Constructing 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 construct a histogram from a frequency distribution table.  Here's our problem statement: The table shows the magnitudes of the earthquakes that have occurred in the past 10 years.  Use the frequency distribution to construct a histogram.  Does the histogram appear to be skewed?  If so, identify the type of skewness.

Part 1

OK, the first part of our problem asks us to construct the histogram.  So to do that I'm going to take my data here and dump it into StatCrunch.  I'm going to resize this window so we can see a little bit better what's going on.  OK, now my data is here in StatCrunch.

You would think that, to construct a histogram, you would go up to Graph and then select Histogram.  However, the data that you have in your data table are frequency counts from a frequency distribution table.  The histogram functionality in StatCrunch is ... has a default setting which is designed to take raw data that hasn't yet been assembled into a frequency distribution table and then make the histogram from that.  Because you already have the data in a frequency distribution table, if you try to use the histogram function, you're going to get something that looks very, very funky.  It will count each one of these numbers as one count.  So instead of the first category having 12 counts, it will only count one.  So you have this basic uniform distribution which is nothing like the actual histogram that you're trying to construct.

How then do we use StatCrunch with a frequency distribution table to get our histogram?  Well now, look at this option right above Histogram.  It says Chart.  You want to go there, and then you want to click on Columns.  In the options window, you want to click on the column where your frequency counts are located.  And then the default is to assemble the plot with horizontal bars.  I don't know why they set that as the default, but since we're looking here for vertical bars, you want to go ahead and select “vertical bars (split)” as our plot option.

And now I'm ready to hit Compute! and, lo and behold, here's my histogram.  The numbers that you see here on the x- or horizontal axis do not correspond with the earthquake magnitudes.  That's OK; we're just looking here for the shape of our distribution inside the histogram.  So now we match what we have with our answer choices.  It looks like Answer choice D is gonna be the one we want.  Excellent!

Part 2

And now the second part of our problem asks us about any skewness in the histogram that we've just constructed.  So to look for skewness, we're looking for a longer tail on either the right or the left.  This histogram is not roughly symmetric; there's a lot more data here on the left than there is on the right, so there's a longer tail here on the right section — hardly anything here on the left.  So this is going to have a longer tail on the right, and so the distribution will be (as a pure statistician would say) skewed to the right.

If you're asking my friends in industry, “How is this distribution skewed?” then they would say the same thing I would say.  It's skewed to the left because the left side of the distribution is where all the data is located.  But the questions that you’re asked in your assignments are created by a pure statistician, and pure statisticians don't look for where the data is when assessing skewness.  They look for where is the longer tail.  So here the longer tail is on the right, so we're gonna say it's skewed to the right.  Nice work!

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