k-mean clustering
rm(list = ls())
mydata<-read.csv("E:\\EXCELR ASSIGMENTS\\assignment\\EastWestAirlines.csv")
View(mydata)
mydata1<-mydata[1:100,]
View(mydata1)
library(readxl)
normalized_data <- scale(mydata1[,2:12]) # Excluding the university name
View(normalized_data)
plot(normalized_data)
# Calculate Distance
d <- dist(normalized_data,method="euclidean") # Distance matrix
d## 1 2 3 4 5
## 2 0.15113328
## 3 0.40432155 0.38480774
## 4 0.16265072 0.11984531 0.47742498
## 5 5.22389111 5.17861077 4.97147609 5.23015427
## 6 0.19921089 0.22173421 0.56512123 0.11243256 5.29355825
## 7 3.35198833 3.28514477 3.01279088 3.36622876 3.24941780
## 8 2.18808810 2.17052779 2.16261565 2.18146534 4.34369098
## 9 13.14974993 13.13643515 13.01393457 13.18318780 11.62474618
## 10 4.42044042 4.36307632 4.13995588 4.43231011 1.43742273
## 11 1.29867420 1.22844418 1.03925563 1.30590455 4.28658964
## 12 5.34366549 5.31333302 5.10640669 5.34606945 2.60365512
## 13 2.24700656 2.15388911 1.92118994 2.24734608 3.89270144
## 14 0.59937112 0.51295520 0.34196523 0.60928157 4.88824897
## 15 0.24539589 0.24796490 0.58982113 0.14442441 5.29230276
## 16 4.34873610 4.31048918 4.13524530 4.33673119 2.56693991
## 17 4.37670584 4.33987323 4.15196126 4.37046032 2.47470313
## 18 2.18153861 2.15397683 2.15122042 2.16812784 4.47058654
## 19 3.49492171 3.45391775 3.25795186 3.50413314 2.64007124
## 20 2.73385310 2.71355942 2.68203217 2.72400058 3.70238724
## 21 5.50195503 5.46660301 5.24700289 5.50803976 2.12596945
## 22 5.72379749 5.71258850 5.59798736 5.74877471 5.14841396
## 23 4.42964210 4.40115207 4.37010969 4.42363442 4.72943895
## 24 1.18795540 1.10660698 0.90058197 1.20702315 4.57750568
## 25 3.73781201 3.75564625 3.46451099 3.85128111 4.80906181
## 26 2.12962033 2.18781988 2.03977793 2.23688546 5.52835251
## 27 2.43450067 2.49350247 2.38688129 2.52730197 5.26568163
## 28 2.09085165 2.16630347 2.07958279 2.19366997 5.75264326
## 29 4.30156499 4.29394182 4.03444612 4.35761225 3.19406480
## 30 3.08598501 3.11008348 2.97012405 3.15732533 4.61368734
## 31 3.33321131 3.37123872 3.06490854 3.44379021 4.27932258
## 32 2.01066816 2.08664191 2.00140434 2.11386710 5.72077128
## 33 4.96461613 4.98078321 4.64722741 5.05588047 4.05162387
## 34 1.97834463 2.05192172 1.94786355 2.08588611 5.64952530
## 35 1.97728790 2.06499562 1.95098209 2.09768726 5.67538722
## 36 5.83232275 5.82718405 5.57721135 5.88104454 2.23669027
## 37 3.04856345 3.08670819 2.99195580 3.12046469 4.78504223
## 38 2.08915490 2.16978824 2.01697018 2.21481863 5.37129845
## 39 3.97220701 3.97042964 3.72814181 4.03092394 3.37831692
## 40 2.87305389 2.92301160 2.87141948 2.94065782 5.29748549
## 41 2.03383130 2.09350999 1.93666519 2.14403938 5.25047804
## 42 4.96679448 4.93718503 4.69812136 5.00084481 3.10959321
## 43 5.46786452 5.44770929 5.27309512 5.51248797 3.96786831
## 44 6.38333472 6.44855864 6.17923857 6.51250183 5.90534182
## 45 3.27300520 3.27866267 2.97582026 3.36253828 4.02819038
## 46 4.60801013 4.61414677 4.41692853 4.65999635 3.81918979
## 47 1.27692139 1.26138651 1.06072979 1.31003798 4.35979152
## 48 2.29668670 2.27076463 2.23656862 2.29117929 4.13928010
## 49 4.07903140 4.01939315 3.80321714 4.07812079 1.91441262
## 50 1.55698515 1.52314396 1.56027009 1.53610811 4.64698745
## 51 6.07024210 6.06968322 6.04112143 6.07913233 5.86251468
## 52 0.38442206 0.29792306 0.64032248 0.22600522 5.25349014
## 53 5.61562562 5.54993137 5.30150585 5.62221707 2.53416048
## 54 2.54398631 2.53609035 2.42971493 2.57545538 3.90789830
## 55 0.34605787 0.36527583 0.61795782 0.31473906 5.27297496
## 56 0.63937388 0.50188441 0.53272976 0.57608014 4.96030705
## 57 3.30597504 3.26758331 3.07025542 3.30631240 3.33314302
## 58 2.38713297 2.36591452 2.35793062 2.38113843 4.14386770
## 59 2.51019505 2.47369861 2.30216102 2.49144807 3.74678929
## 60 4.66313890 4.61722132 4.45390079 4.66965636 1.57634872
## 61 2.45423782 2.41977399 2.19187786 2.48582994 3.69885820
## 62 1.43322924 1.33846127 1.11086436 1.40139468 4.43020080
## 63 0.36475236 0.32821111 0.67339876 0.23189994 5.30399485
## 64 3.42376431 3.46420404 3.18862570 3.51121049 4.96942787
## 65 0.61100280 0.62606863 0.63497604 0.65288745 5.12263958
## 66 10.77189384 10.72566924 10.60738811 10.76887240 7.64678981
## 67 0.77192716 0.63193561 0.64967029 0.70213544 4.92311141
## 68 3.54457996 3.49590321 3.28134168 3.54459115 3.18968971
## 69 3.64490025 3.64486956 3.43927301 3.68967661 3.16915762
## 70 3.60115974 3.59626882 3.39743948 3.65991261 3.58268471
## 71 10.07893512 10.07975430 10.00103907 10.10372010 10.33434638
## 72 4.32296121 4.36019837 4.05466324 4.41732517 4.10010836
## 73 5.44174582 5.51078962 5.22700184 5.57915275 5.81861761
## 74 2.18457287 2.22865413 2.11638715 2.27083336 5.15279503
## 75 3.28505143 3.29195838 2.97770612 3.36967317 3.89875096
## 76 3.44207860 3.43356905 3.12756243 3.52665489 3.95260803
## 77 2.47125841 2.48095410 2.16026124 2.58187447 4.78000386
## 78 3.97021860 3.96830481 3.68270356 4.03623794 3.70100925
## 79 4.53479682 4.52688920 4.29417468 4.57897018 3.10041000
## 80 6.03601673 6.03103813 5.79968920 6.06051399 3.36320853
## 81 3.21953305 3.24046711 3.05782252 3.26314683 4.42407005
## 82 1.52020106 1.52317540 1.49943834 1.54364180 4.64716829
## 83 0.95689753 0.81947536 0.79864875 0.90030861 4.87194760
## 84 0.72258893 0.65187454 0.55250698 0.73138165 4.91687730
## 85 0.76290477 0.63562701 0.61622994 0.71202533 4.90462789
## 86 5.33106308 5.29118277 5.12159852 5.31650323 1.89661280
## 87 2.22986787 2.20532621 2.17696639 2.21925155 4.36440569
## 88 6.43128909 6.45537748 6.20430799 6.51901225 5.40745727
## 89 2.01122311 1.92824258 1.74012332 2.01029155 3.73159057
## 90 2.25996602 2.24207547 2.24110091 2.25280000 4.28131098
## 91 3.10157756 3.06616535 2.98740226 3.08029021 3.41257450
## 92 2.19825506 2.16494899 2.20832327 2.16906664 4.57728413
## 93 4.53049444 4.47348239 4.27127741 4.52804856 2.23060994
## 94 2.92110839 2.92523663 2.85586498 2.94776937 3.89398518
## 95 9.55399826 9.51699332 9.28677349 9.55682023 5.12874666
## 96 1.68016482 1.55468585 1.42190638 1.64544493 4.58584471
## 97 2.42155008 2.31416629 2.10964925 2.41380643 4.36531242
## 98 3.76050317 3.72048771 3.50347646 3.75849161 3.24079488
## 99 0.65109679 0.53754736 0.67732271 0.55941137 5.06403639
## 100 3.16844371 3.12468359 2.99447327 3.16124494 2.99097469
## 6 7 8 9 10
## 2
## 3
## 4
## 5
## 6
## 7 3.45580566
## 8 2.20197767 3.70302948
## 9 13.21525393 12.35225039 12.76937470
## 10 4.50717714 2.52252678 3.45413999 11.63238954
## 11 1.39020953 2.10371019 2.37881866 12.75797376 3.46735901
## 12 5.39799323 3.23640668 4.64019053 12.67136840 2.83634319
## 13 2.34700717 1.33822876 2.86736420 12.50718325 2.94296831
## 14 0.70193181 2.88115266 2.16550192 12.94226564 4.01893253
## 15 0.06917795 3.45690080 2.20258483 13.21235028 4.50541027
## 16 4.38862539 2.79587726 3.52052154 12.71835199 2.43415408
## 17 4.42363334 2.71698866 3.55104128 12.62995111 2.31294900
## 18 2.19292261 3.65352508 0.38071863 12.87682211 3.52195866
## 19 3.56357817 2.28806103 2.49803224 12.31574642 1.76533393
## 20 2.74621941 3.17867997 1.64143892 12.76295631 3.01538029
## 21 5.56513891 3.18680272 4.76129587 12.32825766 2.46173292
## 22 5.77773425 5.70338936 5.03471497 12.05870541 4.79843047
## 23 4.45029980 5.00421743 4.53734631 11.95317639 4.62100846
## 24 1.29578988 2.56036858 2.28656249 12.63586925 3.64308591
## 25 3.91858266 3.50864868 4.15481917 12.06645306 4.03458886
## 26 2.27711575 3.75501680 3.11015003 13.25141794 4.77739086
## 27 2.55409503 4.07563921 3.22530561 12.95133010 4.71837585
## 28 2.21411604 4.05014120 3.12996598 13.41641980 5.04328188
## 29 4.42787069 3.05091768 3.54669538 12.46641046 2.66505661
## 30 3.20102296 4.05657896 2.23408748 12.76819757 3.81498717
## 31 3.50018243 2.55962309 3.90661391 12.57631178 3.74763765
## 32 2.13415442 4.00771893 3.07354816 13.40051459 5.00661664
## 33 5.11944759 2.85710325 5.25755793 12.37289184 3.81455118
## 34 2.11106236 3.91228058 3.04136093 13.34035645 4.92034588
## 35 2.11569679 3.95250146 3.05676301 13.31165887 4.95077458
## 36 5.94104733 4.20010219 5.08985461 11.79012308 2.93306001
## 37 3.14797446 4.35206527 2.19698103 12.75470302 4.04568374
## 38 2.24059032 3.83701682 