Using StatCrunch to construct and evaluate a histogram from a frequency distribution table

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to use StatCrunch to construct and evaluate a histogram from a frequency distribution table.  Here's our problem statement: The table below shows the frequency distribution of the rain fall on 52 consecutive Fridays in a certain city.  Use the frequency distribution to construct a histogram.  Do the data appear to have a distribution that is approximately normal?

Part 1

OK, the first part of this problem asks us to construct a histogram.  So we need to get this information here in the table into StatCrunch.  Notice that we don't have any icon to click on to dump this information directly into StatCrunch.  So what we're going to have to do is input this information in manually.  To do this, we're going to open up our own separate copy here of StatCrunch.  And I'm going to pop that out here so we can take a look at our problem and see everything that's going on just a little bit better.

Alright, so here in StatCrunch, I'm going to enter in this first column here for the classes.  And if you look and see that there's actually a pattern going on here, that actually helps you to input the information in just a little bit more quickly.  And it doesn't take too long once you get going with this; you just gotta keep punching those buttons on your keyboard, and away you'll go with this.  OK.  There's the first column, and now we put in the second column for the frequency counts.  Alright, so now we've got the information here into StatCrunch.

Most people, when they want to make a histogram, they're going to go up to Graph --> Histogram.  The problem with that is that this function in StatCrunch assumes that the numbers you have here in the data table are actual data values, and they're not.  What you have here is a frequency distribution table.  This is a summary of the data that you actually have, not the data itself.  And that's why the histogram feature doesn't work, because the histogram feature assumes that this information is actual data and not summary information.

So what we want to do is go to Graph --> Bar plot --> With Summary so that we can make our graphical representation of the summary Information.  Categories are going to be the class; counts are going to be the frequency.  And then I always like checking this box for Value above bar.  I wish this was selected by default, but it's not.  It's very useful.  So I just go ahead and just check it.  Hit compute!, and look!  Now I've got something that looks more like what I'm asked to choose in my answer options.

So looking at my three answer options here, Answer option C is not going to be right because the high part of the graph is here on the right.  But the one that comes from our summary information is here on the left.  So we're not going to choose Answer options C.  Distinguishing between Answer options A and B --- so if I look here at Answer option A --- I'll blow that up just a little bit --- notice here how the graph goes.  It starts at a high point and comes down and then comes back up a little bit.  That's what we have here.  And notice the values here that we have.  So this bar that comes up here near the end is a 4, which is just under 5, and here we've got 5 and you bring that over and, yeah, you could say that that that might be the case.  If I look at Answer option B, notice how that same point actually goes up closer to 10, so it's well over 5.  So Answer B is not going to be correct.  It's going to be Answer option A.  Excellent!

Part 2

And now the last part of this problem asks, "Do the data appear to have a distribution that is approximately normal?"  Well, a normal distribution starts out small, comes up to a high point in the middle, and then comes back down again.  That's not what we have here.  So looking at our answer options, Answer option A is not going to be correct because we don't conform to that characteristic bell shape that a normal distribution should have.

Answer option B is not going to be correct.  It says that the distribution is approximately uniform.  Uniform means that all of these bars would be coming up to about the same height or level, and that's not what we have here.  And we've got quite a bit of variation among the different classes.  So Answer option B is not going to be correct.

Answer option C is not correct because it says the distribution has no obvious maximum.  That's obviously wrong.  There's an obvious maximum right here on the left side of her distribution.  So yeah, we're not going to select Answer option C.  It must be Answer option D: "No, it is not symmetric."  And that is true that the distribution that we have here is not symmetric.  If we were to take a line down the middle, then each half should be a mirror image of the other half, and that's not what we see here.  So Answer option D is the one we want.  Nice work!

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