Although many universities and summary websites collect student-to-faculty ratios (with “faculty” variously defined), it is hard to find student-to-employee ratios. Total student enrollment is fairly easy to find, and total number of employees not too hard to find for public universities, so one can compute ratios, as I have done for a small number of schools. I’ve not been particularly careful about definitions (like whether headcount or full-time equivalent numbers were used for either student enrollment or employment, nor how student employees are counted), so these numbers should be taken as only roughly indicative and not suitable for direct comparison.
Note: I’ve seen lots of summaries of the growth of administration (variously defined) relative to faculty, but not much about total number of employees.
In 2015, University of California had about 195,000 employees [http://universityofcalifornia.edu/news/ucs-top-10-stories-2015] and about 238,000 students [http://www.universityofcalifornia.edu/sites/default/files/uc_at_a_glance_011615.pdf], for a ratio of only 1.2 students per employee. Note: postdocs are counted as staff, which is correct for the ways postdocs are used at UC, but if one pretended that they were students the ratio could go as high as 1.8 students per employee (actual numbers of postdocs are hard to come by, but the “other academic (postdocs, etc.)” is given as 42,700).
Similarly, University of Michigan had 43,651 students [http://www.ro.umich.edu/report/15enrollmentsummary.pdf] and 45,397 employees [http://orsp.umich.edu/develop-proposal/frequently-required-proposal-data], for 0.96 students per employee.
In contrast, in Fall 2014, California State University (a non-research university) had about 47,417 employees [http://www.calstate.edu/hr/employee-profile/2014/staffing/employees_occupation/em_occupation_headcount.shtml] and 460,200 students [http://www.calstate.edu/AS/stat_reports/2014-2015/f14_01.htm] for ratio of 9.7 students per employee. Michigan State University (a research university without a med school) had about 3.3 students per University employee [Student to University Employee Ratio | Michigan State University].
The California Community Colleges had about 1,555,500 students in Spring 2015 [http://datamart.cccco.edu/Students/Student_Term_Annual_Count.aspx] and 28016.5 full-time equivalents in Fall 2014 [http://employeedata.cccco.edu/asa_code_14.pdf] for 55.5 students per employee.
I suspect that the biggest differences in student-to-employee ratios come from the research/teaching distinction (there are a lot of employees involved in running a research operation), and the biggest differences among research universities come from how large a part of the university budget is dedicated to medical schools, as they have huge numbers of employees and tiny numbers of students. (UCSF has 22,500 employees and 4,560 students+residents [https://www.ucsf.edu/about/facts-figures] for 0.2 students/employee.)
I’m not an economist nor social scientist, so digging up the necessary numbers and doing the appropriate statistical tests to validate this guess is too much bother for me, but I would be interested in reading someone else’s carefully done summary of university employment patterns, particularly for public universities. Anyone know a good source?