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univariate analyse Roebels

*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: Mon, 06 Dec 2010 20:55:30 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t12916690616ghlhv7l54tsw2m.htm/, Retrieved Mon, 06 Dec 2010 21:57:42 +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/2010/Dec/06/t12916690616ghlhv7l54tsw2m.htm/},
    year = {2010},
}
@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 = {2010},
    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 «
40,9545 41,1575 41,539 41,651 41,813 42,304 42,4125 42,463 42,391 42,3173 42,3215 42,1962 42,17 41,922 42,28 42,7017 42,815 43,31 43,43 43,1885 43,1555 42,8993 42,7523 42,55 42,3172 42,2875 42,4705 42,4507 43,0028 42,695 42,29 42,3575 42,565 42,3188 42,0055 41,68 41,575 41,593 41,5745 41,36 41,64 41,8045 41,8 41,6923 41,3725 41,15 41,2235 41,374 41,3557 41,456 40,7955 40,55 40,485 40,5875 40,1 39,557 39,3325 39,282 39,2763 39,2301 39,2537 39,4398 39,382 39,388 39,3572 39,1038 39,0046 39,07 39,089 39,029 38,9655 38,913 38,9199 39,0908 39,1614 39,1144 39,1325 39,1183 39,1906 39,3685 39,4723 39,64 39,35 39,301 39,3261 39,384 39,4305 39,4173 39,4514 39,297 39,355 39,185 39,143 39,1355 39,0437 39,2795 39,5095 39,4907 39,1644 38,849 38,691 38,7665 39,0275 39,14 39,1503 39,1015 39,0387 39,0801 38,581 38,282 38,13 38,2615 38,31 38,235 38,0524 38,0075 38,1375 38,384 38,214 38,35 38,48 38,431 38,091 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean42.26087352342160.108218055794613390.515919114538
Geometric Mean42.191995378499
Harmonic Mean42.1222044154264
Quadratic Mean42.3287123981656
Winsorized Mean ( 1 / 163 )42.26069124236250.108194952126351390.597624120301
Winsorized Mean ( 2 / 163 )42.26077270875760.108137336272207390.80648891126
Winsorized Mean ( 3 / 163 )42.26072993890020.108121228188139390.864316352042
Winsorized Mean ( 4 / 163 )42.2604505091650.108082135375811391.003104835243
Winsorized Mean ( 5 / 163 )42.26030386965380.108012179509197391.254986814292
Winsorized Mean ( 6 / 163 )42.25752016293280.107770447709948392.106751534189
Winsorized Mean ( 7 / 163 )42.2581830957230.107539657253715392.954414909697
Winsorized Mean ( 8 / 163 )42.25784908350310.107392601761178393.489387448466
Winsorized Mean ( 9 / 163 )42.2562507128310.107241289457664394.029677622561
Winsorized Mean ( 10 / 163 )42.25614276985740.107159573809906394.329141741616
Winsorized Mean ( 11 / 163 )42.25414887983710.107021485964592394.819306599957
Winsorized Mean ( 12 / 163 )42.25388981670060.106930878697134395.151431761618
Winsorized Mean ( 13 / 163 )42.25390570264770.106926859327399395.166434031983
Winsorized Mean ( 14 / 163 )42.25374887983710.106895309299338395.281599883062
Winsorized Mean ( 15 / 163 )42.25422851323830.106844591200378395.473725328724
Winsorized Mean ( 16 / 163 )42.25366150712830.106763245673015395.769735556177
Winsorized Mean ( 17 / 163 )42.25259511201630.106685090769102396.049671115372
Winsorized Mean ( 18 / 163 )42.25195356415480.106493745045548396.755260565615
Winsorized Mean ( 19 / 163 )42.24912484725050.106310095770265397.414041828639
Winsorized Mean ( 20 / 163 )42.25031018329940.10615920016378397.990095235426
Winsorized Mean ( 21 / 163 )42.25054114052950.106128082408363398.108965899869
Winsorized Mean ( 22 / 163 )42.253234012220.105812218755986399.32282404606
Winsorized Mean ( 23 / 163 )42.25351507128310.105691135574498399.782960430964
Winsorized Mean ( 24 / 163 )42.25298716904280.105475867690529400.59388080139
Winsorized Mean ( 25 / 163 )42.25374073319760.105377206887208400.976093230718
Winsorized Mean ( 26 / 163 )42.2534494908350.105310954041139401.225588311822
