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Paper CT

*The author of this computation has been verified*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sat, 12 Dec 2009 07:16:31 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj.htm/, Retrieved Sat, 12 Dec 2009 15:18:40 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
349 336 331 327 323 322 385 405 412 411 410 415 414 411 408 410 411 416 479 498 502 498 499 506 510 509 502 495 490 490 553 570 573 572 575 580 580 574 563 556 546 545 605 628 631 626 614 606 602 589 574 558 552 546 607 636 631 623 618 605 619 596 570 546 528 506 555 568 564 553 541 542 540 521 505 491 482 478 523 531 532 540 525 533 531 508 495 482 470 466 515 518 516 511 500 498 494 476 458 443 430 424 476 481 470 460 451 450 444 429 421 400 389 384 432 446 431 423 416 416 413 399 386 374 365 365 418 428 424 421 417 423 423 419 406 398 390 391 444 460 455 456 452 459 461 451 443 439 430 436 488 506 502 501 501 515 521 520 512 509 505 511 570 592 594 586 586 592 594 586 572 563 555 554 601 622 617 606 595 599 600 592 575 567 555 555 608 631 629 624 610 616 621 604 584 574 555 545 599 620 608 590 579 580 579 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean518.8690807799443.60630956638544143.878131155557
Geometric Mean514.087370298814
Harmonic Mean508.97926855051
Quadratic Mean523.336489058373
Winsorized Mean ( 1 / 119 )518.8579387186633.60464885527141143.941326756388
Winsorized Mean ( 2 / 119 )518.8802228412263.60129951005327144.081385453428
Winsorized Mean ( 3 / 119 )518.913649025073.59637276992545144.288059726308
Winsorized Mean ( 4 / 119 )518.9470752089143.58641299241138144.698080312271
Winsorized Mean ( 5 / 119 )519.1281337047353.56143094406586145.763919575562
Winsorized Mean ( 6 / 119 )519.3788300835663.5257904627351147.308478927776
Winsorized Mean ( 7 / 119 )519.3788300835663.5257904627351147.308478927776
Winsorized Mean ( 8 / 119 )519.5348189415043.49805739735400148.520953182327
Winsorized Mean ( 9 / 119 )519.7855153203343.46978465983927149.803393085614
Winsorized Mean ( 10 / 119 )519.7576601671313.46202324184164150.131187418211
Winsorized Mean ( 11 / 119 )519.7576601671313.45613437532448150.386994174187
Winsorized Mean ( 12 / 119 )519.8245125348193.44261145296852150.997148425385
Winsorized Mean ( 13 / 119 )519.8245125348193.43578812169684151.297022436323
Winsorized Mean ( 14 / 119 )519.8635097493043.43168485333155151.489292277118
Winsorized Mean ( 15 / 119 )520.1142061281343.39822826638178153.054522932893
Winsorized Mean ( 16 / 119 )520.1587743732593.39376925208435153.268750977631
Winsorized Mean ( 17 / 119 )520.2061281337053.38906235687898153.495590624885
Winsorized Mean ( 18 / 119 )520.4066852367693.36050091075265154.859855437508
Winsorized Mean ( 19 / 119 )520.4066852367693.35111754888856155.293473787384
Winsorized Mean ( 20 / 119 )520.4623955431753.33604113173226156.011983962836
Winsorized Mean ( 21 / 119 )520.5208913649023.32038046309699156.765436114933
Winsorized Mean ( 22 / 119 )520.3983286908083.31061835447131157.190673454692
Winsorized Mean ( 23 / 119 )520.3983286908083.29962680731656157.714298943408
Winsorized Mean ( 24 / 119 )520.331476323123.29440840449952157.943828583137
Winsorized Mean ( 25 / 119 )520.2618384401113.28901887017336158.181469604244
Winsorized Mean ( 26 / 119 )520.334261838443.2823201303782158.526359760797
