I'm trying to find the average salaries for college graduates of specific universities with specific majors. The issue I'm running into is that there isn't good data available for this issue. However, there is good data for the median salaries of graduates of college X and there's good data for the starting salaries of arbitrary major Y nationwide. I was wondering if there is any mathematically correct way to take the data about nationwide starting salaries for majors and combine it with the median starting salaries from specific colleges.
Example to illustrate the point: Let's say that I know that the average electrical engineering student graduates and gets a starting salary of \$60,000. I also know that this student went to "Fantastic College" whose graduates average starting salary is \$80,000. Is there any way to combine these two statistics to find out the average starting salary of an electrical engineering major at "Fantastic College"?
Also, if this sort of combination is possible, would it be able to be done on both means and medians?