 Hi guys, this is Don. I want to go over a problem that a couple of you have had questions about, wondering an easier way to develop these frequency histograms and relative frequency histograms that you see in some of the MyStatLab problems. Unfortunately, this particular problem and a few of them will require you to do what I call some manual calculations, and that neither Excel, or StatCrunch, or TI, or Minitab, or any software package that I know about will actually give you the exact layout that MyStatLab here is asking for. They're looking for a process and we can do most of the work with the software, but we'll have to do a little bit of manual calculations. So let's first of all, let's work it in StatCrunch. I'm going to open up the data table and then open it in StatCrunch. I'm going to make that a little bit bigger, give us a little more room here. The first thing we need to do, we're told that we have this data and we need to make a histogram using five classes. Okay, so our classes would be equal to five, and I'm going to relabel this class and put that as five. The next thing I want to do is to get some summary statistics for our data and select our data, which is in column ver 1, and I am going to hold the control key down and get the in. I don't need the standard deviation, standard error, I don't need that. I don't need the medium. I do want the medium, I do want the range, the min and the max, and I don't want q1 and q3. So there we've got the data. I click on compute and I'm given this table that has the summary statistics. It shows us the range is 21, our minimum value is 52, our max is 23, and we've got an n of 24. Now when you're doing a histogram and you are given the number of classes and the range, you can calculate the width of the classes by just dividing the range by the number of classes. And so I'm going to go to...let me pause this. The thing I forgot to check is down at the very bottom here, we want to store this output in a data table that I'm going to click compute. And here we've got our data set up for us, our raw data course is in column ver 1. The range is 21, the min, max and n we're given. And I input that one section class. So the first thing I want to do is to come up with the width and I want to go to data, compute, expression, bring this up, click on build, and we want to take the range, I'm going to double click that, and I'm going to divide that by class which is the number and click OK and call this width compute. And we come up with a width of 4.2. Now when we're working with histograms, we don't want fractional widths and the logic is usually to just round up, so our width would be 5. So we've got our data that we need now, we've got the number of classes, we've got the width which is 5, and we've got the starting point. And you can calculate these intervals then by just remembering that the starting point plus the width gives you the starting point of the second class. So that'd be 52 plus 5 is 57 plus 5 is 62 plus 5 is 67, 72. And then because we're dealing with integers here, whole numbers, all we need to remember is that the upper limit for each class cannot duplicate the overlap, the lower limit of the next class. So that would give us 56 and then add 5 to each one of those, 56, 61, 66, 71, 76. So that would give you your answers for that first part. And once we have those, we can go to graph, histogram, we're just going to take our raw data there, and I'm going to first of all get frequency, our bin start with our minimum value of 52, the width we said is 5. And I am going to overlay the value above the bar and everything else I'm going to leave the same. So here we get our frequency distribution, and we've got our values there in each bin 4, 5, 9, 5, 1. And I think if you compare here, we've got 4, 5, 9, 5, 1, and because we've got our n over here of 24, we've got that final value as well. So here we've got the frequency distribution, histogram, and we can convert that, going to edit, and I'm going to make it a relative frequency distribution, leave everything else the same, and click on compute. And now we get our relative frequency distribution. It's, let me move this over here and close this. If we're looking at the three options here, the one that looks like ours, the shape of it, is C. There's a little difference in the labeling on the bottom, it starts at 51, and ours starts at 52, but other than that, it gives us everything we need, and if we blow this up a bit, you can see that's not really quite 51, so that it matches what we have there. The frequency here is a little bit less than 0.4, a little bit more than 0.2, and less than 0.2, and that one is right at 0.2. So you can very quickly get your relative frequency distribution diagram that way. And answering the final question, which class has the greatest relative frequency? Well, it's this middle one. We labeled it 62 to 67, but in the actual one, we know that is 62 to 66, and which has the least is the one on the end, 72 to 76, so you can get your answers using stat crunch.