Winsorized Mean ( 27 / 119 )520.334261838443.26962283078498159.141983270748
Winsorized Mean ( 28 / 119 )520.2562674094713.25063053832236160.047800350135
Winsorized Mean ( 29 / 119 )520.3370473537603.24327835591401160.435519327209
Winsorized Mean ( 30 / 119 )520.3370473537603.22943029565128161.123479907413
Winsorized Mean ( 31 / 119 )520.3370473537603.22943029565128161.123479907413
Winsorized Mean ( 32 / 119 )520.247910863513.22277696134812161.428456608392
Winsorized Mean ( 33 / 119 )520.3398328690813.21449684973641161.872870683245
Winsorized Mean ( 34 / 119 )520.3398328690813.19898744064658162.657666690904
Winsorized Mean ( 35 / 119 )520.4373259052923.19030196690734163.131055086237
Winsorized Mean ( 36 / 119 )520.5376044568253.16518123988504164.457440192502
Winsorized Mean ( 37 / 119 )520.331476323123.15012598334430165.177989411939
Winsorized Mean ( 38 / 119 )520.4373259052923.12393501540807166.596719630325
Winsorized Mean ( 39 / 119 )520.3286908077993.11614296517125166.978439892986
Winsorized Mean ( 40 / 119 )520.2172701949863.10821994203748167.368230014629
Winsorized Mean ( 41 / 119 )520.331476323123.09827160302487167.94249923574
Winsorized Mean ( 42 / 119 )520.331476323123.09827160302487167.94249923574
Winsorized Mean ( 43 / 119 )520.5710306406683.04018046691796171.230305669455
Winsorized Mean ( 44 / 119 )520.6935933147633.02978771041208171.858111221906
Winsorized Mean ( 45 / 119 )520.6935933147633.01042664938449172.963388236423
Winsorized Mean ( 46 / 119 )520.5654596100283.00151195631402173.434411452188
Winsorized Mean ( 47 / 119 )520.6963788300842.99051048558845174.116219066734
Winsorized Mean ( 48 / 119 )520.6963788300842.99051048558845174.116219066734
Winsorized Mean ( 49 / 119 )520.6963788300842.96965704410297175.338893042906
Winsorized Mean ( 50 / 119 )521.253481894152.92372540109929178.284007690382
Winsorized Mean ( 51 / 119 )521.253481894152.92372540109929178.284007690382
Winsorized Mean ( 52 / 119 )521.6880222841232.88865415513277180.598989795005
Winsorized Mean ( 53 / 119 )521.5403899721452.87837353228984181.192741012054
Winsorized Mean ( 54 / 119 )521.8412256267412.83211088605922184.258754908027
Winsorized Mean ( 55 / 119 )521.9944289693592.82008502991170185.098826252662
Winsorized Mean ( 56 / 119 )521.9944289693592.82008502991170185.098826252662
Winsorized Mean ( 57 / 119 )521.83565459612.80912035771855185.764790448464
Winsorized Mean ( 58 / 119 )521.83565459612.78540473006841187.346438010566
Winsorized Mean ( 59 / 119 )521.83565459612.78540473006841187.346438010566
Winsorized Mean ( 60 / 119 )522.002785515322.74804332071332189.954351003397
Winsorized Mean ( 61 / 119 )522.3426183844012.72195263421449191.899966156149
Winsorized Mean ( 62 / 119 )522.5153203342622.68395026074998194.681446961038
Winsorized Mean ( 63 / 119 )522.6908077994432.67074911283648195.709437957771
Winsorized Mean ( 64 / 119 )522.5125348189422.65862108687487196.535165315017
Winsorized Mean ( 65 / 119 )522.5125348189422.63281476498574198.461563558488
Winsorized Mean ( 66 / 119 )523.0640668523682.59195361553648201.803019821442
Winsorized Mean ( 67 / 119 )523.0640668523682.59195361553648201.803019821442
Winsorized Mean ( 68 / 119 )522.8746518105852.55255730052031204.843453153432
Winsorized Mean ( 69 / 119 )522.8746518105852.55255730052031204.843453153432
Winsorized Mean ( 70 / 119 )523.0696378830082.53833412997673206.068078944281