3.04247872 12.98214131 4.67812977
## 39 4.09592590 3.01210622 3.21960958 12.56301502 2.76995983
## 40 2.95506086 4.51025151 2.16513136 13.24180444 4.51773041
## 41 2.18362560 3.67631705 2.98050160 13.01292240 4.55630727
## 42 5.07721930 3.09190469 4.27794581 12.60676135 2.76569135
## 43 5.57372085 5.09501576 4.66313381 11.51142664 3.74081150
## 44 6.53363888 5.70252250 6.04313625 12.19737608 5.43948594
## 45 3.43670706 2.07619790 3.80461747 12.52083483 3.40702292
## 46 4.69087773 4.42825959 3.79313074 11.65545649 3.39645930
## 47 1.35756714 2.33693096 2.40322357 12.76545872 3.61835293
## 48 2.31857069 3.58832452 0.39474398 12.59274848 3.21803285
## 49 4.15100474 2.23457066 3.09834606 12.07957856 1.01496312
## 50 1.55951599 3.46267713 2.41818763 12.61212212 4.01847300
## 51 6.08594111 6.65375452 6.14906292 12.28530074 6.12330332
## 52 0.24120993 3.40422666 2.19410353 13.21981649 4.45995814
## 53 5.70412797 2.82079771 4.86617966 12.11467799 2.05583464
## 54 2.60394527 3.51730554 1.09581180 12.24951327 2.96320347
## 55 0.26885501 3.43794409 2.21407884 13.16173328 4.47984166
## 56 0.67079405 2.97473991 2.17051034 13.01631320 4.09374369
## 57 3.36213335 1.48102625 3.72373536 12.67398729 3.03460948
## 58 2.40098045 3.77633525 0.67084054 12.50583638 3.28917135
## 59 2.53980106 1.91396948 3.09614640 12.90832995 3.34422505
## 60 4.72695685 3.48231805 3.68354616 11.37696371 1.55581530
## 61 2.54642371 1.42528611 3.08906166 12.42966812 2.99208298
## 62 1.49571246 2.31727958 2.36386571 12.87866467 3.58434995
## 63 0.18627463 3.47678495 2.21011715 13.23292456 4.51986082
## 64 3.53135982 3.46312956 3.94298660 12.47469533 4.30263057
## 65 0.65799639 3.23752594 2.24205661 12.99265022 4.29423441
## 66 10.81834399 9.66201101 10.07759962 12.13945883 8.16103303
## 67 0.79504674 2.91936389 2.19139314 12.99947432 4.04485624
## 68 3.60881354 1.20987669 3.89781556 12.56931172 2.85673862
## 69 3.72397705 2.87019028 2.80230173 12.17600071 2.44557681
## 70 3.72199994 3.03046462 2.82397261 12.52493219 2.81280957
## 71 10.12627751 9.97620538 10.22055113 15.50310000 10.15743661
## 72 4.46390301 2.85332196 4.72608243 12.57493506 3.90328328
## 73 5.60264261 4.78745845 5.84910324 12.25208112 5.35781549
## 74 2.30741490 3.80954524 3.00244344 12.86760010 4.50492353
## 75 3.44229249 1.97125958 3.79527995 12.55133042 3.34290596
## 76 3.60775727 1.90116607 3.92305109 12.39191443 3.25458412
## 77 2.66318503 2.73415853 3.20253845 12.64336919 3.86822628
## 78 4.10561128 2.07068568 4.36160404 12.60649501 3.38398442
## 79 4.64141434 3.06943079 3.84141178 12.64074138 2.81089240
## 80 6.11282262 4.26324092 5.41082828 13.04331323 3.88705656
## 81 3.30486351 3.85488861 2.34212101 13.12462005 3.78697269
## 82 1.55276550 3.42945946 2.44547296 12.50985112 4.00708803
## 83 0.99542294 2.82125860 2.24002077 12.94176185 3.95841944
## 84 0.79886737 2.92084592 2.20563237 12.89905786 4.03423186
## 85 0.80094179 2.89402734 2.19110223 12.96135568 4.02023223
## 86 5.36639138 3.43565814 4.53857213 12.43188712 2.56655697
## 87 2.24222855 3.57877902 0.49351418 12.81466309 3.42219307
## 88 6.54747334 5.28148796 6.56457111 11.39277500 5.20272844
## 89 2.09378898 1.81128926 2.66551215 12.31669836 2.92174053
## 90 2.26703485 3.74641927 0.45887187 12.64422288 3.40664721
## 91 3.11439664 3.72144918 1.73907631 12.27972239 2.83204196
## 92 2.18573876 3.79524574 2.79613438 12.52631094 4.11313630
## 93 4.59594572 2.34229747 3.69934869 12.27555120 1.66299742
## 94 2.95855552 3.97964458 1.71035651 12.09306242 3.20109724
## 95 9.61441938 7.36149711 8.83657678 12.34355109 6.11783224
## 96 1.74478688 2.37958285 2.52319073 12.73572992 3.58196204
## 97 2.51324440 2.04072246 2.98397743 12.48737489 3.27321985
## 98 3.81472229 1.61493731 4.07771765 12.65257875 3.04669216
## 99 0.61050320 3.14666636 2.19335347 13.06720580 4.22550294
## 100 3.20893678 2.55430625 2.10187919 12.45087488 2.17026115
## 11 12 13 14 15
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12 4.37300204
## 13 1.08196736 4.13439894
## 14 0.92338250 5.06362374 1.72911037
## 15 1.39216686 5.39646732 2.34571078 0.69628597
## 16 3.47903192 1.24074424 3.35404113 4.09806330 4.38783852
## 17 3.48121927 1.13246808 3.32226658 4.10811298 4.42226533
## 18 2.33760308 4.63321771 2.79549508 2.13378485 2.19149904
## 19 2.64052815 2.37201707 2.46957204 3.17584245 3.56048777
## 20 2.33256180 3.48033714 2.76639493 2.67099655 2.74423822
## 21 4.47908653 0.75684165 4.14241621 5.18316944 5.56245347
## 22 5.52853868 6.33651479 5.49198958 5.54553086 5.77404571
## 23 4.37330204 6.56023109 4.48729724 4.32697083 4.44871889
## 24 0.92948353 4.96324598 1.36727891 0.64719261 1.28688430
## 25 3.39498867 5.65377392 3.24994825 3.52000288 3.95360748
## 26 2.44458309 5.68217002 2.99645741 2.31100965 2.34406462
## 27 2.78900735 5.87830709 3.35143009 2.63791009 2.61362544
## 28 2.58694416 5.85822873 3.25956042 2.38099160 2.28274134
## 29 3.59103171 3.11810971 3.40511651 4.10610722 4.46122214
## 30 3.16536779 5.06172769 3.47067808 3.13118765 3.24769393
## 31 2.68071447 4.13667540 2.76799524 3.18936063 3.53809426
## 32 2.51917822 5.82661182 3.20396430 2.30383398 2.20274687
## 33 4.05540322 3.67427049 3.76443428 4.68851709 5.14314495
## 34 2.44774333 5.76949454 3.11058867 2.24417449 2.17923671
## 35 2.47848383 5.78249296 3.16847239 2.25436112 2.18235829
## 36 5.07659482 3.57060208 4.83670784 5.61827429 5.96380199
## 37 3.27583367 5.31688636 3.70473042 3.17048804 3.19359490
## 38 2.47611984 5.71786906 3.09138114 2.29000692 2.30231647
## 39 3.31394739 3.18215744 3.23423862 3.81122924 4.12995688
## 40 3.24949675 5.41113187 3.80405773 3.08395403 3.00357182
## 41 2.34622176 5.61729560 2.90954826 2.19992324 2.24763688
## 42 4.06293712 2.74841988 3.71078166 4.72650045 5.10523420
## 43 5.14226720 6.03684263 4.92636548 5.28330157 5.59807644
## 44 5.99810097 5.87121503 6.00791593 6.21981036 6.54584859
## 45 2.43766220 4.00193876 2.31199622 3.05293191 3.47341410
## 46 4.34050190 4.98727805 4.31393691 4.36120216 4.68378286
## 47 0.68432400 4.32973169 1.54893090 0.99560173 1.34718000
## 48 2.37925697 4.55769709 2.78051948 2.20285787 2.31450905
## 49 3.11904542 2.23871848 2.67031320 3.69166702 4.14780082
## 50 1.85249354 5.42758970 2.46129755 1.53115737 1.55362015
## 51 6.10471263 7.79309138 6.28510503 6.02749947 6.08235598
## 52 1.34969504 5.36894036 2.26851941 0.67483515 0.20713928
## 53 4.48094828 2.33927796 3.75512100 5.16393684 5.70077925
## 54 2.51664674 4.53422998 2.81672889 2.37660571 2.59775117
## 55 1.39162349 5.37734996 2.33912278 0.67209897 0.21814695
## 56 0.99682019 5.14742610 1.77703827 0.30419174 0.65451242
## 57 2.19107462 2.71575232 2.10950206 3.00483510 3.35773428
## 58 2.52791930 4.74631039 2.95630451 2.32920496 2.39617551
## 59 1.64146308 3.25875867 1.92497102 2.26769852 2.53347243
## 60 3.92823398 3.75049967 3.64470788 4.35579069 4.72330106
## 61 1.32141341 3.60819556 1.32594252 2.07183566 2.53787144
## 62 1.00087223 4.55552908 1.30592051 0.94899267 1.48885379
## 63 1.41593343 5.40729176 2.35703704 0.73126686 0.12827477
## 64 3.19465740 4.93917039 3.34243176 3.14472792 3.51771623
## 65 1.28832105 5.25217947 2.16670556 0.58494721 0.62559116
## 66 10.24334946 9.81650192 9.88047669 10.52041005 10.81655872
## 67 0.98525022 5.12532573 1.70280879 0.38964056 0.77600367
## 68 2.35859787 2.64080106 2.06850252 3.18655621 3.60313759
## 69 2.98098235 2.87392507 3.01750341 3.37308713 3.71413787
## 70 2.99204395 3.58636579 2.99199003 3.46980127 3.75610130
## 71 9.93118519 10.67880407 9.92719786 10.02600360 10.13850513
## 72 3.55032457 3.53962042 3.55021771 4.14350055 4.48864299
## 73 5.02650948 5.85262035 5.06860744 5.27779894 5.61757915
## 74 2.48978837 5.72290142 3.02854114 2.34374229 2.36484960
## 75 2.43581074 3.76361903 2.32327600 3.05762120 3.47667617
## 76 2.51684507 4.03736305 2.20731065 3.15980408 3.64011830
## 77 2.15434670 5.08498944 2.17019333 2.25876540 2.70742972
## 78 2.99944563 3.31662175 2.80410470 3.74279915 4.13523404
## 79 3.73244137 2.49964902 3.59949097 4.35989386 4.66993348
## 80 5.24039526 2.25891842 5.10951929 5.86904170 6.13390924
## 81 3.21555609 4.28785488 3.52072999 3.22616338 3.34294788
## 82 1.83567266 5.37880020 2.48409835 1.46504639 1.53919731
## 83 0.96673250 5.11889212 1.56190123 0.51586503 0.97957851
## 84 1.00338783 5.10624298 1.77136932 0.27044960 0.77470225
## 85 0.96223789 5.10777799 1.68656187 0.31142449 0.77880409
## 86 4.39983154 1.30182324 4.19508263 5.07069947 5.36275157
## 87 2.33696845 4.49351394 2.77439581 2.13998711 2.23426503
## 88 5.85839281 6.16287672 5.67006885 6.12118005 6.53607801
## 89 1.01421388 4.30942042 0.88394657 1.53572804 2.08361758
## 90 2.43684733 4.69358857 2.91139661 2.20489444 2.25742877
## 91 2.99379354 4.35692266 3.19630734 2.94357710 3.10763887
## 92 2.41048493 5.63040537 2.89917222 2.17345888 2.17800145
## 93 3.47220710 1.65436347 3.02756456 4.15935577 4.59091084
## 94 2.98548807 4.84760914 3.33723139 2.81146203 2.94688803
## 95 8.69743229 6.08347851 8.24463966 9.21659852 9.61029522
## 96 1.13975733 4.93582275 1.07724274 1.13444711 1.73101935
## 97 1.65571681 4.82022448 0.97505867 1.84241032 2.50168747
## 98 2.66975077 2.47223551 2.46259579 3.41952634 3.80564313
## 99 1.16782588 5.21877408 1.98515024 0.47964316 0.56352421
## 100 2.42475968 2.76687029 2.45403033 2.90370871 3.19985944
## 16 17 18 19 20
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17 0.23544694
