2.2 is about drawing what's called a histogram it's basically a picture of your distribution so we're going to draw a histogram for each of the examples we just did today the description there says it's a graph with bars of equal width drawn adjacent to each other the horizontal scale represents the classes and the heights of the bars represent the frequencies sounds all scary to me so I'm going to do the one for example B first example B is the one we just finished there's two of them down here A and B I'm gonna do the one for this but we just finished talking about this one then I'll go back to the one we did earlier before the break so I want to make a histogram I have a horizontal axis and a vertical axis like your x's in your eyes from algebra on the horizontal it's going to represent my classes the most common numbers to put on there are the boundaries so I'm going to list and let me make this a little bit longer so I can squeeze them all in here I'm going to list all of my boundaries on that axis starting with negative 0.5 so I'm going to put negative 0.5 here the next one is 1.5 I forgot which one of my adapters now listing all my boundaries 3.5 how far do I have to go 11.5 yes notice that these should be roughly my graph is not they should be all about the same distance this one's a little bit fatter but they should be in the same width use the power of my Eraser to make it a little bit more accurate here so each of these classes that are separated by these boundaries should all be the same width what is that width two two that's the class width from here to here is two from here to here is two right however why do you make them when you draw them is up to you but they should all be evenly spaced or close enough if you're free handing it like me so then I want to just Mark the frequencies my frequencies go from one of the 22. so I am going to mark this scale so it at least goes up to 22 because I have to fit that on my y-axis so maybe I'll count by fives and go up to 20 equal to 20 maybe like here's five again evenly spaced can smaller as I go 15. 20 something like that those should be evenly spaced and I just want to make a bar that goes up to the height for each class so this first class goes up to two two is roughly right here so I'm going to go up to two over and down or this number right here is two it matches up with this two right here if they were marked you do count by ones if you want it just gets really smushed together if I try to mark them all for you it's hard to read everyone okay I just went for this class if you're between these two numbers there's two in that category between those two numbers there's two in that category met class the next one though I had a 22. so it's going to have a much taller bar here 22 is way up there past my 20 about there I'm eyeballing it sorry if you can't read this exactly you don't have to put the numbers on top a lot of times you'll see them written on topic it's hard to read over to your scale other times it'll be a nice perfect number liner you can just look over and see that it's a 22 by looking at the graph 22 in the next class they'll put 11 in the next one 11 roughly here everyone please see what I'm doing there and then I have three and then I have two ones so my graph I don't want to color those in so you can see them this is called a histogram questions on how I just created them micro boundaries find the height space on your frequencies across a little straight lines important um equal width so you have to count evenly spaced what if I had a class that was like a zero what if nobody said anything between six and seven it was a zero what would I have done yeah just skip that one if there was nothing in here between six and seven I just would have no borrowers would have been like a fly line you would sort of see it this bar would just be empty it's okay skip that one but you have to at least keep a space for every possibility in between there uh so it has to have everything is equal width and the other thing is that they are drawn adjacent to each other they have to touch it makes it a histogram because they're touching if I had tried to draw it with my class limits zero to one two to three they wouldn't have touched let me do a little rough quick sketch of what I mean if I had marked my number line 0 1 2 3 4 so far zero to one would have gone you know up here and two to three would have been up here there's this weird space between there see what happens that's why we have to mark it with the boundaries it's like what happens is where is there a good space has to be touching you guys would not be okay if you mark with your boundaries that's the easiest way to do it we don't like The Mark with class limits because you can't tell if the one is on this bar or that bar if you mark the bread at one it's exciting on your problem okay the horizontal scale can be marked using boundaries or midpoints sometimes instead of listing the boundaries like I did there will label just the midpoints they'll label these numbers everything would look the same but instead of lifting the edges they would just put what's in the middle here they'd put 0.5 2.5 4.5 so forth and label those you'd still be able to tell the width and figure out everything else more common is to use the boundaries so that's my histogram that goes with the data we just came up with is it normal is it normal starts low gets high in the middle and goes back down I heard yes I heard no is the middle the highest guys no definitely not right it's much higher over here we call this skewed excuse because we got all this higher part over here that it kind of gets stretched out over there it's not very normal what's your definition of skew excuse like it leans it leans one way or it's not really leaning but it leans one way or the other if you were to draw a bell shape over it in this example it would look something like this rough sketch so it's not highest in the middle it's skewed as a little part that stretches over here to the side if you have skewed left and skewed right where maybe you have something that does that right skewed yeah the book will explain in more details my words leaning over it's not very normal though okay on how to make a histogram