Winsorized Mean ( 71 / 119 )522.6740947075212.48460639284158210.364948030964
Winsorized Mean ( 72 / 119 )522.6740947075212.45694452046796212.733372834959
Winsorized Mean ( 73 / 119 )522.8774373259052.44227262910143214.094622809692
Winsorized Mean ( 74 / 119 )522.8774373259052.44227262910143214.094622809692
Winsorized Mean ( 75 / 119 )522.8774373259052.44227262910143214.094622809692
Winsorized Mean ( 76 / 119 )522.8774373259052.44227262910143214.094622809692
Winsorized Mean ( 77 / 119 )522.8774373259052.41290389805012216.700481833713
Winsorized Mean ( 78 / 119 )522.8774373259052.41290389805012216.700481833713
Winsorized Mean ( 79 / 119 )522.8774373259052.38291206815206219.427919441188
Winsorized Mean ( 80 / 119 )523.3231197771592.35130378313849222.567208682255
Winsorized Mean ( 81 / 119 )523.0974930362122.27604274574851229.827622531836
Winsorized Mean ( 82 / 119 )523.3259052924792.26008934260300231.550981382776
Winsorized Mean ( 83 / 119 )523.5571030640672.21333209186376236.547016594875
Winsorized Mean ( 84 / 119 )523.7910863509752.19727655082417238.381957953589
Winsorized Mean ( 85 / 119 )523.7910863509752.19727655082417238.381957953589
Winsorized Mean ( 86 / 119 )523.7910863509752.19727655082417238.381957953589
Winsorized Mean ( 87 / 119 )523.7910863509752.16531228645337241.9009440938
Winsorized Mean ( 88 / 119 )523.7910863509752.16531228645337241.9009440938
Winsorized Mean ( 89 / 119 )524.7827298050142.09867876718822250.053861510263
Winsorized Mean ( 90 / 119 )524.7827298050142.09867876718822250.053861510263
Winsorized Mean ( 91 / 119 )524.7827298050142.06569379894905254.046717897882
Winsorized Mean ( 92 / 119 )524.7827298050142.06569379894905254.046717897882
Winsorized Mean ( 93 / 119 )524.7827298050142.06569379894905254.046717897882
Winsorized Mean ( 94 / 119 )524.7827298050141.99802086317198262.651276309443
Winsorized Mean ( 95 / 119 )524.7827298050141.99802086317198262.651276309443
Winsorized Mean ( 96 / 119 )525.0501392757661.98059221008801265.097548400655
Winsorized Mean ( 97 / 119 )524.7799442896941.96352893577616267.263667332844
Winsorized Mean ( 98 / 119 )525.3259052924791.92821982452750272.440879722418
Winsorized Mean ( 99 / 119 )525.3259052924791.92821982452750272.440879722418
Winsorized Mean ( 100 / 119 )525.3259052924791.89278797286166277.540809020595
Winsorized Mean ( 101 / 119 )525.0445682451251.87513720761381280.003279820396
Winsorized Mean ( 102 / 119 )525.6128133704741.83895754227011285.821070518914
Winsorized Mean ( 103 / 119 )525.6128133704741.80286774097797291.54263589261
Winsorized Mean ( 104 / 119 )526.4818941504181.74880581652518301.052231857577
Winsorized Mean ( 105 / 119 )526.1894150417831.73041288463767304.083158252696
Winsorized Mean ( 106 / 119 )526.4846796657381.71228375860653307.475134900651
Winsorized Mean ( 107 / 119 )526.4846796657381.67542064172427314.240296767446
Winsorized Mean ( 108 / 119 )526.4846796657381.67542064172427314.240296767446
Winsorized Mean ( 109 / 119 )526.1810584958221.65649966942478317.646340779856
Winsorized Mean ( 110 / 119 )526.4874651810581.63788008394924321.44445148365
Winsorized Mean ( 111 / 119 )526.7966573816161.61924340574632325.335064210937
Winsorized Mean ( 112 / 119 )526.4846796657381.59982819562169329.088261543701
Winsorized Mean ( 113 / 119 )526.4846796657381.56144706696114337.177411137205
Winsorized Mean ( 114 / 119 )526.4846796657381.56144706696114337.177411137205
