What is the median math GRE subject score for admission to a Group 2 or 3 PhD program in applied mathematics?

Question

What are the typical (median or maybe third quartile) scores on the math subject GRE for successful applicants to a math program at the PhD level, in applied math, at a Group 2 or Group 3¹ school?

¹This is a ranking system the American Mathematical Society uses for graduate programs. Generally, Group 1 schools are considered the best, while Group 2 and 3 schools tend to be smaller and less prestigious.

Answer 1

This may not exactly answer your question though... Below are "official" statistics for two group-one (?) pure math programs. Note that whether a score is "acceptable" might also depend on whether you are domestic student or not (based on the Ohio State data).

(Since my reputation is too low to add more than two links in an answer, I can't provide more information at present. But I'll definitely update this answer once my reputation grows...)

Ohio State University: http://www.math.osu.edu/graduate/apply

"There are no a-priori minimum scores for the test set by our program. However, admissions become rare below the 50th percentile. The distribution of percentiles of subject test scores of Ph.D.-applicants we admitted between 2009 and 2012 is depicted below.

The data over the four admission cycles includes 125 domestic (in red) and 129 international (in pink) applicants. The median percentile for domestic students is 67, the one for international students is 95."

University of Pennsylvania: http://www.math.upenn.edu/grad/graddata.html

"Scores on the Advanced Math Subject Test of the GRE should be at least 750, though applicants with somewhat lower scores may be admitted if the rest of their application is sufficiently strong. The average GRE scores of the students who entered our Ph.D. program in the recent past were: Verbal: 597; Quantitative: 789; Advanced Math Subject Test: 820."

Edit: More data...

Cornell: http://www.math.cornell.edu/m/Graduate/app_details.html

"Most successful applicants score 700 or above on their GRE subject test."

Georgia Tech: http://www.math.gatech.edu/academics/graduate/faqs-graduate-admissions#MINGRE

"The PhD entering class in Fall 2006 had the following averages: ... Subj 795"

UIUC: http://www.math.illinois.edu/GraduateProgram/apply-phd.html

"Mathematics subject GRE scores of entering Ph.D. students in 2013: upper quartile 850, median 790, and lower quartile 690."

Penn State: http://www.math.psu.edu/grad/phd/faq.php ("Listed below are the average scores of students accepted to our program for the last several years...")

Answer 2

The NRC data has information on average GRE tests for EVERY math school: https://docs.google.com/spreadsheet/ccc?key=0Amalxehk80PwdHRYSUpuWVVaa0VVVWRidXR6X21LZ0E#gid=0

Here's some caveats: the NRC data is known to have issues. "Average GRE scores" in the spreadsheet doesn't specify what it means. There are several possibilities:

1. it's the mathematics GRE test
2. it's the general test
3. NRC didn't specify which test they wanted when they sent out the survey to the schools, so for some schools it is one and for some schools it is the other

And there are two clear indicators of issues:

1. the prevalence of the number 800
2. the prevalence of the number 777

These wouldn't appear in true averages. So take it with a grain of salt, or maybe a bucket of salt.