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I'm a math professor. I get asked to write a number of recommendation letters to graduate schools where my honest view of the candidate is "this student would fall somewhere in the bottom 25-50% of their student body. I expect there will be dozens of applicants of similar quality and I have no reason to favor this one except that I have a good personal relationship with him or her."

Logically, this candidate deserves to go as much as any of the dozen similar people in the pool, but I feel that a letter which said the above would be a real disservice to them. Should I refuse to write them? Describe their accomplishments and pointedly ignore that (if my estimates are right) they don't particularly make them stand out?

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    Where are you a math professor? At my university (UGA), students who are in the bottom 50% of the student body would almost never apply to grad school in math. On the other hand, some students in the bottom 50% of the student body at Stanford or Princeton might still be strong candidates. – Pete L. Clark Nov 1 '17 at 2:42
  • Why not just say where the student stands relative to other students at your institution? You're probably not in a good position to know what the applicant pool for that graduate program is like. – Brian Borchers Nov 1 '17 at 3:20
  • @PeteL.Clark Possibly these are students with an applied maths or stats component who are applying for MSc programmes with that kind of flavour. (I am speculating here so the OP should correct me if I am misreading) – Yemon Choi Nov 1 '17 at 4:05
  • Upon further reflection: the word "their" is ambiguous. I thought it applied to the student and thus meant that the student falls in that range of students at the OP's university. But maybe "their" refers to the program being applied to? – Pete L. Clark Nov 1 '17 at 12:45
  • If so: you might be able to guess, but you don't know who is in what percentage of their applicant pool or among enrolled students. So there is no need to include speculation like that in your letter. – Pete L. Clark Nov 1 '17 at 12:58
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I've only been a student, so take this with a grain of salt.

Be honest to them about their abilities and your perception of them before you write a letter for them. Grad school is not a small commitment. See my answer here also, for an answer to a related question. An excerpt which I feel is very relevant:

Be very honest. You have information that they don't have that will be useful for them. I would rather you tell them what you know and have them make the decision for themselves, rather than let them keep doing what they're doing and seeing them fail.

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You may respond as follows to these flocks of mediocre students:

I wouldn't be the best person to write a recommendation letter for you, because (a) my standards are so absurdly high that I can only write a strong recommendation letter for about x% of the students in our department, and (b) I believe that our department doesn't give a solid preparation for grad school to many of our students.

Please don't let this discourage you from approaching other members of the department. I am an anomaly.

Similarly, please don't let this response discourage you from going to grad school.

I wish you all the best with your future endeavors, and best of luck with your grad applications.

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    This is such a passive-aggressive answer. – Drecate Nov 4 '17 at 4:23
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    A simpler, direct answer like “I’m sorry, but I cannot write you a strong recommendation letter.” would be much better. There’s no reason to pile insults (to the student and to your colleagues), or to disingenously encourage the student, on top of the bad news. Say no, and then shut up. – JeffE Nov 4 '17 at 17:08
  • @JeffE - Sure. The full response could be held in reserve and sent if the student asks for more of an explanation. – aparente001 Nov 5 '17 at 13:02

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