Winsorized Mean ( 115 / 119 )526.8050139275771.54233643908978341.562969385898
Winsorized Mean ( 116 / 119 )526.8050139275771.50321740132023350.451646890795
Winsorized Mean ( 117 / 119 )526.1532033426181.46329798214465359.566684135977
Winsorized Mean ( 118 / 119 )527.1392757660171.40540807159787375.079157732948
Winsorized Mean ( 119 / 119 )526.8077994428971.38515062050886380.325281339703
Trimmed Mean ( 1 / 119 )519.092436974793.56913936123348145.439105744359
Trimmed Mean ( 2 / 119 )519.3295774647893.53229531675867147.023261334032
Trimmed Mean ( 3 / 119 )519.5580736543913.49583912966041148.621848541658
Trimmed Mean ( 4 / 119 )519.7777777777783.45978544374965150.234107353909
Trimmed Mean ( 5 / 119 )519.9914040114613.42512152819293151.816920868734
Trimmed Mean ( 6 / 119 )520.1700288184443.39480293697452153.225397313349
Trimmed Mean ( 7 / 119 )520.3072463768123.37016069046801154.386480101208
Trimmed Mean ( 8 / 119 )520.4460641399423.34461895998239155.606982549271
Trimmed Mean ( 9 / 119 )520.5659824046923.32222141446868156.692139824746
Trimmed Mean ( 10 / 119 )520.6578171091453.30274973173551157.643739126292
Trimmed Mean ( 11 / 119 )520.7537091988133.28349491019473158.597385847
Trimmed Mean ( 12 / 119 )520.8507462686573.26418412483656159.565369583658
Trimmed Mean ( 13 / 119 )520.9429429429433.24555809459340160.509511079390
Trimmed Mean ( 14 / 119 )521.0362537764353.22689757178562161.466623028916
Trimmed Mean ( 15 / 119 )521.1276595744683.20791587765262162.450537810175
Trimmed Mean ( 16 / 119 )521.2018348623853.19112029062034163.328795969978
Trimmed Mean ( 17 / 119 )521.2738461538463.17405589778790164.229573435408
Trimmed Mean ( 18 / 119 )521.3436532507743.15671303224474165.153958540237
Trimmed Mean ( 19 / 119 )521.4018691588793.14085411201236166.006395255593
Trimmed Mean ( 20 / 119 )521.4608150470223.12505477594483166.86453596301
Trimmed Mean ( 21 / 119 )521.5173501577293.10968469572424167.707469144639
Trimmed Mean ( 22 / 119 )521.5714285714293.09475790120365168.533838581872
Trimmed Mean ( 23 / 119 )521.6325878594253.07986180509256169.368829145809
Trimmed Mean ( 24 / 119 )521.6945337620583.06505879613882170.207023245120
Trimmed Mean ( 25 / 119 )521.7605177993533.04997372875799171.070495748770
Trimmed Mean ( 26 / 119 )521.8306188925083.03459363218736171.960625421984
Trimmed Mean ( 27 / 119 )521.8983606557383.01898266878163172.872261259572
Trimmed Mean ( 28 / 119 )521.966996699673.00345437831153173.788888044674
Trimmed Mean ( 29 / 119 )522.0398671096352.98833376091222174.692624344034
Trimmed Mean ( 30 / 119 )522.1103678929772.97299042374117175.617911084947
Trimmed Mean ( 31 / 119 )522.1818181818182.95774412626112176.547326574158
Trimmed Mean ( 32 / 119 )522.2542372881362.94185540557249177.525461074285
Trimmed Mean ( 33 / 119 )522.3310580204782.92563096737254178.536207691831
Trimmed Mean ( 34 / 119 )522.4054982817872.90914716614716179.573417378418
Trimmed Mean ( 35 / 119 )522.4809688581322.89273869465006180.618100703125
Trimmed Mean ( 36 / 119 )522.5540069686412.87606317618992181.690726161620
Trimmed Mean ( 37 / 119 )522.6245614035092.85990497005299182.741932643246
Trimmed Mean ( 38 / 119 )522.7031802120142.84374736386094183.807882111701
Trimmed Mean ( 39 / 119 )522.7793594306052.82813574787302184.849457747485
Trimmed Mean ( 40 / 119 )522.8602150537632.81218369749157185.926764144230
