Finding the mean, median, mode, and midrange for converted categorical data

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 the mean, median, mode, and mid-range for converted categorical data.  Here's our problem statement: Find the mean, median, mode, and mid-range for the given sample data.  An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas.  Listed below are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4 = wrinkled-green.  Do the results make sense?

Part 1

OK, the first part here is asking us to find the mean.  This is really easy to do in StatCrunch.  But first we need to load our data into StatCrunch.  So I'll click on this icon and open in StatCrunch.  Here's my data in StatCrunch.  I'm gonna resize this window so you can see more of what's going on.  There we go.

OK, so to find the mean, I need to take — that's a statistic of this column, so I'm going to go to Stat –> Summary Stats –> Columns.  I select the column where my data is located.  And then down here under Statistics, I select the mean.  I hit Compute!, and there is my mean value.  I'm asked to round to the nearest tenth.  Nice work!

Part 2

And now the second part asks me for the median.  So I could go through those menu options again, but it's much simpler if I just click on this Options button and click on Edit.  And now I just go and find the median, hit Compute!, and there my results window changes to include the median.  Nice work!

Part 3

The third part asks for the mode.  So I go back into my options window.  Mode is located towards the bottom here.  Excellent!

Part 4

Mid-range — so then I go back into my options window.  And you can go up and down this list, but you're not gonna find mid-range.  How then do we get the mid-range using StatCrunch?  Well, we have to kind of go through it the back door, so to speak.  We can get the range, and then I'm gonna select the min.  But I need to select both of those values, so I'm gonna hit the Ctrl button on my keyboard while I select the second statistic.  So now I got both of these.  That will pop up in my results window.

OK, so the range is 3, and the minimum value is 1.  So I take half the range — and half of 3 is 1.5 — and I add it to the min.  1.5 + 1 = 2.5.  Fantastic!

Part 5

Now the last part of this problem asks, “Do the measures of center make sense?”  Well, you can go through and look at the different answer options here.  Or if we go back and look at how the data were actually established, we see that, even though the data is composed of numbers, these numbers are really categorical data because that's how they're defined.  The 1, the 2, the 3, the 4 — they're really labels to represent the different types of peas according to how the soil affects the phenotype.

So these are categorical data.  And when you're dealing with categorical data, the mean doesn't make sense.  The median doesn't make sense.  Only the mode as a measure of center makes sense when dealing with categorical data.  So I look at my answer options, and it looks like this one matches that sort of thinking.  Well done!

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