## 18 3.50419047 3.53485783
## 19 1.51843583 1.42261772 2.45586365
## 20 2.42815066 2.46834014 1.60898748 1.66469585
## 21 1.60738155 1.46314881 4.78561299 2.44413791 3.68591376
## 22 5.86377985 5.80832847 5.21453253 5.19645631 5.40552985
## 23 5.86546508 5.87005423 4.82471497 5.26466023 5.08754433
## 24 4.05428890 4.03962339 2.27841278 3.03015945 2.78547545
## 25 5.13821847 5.05615084 4.26222530 4.19247833 4.53579751
## 26 4.79836559 4.82192199 3.14505086 4.06172598 3.55853062
## 27 5.00779152 5.03559089 3.38436278 4.31795478 3.77270793
## 28 4.94765240 4.98359230 3.17507730 4.25266156 3.59388109
## 29 2.61876046 2.58153073 3.58121583 2.36529459 3.08095789
## 30 4.11176352 4.13001428 2.33978187 3.25688567 2.85233012
## 31 3.75095198 3.68222352 3.94197678 3.22078050 3.53039785
## 32 4.91104775 4.94673117 3.11776558 4.20820986 3.54263706
## 33 3.87479546 3.73718680 5.28296501 3.69772990 4.63610045
## 34 4.86186841 4.89256751 3.08330387 4.13691235 3.51001231
## 35 4.89597826 4.91895877 3.10642889 4.14981643 3.52531389
## 36 3.62633156 3.56287141 5.27198205 3.79032057 4.61723125
## 37 4.35651860 4.38103688 2.38090891 3.51208545 2.90780292
## 38 4.86803027 4.87716283 3.15744650 4.08056997 3.56344307
## 39 2.57150251 2.54342578 3.23268523 2.18354570 2.70374435
## 40 4.40004534 4.44305195 2.22305981 3.60925209 2.78936514
## 41 4.73881294 4.75717199 3.07287841 3.97851797 3.48913952
## 42 2.48996912 2.46274731 4.26350222 2.62945098 3.50555596
## 43 5.48838397 5.45235960 4.91315165 4.82074220 5.15295382
## 44 5.99351408 5.80760539 6.09968204 5.20122588 5.80160625
## 45 3.55697262 3.49747358 3.81306168 3.00250104 3.40864657
## 46 4.54944914 4.44269812 3.97901228 3.68915842 4.16645587
## 47 3.48925597 3.47765764 2.39232274 2.67692106 2.34142102
## 48 3.46741284 3.48346237 0.64493827 2.38554764 1.70702625
## 49 1.59683610 1.48598867 3.09643726 1.00693500 2.47236658
## 50 4.47330778 4.49758854 2.59555654 3.65992216 3.06972803
## 51 7.25874784 7.24973931 6.41369733 6.76323233 6.59605943
## 52 4.34599145 4.38513767 2.17068186 3.53142712 2.72909274
## 53 2.58030659 2.41828834 4.80697057 2.53751943 4.09246236
## 54 3.58412520 3.54905693 1.28644028 2.33800610 2.01463753
## 55 4.38918815 4.41476265 2.20424904 3.53222866 2.74793910
## 56 4.15065209 4.17271127 2.12450801 3.25649643 2.68079498
## 57 2.30070625 2.27022999 3.70571009 2.31240132 2.78951099
## 58 3.67440051 3.69187584 0.98848713 2.62339155 1.88913341
## 59 2.51500944 2.54171300 3.08750703 2.39763797 2.47467545
## 60 3.32419985 3.25705373 3.88439036 2.81559438 3.45850422
## 61 3.02267133 2.95469632 3.06132389 2.26031283 2.53784456
## 62 3.60708098 3.61993601 2.31734036 2.83387343 2.73839115
## 63 4.39119343 4.42864804 2.19344864 3.57456522 2.74702986
## 64 4.55621933 4.43507118 3.97722325 3.70614217 4.13275711
## 65 4.31524315 4.31825083 2.23150221 3.38055538 2.75257971
## 66 9.77475821 9.73603548 10.34565005 9.64972834 10.17878758
## 67 4.12795032 4.14966593 2.13705226 3.23032860 2.69085628
## 68 2.32078297 2.26532179 3.86926863 2.30186455 2.99576574
## 69 2.40289154 2.25286313 2.80449708 1.37308619 2.12194435
## 70 2.85318586 2.83274860 2.82097442 2.15013876 2.31108800
## 71 10.42381418 10.41198558 10.27304912 10.19154047 10.25898911
## 72 3.56770277 3.46235992 4.77081845 3.43507296 4.05567580
## 73 5.89109629 5.72570224 5.91483035 5.12533938 5.62348444
## 74 4.83083282 4.85683743 3.16100592 4.09743585 3.57603939
## 75 3.34179565 3.28289675 3.80955389 2.89214046 3.36966478
## 76 3.63446582 3.55801534 3.91674932 2.99571970 3.53462277
## 77 4.35919321 4.31765034 3.20544710 3.43120155 3.56239814
## 78 3.12529572 3.06590532 4.37230438 3.02542721 3.63958765
## 79 2.14179833 2.11819411 3.85248051 2.29377896 2.98217512
## 80 2.62018035 2.63617825 5.47375718 3.69516737 4.49883650
## 81 3.31737744 3.36869351 2.40040888 2.88892734 2.73646853
## 82 4.49064192 4.48773327 2.61592671 3.58925043 3.06888169
## 83 4.13078225 4.14707936 2.17446644 3.19793404 2.72855353
## 84 4.16144206 4.16217212 2.17061465 3.19619992 2.70396756
## 85 4.12539872 4.14049649 2.13997283 3.20402251 2.68896484
## 86 1.51877070 1.51352165 4.60781300 2.59505746 3.47053934
## 87 3.39086159 3.40926914 0.34463912 2.32184980 1.59554487
## 88 6.35037031 6.16333143 6.70019421 5.64590308 6.40711987
## 89 3.51302369 3.48372406 2.68104724 2.59803758 2.66543995
## 90 3.61433099 3.62894170 0.66123766 2.53185686 1.72972510
## 91 3.35639013 3.38144019 2.02314311 2.63945140 2.46135643
## 92 4.70499828 4.73411873 3.00563387 3.97104271 3.42178218
## 93 1.34683729 1.19283405 3.64714768 1.27435290 2.69505217
## 94 3.96808262 3.93423901 1.98300148 2.87616714 2.50843715
## 95 6.66766963 6.59904319 9.01852659 7.26121457 8.37622105
## 96 4.01085575 4.00485577 2.43415923 3.02223126 2.92318237
## 97 4.02454733 3.98090396 2.89167701 2.97411828 3.29091561
## 98 2.26031807 2.20256027 4.06097331 2.44806546 3.18720012
## 99 4.22427197 4.24745339 2.15179422 3.34551813 2.70006592
## 100 1.79178248 1.75956722 2.04602377 0.68576056 1.09378839
## 21 22 23 24 25
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22 6.06673258
## 23 6.27674529 4.96947061
## 24 4.99626109 5.27792955 4.03233692
## 25 5.48856212 4.66876636 4.49633929 3.18693898
## 26 5.83489051 6.11417475 4.95624579 2.53255593 2.90091517
## 27 5.95210937 5.77015092 4.02703726 2.77029033 2.87820001
## 28 6.03842093 6.24120588 5.02961354 2.68814704 3.24182823
## 29 3.15816369 5.67070079 5.68209864 3.99398566 3.59289719
## 30 5.15480441 5.39392722 4.91233450 3.18942372 3.27238764
## 31 4.20605548 5.96259051 5.37726430 3.11741811 2.54287302
## 32 6.00652647 6.20935743 4.99274272 2.61685403 3.23806539
## 33 3.61428292 6.45838349 6.31893472 4.48565967 3.52341905
## 34 5.94083638 6.15387073 4.95668001 2.53599028 3.12802216
## 35 5.95253323 6.12862161 4.98178758 2.54808441 3.08736849
## 36 3.25043959 5.61652731 5.17751775 5.38292126 4.50275628
## 37 5.37872766 5.26529769 4.63723248 3.24612573 3.37950581
## 38 5.80670491 5.75674920 4.44603105 2.44412461 2.62678074
## 39 3.29786782 5.68756376 5.69017200 3.75161502 3.58205658
## 40 5.60625118 5.83001847 5.39362648 3.32696724 3.90225650
## 41 5.72326601 5.81102502 4.43366272 2.36056003 2.68109518
## 42 2.79423903 6.22116782 6.24411873 4.59313527 4.35895185
## 43 5.68310937 4.86067447 3.48973452 4.93010025 3.83499960
## 44 5.76007608 6.72183700 7.67341443 6.03694464 4.89373109
## 45 4.03869495 5.91379842 5.22244453 2.91167786 2.49534799
## 46 4.76787421 2.64891891 4.46938402 4.07971765 3.81203815
## 47 4.45778998 5.49387397 4.45758171 1.11709972 3.52585571
## 48 4.62208156 4.82221383 4.33034354 2.22233120 4.04257368
## 49 2.09919630 5.12719421 5.09419130 3.43086988 4.29308683
## 50 5.41593303 5.07713015 2.90045543 1.48809763 3.61231734
## 51 7.59923636 6.33195834 3.27315039 5.85715017 6.15289406
## 52 5.53255501 5.78155894 4.42435882 1.24927138 4.01856868
## 53 2.00825731 6.10782559 6.48122367 4.83328288 5.16538311
## 54 4.52669778 4.54683618 4.19445275 2.26043071 3.71002278
## 55 5.53541825 5.72931417 4.45131530 1.23637435 3.94948665
