 # The Ogive Graph - Sectino 1.8

Folks Jackie Gleason here. And this lesson is on the old I've curve, but first let's take care of the board problem. The mean, age of five people in a room is 30 years. And then one of the people whose age is 50, what a young guy, huh, leaves the room what's. The mean, age of the remaining four people. Okay, this is an excellent s80 type question. Also, you guys.

Well, okay. So if five people in a room are 30 years old, then you multiply 5 x, 13 out I'll, tell you what they add up to. So those five people's ages, add. Up to 150.

So if the 50-year-old dude, the young guy leaves, then the rest of the four people are going to add up to a hundred, because you take away 50 from the 150. And so the average of those four guys you do I'd for into the remaining 100 you get their average is going to be 25 alrighty. Okay.

So here's the OG curve. So it goes like this note, I've graph is a cumulative line graph. And it displays, the total at any given time. So step to construct an give graph, and we're going to go ahead and.

Use the example that we used in the ages of the president's when they got inaugurated all right. So if you want to see that lesson where I got this data that was on, I think the doc Watson stem plots lesson. So all right. So this is so that I have that video on there already so decide on a class interval to make the frequency I'm going to go ahead and use the same frequency table that we had in our prior lesson. So we did a graph of width 40 or five right here.

This is five right here. This is why they. Got to be the same with right here, we're going to use this total that we did right here.

Okay. So we're going to add two columns to the cumulative frequency and relative frequency. Okay. So here's, the same data that we just had, and then we're going to add two columns one for cumulative and one for relative. Ok. So this to just goes right here, and then I'm going to take that too, so I made a total right there, I'm going to take that too, and I'm going to divide it. By 43 2 / 43 gets me, four-point-seven.

Percent, and if you can see a tiny little font size that says to over 43, okay, this next number here is going to be eight because I keep adding that's. What cumulative means I'm going to go to plus this. Next number is going to be 8 so 8 is going to go here all right. And then. So then this is going to be 8 / 43 and eight / 43 gets me, 18.6 percent. Okay. Now, I'm going to go 8 plus 13 is 21.

Okay, you guys get the idea right? Can I go kind of fast good? Thank you. So it gets 4.8 percent.

Notice the. Percentages keep increasing because I'm going to get down here, that's going to be a total of all of them when I get down here and that's, why it's an it's called a cumulative frequency? We keep adding the priors. So look, 21, plus this 12 is 33 33 /. 43 is going to be the percentage is going to be. Seventy-six point seven thirty.

Three, plus seven is 40 okay. And then and then 40, plus three is 43 okay? So it adds up to a hundred percent of the data. Alright.

So we're going to use that to make. Our cumulative relative frequency gram, which is a graph, which is an give graph, okay, so label and scale, your axes. And you title of your graph, just like we've done before, and I'm going to use the title age at inauguration and relative cumulative frequency, we're going to leave some spaces for about two to three lines for step number four before the graph.

So we're going to have a step number four right here, but leave a few spaces in your notes right here to put that. Okay, all right so going to. Start this graph member, you left the space right there?

Okay, this graph. So we probably pause it right here. So you can go ahead and crank out this graph, right here, it's the same graph. Right there? Ok, notice a little springboard goes from 0 to 35 right there.

And then they start going up by fives, right there, ok, and then alrighty. So now you got all that down. So, so now we're going to plot your points at the left end point of the next class interval. So what that means is this 4.7 is going to be graphed. At the left point of the next class interval of 45, so I'm going to put 0 at the 40 and then 4.7 at the four five, and then 18.6 is going to go at the next two left intervals, 50, you guys get it, and then 48.8 is going to go into 55 and so on all right. So that's, what that I just said, right there, okay, so-and-so on and so on.

So here we go there's that zero starts at the 40. And then the first one is 4.7, and then go ahead and connect them. Okay. And then the next one went up to 18.6. So here we go 18.6. The next one goes 48.8, and then seventy-six point seven and a 93 and then, and then finally the year one hundred percent right there?

Okay, so great went all the way up to the hundred percent there's, my beautiful, give, cure, isn't that a beauty and hang nicely on like a Christmas tree, ornament, wouldn't it. Ok. So the piece percentile like the 50th percentile of a distribution is the value where p % of the observations fall at or below that percentile. So Bill Clinton was 46. So what was his percentile. So if you go down here, here's old, Billy, right here bill was 46.

So if I go straight up and straight over right, there that'll tell me that he is about I'm guessing estimating about in the eighth percentile. That means eight percent of the president's was at or below him. So his graph you would estimate Clinton to be about eight percent tile or about eight percent of the U.S. presidents were the same age or younger. Okay, pretty groovy. Huh? All right.

So in other words, Clinton was younger than about.Ninety-two percent of all US presidents. He was a young dog. They columns. One of his nicknames is the big dog all right. So what age corresponds to the 60th percentile, so we're going to go backwards? So I'll just go over the sixty percent towel and then go straight down. Okay and I get about what about fifty-five percent right there.

Well, at 57, I, guess 50 55 and 57 years old. Okay. So about sixty percent of all presidents were 57 years old or younger when they took office. Okay. So to find the. Center of the distribution, you just find the 50th.

So you just go over 50, and then it goes down to about I. Don't know, about 56 I would say, so the center is about fifty-six percent. Okay, I'm.

Sorry, 56 years, old, all right, isn't that pretty cool. Okay, so that would be your homework assignment for this lesson all right. Good job.

You guys.