Constructing and interpreting a relative frequency distribution from categorical data
Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to construct and interpret a relative frequency distribution from categorical data. Here's our problem statement: Among fatal plane crashes that occurred during the past 70 years, 620 were due to pilot error, 85 were due to other human error, 308 were due to weather, 267 were due to mechanical problems, and 386 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?
OK, I actually think this problem is a little bit easier to solve in Excel, but I'm going to solve it in StatCrunch. In StatCrunch, we're actually going to have it do everything for us. Now we can actually calculate this stuff out, and I could take my calculator and do all the old school calculations, and that's a legitimate way to approach this problem. But I'm lazy. I'm going to have StatCrunch do everything for me.
So I know it's tempting to say, "OK, we're going to make a bar plot, and we've got data here, so why don't we just press With Data?” Well, this isn't actual data. This is actually a summary of the data. We don't have the actual individual counts. We just have a summary of the counts. So because this is a summary, I'm going to select With Summary after selecting Bar Plot. The categories are the cause, and the counts are in the frequency column. I'm going to select Relative frequency. Or if I wanted to, since these are in percent form here, let's just go ahead and just select Percent. And then all we have to do is just take the numbers straight over. I'm going to tick Value above bar. This is what's going to give me the numbers that I need on my graph to put here into the answer fields in my assignment.
And that's all I need to do. Hit Compute!, and out comes this wonderful little bar graph. Now notice how that, first of all, everything's just really small as far as the typeface goes. You can barely see it. And there's actually a zoom feature that we can use. But first I want to make sure that we get this in the right order, which I didn't do previously. So back in my options menu, I need to make sure I order by worksheet. And that way it'll put in the same order that we have here in our assignment.
Now I've got this ordered correctly. Now to get the zoom feature, there's these three bars that you see here in the lower left. Go ahead and click on that, and then hit Zoom. And now, when I click on the zoom tool, I can zoom in on area, I can move this around, and now there's the number I need to put in for pilot error, 37.2. I hit the X to go back. Whoops, that's not what I wanted to do. I want to go back this way. And now I just go ahead and just do the same thing for each of the following categories. And it really is that simple.
Now to do this the old school way, I'd have to take the sum of the numbers that are listed here, and I could do that easily enough in StatCrunch. And then once I have that sum, I go ahead and divide by the --- each of these counts by the total sum, and that gives me the same percentages that you'll see here. And I can show you that in a moment as soon as I get done with all of this business. So we've got two more numbers to put in. I'm going to put that in here. And we've got one more. Excellent!
Now to illustrate what I was showing you before, just very quickly, if you go up to Stat --> Summary stats --> Columns, at the frequency, we want to get the sum. The sum is 1666. So if I take that 1666 and divide it into each one of these numbers, I'm going to get the same numbers out. So if I took the first number, 620 for pilot error, and I divided by 1666, notice we get the same 37.2% that is the correct answer. And we can do the same thing for each of the others in succession. But like I said, I'm lazy. I just let StatCrunch do all that calculating for me.
The next part of the problem asks, “What is the most serious threat to aviation safety, and can anything be done about it?" Well, the most serious threat is going to be the category with the largest percentile. And that's going to be the 37.2% related to pilot error. Can you do something about pilot error? Yeah, you could probably train your pilots better. So let's see, we got --- yeah, right here, Answer option D: "Pilot errors are the most serious threat. Pilots could be better trained." So I go ahead and select that one. Excellent!
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