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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!



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