Constructing a relative frequency distribution from a frequency counts table 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 relative frequency distribution from a frequency events table in StatCrunch.  Here's our problem statement: Construct one table that includes relative frequencies based on the frequency distribution shown below.  Then compare the amounts of tar in non-filtered and filtered cigarettes.  Do the cigarette filters appear to be effective?  (Hint: the filters reduce the amount of tar ingested by the smoker.)

Part 1

OK, the first part of this problem asks us for our relative frequency distributions.  And to do that, we need to take a look at the data that's being provided.  So here's the data.  We're going to dump this in StatCrunch.  I've actually worked this problem out before in a previous post and video showing you how to do this in Excel, because I think Excel is a little bit quicker with this.  But I got a request to do this in StatCrunch, and so here we go.  Today I'm going to download this data here into StatCrunch.

OK, here's my data in StatCrunch, and now I'm going to resize this window a bit so we can get a better view of everything that's going on.  Great.  OK, so in StatCrunch, to make a relative frequency distribution, you want to make the graphical portion.  Go to Graph --> Bar Plot --> With Summary.  It might be tempting to come down here and select Histogram, but you don't want to do that because that's not going to give you what you need.  You want to go up here to Bar Plot, and then you want to select With Summary because the data that we're given are frequency counts and not the actual data themselves.

Here in my options window, I'm going to select my categories.  So the first one that I make is for the non-filtered cigarettes, and then I select its frequency for the counts.  Down here under Type, it will be tempting to select Relative Frequency.  But this is actually going to give you a number in decimal form.  And notice here in your assignment, you're asked for percentages.  So we want to click on Percent under Type.

And then under Order By, we want to make sure that we select Worksheet.  What this does is it gives us the columns in our relative frequency distribution according to the order that's in the worksheet.  We don't want to do it by, you know, whether the values are Counts Ascending or Descending.  We want it as the order of the worksheet because that's going to match the order of the categories here in our assignment.  And then the real kicker right here --- check this box next to Value above bar.  This will give us the numbers that we need to stick into our answer fields here in our assignment.

Once I've done that, I hit Compute!, e viola!  Here we have our relative frequency distribution.  And the numbers on the tops of the bars represent the percentages that form our relative frequency distribution.  So now all I've got to do is just match up the columns here with the columns here and take the numbers straight off the top.  So first we have 4 - 7.  There's no column for that here, so I'm just going to press zero. 8 - 11 — similarly, there's nothing there. 12 - 15 — there's a 4.  And you see I'm just coming down here and just taking that number off the top.  If there's no column there, then obviously the number I need to put in is zero.  And I just do it one after the other, and eventually that gets me everything I need for that.

Now I need to go and do the same thing for the non-filtered --- actually that was the non-filtered.  Now I do the same thing for the filtered cigarettes.  I could just come in here into my options window and change everything up.  But I know further on down the problem --- see here, it says, "Do the cigarette filters appear to be effective?"  I'm going to have to compare the two graphs in order to get the answer to that question.  So I'm going to make a separate graph.  So just come in, and look at the same menu options I did before.  Well, this time I'm going to select the filtered cigarettes, and you can see I'm selecting the same options there that I did before.

OK, here's my new graph.  And now I'm going to fill in the numbers here from those actual columns and make sure everything matches up.  And then that's the last column there.  So the rest of these are going to be zero.  So I'll go ahead and put that in here.  And I check my answer.  Excellent!

Part 2

Now the second part of this problem asks, "Do cigarette filters appear to be effective?"  Well, as I just mentioned a moment ago, I'm going to have to compare my graphs to get that.  So let's move this down here a little bit and then we're going to do the same thing here.  And then I'm going to slide this up above the other one, but we're gonna move it over so that we match columns up.  So now I've got 12 - 15; here's my first column.  I'm going to match this up to 12 - 15 here.

So now I've got a better picture of what's going on.  And we notice here on the horizontal axis of our graphs, we're looking at the amount of tar in the cigarettes.  So here are the non-filtered, here are the filtered, and it looks like for the higher tar levels, the non-filtered cigarettes seem to be capturing that out.  And the filtered cigarettes?  Not so much so.

So would I say that do they appear to be effective?  Yeah, because the higher tar (what you're trying to get out then) that, you know, the non-filtered cigarettes --- of course, they're letting all that stuff through.  But the filtered cigarettes, they're actually capturing a lot of that stuff, and you don't see the higher tar levels for the filtered cigarettes.  So it does appear that the filters are working in the cigarettes; they are effective.  So I come over here and select the answer option that matches that.  Excellent!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.