## 56 5.27184819 5.61881447 4.32347023 0.76731704 3.72598003
## 57 2.85089235 5.96026536 5.18860839 2.92135632 4.27314374
## 58 4.77169777 4.69694668 4.02084523 2.32290242 4.06449494
## 59 3.47022933 5.81852796 4.85405389 2.33421154 4.20856320
## 60 3.30693536 4.39328354 3.53484263 3.97846419 4.27793743
## 61 3.64860456 5.52148940 4.73408466 1.87215664 3.48890355
## 62 4.66686549 5.50075149 4.35252976 0.93866107 3.56723650
## 63 5.57429132 5.79218933 4.44939749 1.31029122 4.04726728
## 64 4.94987231 5.61790303 5.42930723 2.99560583 3.75583260
## 65 5.38268391 5.59106158 4.42939133 1.01667816 3.74456063
## 66 9.16760247 8.30017170 6.97395264 10.06768997 9.37651363
## 67 5.24288256 5.61313702 4.31399391 0.73786678 3.74854599
## 68 2.70953082 5.96050907 5.25466661 3.02920525 4.26406768
## 69 2.90836030 5.14039804 5.48133510 3.23738724 4.21579459
## 70 3.67895020 5.58459508 5.47214924 3.41405290 3.46341962
## 71 10.63075513 6.70036508 10.28517849 9.95832749 8.80887714
## 72 3.60965618 6.30836206 6.01029031 4.05960632 3.53515504
## 73 5.74289766 6.61987075 6.78978303 5.08071820 3.85081573
## 74 5.75510879 5.55336028 3.85880414 2.41507615 2.69536415
## 75 3.82237688 5.89764620 5.23447800 2.93578855 2.64788941
## 76 4.01916416 5.88894628 5.24431639 2.93778214 2.43330948
## 77 5.12099802 5.66219296 4.81956109 2.11274064 1.91192427
## 78 3.37820927 6.23447568 5.63786266 3.62421762 3.34190325
## 79 2.65709319 6.02346498 6.05649638 4.30194882 4.21550199
## 80 2.46939273 6.87963716 6.89195681 5.83705169 5.75254945
## 81 4.52225126 5.64774984 5.41854371 3.38909982 3.93024493
## 82 5.37292564 5.02641297 3.13051922 1.40710607 3.48702470
## 83 5.21812613 5.59115313 4.30076569 0.65644566 3.68429393
## 84 5.21357729 5.51972532 4.33996260 0.62118235 3.58819356
## 85 5.22014002 5.57824506 4.31346574 0.65790717 3.69993357
## 86 1.14854202 5.95707100 5.75927544 4.93476362 5.69316341
## 87 4.64178416 5.13951537 4.83400851 2.25978120 4.27989740
## 88 5.75164147 6.09650413 6.10185895 5.71232227 4.99324765
## 89 4.27529526 5.17606159 3.79416808 1.11818541 3.24362796
## 90 4.78514064 4.91951004 4.39991789 2.27649307 4.22024201
## 91 4.29021510 4.41131729 3.48520136 2.82256342 4.23693060
## 92 5.59175030 5.08502358 2.40206277 2.10165272 3.92821027
## 93 1.58276737 5.67318900 5.82639120 3.94358737 4.82646377
## 94 4.79072505 4.38756159 3.70984937 2.68901882 3.99924399
## 95 5.50959314 7.83182002 7.67031536 8.86310502 8.44006346
## 96 4.97424869 5.51178066 4.32922153 0.79228737 3.53785245
## 97 4.78150478 5.46319918 4.49487926 1.34462157 3.35852421
## 98 2.58369689 6.04807603 5.42266257 3.29814568 4.54980248
## 99 5.35242300 5.65411853 4.36424137 0.94045052 3.94639787
## 100 2.88719173 5.21701611 5.13579489 2.82829853 4.40312465
## 26 27 28 29 30
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27 1.26160206
## 28 0.44333877 1.26592773
## 29 3.58986176 3.84090711 3.85173064
## 30 2.22790789 2.32890135 2.35333711 2.58356984
## 31 2.52807441 2.90775143 2.79919650 2.58284421 3.19771647
## 32 0.45208643 1.26818157 0.08039671 3.85098422 2.35290324
## 33 4.40068761 4.68291492 4.69609093 3.03362508 4.68416468
## 34 0.34970274 1.25427061 0.17025368 3.78408304 2.31542673
## 35 0.49528009 1.28843177 0.33161702 3.82863251 2.36243728
## 36 5.34465655 4.95238488 5.57013777 2.79089260 4.38284132
## 37 2.31725261 2.23380196 2.35773359 2.98504546 0.71369558
## 38 0.79425869 0.93122664 0.85109641 3.71124406 2.28344414
## 39 3.30314642 3.62163502 3.54129739 0.53657474 2.29795161
## 40 2.17102063 2.47227768 2.12066877 3.23129243 1.04548855
## 41 0.56924940 0.77741103 0.73623645 3.58092211 2.16862026
## 42 4.38222645 4.66940421 4.65011549 1.16993443 3.54494718
## 43 4.97803394 4.26160549 5.20412078 4.15270992 3.83028548
## 44 6.09602445 6.27819160 6.28342175 5.13906800 5.67054003
## 45 2.52033881 2.93480111 2.84828912 2.36259453 3.12127620
## 46 5.11458623 4.79496997 5.27450513 4.45456306 4.29053604
## 47 2.63509786 2.92963959 2.72425168 3.77705116 3.35660275
## 48 3.25657768 3.32367223 3.30722687 3.52436274 2.35342094
## 49 4.54376165 4.66824168 4.78262280 2.41799248 3.66382855
## 50 2.82886753 2.45576602 2.84269349 4.47432607 3.33769529
## 51 6.53161760 5.44918241 6.56044500 7.19781493 6.41033027
## 52 2.43200320 2.69950121 2.38494502 4.47120727 3.29460167
## 53 5.88716385 6.14569433 6.18938882 3.24402440 5.15475081
## 54 3.41726835 3.39326452 3.51337734 3.51531381 2.48515813
## 55 2.46316740 2.72160928 2.41192467 4.50970473 3.33320032
## 56 2.44154814 2.75010663 2.49330432 4.23514002 3.22941250
## 57 3.95937359 4.20556101 4.12478920 3.34346408 4.34268703
## 58 3.35380695 3.27779520 3.38629838 3.70552826 2.43431339
## 59 3.42289904 3.66620505 3.52664463 3.48383282 3.92741782
## 60 5.10097115 4.68447520 5.30259527 3.51292276 4.10289760
## 61 3.32251107 3.61302957 3.51361954 3.45983960 3.81691033
## 62 2.66540899 2.99101548 2.81776949 3.79808514 3.29251135
## 63 2.45324559 2.71084617 2.39070042 4.52378134 3.32498915
## 64 4.19269166 4.40595734 4.34390814 4.68930616 4.63364440
## 65 2.54909854 2.81798990 2.55164067 4.43013892 3.36856287
## 66 10.91249857 10.14764718 11.09744083 9.60599123 10.09187450
## 67 2.52219515 2.82921215 2.58745023 4.24047705 3.27527892
## 68 4.16542108 4.42056942 4.36631944 3.34627721 4.48879657
## 69 4.33927248 4.55987587 4.49425202 3.07211446 3.66867352
## 70 3.01601019 3.35168141 3.23869504 1.26225680 1.94950194
## 71 9.88625671 9.81863198 9.96102484 10.00899159 9.99095606
## 72 3.85754879 4.12053808 4.07410427 2.97389322 4.28532243
## 73 5.11877774 5.29186645 5.31794445 5.04710126 5.48351407
## 74 1.24292720 0.84384906 1.30626388 3.73237920 2.32278714
## 75 2.63178155 3.02410119 2.94076979 2.29894082 3.20479447
## 76 2.78971374 3.19684514 3.14522833 2.44796962 3.29363157
## 77 1.58252525 2.15829352 1.99363288 3.06748987 2.50008885
## 78 3.40338294 3.72750058 3.67675148 2.34241935 3.82264974
## 79 4.00722065 4.27887477 4.22232458 0.92660858 3.18401606
## 80 5.66404913 5.73072736 5.82595297 2.83921027 5.00255040
## 81 2.71438933 3.00168831 2.79972103 2.34217531 1.63731595
## 82 2.88748902 2.55276580 2.90836425 4.51504755 3.41588681
## 83 2.56935169 2.88663213 2.66513438 4.21065268 3.28765783
## 84 2.52011187 2.82274886 2.58728277 4.24578998 3.28992773
## 85 2.53615011 2.84247928 2.60626892 4.23786994 3.28626459
## 86 5.76435742 5.72077374 5.91806038 3.35665515 5.04746948
## 87 3.29551049 3.52552196 3.33431630 3.60701474 2.52307499
## 88 6.83767800 6.67852160 7.05109321 6.28596160 6.88806589
## 89 3.04884805 3.10490376 3.25293136 3.68369559 3.46834241
## 90 3.36032103 3.39155539 3.38244350 3.77765014 2.52961077
## 91 3.93742680 3.63880244 4.01225674 3.63614858 2.95296885
## 92 3.30945439 2.68563593 3.31702576 4.77064093 3.65203458
## 93 5.00176367 5.24601774 5.23067020 2.68105881 4.26788820
## 94 3.86821406 3.55381899 3.92316286 4.03453679 2.97494999
## 95 9.73867253 9.35639665 9.95974384 7.28061170 8.98719455
## 96 2.91402023 3.24626881 3.10647114 4.07730520 3.46634270
## 97 3.34041005 3.67903337 3.61134718 4.00608667 3.74344131
## 98 4.44781647 4.67889775 4.62733173 3.55426585 4.75209219
## 99 2.66620731 2.93528129 2.68082617 4.44740875 3.42529918
## 100 3.98517415 4.22188140 4.12206662 2.79914090 3.23030335
## 31 32 33 34 35
## 2
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## 32 2.79279270
