The following data are for Fall 2003 courses with enrollments over 150 students. Determine which clustering method works "best" for these data and which variables are most useful in the clustering algorithm. You want a method that gives reasonable separartion of the data and makes sense.
The variables are: Section GPA (a measure of the grades awarded in the course), the Average Cumulative GPA (a measure of the overall GPA of the students in the course. It includes the student's grade for the section under consideration.), GPA/Total Grades (a measure of the retention rate since students who withdraw before the automatic withdrawal deadline do not get GPA grades in the course.)
The math department prides itself on giving out some of the lowest grades in the university. Do the large-lecture math courses cluster together? Which other courses are in that cluster? Do all the courses in the cluster have relatively low section GPAs?
DEPT CRSE SECTGPA AVECUMGPA GPA/Total_Grades Concatenated_Dept/Course CSCI A201 2.54 2.82 0.562500 CSCIA201 BIOL L112 2.55 3.00 0.718750 BIOLL112 ANTH E105 2.59 2.92 0.745223 ANTHE105 AST A100 3.12 2.94 0.782895 AST A100 HIST H205 2.80 2.95 0.797386 HISTH205 MUS A101 2.29 2.70 0.778481 MUS A101 CLAS C101 2.76 2.94 0.776398 CLASC101 CHEM C342 2.37 3.19 0.649485 CHEMC342 MUS T109 3.10 3.16 0.824675 MUS T109 BUS A100 2.66 3.05 0.730337 BUS A100 HIST H105 3.05 2.96 0.861842 HISTH105 BUS A100 2.51 3.09 0.798780 BUS A100 BUS A100 2.58 3.06 0.775148 BUS A100 BIOL L318 3.03 3.25 0.851613 BIOLL318 PHYS P201 2.71 3.14 0.830189 PHYSP201 BUS A100 2.51 2.93 0.826087 BUS A100 BUS A100 2.53 3.08 0.817073 BUS A100 HIST H105 3.12 2.87 0.870968 HISTH105 PHYS P150 3.10 2.97 0.813253 PHYSP150 CHEM C117 3.26 3.27 0.894737 CHEMC117 BIOL L111 2.45 3.02 0.913333 BIOLL111 GEOG G120 2.90 3.01 0.826347 GEOGG120 BUS A100 2.60 3.09 0.827381 BUS A100 BIOL Q201 2.68 3.17 0.927152 BIOLQ201 BUS X220 3.89 3.13 0.921053 BUS X220 HPER F255 3.37 2.92 0.886076 HPERF255 PSY P211 3.21 3.11 0.853659 PSY P211 BUS L201 2.73 3.08 0.795455 BUS L201 CLAS C102 2.70 2.91 0.829412 CLASC102 MUS F450 3.99 3.63 0.815029 MUS F450 REL R153 3.18 3.09 0.810345 REL R153 BUS A100 2.75 3.16 0.855422 BUS A100 GEOG G109 2.75 2.90 0.740933 GEOGG109 BUS A100 2.74 3.04 0.852071 BUS A100 BUS A100 2.62 2.91 0.852071 BUS A100 HPER H263 3.46 2.90 0.941558 HPERH263 COAS E104 3.85 3.13 0.929487 COASE104 PHYS P202 2.97 3.24 0.929487 PHYSP202 CHEM C343 3.26 3.31 0.900621 CHEMC343 BUS A100 2.43 3.01 0.828571 BUS A100 PHYS P201 2.74 3.13 0.792350 PHYSP201 CJUS P290 3.11 2.99 0.941935 CJUSP290 BIOL M200 2.99 3.26 0.901235 BIOLM200 EDUC M135 3.71 3.31 0.884848 EDUCM135 BUS A100 2.51 3.04 0.874251 BUS A100 CLAS C205 2.58 3.01 0.880240 CLASC205 JOUR J300 2.96 3.07 0.973684 JOURJ300 MUS Z320 2.87 2.92 0.840909 MUS Z320 BIOL L104 3.17 3.06 0.974026 BIOLL104 BUS Z574 4.00 3.55 0.993464 BUS Z574 BIOL L112 2.82 3.07 0.821622 BIOLL112 BUS L201 2.36 2.99 0.885057 BUS L201 BIOL L211 2.45 3.19 0.950920 BIOLL211 BUS L201 2.84 3.06 0.911765 BUS L201 JOUR J110 2.83 2.96 0.906433 JOURJ110 FOLK F131 3.11 2.94 0.918605 FOLKF131 POLS Y100 3.32 3.10 0.952663 POLSY100 HIST H101 2.84 3.00 0.941520 HISTH101 JOUR J110 2.96 3.04 0.941520 JOURJ110 ANTH A105 2.94 2.97 0.830769 ANTHA105 POLS Y100 3.40 3.09 0.958824 POLSY100 BUS L201 2.49 3.11 0.947674 BUS L201 REL R170 2.77 3.00 0.881081 REL R170 BUS A200 3.21 3.04 0.942857 BUS A200 BUS L201 2.86 3.09 0.959538 BUS L201 LLC Q199 3.92 3.11 0.766055 LLC Q199 CJUS P100 2.80 2.85 0.943820 CJUSP100 MUS X050 3.97 3.09 