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

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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