For the three clusters identified in the accompanying Distance Matrix After Second Clustering table, find the average and standard deviations of each numerical variable for the schools in each cluster and compare them with the average and standard deviation for the entire data set. Does the clustering show distinct differences among these clusters? Click to view the Colleges and Universities data. Click to view the Distance Matrix After Second Clustering data. Compute the overall mean and overall standard deviation for each numerical variable. Median Acceptance Expenditures SAT Rate /Student Top 10% HS Graduation % Overall Mean % Overall Stdev (Round to two decimal places as needed. Type N if the solution is undefined.) % A B C D E F G 1 School Type Median SAT Acceptance Rate Expenditures/Student Top 10% HS Graduation % 23456580 Amherst Lib Arts 1315 22 26636 85 93 Barnard Lib Arts 1220 53 17653 69 80 Bates Lib Arts 1240 36 17554 58 88 5 Berkeley University 1176 37 23665 95 68 6 Bowdoin Lib Arts 1300 24 25703 78 90 7 Brown University 1281 24 24201 80 90 8 Bryn Mawr Lib Arts 1255 56 18847 70 84 9 Cal Tech University 1400 31 102262 98 75 10 Carleton Lib Arts 1300 40 15904 75 80 11 Carnegie Mellon University 1225 64 33607 52 77 12 Claremont McKenna Lib Arts 1260 36 20377 68 74 13 Colby Lib Arts 1200 46 18872 52 84 14 Colgate Lib Arts 1258 38 17520 61 85 15 Columbia University 1268 29 45879 78 90 16 Cornell University 1280 30 37137 85 83 17 Davidson Lib Arts 1230 36 17721 77 89 18 Duke University 1310 25 39504 91 91 19 Georgetown University 1278 24 23115 79 89 20 Grinnell Lib Arts 1244 67 22301 65 73 21 Hamilton Lib Arts 1215 38 20722 51 85 22 Harvard University 1370 18 46918 90 90 23 Haverford Lib Arts 1285 35 19418 71 87 24 Johns Hopkins University 1290 48 45460 69 86 25 Middlebury Lib Arts 1255 25 24718 65 92 26 MIT University 1357 30 56766 95 86 27 Mount Holyoke Lib Arts 1200 61 23358 47 83 28 Northwestern University 1230 47 28851 77 82 29 Oberlin Lib Arts 1247 54 23591 64 77 30 Occidental Lib Arts 1170 49 20192 54 72 31 Pomona Lib Arts 1320 33 26668 79 80 32 Princeton University 1340 17 48123 89 93 33 Rice University 1327 24 26730 85 88 34 Smith Lib Arts 1195 57 25271 65 87 35 Stanford University 1370 18 61921 92 88 36 Swarthmore Lib Arts 1310 24 27487 78 88 37 U Michigan University 1195 60 21853 71 77 38 U of Chicago University 1300 45 38937 74 73 39 U of Rochester University 1155 56 38597 52 73 40 U Pennsylvania University 1280 41 30882 87 86 41 UVa 42 UCLA 43 UNC University 1218 37 19365 77 88 University 1142 43 26859 96 61 University 1109 32 19684 82 73 44 Vassar Lib Arts 1287 43 20179 53 84 45 Washington U (MO) University 1225 54 39883 71 76 46 Washington and Lee Lib Arts 1234 29 17998 61 78 47 Wellesley Lib Arts 1250 49 27879 76 86 48 Wesleyan (CT) Lib Arts 1290 35 19948 73 91 49 Williams Lib Arts 1336 28 23772 86 93 50 Yale 51 University 1350 19 52468 90 93