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OK - I figured out what is going on!  The way functions work is not how I expected (and others asking this and similar questions).

Aggregate / Statistical functions are applied to the breakdown rows of data in the freeform table - as opposed to the raw data.  Here is a simple example.  You can see that the mean pageviews per visit column has the same value for all rows:

Screen Shot 2018-03-07 at 1.43.25 PM.png

Pageviews per visit is defined like this:

Screen Shot 2018-03-07 at 1.45.41 PM.png

Mean pageviews per visit is defined like this (note it includes a function):

Screen Shot 2018-03-07 at 1.46.09 PM.png

Why does the mean function return 6.66 and why does the summary in the "Pageviews per Visits" column return 6.71?

6.66 is the average of the values in the "Pageviews per Visits" column - the average of 7 values.  That is how the Adobe functions work in calculated metrics.  The overall value in the "Pageviews per Visits" column is the total number of pageviews over the 7 days divided by the total number of visits over the 7 days.  The math for these helps you see why they are not the same thing:

RB 2018-03-07 16.48.41.jpg