The solution that first popped into my head involved the use of an SQL JOIN to take advantage of the one-to-many relationship between markers and windows.   Coding off the top of my head, something like:

  SELECT m.coordinate, AVERAGE(i.quantitativeValue) 
    FROM markers m 
      INNER JOIN intervals i
        ON  (m.coordinate >= i.lowCoordinate) 
        AND (m.coordinate <= i.highCoordinate)
    GROUP BY m.coordinate
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Looking over the SQL I’ve just written, I wonder if this is, indeed, the solution to your problem.   The more I look at it, the more that I think that it is.   This will equally accommodate there being just one intervals row for each marker, or more than one.