Finding a five-number summary and constructing a boxplot

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find a five-number summary and construct a boxplot.  Here's our problem statement: Listed below our amounts of strontium-90 (in millibecquerels) in a simple random sample of baby teeth obtained from residents in a region born after 1979.  Use the given data to construct a boxplot and identify a five-number summary.

Part 1

OK, here we have our data set, and the first part of this problem is asking us to construct a five-number summary.  This is really easy to do once we dump our data into StatCrunch.  So here's my data in StatCrunch.  I'm going to resize this window so we can see a little better what's gonna happen here.  Great!

Now, to get the five-number summary, I'm going to go into Stat –> Summary Stats –> Columns because I'm looking for summary statistics on data that are listed in a column.  I select the column where my data are located.  And then I come down here and select the specific statistics for the five-number summary.  To do that on an individual basis, I'm going to use the Ctrl-click option.  So I press the Ctrl button on my keyboard, and then with the left button on my mouse I'm going to click the individual statistics I want for my five-number summary.

What are the statistics for the five-number summary?  Well, if you need a review of that, here you go.  The five-number summary is the minimum, the first quartile, the median (which is also the second quartile), the third quartile, and the maximum.  So these are the numbers that I want to select for my five-number summary.

In order to put the answers in the proper order, I'm going to list them in the proper order when I calculate them in StatCrunch.  So the first one I want to select is the min.   So I come down here and select the min.  And then pressing the Ctrl button and keeping it pressed on my keyboard, I'm going to select the next four numbers for my five-number summary.  So after the min, we have the first quartile, and then the median, and then the third quartile, and then the minimum — excuse me — the maximum.

Notice how the numbers that I selected are listed here.  This is the order in which they will appear in the results window.  So if I select them in a different order, they'll appear in a different order.  This helps me to know what order the numbers are going to be in the results window before I select Compute!.  This is the order I want.  So now I'm going to go down here and click Compute!.

Now, here in my results window is my five-number summary, and it's in the order than I need to put them in the answer fields.  So I'm going to do that now.  Fantastic!

Part 2

And now the second part of this problem asks us to construct a boxplot.  I can do that very easily in StatCrunch by going to Graph –> Boxplot.  Here I select the column where my data is located.  And then, for some reason, the default selection for StatCrunch is to draw the boxplot vertically.  But for all the homework assignments that you're going to have here, the boxplots are drawn horizontally.  So you want to come down here under Other options and click this box next to Draw boxes horizontally.

The other default options are fine for our purpose, so we're going to select Compute!.  And now here we have our boxplot.  So we just match the one that we drew with the right answer here.  And notice how we've got different numbers here on our axes.  We can change the numbers that are listed here on the axis if we wanted to.  Here I've got it set from about 120 to about 180 (it’s what it came up to be).  So let's see what matches here.  We've got the edge of our whisker a little to the left of 120, so that ... that ... so A and D are not going to be correct.  And I want — let's just go ahead and just change this axis here.  I want to go full-out to 180.  OK, see this whisker here on answer B; it goes almost to 200, but we're not even past 180 yet, so this has got to be the right answer here — answer option C.   And the edges of the boxes look good.  Everything seems to match up, so we're gonna select answer C.  Fantastic!

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.