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? Compute the overall mean and overall standard deviation for each numerical variable.       Median   SAT  Acceptance  Rate   Expenditures   /Student  Top 10% HS   Graduation %  Overall Mean enter your response here enter your response here​% ​$enter your response here enter your response here enter your response here Overall Stdev enter your response here enter your response here​% ​$enter your response here enter your response here enter your response here ​(Round to two decimal places as needed. Type N if the solution is​ undefined.)   Colleges and Universities School Type  Median SAT   Acceptance Rate   Expenditures/Student   Top 10% HS   Graduation %    Amherst Lib Arts 1315 22 $26,636 85 93   Barnard Lib Arts 1220 53 $17,653 69 80   Bates Lib Arts 1240 36 $17,554 58 88   Berkeley University 1176 37 $23,665 95 68   Bowdoin Lib Arts 1300 24 $25,703 78 90   Brown University 1281 24 $24,201 80 90   Bryn Mawr Lib Arts 1255 56 $18,847 70 84   Cal Tech University 1400 31 $102,262 98 75   Carleton Lib Arts 1300 40 $15,904 75 80   Carnegie Mellon University 1225 64 $33,607 52 77   Claremont McKenna Lib Arts 1260 36 $20,377 68 74   Colby Lib Arts 1200 46 $18,872 52 84   Colgate Lib Arts 1258 38 $17,520 61 85   Columbia University 1268 29 $45,879 78 90   Cornell University 1280 30 $37,137 85 83   Davidson Lib Arts 1230 36 $17,721 77 89   Duke University 1310 25 $39,504 91 91   Georgetown University 1278 24 $23,115 79 89   Grinnell Lib Arts 1244 67 $22,301 65 73   Hamilton Lib Arts 1215 38 $20,722 51 85   Harvard University 1370 18 $46,918 90 90   Haverford Lib Arts 1285 35 $19,418 71 87   Johns Hopkins University 1290 48 $45,460 69 86   Middlebury Lib Arts 1255 25 $24,718 65 92   MIT University 1357 30 $56,766 95 86   Mount Holyoke Lib Arts 1200 61 $23,358 47 83   Northwestern University 1230 47 $28,851 77 82   Oberlin Lib Arts 1247 54 $23,591 64 77   Occidental Lib Arts 1170 49 $20,192 54 72   Pomona Lib Arts 1320 33 $26,668 79 80   Princeton University 1340 17 $48,123 89 93   Rice University 1327 24 $26,730 85 88   Smith Lib Arts 1195 57 $25,271 65 87   Stanford University 1370 18 $61,921 92 88   Swarthmore Lib Arts 1310 24 $27,487 78 88   U Michigan University 1195 60 $21,853 71 77   U of Chicago University 1300 45 $38,937 74 73   U of Rochester University 1155 56 $38,597 52 73   U Pennsylvania University 1280 41 $30,882 87 86   U Va University 1218 37 $19,365 77 88   UCLA University 1142 43 $26,859 96 61   UNC University 1109 32 $19,684 82 73   Vassar Lib Arts 1287 43 $20,179 53 84   Washington U (MO) University 1225 54 $39,883 71 76   Washington and Lee Lib Arts 1234 29 $17,998 61 78   Wellesley Lib Arts 1250 49 $27,879 76 86   Wesleyan (CT) Lib Arts 1290 35 $19,948 73 91   Williams Lib Arts 1336 28 $23,772 86 93   Yale University 1350 19 $52,468 90 93   Distance Matrix After Second Clustering   Pomona/Rice Occidental/Princeton Oberlin   Pomona/Rice 0 1.5795 3.2343   Occidental/Princeton   0 0.0000   Oberlin     0

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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?

Compute the overall mean and overall standard deviation for each numerical variable.
 