Winsorized Mean ( 27 / 163 )42.25377942973520.105167092045728401.777577070997
Winsorized Mean ( 28 / 163 )42.25494847250510.104924037414499402.719429348474
Winsorized Mean ( 29 / 163 )42.25500753564150.104651512062768403.768724433698
Winsorized Mean ( 30 / 163 )42.25494643584520.10464775096226403.782652252928
Winsorized Mean ( 31 / 163 )42.25725091649690.104383981018921404.82505556899
Winsorized Mean ( 32 / 163 )42.25848920570260.104291522103091405.19582372123
Winsorized Mean ( 33 / 163 )42.26008207739310.10411566705408405.895512876482
Winsorized Mean ( 34 / 163 )42.26166782077390.103978775697099406.445137841269
Winsorized Mean ( 35 / 163 )42.26194582484720.10393806223856406.607020706689
Winsorized Mean ( 36 / 163 )42.26260570264770.103691996245164407.578282153274
Winsorized Mean ( 37 / 163 )42.26227413441960.10347970783204408.411223995881
Winsorized Mean ( 38 / 163 )42.263465987780.103324555253261409.036031020769
Winsorized Mean ( 39 / 163 )42.2619171079430.10287204028023410.820248075364
Winsorized Mean ( 40 / 163 )42.26737535641550.102383378262104412.834349421545
Winsorized Mean ( 41 / 163 )42.27018940936860.101823990535268415.129962862024
Winsorized Mean ( 42 / 163 )42.26884643584520.101646473463102415.841740453384
Winsorized Mean ( 43 / 163 )42.26840855397150.101580863579122416.106017065394
Winsorized Mean ( 44 / 163 )42.26827413441950.101457077820377416.612374833551
Winsorized Mean ( 45 / 163 )42.26859490835030.10135772062138417.023929200655
Winsorized Mean ( 46 / 163 )42.27103075356420.101133343805763417.97323378084
Winsorized Mean ( 47 / 163 )42.27189226069250.100956747643127418.712896834987
Winsorized Mean ( 48 / 163 )42.26964378818740.100700087374304419.757766754166
Winsorized Mean ( 49 / 163 )42.26909490835030.100538393224824420.427396465627
Winsorized Mean ( 50 / 163 )42.26900325865580.100404858888457420.985634824843
Winsorized Mean ( 51 / 163 )42.26919022403260.100194295392001421.87222394906
Winsorized Mean ( 52 / 163 )42.26999511201630.100078564361371422.368120303812
Winsorized Mean ( 53 / 163 )42.27102057026480.099933125323793422.993080955915
Winsorized Mean ( 54 / 163 )42.26902993890020.0997230137539583423.864345327434
Winsorized Mean ( 55 / 163 )42.26904114052950.0996025037984078424.377295033473
Winsorized Mean ( 56 / 163 )42.2726338085540.0992787480608477425.797410163202
Winsorized Mean ( 57 / 163 )42.27309816700610.099029549478575426.873578538816
Winsorized Mean ( 58 / 163 )42.27440936863540.0988083187545123427.84261387612
Winsorized Mean ( 59 / 163 )42.27373645621180.0984283480236086429.487411960549
Winsorized Mean ( 60 / 163 )42.27316211812630.0983731617226907429.722511484304
Winsorized Mean ( 61 / 163 )42.27280183299390.0982037691800925430.460074862007
Winsorized Mean ( 62 / 163 )42.27049103869650.0979959936927795431.349175061338
Winsorized Mean ( 63 / 163 )42.26943890020370.0979023389587506431.751062842463
Winsorized Mean ( 64 / 163 )42.2711334012220.0976108696156712433.057645809924
Winsorized Mean ( 65 / 163 )42.27183503054990.0974860141229078433.619482865047
Winsorized Mean ( 66 / 163 )42.27254745417520.0973791642810683434.102590284742
Winsorized Mean ( 67 / 163 )42.27219266802440.0973293373681427434.321180140498
Winsorized Mean ( 68 / 163 )42.27202647657840.0971389246315007435.170830199516
Winsorized Mean ( 69 / 163 )42.27070549898170.0970262171377757435.662718241998
Winsorized Mean ( 70 / 163 )42.27094786150710.0968554249726265436.433456086263
Winsorized Mean ( 71 / 163 )42.27103462321790.0967915546052464436.722344171613
Winsorized Mean ( 72 / 163 )42.27131323828920.096553741201669437.800883862163
