2.3 Histograms

Welcome back now. Module two. Lecture three. We’re going to talk about a tool called a Histogram. It’s a bar chart. But guess what? The bars just fall into whatever place they belong in. We don’t just move the tallest bar off to the left like we did on Pareto chart. The histogram will show us how things are actually happening in the world. It’s a graphic display where the data is grouped into ranges, each bar is plotted as a range of data. Shows us information as it actually exists. Allows us to make decisions. What we’re looking at, with all of these tools is, what are causing these problems and what kind of solutions can we put in place to deal with these problems? Histogram is a thing that will help us focus in on areas where we want to put our efforts. One way to display and examine what’s going on. You’re looking at what’s going on out here in the world. Three most common characteristics. We have shape, we have central tendency, and we have dispersion. So, let’s talk about those three things, cuz they’re going to all give us some good information that will help us focus in on where to look to solve some of our problems. Shape. Let’s take a look at what the shape of this Histogram is like. So we can have the shape of a Histogram like this, or we can have these other shapes. Skewed to the right, skewed to the left, uniform, or the typical bell shaped curve. In most situations, if you gather enough samples of what’s going on you will get something that’s very close to a bell shaped curve. It may be skewed one direction or the other, but very close to a bell shaped curve. This one’s skewed off to the right. What happened here? Well, this is a class that’s gotten some grades. Let’s say this is a class in biology that happens to be at a Big Ten university, who accepts every student that applies from that state. You can’t turn down a student. They get to come to the university no matter what their SAT or ACT scores might happen to be. It doesn’t make any difference. They all get to come there. So, right away in their freshman year, there’s a couple of classes the university puts in to just to start to weed out the people that really can’t keep up, or the people that just won’t. Or, it might focus some of those people that are having a hard time going to school and taking care of their classwork instead of gee, it’s my freshman year, I think partying’s kinda fun. And, it may refocus those people. So these classes are not easy to get through. And you may end up with a lecture class of 600 people, and this is what the grade dispersion looks like. Skewed off to the left, purposely made to be a very hard class. Very few people get A’s and B’s, lot of people get less than C’s. Or, we may have a class that’s designed really well. The instructor’s laid the class out well, there’s a lot of transfer of knowledge from the instructor to the students. It’s been laid out so that people can actually do the work, understand it, it’s clear, and all you have to do is just do the work required by the class and you’re able to get a good grade. This is the kind of class where everybody comes in with an A and it’s really theirs to lose. It’s very hard to lose that. You have to work pretty hard at doing that, although some people do, so a different way to look at a class. And so you’ll see different shapes to the classes because of this. One of them is a pretty tough class to get through. This one, this is an easier class to get through. Designed better and designed purposely to transfer knowledge. We may end up with a curve shaped like this. We may end up with a bell-shaped curve, like this. In the old days when people used to use the bell-shaped curve to give people grades, didn’t make any difference as to what you did, it just made a difference how you compared to the other people in the class. There’s another element that comes into play with this, and why we wanna look at Central tendency. If we are doing something for a group of stakeholders, they have some expectations. They want it to be at least this good, and they don’t want it really any better than this. Because they now start to perceive that it if it’s better than that, they’re having to pay more money than they really need to. So we don’t want to put too many extra things in there because now people say, eh, too much. [INAUDIBLE] I don’t wanna pay for that extra. So you have an idea, of, well, you know, I’m kinda lookin’ at this range in here. We want all of the things that we do to fall within that range, someplace. All of our efforts to fall in there. It maybe that we have a curve that’s pushed off to the right here, where we’re taking care of everything that our stakeholders need. And. we’re giving them some extra. Now in this class that we’re looking at, most people in the class are doing fine. But we have a whole bunch of people up here that they’re not even challenged by this class. Class needs to be redesigned so that it takes care of everybody. We also have another class that may not have been designed quite right, because there’s a bunch of people that are just left behind. It’s challenging to the most to the higher level students in the class, but some of the other students, they’re not able to keep up at all. It’s not a value to them at all, in either of these cases. So we need to figure out, how we put this class together so everybody is getting something out of this class. This is what it would look like. Now, we get it put together so everybody’s getting something out of the class. Central tendency. Three measures of central tendency, mean, median, and mode. And I’m sure you’ve all heard these terms before. We’ll just quickly go over them one more time. We’re just talking about kind of where’s the middle of this histogram? However you want to define middle, that’s what these three things are all about, the middle. Mean. The mean is the sum of all the measures divided by the total number of measures, which means, what we’re looking at is the average. And most of the time, when people talk about, we’re gonna look at the center of something, we’re talking about the mean. If we take a look at, let’s just examine the mean one more time. Mean is just that average piece. Median, now, is the middle. We just draw a line down the middle so that this thing is divided into two equal parts. Doesn’t have anything to do with the average, just the middle part. If you think as the median as the median strip in the freeway, that’s what it is. Just that dividing piece right in the middle. And then we have mode. Mode is simply when we put all these numbers together. A plus, A, A minus, B plus, C, D. Other, incomplete. One of those comes up the most. Which thing comes up the most? That’s the mode. It’s the easiest to identify. So, we just look at all the numbers and, numbers or values and say, oh, that one. That one comes up the most number of times. And, a lot of times, it’s the least useful way to do things. The mean or the median are usually much more useful measures of central tendency than the mode. Although the mode is there for you for some, sometimes when you may be able to use that. We’re also looking at Dispersion, what does the shape of this thing look like? Is it all squished out here? And it just, thinks just sort of happen all along the way, or gee, you know, kind of in the middle here there’s kind of a area where people are starting to do better, or, this third one. Yeah, we’ve really got something that’s working really well, and most everybody is hovered around that central part there, and everybody’s getting a lot out of this class. So we’re looking at the voice of the customer and these are our specification limits out here. Upper and lower that we’ve been talking about and these are all our data points along the way. So what does this curve look like compared with what people are expecting from us? Dispersion and standard deviation. There’s all kinds of calculations you get into with standard deviations and dispersion. And one of the things that comes out of all of this is a term that we hear once in a while called Six Sigma. All we’re trying to do if you hear that term Six Sigma is it means, we’re just trying to do almost everything right. Simply what we’re trying to do. We’re trying to make sure that all of that histogram is within those requirements that our customers have given us. So dispersion might look like this, where everything is pretty centrally located around that mean or, you know, we’ve got some things starting to spread out a little farther from the mean. Some customer’s really, really happy. Some customer, eh, not quite so happy. Or A, we have almost all of our customers equally happy. Everybody’s happy with this thing. The value of Histograms. Give us three measures, the shape, central tendency, and the dispersion. And we can make well-founded decisions based on the information that we get from these things, and then we can have effective actions that we take.