 
  Median  
SAT
 Acceptance 
Rate
  Expenditures  
/Student
 Top 10% HS 
 Graduation % 
Overall Mean
enter your response here
enter your response here​%
​$enter your response here
enter your response here
enter your response here
Overall Stdev
enter your response here
enter your response here​%
​$enter your response here
enter your response here
enter your response here
​(Round to two decimal places as needed. Type N if the solution is​ undefined.)
 
Colleges and Universities
School
Type
 Median SAT 
 Acceptance Rate 
 Expenditures/Student 
 Top 10% HS 
 Graduation % 
 
Amherst
Lib Arts
1315
22
$26,636
85
93
 
Barnard
Lib Arts
1220
53
$17,653
69
80
 
Bates
Lib Arts
1240
36
$17,554
58
88
 
Berkeley
University
1176
37
$23,665
95
68
 
Bowdoin
Lib Arts
1300
24
$25,703
78
90
 
Brown
University
1281
24
$24,201
80
90
 
Bryn Mawr
Lib Arts
1255
56
$18,847
70
84
 
Cal Tech
University
1400
31
$102,262
98
75
 
Carleton
Lib Arts
1300
40
$15,904
75
80
 
Carnegie Mellon
University
1225
64
$33,607
52
77
 
Claremont McKenna
Lib Arts
1260
36
$20,377
68
74
 
Colby
Lib Arts
1200
46
$18,872
52
84
 
Colgate
Lib Arts
1258
38
$17,520
61
85
 
Columbia
University
1268
29
$45,879
78
90
 
Cornell
University
1280
30
$37,137
85
83
 
Davidson
Lib Arts
1230
36
$17,721
77
89
 
Duke
University
1310
25
$39,504
91
91
 
Georgetown
University
1278
24
$23,115
79
89
 
Grinnell
Lib Arts
1244
67
$22,301
65
73
 
Hamilton
Lib Arts
1215
38
$20,722
51
85
 
Harvard
University
1370
18
$46,918
90
90
 
Haverford
Lib Arts
1285
35
$19,418
71
87
 
Johns Hopkins
University
1290
48
$45,460
69
86
 
Middlebury
Lib Arts
1255
25
$24,718
65
92
 
MIT
University
1357
30
$56,766
95
86
 
Mount Holyoke
Lib Arts
1200
61
$23,358
47
83
 
Northwestern
University
1230
47
$28,851
77
82
 
Oberlin
Lib Arts
1247
54
$23,591
64
77
 
Occidental
Lib Arts
1170
49
$20,192
54
72
 
Pomona
Lib Arts
1320
33
$26,668
79
80
 
Princeton
University
1340
17
$48,123
89
93
 
Rice
University
1327
24
$26,730
85
88
 
Smith
Lib Arts
1195
57
$25,271
65
87
 
Stanford
University
1370
18
$61,921
92
88
 
Swarthmore
Lib Arts
1310
24
$27,487
78
88
 
U Michigan
University
1195
60
$21,853
71
77
 
U of Chicago
University
1300
45
$38,937
74
73
 
U of Rochester
University
1155
56
$38,597
52
73
 
U Pennsylvania
University
1280
41
$30,882
87
86
 
U Va
University
1218
37
$19,365
77
88
 
UCLA
University
1142
43
$26,859
96
61
 
UNC
University
1109
32
$19,684
82
73
 
Vassar
Lib Arts
1287
43
$20,179
53
84
 
Washington U (MO)
University
1225
54
$39,883
71
76
 
Washington and Lee
Lib Arts
1234
29
$17,998
61
78
 
Wellesley
Lib Arts
1250
49
$27,879
76
86
 
Wesleyan (CT)
Lib Arts
1290
35
$19,948
73
91
 
Williams
Lib Arts
1336
28
$23,772
86
93
 
Yale
University
1350
19
$52,468
90
93
 
Distance Matrix After Second Clustering
 
Pomona/Rice
Occidental/Princeton
Oberlin
 
Pomona/Rice
0
1.5795
3.2343
 
Occidental/Princeton
 
0
0.0000
 
Oberlin
 
 
0
 
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