Winsorized Mean ( 73 / 163 )42.27097128309570.0964807476652244438.128562495914
Winsorized Mean ( 74 / 163 )42.26815295315680.0962437820638193439.178012820909
Winsorized Mean ( 75 / 163 )42.26731283095720.0961423605616408439.632567622031
Winsorized Mean ( 76 / 163 )42.26599714867620.0960611730133718439.990433416763
Winsorized Mean ( 77 / 163 )42.26591873727090.0959280716781988440.60010795439
Winsorized Mean ( 78 / 163 )42.26383767820770.095602433175708442.079100649362
Winsorized Mean ( 79 / 163 )42.26423991853360.0955661152421004442.251312732179
Winsorized Mean ( 80 / 163 )42.26420733197560.0953722951536658443.149735086889
Winsorized Mean ( 81 / 163 )42.26442179226070.0951699007436255444.094419160057
Winsorized Mean ( 82 / 163 )42.26330285132380.0949974237573685444.8889367702
Winsorized Mean ( 83 / 163 )42.26450305498980.0948210753057953445.728999789214
Winsorized Mean ( 84 / 163 )42.2688997963340.0944930397322306447.322891888264
Winsorized Mean ( 85 / 163 )42.27018085539710.0940785789539658449.307178375649
Winsorized Mean ( 86 / 163 )42.26671283095720.0938885470779593450.179645402985
Winsorized Mean ( 87 / 163 )42.26915804480650.0937285691092023450.974110098268
Winsorized Mean ( 88 / 163 )42.25324276985740.0927590302321237455.516219435685
Winsorized Mean ( 89 / 163 )42.24947250509170.092502518975811456.738616125034
Winsorized Mean ( 90 / 163 )42.24905091649690.0924116183508918457.183324677586
Winsorized Mean ( 91 / 163 )42.24035865580450.0919081649534717459.593102279744
Winsorized Mean ( 92 / 163 )42.24032118126270.0916213993049082461.031172867056
Winsorized Mean ( 93 / 163 )42.24070.0915965502159978461.160381044814
Winsorized Mean ( 94 / 163 )42.23763686354380.0913506233889188462.368348420788
Winsorized Mean ( 95 / 163 )42.23978452138490.090894491924055464.712257335433
Winsorized Mean ( 96 / 163 )42.24021466395110.090827708378623465.058685482509
Winsorized Mean ( 97 / 163 )42.23985906313640.0907522198323204465.44160728169
Winsorized Mean ( 98 / 163 )42.23916048879840.0903114240516779467.705618999301
Winsorized Mean ( 99 / 163 )42.23361568228110.089915173961102469.705098947499
Winsorized Mean ( 100 / 163 )42.23263808553970.0898143506347407470.221493414705
Winsorized Mean ( 101 / 163 )42.22827718940940.0893284736832802472.730311492083
Winsorized Mean ( 102 / 163 )42.22401853360490.0887950472229603475.522226229378
Winsorized Mean ( 103 / 163 )42.22192077393080.0886434866682302476.311597849897
Winsorized Mean ( 104 / 163 )42.21444378818740.088180132797743478.729646336707
Winsorized Mean ( 105 / 163 )42.20396517311610.0875118883694507482.265506544011
Winsorized Mean ( 106 / 163 )42.207332993890.0871175130529635484.487349498026
Winsorized Mean ( 107 / 163 )42.20105682281060.0864918379988538487.919528584533
Winsorized Mean ( 108 / 163 )42.1973835030550.0860869484988455490.1716722323
Winsorized Mean ( 109 / 163 )42.19767209775970.0858107270157667491.752879450682
Winsorized Mean ( 110 / 163 )42.19731364562120.0852679726659007494.878819401041
Winsorized Mean ( 111 / 163 )42.19595723014260.0848954531556705497.034360047163
Winsorized Mean ( 112 / 163 )42.19657311608960.0847659955505975497.800714095337
Winsorized Mean ( 113 / 163 )42.19664215885950.0844656865463008499.571410406152
Winsorized Mean ( 114 / 163 )42.19524908350310.0842194906916296501.015248809819
Winsorized Mean ( 115 / 163 )42.19841099796330.083961642814264502.591535652925
Winsorized Mean ( 116 / 163 )42.20230916496940.0837085502222437504.157688228067
Winsorized Mean ( 117 / 163 )42.20373890020370.0833638915259702506.259222400336
Winsorized Mean ( 118 / 163 )42.21166965376780.0828108304458308509.736098847358
