 Hi, this is Dr. Don. I'm going to take a few minutes and show you how to solve this histogram problem from my stats lab using StatCrunch. Now I'm not going to get into the details and theory of how you construct a histogram. I've got another video on that. Here I just want to show you the mechanics of how I would approach this to use StatCrunch and cheat a little bit to use a simple calculator for some things that are faster. The question is, we've got this data set here of 20 patients. That's the number of days they were hospitalized for you to construct a histogram, a frequency distribution and a frequency histogram, I should say, using six classes. That's important. And then we need to describe the shape of the histogram and we'll talk about that. One of the things that jumps out at me when I look at this problem is that in addition to the histogram, we've got to give them some other intermediate information. They want the class, and that means the class limits, the lower limit and the upper limit. They want the frequency, which would be the number of patients that fall into that class and then the midpoint of that class. So to start, I would just click on the little rectangle here and open in StatCrunch. And I've already done that. And over here on the right side, I've got the data in the column that's labeled Variable 1. First thing we need to do in order to do this is to find the range of the data and the minimum and maximum values is what we need to get that range if we do it manually. With a small data set, you could probably inspect it, but let me show you how you would do it just so using StatCrunch in case you have a bigger data set. We're going to start with going to Summary Stats. Here we go. And our data is in column 1, Variable 1. And the statistics we need, I'm going to scroll down here. I'm going to get the range, the min and the max. And one of the things I like to do is to store it in a data table. Makes it easier to do things. And then I'm going to hit Compute. And drag that out or just close that. And there you can see there's the column, the Variable 1. The range is 11. Min is 3. The max is 14. 14 minus 3 is 11. That's how you get that. So we know the minimum value is 3. I'm just going to click over there and go ahead and put 3 in there. The first thing we need to do is to get the bin width. That's how we will determine what these class limits are. The way we do that, we take the range and we divide it by the number of classes, which is 6 in this case. Now, you can do this in StatCroach if you want using data, compute, create an expression. I find that to take more time to be clunky. I like just to use a simple calculator. Here I'm going to use my Windows calculator. And I'm going to take the range, which would be 11. And I want to divide that by number of classes, which is 6, and hit equal. That gives me 1.833. The standard way of coming up with a bin width when you're using integer data like this is to round up up to the next integer. So 1.83333 becomes 2 for my bin width. So now that I know the bin width, I can just add it. So 3 plus 2 is 5, 5 plus 2 is 7, 7 plus 2 is 9, 9 plus 2 is 11, 11 plus 2 is 13. So those are my lower limits for each of my bins for the upper limits. Remembering that we've got integer data here and that a data point cannot fall into two bins. In this case, that just means this would be 4 for my upper class limit. Then I can add my 2 again. 6, 10, and so up to 14. So those are my class lower limits and upper limits. Now we're going to get the actual frequencies and here I'm going to jump back into stat crunch. I'm going to go to graph histogram and then pick my data column, which is variable 1. And we want to go down here our bins. They start at the minimum value, so that's 3, and the bin width is 2, and we just click compute. And so here is our histogram we need. So I can hover and see that my frequency is 3, and I just put 3 in there. My next frequency is 8, 8, and so on until I complete it. It goes up and it says the last one has a frequency of 1. Finally, we need to get the midpoints of the class. So we just take the upper limit and the lower limit, add those together to get 7 and divide by 2, which gives me 3 points. Now you can do that for each one of those, but because we know the bin width is 2, we can just add 2 each time. 5.5, 7.5, all the way up to 13.5. So that's it. Here's our histogram, and we just compare that to the answer options. When you actually go through this, they'll give you some ones to pick. And you just pick the ones that matches what you actually have here. And then final thing is this skewed data, or uniform data, or normally distributed data, it's skewed. Remember, we got this tail over here toward the upper limit. So that's got an upper skew, a positive skew. I hope this helps.