## 33 1.93641683 4.68973841
## 34 2.70180855 0.13041026 4.59673739
## 35 2.64367406 0.30332320 4.54422797 0.25341181
## 36 3.98321906 5.56716185 3.67773747 5.50630741 5.52006363
## 37 3.42799249 2.35444490 4.97616626 2.33481896 2.35836991
## 38 2.51203547 0.83679898 4.36934435 0.77147176 0.68846585
## 39 2.42883870 3.53776231 3.12680881 3.47407560 3.51214960
## 40 3.53445110 2.11675463 5.17733943 2.12227011 2.14714548
## 41 2.50972301 0.72137802 4.35904262 0.64179887 0.68978725
## 42 3.16961802 4.64788909 3.20238868 4.58370514 4.65690890
## 43 4.97838315 5.20083789 5.58429075 5.13873487 5.18293163
## 44 4.48424477 6.27195569 4.16690582 6.18437937 6.01173498
## 45 0.76304183 2.83890786 2.08689970 2.74079986 2.74634042
## 46 4.58842147 5.23449360 4.98439248 5.15945812 5.08396566
## 47 2.68476553 2.65299614 4.00976855 2.58764897 2.55791555
## 48 3.91095203 3.25012302 5.18561020 3.20842087 3.21952733
## 49 3.58537438 4.74249289 3.75075488 4.66465148 4.70244762
## 50 3.75412121 2.77601130 5.19604107 2.74017024 2.75928601
## 51 6.76083531 6.52983645 7.50671691 6.50358740 6.48478660
## 52 3.61781492 2.30570737 5.19666411 2.28177156 2.30401436
## 53 4.39342866 6.15748281 3.77188202 6.06631816 6.10539341
## 54 3.73531951 3.45788339 4.88686996 3.39653469 3.36241359
## 55 3.54296176 2.33155066 5.11409387 2.30235624 2.28646191
## 56 3.41438616 2.41620336 4.90902035 2.36582541 2.39952647
## 57 2.70560997 4.07779253 3.08045859 4.01408784 4.02726184
## 58 4.05553184 3.32980562 5.34784162 3.29263607 3.30015138
## 59 2.83182757 3.47092389 3.66074888 3.42220116 3.44050391
## 60 4.36172356 5.26563718 4.62645643 5.19524390 5.21667971
## 61 2.38371102 3.45630124 3.21640552 3.37122060 3.34970436
## 62 3.15643017 2.75005427 4.39807913 2.68229869 2.73021290
## 63 3.63474274 2.31098372 5.22076885 2.28949083 2.29886705
## 64 3.36826798 4.29153411 3.84677615 4.20354134 4.05707445
## 65 3.38004533 2.47214480 4.87967469 2.42365389 2.38195088
## 66 10.36996939 11.07954349 10.21719051 11.02580699 11.06612868
## 67 3.45805787 2.51126424 4.92289709 2.45887791 2.49981721
## 68 2.80913920 4.32044668 2.98888783 4.24823693 4.26766372
## 69 3.24915293 4.44610126 3.62925015 4.37038177 4.30338897
## 70 2.48664710 3.23025810 3.49846120 3.16619045 3.21071363
## 71 9.80203980 9.95793253 10.12264920 9.93488135 9.94161212
## 72 1.44771792 4.06355144 1.10473191 3.98694618 3.90981363
## 73 3.36704501 5.30501170 3.19191683 5.21173914 5.03145884
## 74 2.85711879 1.29072789 4.61858269 1.25657997 1.31548519
## 75 0.74253423 2.92856583 1.92620883 2.83529450 2.83519697
## 76 1.12023978 3.13323344 2.07403693 3.02721510 3.04066851
## 77 1.87887444 1.97536461 3.41742382 1.84769650 1.85483960
## 78 1.35855978 3.66792047 1.62460710 3.58951373 3.60355856
## 79 2.74542653 4.21732252 2.98904611 4.16160362 4.20183512
## 80 4.19575867 5.82156251 3.72178739 5.78421601 5.81476633
## 81 3.25149153 2.78927823 4.46325303 2.76723555 2.80739422
## 82 3.58141874 2.83885681 4.98248196 2.79089198 2.75277720
## 83 3.45658445 2.59091705 4.89230738 2.53157516 2.58064341
## 84 3.29379594 2.50960747 4.74759496 2.44823552 2.44102414
## 85 3.41433649 2.52959519 4.86850235 2.47363740 2.50225068
## 86 4.47329573 5.88432875 4.22634424 5.83542944 5.86735946
## 87 3.93131855 3.27470725 5.19648804 3.23505897 3.24039073
## 88 5.22100197 7.01522084 4.68873638 6.91650742 6.77681467
## 89 2.93843145 3.19068531 4.01605336 3.10581380 3.13622060
## 90 4.04032212 3.32237285 5.33436137 3.28513646 3.28143615
## 91 4.29339987 3.96182120 5.28472717 3.92226277 3.94640346
## 92 4.16013129 3.25721367 5.50829372 3.22858665 3.25412125
## 93 3.75548139 5.19182457 3.67182554 5.11683433 5.15011016
## 94 4.15273042 3.86812542 5.24221760 3.81694019 3.76521411
## 95 8.25016724 9.93766430 7.26453023 9.87361494 9.88658877
## 96 3.45599013 3.03991291 4.68458916 2.96015365 3.02259394
## 97 3.44879215 3.55281510 4.40169952 3.45437548 3.50688383
## 98 3.04557623 4.58055353 3.06926991 4.51327783 4.51833794
## 99 3.60534073 2.60181267 5.07723431 2.55963830 2.57522367
## 100 3.45630087 4.07088827 4.16903549 4.01120543 4.02594123
## 36 37 38 39 40
## 2
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## 37 4.55175718
## 38 5.16163728 2.18700086
## 39 3.12274870 2.71722277 3.45373276
## 40 5.16434377 1.04577801 2.29088347 2.84774172
## 41 5.07113685 2.18245966 0.48083260 3.32265630 2.24101080
## 42 2.92381837 3.96574921 4.58818390 1.41767138 4.13887159
## 43 3.47504975 3.79755202 4.65601492 4.33193598 4.75759336
## 44 5.61622994 5.77412824 5.80348515 5.04643573 5.96810467
## 45 3.89803170 3.41676260 2.61999446 2.24317568 3.55744405
## 46 4.39526108 4.28696221 4.72777103 4.42313514 4.79142928
## 47 5.14645159 3.41246431 2.54826544 3.48812131 3.36031542
## 48 4.96085348 2.29258239 3.13296034 3.23684275 2.40933318
## 49 3.33272846 3.95264742 4.55257396 2.43580853 4.21582656
## 50 5.33201275 3.15570266 2.48724207 4.26642632 3.44387066
## 51 6.08754316 6.27150801 6.07061186 7.15740269 6.84825209
## 52 5.97513365 3.25548668 2.42149748 4.14745754 3.07418654
## 53 3.84405877 5.52542197 5.96839729 3.41226123 5.76666656
## 54 4.71421882 2.44403870 3.18241001 3.25264663 2.70321104
## 55 5.98070100 3.27569258 2.38368100 4.17884016 3.10071093
## 56 5.74942772 3.26139184 2.45632226 3.93905916 3.15987549
## 57 4.29199367 4.52393226 3.97872405 3.21789292 4.56687090
## 58 4.94745010 2.27726981 3.15275271 3.43665271 2.51470984
## 59 4.62856593 4.06180927 3.44484491 3.29889634 4.02706983
## 60 2.87536109 4.10758721 4.80976167 3.61928365 4.79964060
## 61 4.64459880 3.96560190 3.26132089 3.24603570 4.03042425
## 62 5.26216297 3.44174049 2.73010847 3.58603698 3.42326253
## 63 6.01538164 3.27023349 2.41878734 4.19434553 3.07971906
## 64 5.56704742 4.71258158 3.90101870 4.53112677 4.79498690
## 65 5.86529097 3.33611592 2.42268387 4.11071748 3.21447003
## 66 7.77402204 9.88650284 10.46312251 9.92168300 10.86284972
## 67 5.74986564 3.31962036 2.54922511 3.95177088 3.23062442
## 68 4.24213716 4.70319609 4.19677200 3.26430913 4.78462480
## 69 4.17166352 3.81420156 4.19839397 2.84936856 3.90305351
## 70 3.55146095 2.33578668 3.16570758 0.83619954 2.44613794
## 71 10.24393263 10.01552207 9.82920253 10.00607801 10.18314668
## 72 3.77581506 4.49687743 3.77798996 2.93702717 4.61142542
## 73 5.55364853 5.55575894 4.78237372 4.95185290 5.76825008
## 74 4.99351304 2.14062720 0.81617602 3.53756400 2.47373879
## 75 3.78052584 3.49891063 2.71659140 2.20454434 3.62760346
## 76 3.93357585 3.61302489 2.89082599 2.36504571 3.79543624
## 77 4.76813010 2.78375859 1.70811795 2.88795328 2.90923791
## 78 3.54407841 4.11605713 3.50337401 2.33394460 4.24555751
## 79 2.85844140 3.54120761 4.15023969 0.96756100 3.65358301
## 80 2.82587755 5.26993247 5.72984133 3.07783100 5.42499598
## 81 4.27889924 1.94994289 2.86690427 2.11656465 1.80673825
## 82 5.33558894 3.25783367 2.48163901 4.28408686 3.50599262
## 83 5.72679925 3.35441796 2.61250973 3.93143082 3.29249573
## 84 5.71418454 3.31553766 2.45875854 3.94868993 3.23985248
## 85 5.73462007 3.32868086 2.54012745 3.94841876 3.24736746
## 86 3.14130528 5.20320031 5.71045496 3.46824730 5.46288695
## 87 5.23093735 2.56710974 3.27197854 3.27141962 2.43972090
## 88 5.82289067 6.84266556 6.33817352 6.33039212 7.35467406
## 89 4.72541142 3.58999291 2.96139729 3.50022895 3.79144371
## 90 5.13893366 2.47187992 3.22831175 3.45982099 2.50404331
## 91 4.28987682 2.83638106 3.68440771 3.53084802 3.29983527
## 92 5.27051778 3.47715497 2.95222288 4.59136868 3.83732678
## 93 3.66406157 4.56512091 5.06201522 2.67425537 4.71467291
## 94 4.69876992 2.82474474 3.50190527 3.81080562 3.21029120
## 95 5.32638031 9.02903041 9.45983741 7.68003630 9.70313626
## 96 5.55839129 3.62171846 2.99127824 3.85645317 3.65557655
## 97 5.40242407 3.97162435 3.41026059 3.85345046 4.09792402
## 98 4.30322704 4.95266186 4.45087703 3.49291350 5.02047251
## 99 5.91028736 3.42239989 2.63864376 4.14241373 3.30028280
## 100 4.21338189 3.40789393 3.99143038 2.53662864 3.43691670
## 41 42 43 44 45
## 2
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## 42 4.40579341
