Take some people and 'partition' them, that is, for
some positive integer n, have n boxes and put each
person in some one of the n boxes. Each box is a
'partition'. Have no empty boxes.
Okay, pick a measure. Might pick accuracy with a
bow and arrow, skill at adding a column of numbers,
ability to memorize a passage of music, distance on
a broad jump -- you get it, essentially anything.
Now apply the measure to each of the people, and for
each partition get an average for the measures of
the people in that partition.
Now rank the partitions on the averages. Typically
will have no ties -- assume no ties. So, there is
no ambiguity in the ranking.
Note: Likely picking a different measure will
result in a different ranking.
Now pick one more box, A, and move some people from
the partitions into box A from some of the other
boxes, and get the score of the people in box A.
So, here we have an experiment with any people with
any partitions with any measure and have said
nothing, zip, zilch, zero, about ethnicity, race,
income, parent's education, school systems, teachers
unions, school budgets, etc.
Claim: Essentially always, the score of box A will
be significantly lower than the score of the best
partition and significantly higher than the score of
the worst partition. That is, the score of box A
will be, in the word of the OP, 'middling'.
So, just this little thought experiment is enough to
explain the fact that the US is not either the best
or the worst in the world on the PISA tests.
But, if in each partition the people are
homogeneous, then typically the result will be the
same except the difference between partition at the
top of the ranking and the bottom of the ranking
will be larger. Net, both the top and the bottom of
the rankings will have homogeneous populations, and
the diverse partition A will be middling.
For more, if want to compare the school, home life,
etc. of Finland what those aspects of the US, then
compare PISA scores of students in Finland, native
to Finland, with the PISA scores of US students of
recent, native Finnish descent.
Of course, there was
"McKinsey's report, The Economic Impact of the
Achievement Gap in America's Schools"
of 2009. The URLs of the PDFs are no longer live.
There in the "supporting materials" on page 24 is a
bar graph of
"PISA Science Literacy Scale for 15-year-old
students, 2006"
with
Finland 563
Hong Kong 542
Canada 534
Japan 531
Australia 527
US whites 523
...
US average 489
...
Greece 473
Israel 454
US Latinos 439
Now, how can Israel be so low?
Exercise for the reader!