Trimmed Mean ( 41 / 119 )522.9458483754512.79587324104716187.042044931761
Trimmed Mean ( 42 / 119 )523.0290909090912.77930012546835188.187337566127
Trimmed Mean ( 43 / 119 )523.1135531135532.76197291727959189.398509247076
Trimmed Mean ( 44 / 119 )523.1918819188192.7465336463235190.491706744304
Trimmed Mean ( 45 / 119 )523.2676579925652.7308592210976191.612827915110
Trimmed Mean ( 46 / 119 )523.344569288392.71531933256985192.737761268426
Trimmed Mean ( 47 / 119 )523.426415094342.69942928315420193.902621698884
Trimmed Mean ( 48 / 119 )523.5057034220532.68328844569130195.098556870647
Trimmed Mean ( 49 / 119 )523.5862068965522.66637738910864196.366129204082
Trimmed Mean ( 50 / 119 )523.6679536679542.64957628071411197.642150361799
Trimmed Mean ( 51 / 119 )523.7354085603112.63403464171787198.833910634805
Trimmed Mean ( 52 / 119 )523.8039215686272.61773324540844200.098280635504
Trimmed Mean ( 53 / 119 )523.8616600790512.60219373404069201.315395247532
Trimmed Mean ( 54 / 119 )523.9243027888452.58631261380031202.575782986649
Trimmed Mean ( 55 / 119 )523.9799196787152.57164756923248203.752616006827
Trimmed Mean ( 56 / 119 )524.0323886639682.55676395387742204.959236799805
Trimmed Mean ( 57 / 119 )524.0323886639682.54112116097747206.220937714907
Trimmed Mean ( 58 / 119 )524.1440329218112.52513117165562207.571012074653
Trimmed Mean ( 59 / 119 )524.1440329218112.50932919538176208.878147150426
Trimmed Mean ( 60 / 119 )524.263598326362.49270372051854210.319258566879
Trimmed Mean ( 61 / 119 )524.263598326362.4768239504307211.667687659106
Trimmed Mean ( 62 / 119 )524.3702127659572.46124642787182213.0506749864
Trimmed Mean ( 63 / 119 )524.3702127659572.44646172403690214.338204278421
Trimmed Mean ( 64 / 119 )524.4588744588742.43144807827308215.698159111573
Trimmed Mean ( 65 / 119 )524.5065502183412.41611443895447217.086799268213
Trimmed Mean ( 66 / 119 )524.5550660792952.40103345094734218.470536456845
Trimmed Mean ( 67 / 119 )524.5911111111112.38688705346451219.780450168214
Trimmed Mean ( 68 / 119 )524.6278026905832.37194184171942221.180719300555
Trimmed Mean ( 69 / 119 )524.6696832579192.35780684615443222.524454924564
Trimmed Mean ( 70 / 119 )524.7123287671232.342857201143223.962573780055
Trimmed Mean ( 71 / 119 )524.7511520737332.32766923810283225.440601045805
Trimmed Mean ( 72 / 119 )524.82.31385646788355226.807499637187
Trimmed Mean ( 73 / 119 )524.8497652582162.30039450417526228.156415912838
Trimmed Mean ( 74 / 119 )524.8957345971562.28676342933531229.536526543862
Trimmed Mean ( 75 / 119 )524.9425837320572.27230140519241231.018025395978
Trimmed Mean ( 76 / 119 )524.9903381642512.25695606504104232.609906012816
Trimmed Mean ( 77 / 119 )525.0390243902442.24067058758912234.322272670685
Trimmed Mean ( 78 / 119 )525.0886699507392.22468802153782236.028002518650
Trimmed Mean ( 79 / 119 )525.1393034825872.20770980309658237.866092158496
Trimmed Mean ( 80 / 119 )525.1909547738692.19102427513007239.701111820266
Trimmed Mean ( 81 / 119 )525.2335025380712.17476401972035241.512871178368
Trimmed Mean ( 82 / 119 )525.2820512820512.16081880572343243.093983581927
Trimmed Mean ( 83 / 119 )525.3264248704662.14669054867620244.714556177843
Trimmed Mean ( 84 / 119 )525.3664921465972.13373709520421246.218942965097
Trimmed Mean ( 85 / 119 )525.4021164021162.12063989492006247.756404876049
Trimmed Mean ( 86 / 119 )525.4385026737972.10663924147021249.420257787991