## 43 4.57630147 4.73612581
## 44 6.00444758 5.76236217 6.59882240
## 45 2.51591398 2.79986974 4.76071921 4.94303954
## 46 4.77571002 5.15363975 4.16680968 4.87801507 4.66360849
## 47 2.50826504 4.32225199 5.36636544 5.69995818 2.62165274
## 48 3.09082973 4.25321365 4.47012341 5.94633392 3.79340551
## 49 4.40764627 2.46751235 4.43954521 5.57444749 3.25401989
## 50 2.44999738 5.13086982 4.52766508 6.66193508 3.62827906
## 51 5.99103455 7.71837569 4.89622383 8.34994359 6.74799793
## 52 2.33955200 5.08432228 5.59524912 6.67279105 3.51346454
## 53 5.81960981 2.74923355 5.47861241 5.84181834 4.00227700
## 54 3.18641871 4.30203055 4.20347319 5.29267533 3.68521890
## 55 2.35362027 5.15997575 5.63296882 6.43369892 3.49922147
## 56 2.34076359 4.81526330 5.36003954 6.48773349 3.23686603
## 57 3.87319358 3.36964233 5.70780633 5.85599729 2.49369430
## 58 3.13068241 4.44685243 4.28401634 6.03977746 3.94990945
## 59 3.33183244 3.74805027 5.63952225 6.14468429 2.68687299
## 60 4.74340608 3.78042260 3.02880747 5.92902560 4.11603913
## 61 3.20421587 3.77901780 5.33365903 5.28641942 2.20579260
## 62 2.56573445 4.32124296 5.15983977 6.35679034 2.91152884
## 63 2.35700333 5.15102879 5.64467856 6.63604282 3.55684219
## 64 4.03193862 5.39110204 5.99160079 4.25265429 3.66013368
## 65 2.41956088 5.09243218 5.55332869 6.10605282 3.35540768
## 66 10.47558301 9.70909643 6.73634361 11.24161484 10.13477724
## 67 2.42227772 4.79934347 5.35097754 6.53513447 3.25526219
## 68 4.07837768 3.29346592 5.67058821 5.85413976 2.52824610
## 69 4.21902851 3.54248428 5.21974298 4.17176711 3.30322776
## 70 3.03595362 1.91059422 4.26095948 5.10985290 2.24769515
## 71 9.81065020 10.21988327 10.20273553 11.06527055 9.76306461
## 72 3.80903726 3.32383955 5.64029899 4.18366040 1.87311570
## 73 5.00573736 5.66165513 6.40606499 2.22506556 3.88660404
## 74 0.83574848 4.55690732 4.22430249 6.27555770 2.81621047
## 75 2.61661615 2.73913797 4.83186889 4.94199726 0.38856333
## 76 2.77556767 2.79355240 4.70507312 4.92814793 0.47107434
## 77 1.57655670 3.81294658 4.50967204 5.27959548 1.69698745
## 78 3.39488204 2.43437376 5.17215010 5.17819264 1.10051562
## 79 4.01863160 0.91974477 4.79124545 5.30301769 2.55844107
## 80 5.61124603 2.50794752 5.82047231 6.33804327 4.14843381
## 81 2.74181507 3.26617711 4.59944381 5.86408713 3.24228675
## 82 2.50036189 5.21865590 4.67065945 6.17251479 3.55377791
## 83 2.47149598 4.74669175 5.28630976 6.53257820 3.21464487
## 84 2.39712646 4.86149704 5.36633795 6.15830781 3.17468227
## 85 2.42901320 4.80855686 5.34826207 6.43182263 3.22852327
## 86 5.60147022 3.05004791 5.44153923 6.44425026 4.28404748
## 87 3.20726614 4.29353123 4.97030959 5.94359281 3.83053935
## 88 6.53994743 6.75387797 6.35443825 4.01463317 5.46528785
## 89 2.81741795 4.08647315 4.62820339 5.96886470 2.60982532
## 90 3.18329433 4.49458136 4.66611073 5.95800225 3.95708098
## 91 3.62949594 4.31530929 3.76889062 6.32953420 4.15836284
## 92 2.86737854 5.38790180 4.33435471 6.97411150 4.02552943
## 93 4.92869820 2.41072884 5.23144621 5.63375668 3.43196883
## 94 3.52912427 4.81810736 4.03604950 5.45371061 4.16250116
## 95 9.43397200 7.09051821 7.07172539 8.95487956 8.12615635
## 96 2.81746348 4.52316480 5.11526076 6.47833757 3.10006400
## 97 3.24104914 4.38068360 4.99865097 6.24438492 3.02800574
## 98 4.35257699 3.52604524 5.91247984 5.88264177 2.86695297
## 99 2.55553347 5.02944818 5.54310690 6.54546411 3.46797619
## 100 3.89669997 3.09230303 4.99762451 5.50156502 3.25542755
## 46 47 48 49 50
## 2
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## 47 4.14601981
## 48 3.57057581 2.40076996
## 49 3.69681667 3.24785799 2.92694631
## 50 4.10723768 1.90098538 2.34405939 3.96367619
## 51 5.32621284 6.05400892 6.04720271 6.59193406 4.87666513
## 52 4.72353532 1.37187452 2.29964093 4.09371193 1.53065084
## 53 4.84159302 4.64080806 4.69424339 1.88475994 5.58657582
## 54 2.96762167 2.43745590 0.84794935 2.83853922 2.45883194
## 55 4.59095947 1.26553145 2.30728717 4.13022284 1.56205802
## 56 4.51585244 1.16506552 2.21708049 3.75466431 1.50574254
## 57 4.67519804 2.16298038 3.66685685 2.54861119 3.49302821
## 58 3.50244164 2.54123771 0.42266297 3.10311280 2.20131223
## 59 4.53373238 1.52653307 3.08441715 2.77765521 2.80498429
## 60 3.23143250 4.02419672 3.40289828 2.31189973 3.78984178
## 61 4.11244798 1.23857801 3.00565839 2.68255219 2.73628980
## 62 4.27987790 1.19631247 2.34548306 3.18186014 1.87349160
## 63 4.71861775 1.38091126 2.31950061 4.15516574 1.55163705
## 64 3.64187081 2.69604050 3.82940642 4.12684496 3.72706795
## 65 4.34276143 1.05586074 2.28713036 3.97409740 1.60928198
## 66 8.66967561 10.38027101 9.76237504 8.98014114 9.39859012
## 67 4.52179392 1.20017639 2.22616594 3.70672994 1.52849656
## 68 4.67582653 2.38624926 3.81463940 2.40743673 3.67836947
## 69 3.27081342 2.73588799 2.67146861 2.06521669 3.86794400
## 70 4.40582737 3.22659132 2.85715777 2.54622778 3.92407864
## 71 8.57366003 9.98595030 10.19284913 10.20872112 9.98119761
## 72 4.79514882 3.39444761 4.69588907 3.70805056 4.64391311
## 73 4.93316026 4.72252674 5.75572712 5.48903110 5.70365659
## 74 4.72471437 2.67272413 3.04642251 4.45139916 2.14653934
## 75 4.59145467 2.56281577 3.78193579 3.13358493 3.63483059
## 76 4.65186925 2.75096356 3.88315569 3.16858589 3.73943672
## 77 4.42161499 2.38344330 3.20843211 3.74683115 2.94114225
## 78 5.00420335 3.12464451 4.34115746 3.15496843 4.24287470
## 79 4.81056881 3.87757526 3.84471614 2.41138540 4.77235276
## 80 5.70772803 5.25474773 5.39232118 3.51076595 6.07299322
## 81 4.38209356 3.27297587 2.48734252 3.31416162 3.64802744
## 82 3.79805809 1.68611546 2.36735935 3.95992834 0.70217998
## 83 4.51386865 1.27065059 2.25504813 3.64176254 1.58731922
## 84 4.30179720 0.97838676 2.22114236 3.72315700 1.55982801
## 85 4.45123709 1.12594842 2.21644139 3.69027505 1.52933359
## 86 4.80257975 4.40099527 4.41496366 2.22855968 5.07364733
## 87 3.79749154 2.31667650 0.62236793 2.97953588 2.62137077
## 88 4.57568212 5.54250160 6.30547600 5.65204471 6.02413462
## 89 3.92201728 1.31590336 2.54872044 2.80246427 1.82253636
## 90 3.57573232 2.40027481 0.44815270 3.11180752 2.35820326
## 91 3.18370998 2.99405443 1.48869829 2.75392330 2.44378335
## 92 4.10547697 2.46038263 2.71901659 4.15528831 0.80461801
## 93 4.33935427 3.57895189 3.56707104 0.97185667 4.58010399
## 94 2.69706487 2.82586492 1.49932738 3.24393296 2.45034360
## 95 7.26183392 8.66843805 8.57180472 6.52321675 8.71580134
## 96 4.41943478 1.56520406 2.46182892 3.31501062 1.97276422
## 97 4.30053940 2.02988980 2.85769112 3.10301894 2.55127504
## 98 4.69065823 2.58237457 3.99347245 2.54742758 3.88842194
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## 52 6.09239779
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## 100 6.65534148 3.16344340 3.08847775 2.08592883 3.17114378
## 56 57 58 59 60
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## 57 3.08497352
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## 66 10.53725412 9.99949314 9.50746249 10.19420536 6.98386833
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## 72 4.37033530 2.63400548 4.84628526 3.05366159 4.56138058
## 73 5.55977390 4.94156175 5.83221307 5.22705562 5.77296402
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## 78 3.90177840 2.14537795 4.50483439 2.63222882 4.15548525
## 79 4.47290198 3.04091526 4.03537363 3.32922752 3.69830374
## 80 5.97700655 3.84141591 5.54121984 4.19014097 4.49454674
## 81 3.33318604 3.90394011 2.70208543 3.36254032 4.28824296
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## 83 0.33719951 3.05886259 2.38022847 2.37239749 4.31600689
## 84 0.42736486 3.03927584 2.33894649 2.33100344 4.36125686
## 85 0.16052683 3.04161676 2.33845295 2.31289507 4.35376598
## 86 5.11810245 2.88484141 4.50481205 3.31994089 3.00019634
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## 88 6.34375895 5.48587195 6.26884323 5.85291580 5.14495581
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## 99 0.32404512 3.15636942 2.34426499 2.37137074 4.50027793
## 100 2.94599615 2.38929808 2.24271581 2.31389386 2.95521467
## 61 62 63 64 65
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## 62 1.90637186
## 63 2.56356056 1.48710286
## 64 2.73051129 3.12308773 3.57293774
## 65 2.21846245 1.40192417 0.66597476 2.96112465
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## 70 3.06391917 3.40354702 3.81909343 4.55182663 3.75792652
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## 74 3.35828312 2.68460156 2.45732101 4.25734019 2.56275648
## 75 2.13264995 2.84006756 3.55704046 3.51737773 3.35066007
## 76 2.19900662 2.98404684 3.71744967 3.70983624 3.48519856
## 77 2.61488264 2.29422875 2.80590418 3.36244524 2.59571260
## 78 2.46020332 3.44496988 4.20192350 4.07088407 4.03106472
## 79 3.43564382 4.04540387 4.72281788 4.90858570 4.64961657
## 80 4.75739396 5.37789222 6.17205391 5.90283830 6.11665620
## 81 3.73427702 3.07223622 3.40358433 4.36209354 3.46230279
## 82 2.53157122 1.91467160 1.55983817 3.17378638 1.36125076
## 83 2.15686748 0.92893122 0.95902232 3.47468072 0.98055303
## 84 2.03729361 1.05963719 0.79400244 3.02482246 0.45562707
## 85 2.12820556 0.93638678 0.76448098 3.32072387 0.73119424
## 86 3.77689506 4.56591209 5.36167745 5.27919542 5.27237969
## 87 2.95609827 2.27614285 2.23455125 3.73819302 2.19679132
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## 95 8.00015678 8.61178314 9.61814669 8.45027346 9.41665741
