince Albert than any other tobacco on earth? Try P.A. today. Saturday night, be sure to listen to Prince Albert's Grand Ole Opry. You'll hear Red Foley, Grand Ole Opry's sensational new singer. He's got a voice that romantic his moonlight on the mountains, warm as southern hospitality. And the way Red Foley sings our great American folk songs make mighty fine listeners. Remember Grand Ole Opry Saturday night on NBC, with a duke of a duke, mini pearl, and Red Foley. Be sure to listen at this very same time next week for the Abbott and Costello show for Camel Cigarette. Thursday night is all star night on NBC. Stay tuned in for Rudy Valley over most of these stations. This is Cam Niles in Hollywood, wishing you all a pleasant good night for Camel. This is NBC, The National Broadcasting Company.


Statistics and Excel, Correlation Random Number Generation Example. Got data? Let's get stuck into it with Statistics and Excel. You're not required to, but if you have access to OneNote, we're in the icon left-hand side. OneNote Presentation 1730, Correlation Random Number Generation Example tab. We're also uploading transcripts to OneNote so that you can go to the View tab, Immersive Reader Tool, change the language if you so choose, be able to then either listen to or read the transcript in multiple languages using the timestamps to tie in to the video presentations. OneNote desktop version here thinking about correlation, having different datasets to see whether or not there's a mathematical relation or correlation between them. In other words, are the data points and the different datasets moving together in some way, shape, or form. If there is a mathematical relation or correlation between the different datasets, the next logical question would be, is there a cause and effect relationship which is causing the correlation or mathematical relation between the different datasets. And if there is a causal relation between the different datasets, the next logical question would be, what's the causal factor in the causal relationship which is causing the correlation or mathematical relation between the different datasets. Now, in prior presentations, we thought about a perfect positive and a perfect negative correlation which are great to consider in theory, but which are not usually the examples we have in practice where we don't have a perfect correlation, we usually have some kind of trend. We saw that in another example where we had a very simple trend of only four data points so we can really analyze the formula that we're putting together in a simple small or low data point example. This time we'll have more data points, but we'll actually generate the data points to get a conceptual understanding of how we're generating the data points and then what we might assume would happen therefore with the correlation and then we'll map that out. We'll also take a look at what it means to have randomness to some degree and what randomness kind of looks like as we go through here. So we're just going to imagine we generate and excel our data, random data one with this formula, random between and then we're just picking the low number, the bottom number, one to a hundred. Excel generating random numbers then between one and a hundred. We're going to do that two times over so we then created a second dataset, same fashion to do so and that's going to be the data that we will be using. So when we do this in Excel, Excel will keep on regenerating these random numbers. So we're going to imagine that we copy this information over, paste it over here so now we have static numbers which will not keep shuffling around that are randomly generated. Now if I was to just think about how we created those numbers we can make some assumptions based on what we've done in the past. Well first I randomly generated numbers not in accordance to a normal distribution or a Poisson distribution or anything like that but more towards like a uniform distribution because we had random numbers which could equally come up between a certain interval between zero or one and a hundred. We also know that we generated these two datasets the same way so they're kind of related in that way, they're going to be numbers between one and a hundred but they're not connected in any other way in terms of how we created the two datasets so we might have a hypothesis then that they wouldn't be highly correlated between them because they're not exactly connected. So we'll kind of test those out as we go. Now first I want to look at it pictorially. Let's say we took just this first dataset and we made a histogram of it. We counted all of the numbers here and see how many fall into the buckets of one to eighteen, eighteen to thirty-five and so on and so forth and you can see that it's not a bell curve type of shape or anything like that. It's going to if we did this indefinitely it would tend towards a uniform distribution or a straight line type of distribution. If we did this indefinitely we would expect kind of an even outcome because they all have kind of an equal chance. Now if we did this for the second one, same kind of thing. It looks different here just because of the randomness that happened here but you would expect the same kind of trend line where it would trend towards a uniform distribution. It's not a bell curve or anything like that. It would tend towards a straight line type of distribution. Now the fact that these both are kind of similar in nature may give us some understanding about the datasets but doesn't necessarily mean that they're correlated either. So then we're going to do our mathematical calculations so we'll say okay let's do the mean and the standard deviation for the first dataset which would be the average formula, the average summing up all of the data dividing by the data points gives us 48.82. The standard deviation is going to be the standard deviation of a sample this time of the first dataset that's a measure of the spread 29, 34, 30, 73. I got dyslexic there for a second. If we did that with a mean summing up all of this stuff and taking the average divided by the units we get to the 49, 51 and for the standard deviation if we took all of this with the standard div.s we get 26, 56. Now these could give us some indication where it's like the mean is similar and the standard deviations are similar. So we might kind of start to think well maybe they're kind of related in that way and these will kind of together but it doesn't necessarily mean that there's a relation because again there's not like a direct relationship in the way we created the numbers other than we created them in a similar fashion in terms of the random numbers between a certain interval. So let's do our calculations here and say that actually before I do that let's actually graph this thing out. If I took these two and made a scatter plot of them graphing them together it would look something like this. So now we've got the scatter plot. If I was to do this it would automatically take the first random and make it on the left. I'm sorry make it the X. So the random one is the X. In this case I don't really know which should be the independent or dependent. So normally we put the independent factor over here if we know it but we don't really know what it is. There isn't really one here because we made them completely separately. We just used in essence the same technique to make the two data sets. So you can see here that if we plot these together we get somewhat of a random jumble of data points. So somewhat of a random jumble and if we plot the curve and they're the trend line we get a little bit of a correlation but downward sloping but not a high correlation obviously you can't really see it. If you didn't have the trend line you wouldn't even see a general pattern right here generally with the dots. Now if I was to switch the X and Y's then remember you're still going to get that slight downward sloping it's not going to change to an upward sloping line and so now we just changed the X and the Y's. In this case we can see the same relation and we don't know which is the independent or dependent factor. Now just to get an idea of what randomness looks like versus what often people have in their mind of randomness we did another data set just to kind of show this and this one we actually kind of put a system together to create our two data sets. What we did is we just took, we counted by five five, ten, fifteen, twenty, twenty, five, thirty, up to a hundred here and then we did the same thing here but we staggered it, that's our starting point. I staggered it and we made, we said five, ten, fifteen, twenty.