Constructing a frequency polygon in StatCrunch

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to construct a frequency polygon in StatCrunch.  Here's our problem statement: The given data represent the number of people from a town age 25 to 64 who subscribed to a certain print magazine.  Construct a frequency polygon.  Does the graph suggest that the distribution is skewed?  If so, how?

Part 1

OK, the first thing we need to do for this first part that's asking us to construct the frequency polygon is take the data and put it into StatCrunch.  So here I've got my data in StatCrunch.  And I'm going to resize this window so we can see the better everything that's going on.  Excellent.

OK, now before we actually go and make the frequency polygon, we need to manipulate our data set a little bit.  We can't just dump this in.  We could, but we'll end up with something that's only partially correct.  The frequency polygon is constructed by looking at the midpoints for each of your classes or categories here.  And so it's almost like you're making a bar graph, but you're putting the dot at the midpoint on the top of each of the bars on your graph.  So we need to change these age limits a little bit.

And we also need to add in a couple of new categories, because the frequency polygon they want you to construct, it includes not just the data they give you but also the category before and the category after the data that they give you.  So we need to go ahead and put that into our data set here.

To do that I'm going to click on this little arrow and say Insert 1 Above.  And then the midpoint — I need to replace all of these ages with midpoints.  OK, so what's the midpoint for this first category?  Well, I just simply — if I take my calculator, I'm going to take the upper limit, subtract out the lower limit, divide by 2, and then add that to my lower limit.  So there's my midpoint.  I need to replace this first category with 29.5.

And then I can do the same calculation here.  Notice how it's apart by ten.  Notice how categories here — the lower limits are separated by 10.  The upper limits are separated by tens, so it only makes sense that the midpoints are gonna be separated by 10.  So I can just add 10 to the one that came before to get the next one in line.  And of course, for this column here that’s after the data set, I just add another 10.  And then for this column before the first category given in my data set, I'm gonna subtract 10 out.  And there's no data in either of those categories, so I'm just going to put zeros there.

OK, now I'm ready to actually make my frequency polygon.  To do that, I go to Graph and for this I'm gonna go Chart –> Columns.  Here in the options window, I want to select People, because this is where the actual frequency counts are located.  And then down here, I want to put under Plot, I want to select “points with connected lines.”  All the other default options are good for our purpose, so we'll just hit Compute!.  And I've got the basic shape for my frequency polygon here.  So it's going to match up with Answer option C.

If I really wanted to get the label on the x-axis correct, I mean, I could always go back to my options window and say the row labels are in Age.  And now the numbers actually match up with what you see here in your answer option.  So I'm going to check my answer.  Nice work!

Part 2

Now the second part of this problem asks, “Does the graph suggest that the distribution is skewed?  If so, how?”  Well, just look at your graph.  It's not symmetrical.  It's actually — all the data is just pushed over here on the right.  So my friends in industry and I would say this is skewed to the right.  But since this question in your assignment is made by a pure statistician, they look for where the longer tail is.  And that's going to be here on the left, so we're gonna say that the distribution appears to be skewed to the left.  Good job!

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