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## 99 2.28322234 1.15405693 0.51038167 3.37327451 0.58802513
## 100 2.22894080 2.68641953 3.20022190 3.80533434 3.05969109
## 66 67 68 69 70
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## 67 10.49651122
## 68 9.86974098 3.23085644
## 69 9.95155178 3.53346268 2.75147630
## 70 9.96534335 3.58833976 3.33361101 2.79096565
## 71 13.11054296 10.07863794 10.12831792 10.30856380 9.98651807
## 72 10.42446659 4.40639773 2.70031084 3.25611041 3.24809787
## 73 11.01839207 5.61170240 4.95720966 4.23996875 4.97789722
## 74 9.86466328 2.51667537 4.19162925 4.37912340 3.23987941
## 75 10.12085374 3.26667939 2.33253289 3.19008799 2.32076709
## 76 10.01297577 3.33786473 2.52019479 3.32178020 2.33309531
## 77 10.34365770 2.49259307 3.47682322 3.66880731 2.70659223
## 78 10.08136032 3.91041791 2.14739432 3.40883878 2.57577862
## 79 9.89168751 4.47801381 3.06602702 3.01779812 1.56018075
## 80 9.84106937 5.98088638 3.85873930 4.26560440 3.75795891
## 81 10.43862856 3.37549762 4.07659074 3.40220549 2.25579482
## 82 9.61186093 1.58579557 3.62088054 3.56793704 3.95540920
## 83 10.42809897 0.22220794 3.19914252 3.53483706 3.55669273
## 84 10.53140700 0.48151943 3.21258493 3.31524474 3.59587780
## 85 10.49237310 0.13226986 3.20681722 3.46183179 3.58785126
## 86 8.79156460 5.09001578 2.83860276 3.23636724 3.78243121
## 87 10.31350213 2.16532629 3.76359645 2.57721311 2.91147644
## 88 9.04479658 6.35278366 5.38530047 4.76078438 6.36400096
## 89 9.50692984 1.52712887 2.26327080 2.95546354 3.21033960
## 90 9.97540657 2.23227214 3.92235688 2.69723719 3.06088883
## 91 8.58358144 2.94760472 3.87292144 3.03860234 3.38370119
## 92 9.08754613 2.14142668 3.97591338 4.19967188 4.27359359
## 93 9.44696072 4.17073455 2.24266145 2.18940429 2.80259488
## 94 9.15793998 2.91640000 4.15567375 2.67407738 3.49828879
## 95 6.15373835 9.26679978 7.17638004 7.51174144 8.14592827
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## 97 9.93156490 1.76496274 2.88921209 3.41327725 3.58137733
## 98 9.95499388 3.48163943 0.56972540 2.77932138 3.65027759
## 99 10.62319202 0.37733503 3.35356624 3.54314762 3.77887911
## 100 9.80240945 2.92249720 2.45833570 1.50285944 2.32888974
## 71 72 73 74 75
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## 72 10.04768035
## 73 10.58126827 3.12909461
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## 75 9.77400614 1.64012488 3.89688893 2.90974913
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## 83 10.06863847 4.42060252 5.61021442 2.56132449 3.24001925
## 84 10.06605813 4.20758482 5.22142222 2.52987348 3.18072177
## 85 10.07416810 4.35134854 5.50563143 2.53243591 3.23854299
## 86 10.60550673 4.03753292 6.33013460 5.55249810 4.06739306
## 87 10.28818758 4.68287585 5.78161195 3.30121113 3.80371010
## 88 11.00458956 4.80423241 3.30046592 6.47084241 5.41263777
## 89 9.89615073 3.68811196 5.00794750 2.83770618 2.61567659
## 90 10.25834311 4.80817128 5.78133422 3.19524410 3.94647116
## 91 10.17473074 4.85813837 6.11641254 3.38149957 4.07496739
## 92 10.04570171 4.98085523 6.04583399 2.55992063 4.02456478
## 93 10.40533520 3.65976000 5.57717870 5.02075505 3.30517920
## 94 10.22130398 4.76799688 5.32846926 3.43637605 4.14228806
## 95 12.31583569 7.55772572 8.92155409 9.13428480 7.91647850
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## 97 10.05923956 4.28102742 5.35750291 3.33503776 3.06763021
## 98 10.22477224 2.72816547 5.01780081 4.46659670 2.61570565
## 99 10.14456908 4.50190190 5.62872059 2.64429397 3.46488978
## 100 10.24382223 3.78160680 5.38304999 3.99004328 3.17328152
## 76 77 78 79 80
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## 77 1.76091169
## 78 1.24460550 2.72629089
## 79 2.67433502 3.59607492 2.20544647
## 80 4.30929607 5.31746929 3.35348821 2.26902559
## 81 3.49699478 2.90420028 3.62790815 2.78119744 4.13033921
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## 83 3.26783373 2.44138303 3.88312092 4.46233921 5.99865076
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## 85 3.30813130 2.46235706 3.89088469 4.47744007 5.98230028
## 86 4.32540979 5.27389037 3.66323417 2.85465188 2.47119263
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## 88 5.34159740 5.78124807 5.58272176 6.45198553 7.07917732
## 89 2.56094917 2.40000196 3.11166051 3.87368512 5.28398348
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## 94 4.22978556 3.64362059 4.69155998 4.36235761 5.68811644
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## 98 2.90165447 3.78801369 2.40410398 3.23760137 3.73936423
## 99 3.57423792 2.73237078 4.10013727 4.65466469 6.10965992
## 100 3.28153944 3.55141207 3.36145893 2.70180818 4.11871557
## 81 82 83 84 85
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## 82 3.71240365
## 83 3.43378384 1.65895461
## 84 3.40270457 1.41187726 0.57737381
## 85 3.38955777 1.53225125 0.26204313 0.35579958
## 86 4.40513567 5.11762975 5.08479369 5.11943932 5.08564614
## 87 2.46156470 2.57925480 2.20753145 2.14958590 2.15262387
## 88 7.04561487 5.56615296 6.32106360 5.99284300 6.24251146
## 89 3.63848814 1.78129757 1.42313037 1.52485818 1.49148244
## 90 2.68623930 2.30601768 2.27680028 2.19613081 2.21532093
## 91 2.83448710 2.57212017 2.97202494 2.97754114 2.94575341
## 92 3.99458681 1.10482124 2.18392607 2.19394436 2.14924371
## 93 3.85978158 4.55636246 4.10908776 4.18036408 4.15326554
## 94 3.28830552 2.21054915 2.94691834 2.75202153 2.86452691
## 95 8.48118614 8.76219163 9.23337363 9.24263158 9.24526010
## 96 3.61166079 2.04220964 0.76350449 1.14368449 0.96327701
## 97 3.89701872 2.54581297 1.57353737 1.81970678 1.73661845
## 98 4.17816335 3.79651473 3.47384470 3.43705676 3.45213241
## 99 3.48738295 1.49396862 0.56746067 0.45108643 0.35247836
## 100 2.95322484 3.31034354 2.90726285 2.90857041 2.90250070
## 86 87 88 89 90
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## 87 4.49120105
## 88 6.23891091 6.49048655
## 89 4.18651840 2.64013736 5.37986103
## 90 4.56186854 0.58914056 6.34931560 2.60849007
## 91 3.87704642 1.93871015 6.11449381 2.80936527 1.66781206
## 92 5.14701293 3.02786406 6.17753044 2.15940679 2.67721280
## 93 1.98227911 3.53159916 5.82153107 3.26453195 3.72605161
## 94 4.56909209 1.84326080 5.47858297 2.79500975 1.36377489
## 95 5.42527780 8.86772601 7.30354669 8.12825949 8.78781343
## 96 4.92245194 2.43962374 6.11765318 1.15855338 2.54037640
## 97 4.86658178 2.85702458 5.75234182 1.29643902 2.97140988
## 98 2.71435133 3.92102975 5.34723612 2.59906389 4.08844208
## 99 5.18114603 2.15536100 6.34895709 1.72565196 2.19819459
## 100 2.85672431 1.91969786 5.88578130 2.47253975 2.11077304
## 91 92 93 94 95
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## 92 2.51817743
## 93 3.56424303 4.81924312
## 94 1.56457828 2.52670665 3.95788718
## 95 7.42250751 8.59484504 6.61645062 8.18907646
## 96 3.04324293 2.47413510 3.79320933 3.10485523 8.91262805
## 97 3.30347810 2.96967389 3.57540079 3.34978742 8.59357786
## 98 3.95797006 4.16563474 2.36595948 4.27417023 6.97972883
## 99 2.98209733 2.12811739 4.32107266 2.86567339 9.38056934
## 100 2.44417729 3.68250918 1.73354786 2.61526010 7.66086090
## 96 97 98 99
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## 96
## 97 0.83716203
## 98 3.29045973 3.22026183
## 99 1.27556863 2.04904854 3.56578610
## 100 2.83739761 2.94264913 2.62345576 2.99475119plot(d)#plottting the data
str(d)## 'dist' num [1:4950] 0.151 0.404 0.163 5.224 0.199 ...
## - attr(*, "Size")= int 100
## - attr(*, "Labels")= chr [1:100] "1" "2" "3" "4" ...
## - attr(*, "Diag")= logi FALSE
## - attr(*, "Upper")= logi FALSE
## - attr(*, "method")= chr "euclidean"
## - attr(*, "call")= language dist(x = normalized_data, method = "euclidean")km <- kmeans(mydata1,4) #kmeans clustering
str(km)## List of 9
## $ cluster : Named int [1:100] 4 4 4 4 2 4 2 4 1 2 ...
## ..- attr(*, "names")= chr [1:100] "1" "2" "3" "4" ...
## $ centers : num [1:4, 1:12] 54.2 54.8 51.1 49.1 555560 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:4] "1" "2" "3" "4"
