<p>It may also depend on what “mediocre HS” actually means.</p>
<p>Suppose two high schools have similar not very good rankings in terms of test scores, students going to college, etc. But:</p>
<ul>
<li>School A offers courses so that a college bound student who takes them will be well prepared for college, without needing remedial courses. If AP courses are offered, students who do well in them do well in the AP tests, and are well prepared for subsequent courses in college.</li>
<li>School B offers courses that are low quality so that a student who does well in the most rigorous and advanced courses is still likely to need remedial courses in college. If AP courses are offered, students taking them typically score 1 on the AP test.</li>
</ul>
<p>If School A is the “mediocre HS”, the advantage of going to an elite HS is much less than if School B is the “mediocre HS”. Indeed, a good, but not great, student may find an elite HS to be too competitive relative to School A, and may not be academically able to take more rigorous and advanced courses than s/he would have taken at School A. On the other hand, attending School B is generally undesirable for any college-bound student.</p>
<p>There can also be non-academic issues at some “mediocre HSs” but not others. E.g. the presence of criminal gangs.</p>