2, 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 Meanenter your response hereenter your response here%$enter your response hereenter your response hereenter your response hereOverall Stdeventer your response hereenter your response here%$enter your response hereenter your response hereenter your response here(Round to two decimal places as needed. Type N if the solution is undefined.) Colleges and UniversitiesSchoolType Median SAT Acceptance Rate Expenditures/Student Top 10% HS Graduation % AmherstLib Arts131522$26,6368593 BarnardLib Arts122053$17,6536980 BatesLib Arts124036$17,5545888 BerkeleyUniversity117637$23,6659568 BowdoinLib Arts130024$25,7037890 BrownUniversity128124$24,2018090 Bryn MawrLib Arts125556$18,8477084 Cal TechUniversity140031$102,2629875 CarletonLib Arts130040$15,9047580 Carnegie MellonUniversity122564$33,6075277 Claremont McKennaLib Arts126036$20,3776874 ColbyLib Arts120046$18,8725284 ColgateLib Arts125838$17,5206185 ColumbiaUniversity126829$45,8797890 CornellUniversity128030$37,1378583 DavidsonLib Arts123036$17,7217789 DukeUniversity131025$39,5049191 GeorgetownUniversity127824$23,1157989 GrinnellLib Arts124467$22,3016573 HamiltonLib Arts121538$20,7225185 HarvardUniversity137018$46,9189090 HaverfordLib Arts128535$19,4187187 Johns HopkinsUniversity129048$45,4606986 MiddleburyLib Arts125525$24,7186592 MITUniversity135730$56,7669586 Mount HolyokeLib Arts120061$23,3584783 NorthwesternUniversity123047$28,8517782 OberlinLib Arts124754$23,5916477 OccidentalLib Arts117049$20,1925472 PomonaLib Arts132033$26,6687980 PrincetonUniversity134017$48,1238993 RiceUniversity132724$26,7308588 SmithLib Arts119557$25,2716587 StanfordUniversity137018$61,9219288 SwarthmoreLib Arts131024$27,4877888 U MichiganUniversity119560$21,8537177 U of ChicagoUniversity130045$38,9377473 U of RochesterUniversity115556$38,5975273 U PennsylvaniaUniversity128041$30,8828786 U VaUniversity121837$19,3657788 UCLAUniversity114243$26,8599661 UNCUniversity110932$19,6848273 VassarLib Arts128743$20,1795384 Washington U (MO)University122554$39,8837176 Washington and LeeLib Arts123429$17,9986178 WellesleyLib Arts125049$27,8797686 Wesleyan (CT)Lib Arts129035$19,9487391 WilliamsLib Arts133628$23,7728693 YaleUniversity135019$52,4689093 Distance Matrix After Second Clustering Pomona/RiceOccidental/PrincetonOberlin Pomona/Rice01.57953.2343 Occidental/Princeton 00.0000 Oberlin 0

The data relating to colleges and universities are given. Over all mean=1n∑ XiStandard…

Answered: 2, For the three clusters identified in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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2, 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

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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