0.982659 MUS X050 BUS X420 3.97 3.23 0.960894 BUS X420 GEOG G107 3.17 2.95 0.910526 GEOGG107 GEOL G103 2.50 2.84 0.812207 GEOLG103 CHEM C117 3.07 3.19 0.896907 CHEMC117 HIST H106 2.38 2.91 0.753247 HISTH106 CMCL C205 2.51 2.91 0.864734 CMCLC205 PHSL P215 2.75 3.04 0.918367 PHSLP215 BUS X420 3.96 3.23 0.957672 BUS X420 MUS Z320 3.04 2.96 0.916256 MUS Z320 PHYS Q202 2.91 3.11 0.945000 PHYSQ202 BUS G302 3.13 3.21 0.935644 BUS G302 BUS X420 3.98 3.24 0.954774 BUS X420 BUS Z302 3.14 3.12 0.900943 BUS Z302 HPER P211 3.36 2.91 0.906103 HPERP211 BUS Z302 3.11 3.18 0.956098 BUS Z302 BUS Z302 3.27 3.24 0.929245 BUS Z302 MSCI M131 2.88 3.08 0.925234 MSCIM131 HPER H318 2.75 2.81 0.912442 HPERH318 PSY P101 2.87 2.99 0.872247 PSY P101 HPER R160 2.91 2.87 0.917051 HPERR160 HIST A300 2.11 2.96 0.858974 HISTA300 AST A100 2.74 2.92 0.867521 AST A100 POLS Y103 2.69 2.98 0.902655 POLSY103 ECON E201 2.52 3.04 0.811024 ECONE201 AST A105 2.85 2.97 0.888889 AST A105 CHEM C101 2.75 2.92 0.888889 CHEMC101 EDUC U211 3.94 3.09 0.945701 EDUCU211 FINA A101 2.94 2.97 0.901709 FINAA101 PSY P101 2.57 2.91 0.796226 PSY P101 MATH M118 2.51 2.89 0.739583 MATHM118 PSY P101 2.78 2.95 0.830116 PSY P101 MATH M118 2.46 2.90 0.749129 MATHM118 MATH M118 2.55 2.99 0.774194 MATHM118 AST A105 2.93 3.05 0.924051 AST A105 HPER P212 3.08 2.95 0.916667 HPERP212 JOUR C201 2.69 2.83 0.827068 JOURC201 ECON E370 2.85 3.12 0.864341 ECONE370 MATH M118 2.51 3.01 0.758503 MATHM118 MATH M119 2.46 3.00 0.780488 MATHM119 BUS X220 3.88 3.14 0.907258 BUS X220 PSY P101 3.62 3.06 0.865900 PSY P101 PSY P101 3.12 3.09 0.890196 PSY P101 ENG W143 3.05 3.00 0.869732 ENG W143 FOLK F101 3.10 2.84 0.838235 FOLKF101 MATH M118 2.54 2.82 0.790378 MATHM118 BUS A200 2.84 2.85 0.954733 BUS A200 BUS X220 3.95 3.16 0.935743 BUS X220 PSY P101 2.99 2.91 0.914063 PSY P101 CHEM C103 2.90 3.04 0.864964 CHEMC103 ECON E201 2.46 2.99 0.759615 ECONE201 PSY P101 2.91 3.09 0.912214 PSY P101 MATH M119 2.63 3.05 0.826990 MATHM119 PSY P102 2.63 2.88 0.930233 PSY P102 BIOL L111 2.76 3.11 0.876364 BIOLL111 PSY P101 3.11 3.05 0.934363 PSY P101 BIOL L111 2.49 2.89 0.910448 BIOLL111 BUS X220 3.95 3.35 0.983936 BUS X220 CJUS P100 2.74 2.96 0.907407 CJUSP100 MATH M119 2.56 2.94 0.824916 MATHM119 PSY P101 3.27 3.01 0.953488 PSY P101 PSY P101 3.27 3.01 0.942529 PSY P101 CMCL C190 2.91 2.95 0.852234 CMCLC190 BUS X100 2.88 2.93 0.965116 BUS X100 POLS Y103 2.74 2.90 0.896429 POLSY103 PSY P102 3.03 3.14 0.940959 PSY P102 BUS X100 3.06 3.06 0.969697 BUS X100 BUS X100 2.94 3.01 0.970149 BUS X100 BUS X201 3.19 3.19 0.844156 BUS X201 BUS X100 3.02 3.04 0.992424 BUS X100 ENG L141 3.25 3.06 0.929577 ENG L141 CJUS P202 3.59 2.99 0.934483 CJUSP202 HPER H160 3.54 2.97 0.954545 HPERH160 COAS X112 3.17 2.80 0.904605 COASX112 CHEM C126 2.85 3.16 0.864615 CHEMC126 CHEM C341 2.71 3.22 0.820290 CHEMC341 ECON E201 2.47 2.95 0.796657 ECONE201 BUS X201 3.36 3.32 0.911392 BUS X201 HIST A300 3.44 3.07 0.938312 HISTA300 HIST H106 2.94 2.90 0.913846 HISTH106 HIST H105 2.95 2.91 0.871345 HISTH105 ECON E202 2.57 2.96 0.837989 ECONE202 CHEM C106 2.71 3.08 0.862464 CHEMC106 ECON E201 2.43 2.96 0.881356 ECONE201 COAS X112 2.97 2.71 0.927374 COASX112 ANAT A215 2.54 3.00 0.877922 ANATA215 CJUS P100 2.72 2.89 0.939058 CJUSP100 CJUS P200 3.17 2.90 0.939560 CJUSP200 MUS Z401 3.44 3.04 0.914667 MUS Z401 MUS Z301 2.91 2.98 0.917553 MUS Z301 MUS Z201 3.11 3.00 0.907895 MUS Z201 SOC S100 2.78 2.92 0.882494 SOC S100 PSY P101 2.79 2.88 0.929412 PSY P101 MUS X070 3.82 3.47 0.955036 MUS X070 MUS X040 3.96 3.64 0.946839 MUS X040