Trimmed Mean ( 87 / 119 )525.4756756756762.09167212064843251.222775543222
Trimmed Mean ( 88 / 119 )525.5136612021862.07715898254072252.996359748733
Trimmed Mean ( 89 / 119 )525.5524861878452.06162540383706254.921425206391
Trimmed Mean ( 90 / 119 )525.5698324022352.04822191555177256.598090476271
Trimmed Mean ( 91 / 119 )525.5875706214692.03384382238846258.420811291321
Trimmed Mean ( 92 / 119 )525.6057142857142.01999686456791260.201252539144
Trimmed Mean ( 93 / 119 )525.6057142857142.00512331117883262.131366861775
Trimmed Mean ( 94 / 119 )525.6432748538011.98914529242116264.255847401672
Trimmed Mean ( 95 / 119 )525.6627218934911.97533194427651266.113613672168
Trimmed Mean ( 96 / 119 )525.6826347305391.96045402242791268.14331206784
Trimmed Mean ( 97 / 119 )525.6826347305391.94532479599009270.228722634972
Trimmed Mean ( 98 / 119 )525.7177914110431.92987548554785272.410212652555
Trimmed Mean ( 99 / 119 )525.7267080745341.91506344010594274.521823697626
Trimmed Mean ( 100 / 119 )525.7358490566041.89906208817908276.839737009709
Trimmed Mean ( 101 / 119 )525.7452229299361.88365899126619279.108493292903
Trimmed Mean ( 102 / 119 )525.7612903225811.86792842138804281.467578897853
Trimmed Mean ( 103 / 119 )525.7647058823531.85287838225813283.755647924176
Trimmed Mean ( 104 / 119 )525.768211920531.83852430767158285.972945653568
Trimmed Mean ( 105 / 119 )525.7516778523491.82585543067233287.948141468547
Trimmed Mean ( 106 / 119 )525.7414965986391.81306743784898289.973492228386
Trimmed Mean ( 107 / 119 )525.7241379310351.80010330585366292.052204015992
Trimmed Mean ( 108 / 119 )525.7062937062941.78800715383802294.018003550963
Trimmed Mean ( 109 / 119 )525.6879432624111.77475642268324296.202868485821
Trimmed Mean ( 110 / 119 )525.6762589928061.76136599212213298.448057555296
Trimmed Mean ( 111 / 119 )525.6569343065691.74776548613537300.759420229136
Trimmed Mean ( 112 / 119 )525.629629629631.73392453053277303.144468155211
Trimmed Mean ( 113 / 119 )525.6090225563911.71993374516939305.598412748525
Trimmed Mean ( 114 / 119 )525.6090225563911.70691214127036307.92974626404
Trimmed Mean ( 115 / 119 )525.5658914728681.69253823544545310.519361079336
Trimmed Mean ( 116 / 119 )525.5354330708661.67786993045077313.215836062857
Trimmed Mean ( 117 / 119 )525.5041.66422020875418315.765904797772
Trimmed Mean ( 118 / 119 )525.5041.65179419950654318.141327870620
Trimmed Mean ( 119 / 119 )525.4462809917361.64161406887632320.079055701199
Median523
Midrange479
Midmean - Weighted Average at Xnp526.071038251366
Midmean - Weighted Average at X(n+1)p526.071038251366
Midmean - Empirical Distribution Function526.071038251366
Midmean - Empirical Distribution Function - Averaging526.071038251366
Midmean - Empirical Distribution Function - Interpolation526.071038251366
Midmean - Closest Observation526.071038251366
Midmean - True Basic - Statistics Graphics Toolkit526.071038251366
Midmean - MS Excel (old versions)526.071038251366
Number of observations359
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj/1vybe1260627387.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj/1vybe1260627387.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj/2799h1260627387.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/12/t1260627517xmqyvh82lut3kpj/2799h1260627387.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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