So in recent videos, we've seen how to take a data set and turn it into a frequency distribution and then a histogram. The problem was that we had to do all that stuff by hand, which can be very time-consuming and very frustrating, especially when you start getting larger and larger data sets of 20 or 30 numbers. So what I want to do in this video is to show you how you can take this data and immediately just get a histogram right out of a TI 84 graphing calculator so we can much more quickly answer questions about the shape of the distribution. Is it normal? Is it skewed?
Etcetera. So the most important thing here is if you have a TI 84, I want you to take it out and follow exactly along with what I'm doing here. I'm going to have a list of steps for you to refer back to later, but the most important thing is that you're sitting here doing exactly what I'm doing. Alright. So let's get started over here.
We've got a pretty familiar setup of a problem. We've got the datasets for the time that students spent studying for their exams. Now a couple of things. If you run these types of problems on a quiz or a test and you have to show your work and do this stuff by hand, then you're going to have to, and there's no way around it. But if you have access to a graphing calculator and you can use it, these steps are going to be really helpful.
Alright? Now, one of the things I want also to point out here is that in previous problems, we have fewer numbers, like five or six numbers. It's usually easy to tell which one of these shapes the distribution is. But here, all the numbers are randomized, and I don't really see any clear patterns in the data. So I have to create a histogram.
The first thing is I have to take this data that's on the page and then put it into my calculator. So that's the first step. We're going to input this list as this data as a list. So here's how you're going to do this. You're going to go to your calculators and you're basically going to hit the stat button over here.
It's going to bring up a menu. You're going to go to edits. When you hit that button, it should come up with a bunch of columns where you just input these numbers. And all you have to do is just type each number and hit enter. So, for example, I'm just going to go 49 and then enter, 25, enter, 55, so on and so forth.
So I'm just going to fly through this and typing all the numbers. By the way, if you ever mess up one of the numbers, let's say you mistype a number, you can always just hit the up button and then type over it again. That's 5 and then 72. Also notice here, so we've got 68, 28, that these numbers don't necessarily have to be in any particular order. You can input them exactly how they are in the table.
Alright. So 63, 53, 33, 42, 37, 12, 95, and 21. When you're done, you should basically see this L1 contains twenty-one, which means you've typed 20 numbers in. Alright. So that's the first step, and you should see something like this once you're done.
Alright? So now let's go ahead into the second step. We're going to have to graph the default histogram. So one of the things we're going to do is we're going to open up the stat plot button. You're going to hit the second key and then go to the y equals.
Above it, it says stat plot. And, basically, you're going to turn on these plots and tell it what type of graph to do. You're going to turn it on, and then we want a histogram, which is a bar graph. There are other types of shapes that you can do here, like line graphs and things like that. We want a bar graph, something that looks like this.
So you're going to select that, and then it's automatically going to point to L1, that list that you just populated in step one. Okay? So now what I'm going to do is I'm going to quit out of this window. So I'm going to hit the second and then mode button, which is quit, to get out to the main screen. And now what you're going to do here is, once you're done with this, is you're going to have to tell the graphing calculator, like, a good window to fit this information in.
It's going to try to do its best. So we're going to go to the zoom button over here. And if you scroll all the way down to option nine, which is zoom stat, it's basically kind of like an auto feature. It's going to try to do its best at figuring out what the classes are going to be. When you hit that button, you should see something that looks like this.
All right. You should see something that looks kind of like this. Alright. So let's take a look at our graph here. One of the things you can do is you can hit the trace button.
That trace button basically will allow you to sort of toggle through each of these classes and see the frequencies and also where the class limits are. So if you'll notice here, the min and the max, the five and the 27 are basically what the class limits are. Notice how that's a number of 22. If you look through the problem, though, we're actually told specifically to use a class width of 15. So in other words, the calculator kind of just guessed at a class width of 22, but you can adjust it.
And I'm going to show you how to do that in this next step. So now when we're done with defaulting the default graphing the default histogram, now what we can do is adjust the boundaries a little bit, and we can do that all in the window function. So let's go ahead and open up the window key now. It's you should see something that looks like this. And, basically, what we're going to do here is we're going to adjust some of these numbers a little bit.
Alright? So what I'm going to do is I'm just going to reset these numbers, and the x-scale is going to be the thing that you're set to the desired class width. So in other words, I want to set this to, the number five, and I want to go all the way down over here to the xscl, and I want to set this from 22. Remember, that was the previous class width the one automatically did. I want to set this to 15.
And once you do that, all of a sudden, if you go back to the graph button, you're going to see that your histogram has changed a lot. And now we can clearly start to see some patterns that are emerging. Alright? So you're going to set the xscl, the x scale to the desired class width. And then one of the things you can also do to further tweak this is go back into the window key.
We're going to go back into the window. And basically, we're going to set the XMin to be the minimum of the data set, which is five, and the XMax to be a number that's near the maximum. So the maximum here is 95, but I'm going to go ahead and change this to something like 125. So it just makes the window a little bit tighter. Another thing you can also do, this is totally optional, is you can adjust the y min and y max and y scale values.
So this basically just tells the bars how tall to be. Right? So go back to the window and set this to, I noticed there's a bunch of decimals here. What I'm going to do is I'm just going to set this to negative one, and then I'm going to set this to six. Oops.
This is going to be negative one. I'm going to delete this and then I'm going to go and make this a six. If you go back to the graph function or the graph window, you should see a really beautiful histogram that looks like this. And you'll see that the data is pretty well contained within the window here. Go ahead and hit the trace button.
And if you hit the trace button, what you're going to see here is that your class widths are 15, and it shows you the frequencies for each one of those things. You've got n equals three and four, that n actually equals f. And so this is what your histogram is going to look like. Alright. So now we can go back to our question here.
That's all the steps that you need. Is this distribution, is it normal? Is it skewed? Is it uniform? Or none of these?
So it's definitely not uniform. Uniform means that all the data values are equally spread out, and that's definitely not what we see here. Let's see. Is it a normal distribution? Well, remember, normal tends to sort of do this bell curve shape that's symmetrical, so it's definitely not normal.
Is it skewed right? Is it skewed left? It looks like one of these because the data peaks towards the left or the right. We just have to figure out which one. Which one is it?
Is it skewed right or is it skewed left? Well, remember, when it's skewed to the right, that means the data peaks to the left and it trails to the right. So that, so skewed right just means that the data trails off to the right, and that's exactly what the right answer is. Alright. Skewed left would have been if it peaked to the right.
So it's definitely not skewed left, and it's definitely not none of these. So the right answer is that this data set is skewed to the right. All right? So hopefully this makes sense, folks. Let me know if you have any questions, and let's get some practice.