## .. ..$ : chr [1:12] "ID." "Balance" "Qual_miles" "cc1_miles" ...
## $ totss : num 1.41e+12
## $ withinss : num [1:4] 1.99e+10 1.80e+10 3.77e+10 3.84e+10
## $ tot.withinss: num 1.14e+11
## $ betweenss : num 1.29e+12
## $ size : int [1:4] 4 27 9 60
## $ iter : int 3
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"fit <- kmeans(d, 5) # 5 cluster solution
final2<- data.frame(mydata1, fit$cluster) # append cluster membership
final2## ID. Balance Qual_miles cc1_miles cc2_miles cc3_miles Bonus_miles
## 1 1 28143 0 1 1 1 174
## 2 2 19244 0 1 1 1 215
## 3 3 41354 0 1 1 1 4123
## 4 4 14776 0 1 1 1 500
## 5 5 97752 0 4 1 1 43300
## 6 6 16420 0 1 1 1 0
## 7 7 84914 0 3 1 1 27482
## 8 8 20856 0 1 1 1 5250
## 9 9 443003 0 3 2 1 1753
## 10 10 104860 0 3 1 1 28426
## 11 11 40091 0 2 1 1 7278
## 12 12 96522 0 5 1 1 61105
## 13 13 43382 0 2 1 1 11150
## 14 14 43097 0 1 1 1 3258
## 15 15 17648 0 1 1 1 0
## 16 16 28495 0 4 1 1 49442
## 17 17 51890 0 4 1 1 48963
## 18 18 13958 0 1 1 1 4291
## 19 19 91473 0 3 1 1 27408
## 20 20 23354 0 3 1 1 10447
## 21 21 120576 0 5 1 1 58831
## 22 22 185681 2024 1 1 1 13300
## 23 23 20584 0 1 1 1 3450
## 24 24 66275 0 1 1 1 2533
## 25 25 205651 500 1 1 1 4025
## 26 26 20726 0 1 1 1 1375
## 27 27 18521 0 1 1 1 1227
## 28 28 8828 0 1 1 1 0
## 29 29 59763 0 3 1 1 33772
## 30 30 19221 0 1 1 1 4655
## 31 31 177926 0 3 1 1 20797
## 32 32 10021 0 1 1 1 0
## 33 33 276571 0 4 1 1 42044
## 34 34 18047 0 1 1 1 100
## 35 35 43832 0 1 1 1 0
## 36 36 123759 0 4 1 1 50572
## 37 37 23193 0 1 1 1 650
## 38 38 68666 0 1 1 1 350
## 39 39 59990 0 3 1 1 27878
## 40 40 2176 0 1 1 1 0
## 41 41 34616 0 1 1 1 1750
## 42 42 10470 0 4 1 1 38094
## 43 43 60313 0 1 1 1 10000
## 44 44 619393 0 3 1 1 15008
## 45 45 121260 0 3 1 1 18493
## 46 46 288865 967 1 1 1 23600
## 47 47 92336 0 2 1 1 11214
## 48 48 36924 0 1 1 1 5900
## 49 49 70312 0 3 1 1 34678
## 50 50 17051 0 1 1 1 1150
## 51 51 108137 0 1 1 1 6368
## 52 52 1300 0 1 1 1 370
## 53 53 118531 0 4 1 1 44577
## 54 54 121395 0 1 1 1 4970
## 55 55 38348 0 1 1 1 0
## 56 56 14448 0 1 1 1 1625
## 57 57 75971 0 4 1 1 34339
## 58 58 36298 0 1 1 1 3100
## 59 59 38077 0 3 1 1 34024
## 60 60 95118 0 3 1 1 23188
## 61 61 134457 0 3 1 1 15588
## 62 62 19918 0 1 1 1 17601
## 63 63 10120 0 1 1 1 0
## 64 64 362642 0 1 1 1 28079
## 65 65 80250 0 1 1 1 895
## 66 66 53914 0 3 1 1 33767
## 67 67 9375 0 1 1 1 1750
## 68 68 83237 0 4 1 1 35287
## 69 69 230715 0 3 1 1 24047
## 70 71 47457 0 3 1 1 12621
## 71 72 84409 5031 2 1 1 15436
## 72 73 252386 0 4 1 1 39787
## 73 74 550367 0 3 1 1 12500
## 74 75 12646 0 1 1 1 631
## 75 76 123867 0 3 1 1 25308
## 76 78 129871 0 3 1 1 15776
## 77 79 109380 0 1 1 1 7537
## 78 80 111157 0 4 1 1 32883
## 79 81 49238 0 4 1 1 38037
## 80 82 38896 0 5 1 1 76988
## 81 83 4340 0 1 1 1 32685
## 82 84 88443 0 1 1 1 1200
## 83 85 8454 0 1 1 1 498
## 84 86 61990 0 1 1 1 1625
## 85 87 24093 0 1 1 1 1750
## 86 88 35418 0 5 1 1 58557
## 87 89 40284 0 1 1 1 7719
## 88 90 609477 0 3 1 1 21422
## 89 91 62553 0 2 1 1 7672
## 90 92 48433 0 1 1 1 3500
## 91 93 20508 0 1 1 1 22250
## 92 94 2000 0 1 1 1 2000
## 93 95 78629 0 4 1 1 36679
## 94 96 143566 0 1 1 1 5000
## 95 97 185549 0 5 1 1 110859
## 96 98 16796 0 1 1 1 2875
## 97 99 57346 0 1 1 1 5560
## 98 100 102062 0 4 1 1 44247
## 99 101 22324 0 1 1 1 1375
## 100 102 64824 0 3 1 1 20184
## Bonus_trans Flight_miles_12mo Flight_trans_12 Days_since_enroll Award.
## 1 1 0 0 7000 0
## 2 2 0 0 6968 0
## 3 4 0 0 7034 0
## 4 1 0 0 6952 0
## 5 26 2077 4 6935 1
## 6 0 0 0 6942 0
## 7 25 0 0 6994 0
## 8 4 250 1 6938 1
## 9 43 3850 12 6948 1
## 10 28 1150 3 6931 1
## 11 10 0 0 6959 0
## 12 19 0 0 6924 1
## 13 20 0 0 6924 0
## 14 6 0 0 6918 0
## 15 0 0 0 6912 0
## 16 15 0 0 6912 1
## 17 16 0 0 6910 1
## 18 5 0 0 6905 1
## 19 17 0 0 6903 1
## 20 5 0 0 6896 1
## 21 23 250 2 6896 1
## 22 16 1800 9 6896 1
## 23 11 3450 11 6884 0
## 24 11 150 1 6884 0
## 25 21 700 4 7932 0
## 26 4 0 0 7924 0
## 27 2 1227 2 7917 0
## 28 0 0 0 7914 0
## 29 20 100 1 7907 1
## 30 8 500 1 7896 1
## 31 13 0 0 7886 0
## 32 0 0 0 7879 0
## 33 23 0 0 7872 0
## 34 1 0 0 7868 0
## 35 0 0 0 7865 0
## 36 23 2500 5 7865 1
## 37 4 550 3 7861 1
## 38 2 350 2 7861 0
## 39 17 0 0 7854 1
## 40 0 0 0 7847 1
## 41 4 500 1 7850 0
## 42 26 0 0 7840 1
## 43 26 3250 9 7829 1
## 44 14 0 0 7819 1
## 45 18 0 0 7808 0
## 46 14 2000 4 6884 1
## 47 6 0 0 6884 0
## 48 6 300 2 6879 1
## 49 24 500 1 6875 1
## 50 4 1150 4 6868 0
## 51 5 6368 5 6844 0
## 52 1 0 0 6868 0
## 53 38 0 0 6868 1
## 54 8 650 2 6889 1
## 55 0 0 0 6861 0
## 56 6 0 0 6856 0
## 57 14 0 0 6869 0
## 58 5 600 3 6865 1
## 59 8 0 0 6837 0
## 60 23 2200 7 6865 1
## 61 14 0 0 6861 0
## 62 11 0 0 6863 0
## 63 0 0 0 6864 0
## 64 8 0 0 6835 0
## 65 2 0 0 6833 0
## 66 45 5550 29 6826 1
## 67 7 0 0 6826 0
## 68 18 0 0 6837 0
## 69 12 0 0 6826 1
## 70 16 0 0 7766 1
## 71 16 1150 4 7766 0
## 72 13 0 0 7787 0
## 73 13 50 1 7801 0
## 74 4 631 4 7787 0
## 75 17 0 0 7759 0
## 76 22 0 0 7752 0
## 77 16 0 0 7749 0
## 78 19 0 0 7771 0
## 79 18 0 0 7801 1
## 80 16 556 1 7771 1
## 81 5 0 0 7733 1
## 82 3 1200 3 6837 0
## 83 9 0 0 6821 0
## 84 6 0 0 6833 0
## 85 7 0 0 6819 0
## 86 18 900 3 6813 1
## 87 5 0 0 6827 1
## 88 22 1200 8 6820 0
## 89 16 700 1 6819 0
## 90 4 500 1 6807 1
## 91 8 1250 5 6794 1
## 92 4 2000 4 6809 0
## 93 25 0 0 6817 1
## 94 5 1500 3 6785 1
## 95 39 2950 16 6778 1
## 96 16 0 0 6773 0
## 97 23 0 0 6766 0
## 98 16 0 0 6758 0
## 99 4 0 0 6753 0
## 100 13 0 0 6770 1
## fit.cluster
## 1 4
## 2 4
## 3 4
## 4 4
## 5 3
## 6 4
## 7 5
## 8 1
## 9 2
## 10 5
## 11 4
## 12 3
## 13 4
## 14 4
## 15 4
## 16 5
## 17 5
## 18 1
## 19 5
## 20 1
## 21 3
## 22 3
## 23 3
## 24 4
## 25 5
## 26 4
## 27 4
## 28 4
## 29 5
## 30 1
## 31 5
## 32 4
## 33 5
## 34 4
## 35 4
## 36 3
## 37 1
## 38 4
## 39 5
## 40 1
## 41 4
## 42 5
## 43 3
## 44 3
## 45 5
## 46 3
## 47 4
## 48 1
## 49 5
## 50 4
## 51 3
## 52 4
## 53 3
## 54 1
## 55 4
## 56 4
## 57 5
## 58 1
## 59 5
## 60 5
## 61 5
## 62 4
## 63 4
## 64 5
## 65 4
## 66 2
## 67 4
## 68 5
## 69 5
## 70 5
## 71 2
## 72 5
## 73 3
## 74 4
## 75 5
## 76 5
## 77 4
## 78 5
## 79 5
## 80 3
## 81 1
## 82 4
## 83 4
## 84 4
## 85 4
## 86 3
## 87 1
## 88 3
## 89 4
## 90 1
## 91 1
## 92 4
## 93 5
## 94 1
## 95 2
## 96 4
## 97 4
## 98 5
## 99 4
## 100 5final3 <- final2[,c(ncol(final2),1:(ncol(final2)-1))]
x<-aggregate(mydata1[,2:12], by=list(fit$cluster), FUN=mean)
# k clustering alternative for large dataset - Clustering Large Applications (Clara)
#install.packages("cluster")
library(cluster)
xds <- rbind(cbind(rnorm(5000, 0, 8), rnorm(5000, 0, 8)),
cbind(rnorm(5000, 50, 8), rnorm(5000, 50, 8)))
xcl <- clara(xds, 5)
clusplot(xcl)
str(xcl)## List of 10
## $ sample : int [1:50] 154 330 646 928 942 1273 1279 1309 1490 1849 ...
## $ medoids : num [1:5, 1:2] -4.586 0.639 51.688 40.857 53.458 ...
## $ i.med : int [1:5] 1849 2087 9515 8602 5361
## $ clustering: int [1:10000] 1 2 2 1 1 2 2 2 1 2 ...
## $ objective : num 7.66
## $ clusinfo : num [1:5, 1:4] 2406 2594 1772 1448 1780 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : NULL
## .. ..$ : chr [1:4] "size" "max_diss" "av_diss" "isolation"
## $ diss : 'dissimilarity' num [1:1225] 17.85 16.19 7.51 7.8 15.14 ...
## ..- attr(*, "Size")= int 50
## ..- attr(*, "Metric")= chr "euclidean"
## $ call : language clara(x = xds, k = 5)
## $ silinfo :List of 3
## ..$ widths : num [1:50, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:50] "154" "1490" "3231" "4338" ...
## .. .. ..$ : chr [1:3] "cluster" "neighbor" "sil_width"
## ..$ clus.avg.widths: num [1:5] 0.185 0.434 0.313 0.692 0.307
## ..$ avg.width : num 0.341
## $ data : num [1:10000, 1:2] -6.3 1.09 2.22 6.81 -3.07 ...
## - attr(*, "class")= chr [1:2] "clara" "partition"y<-xcl$clustering
y <- as.data.frame(y)
#Partitioning around medoids
xpm <- pam(xds, 2)
clusplot(xpm)