Winsorized Mean ( 119 / 163 )42.21215437881870.0826449693330355510.764959071083
Winsorized Mean ( 120 / 163 )42.21276537678210.0820906673129391514.221247780361
Winsorized Mean ( 121 / 163 )42.21461364562120.0816307348832942517.141168776375
Winsorized Mean ( 122 / 163 )42.21759531568230.0810136436782572521.117103229525
Winsorized Mean ( 123 / 163 )42.21521547861510.0806970905524795523.131815404935
Winsorized Mean ( 124 / 163 )42.2104171079430.0799227001981754528.140528326477
Winsorized Mean ( 125 / 163 )42.23803930753560.0778515350128074542.546005041353
Winsorized Mean ( 126 / 163 )42.2555663951120.0767417730323558550.620147612386
Winsorized Mean ( 127 / 163 )42.26177413441960.0763505380822801553.522937701835
Winsorized Mean ( 128 / 163 )42.27108085539710.0755532098904594559.487557400721
Winsorized Mean ( 129 / 163 )42.27108085539710.0754390505605311560.334210747781
Winsorized Mean ( 130 / 163 )42.30735376782080.0729234622294682580.161068528154
Winsorized Mean ( 131 / 163 )42.31335682281060.0724235272264261584.248771680527
Winsorized Mean ( 132 / 163 )42.34198818737270.0703377371503526601.981097243195
Winsorized Mean ( 133 / 163 )42.34185274949080.0701571126020935603.52901051728
Winsorized Mean ( 134 / 163 )42.34501853360490.0697600265282592607.009782550058
Winsorized Mean ( 135 / 163 )42.34829042769860.0695615007372961608.789200618743
Winsorized Mean ( 136 / 163 )42.35216822810590.0690303766670788613.529438385696
Winsorized Mean ( 137 / 163 )42.37585723014260.0673630089918106629.067167045556
Winsorized Mean ( 138 / 163 )42.39682423625250.0657576332567174644.743767932395
Winsorized Mean ( 139 / 163 )42.40333543788190.0651770563543747650.586844660955
Winsorized Mean ( 140 / 163 )42.40487515274950.0650226914615828652.155027722952
Winsorized Mean ( 141 / 163 )42.4112503054990.0645584555570552656.943384713052
Winsorized Mean ( 142 / 163 )42.41165519348270.0644887819574468657.659423951722
Winsorized Mean ( 143 / 163 )42.42094582484720.0637704578376023665.213129453709
Winsorized Mean ( 144 / 163 )42.42302810590630.063635967512452666.651734297984
Winsorized Mean ( 145 / 163 )42.42689674134420.06314816406299671.862711622519
Winsorized Mean ( 146 / 163 )42.42954317718940.0627557714683682676.105833526018
Winsorized Mean ( 147 / 163 )42.44600957230140.0617339196186086687.563819607314
Winsorized Mean ( 148 / 163 )42.4475167006110.0614884385095263690.333300528272
Winsorized Mean ( 149 / 163 )42.4431164969450.0612828398935954692.577507351788
Winsorized Mean ( 150 / 163 )42.45060122199590.0606572674672443699.84361304966
Winsorized Mean ( 151 / 163 )42.46440957230140.0596515157867264711.87477823909
Winsorized Mean ( 152 / 163 )42.46524541751530.0593000385651445716.108225981417
Winsorized Mean ( 153 / 163 )42.46240977596740.0591191716051437718.251095593379
Winsorized Mean ( 154 / 163 )42.46959226069250.0586868050165307723.665093861043
Winsorized Mean ( 155 / 163 )42.47890488798370.0578415506351238734.401211958324
Winsorized Mean ( 156 / 163 )42.50610162932790.0559349624751337759.920088410255
Winsorized Mean ( 157 / 163 )42.54805356415480.0535029515705859795.246847419652
Winsorized Mean ( 158 / 163 )42.56340305498980.0526077888044359809.070368139116
Winsorized Mean ( 159 / 163 )42.56453645621180.0522291287605908814.957811211445
Winsorized Mean ( 160 / 163 )42.55854052953160.0516954261011227823.255435525026
Winsorized Mean ( 161 / 163 )42.55614684317720.0515425930433995825.650095006752
Winsorized Mean ( 162 / 163 )42.56267963340120.0509624037895554835.178022786365
Winsorized Mean ( 163 / 163 )42.57326965376780.0501558393230995848.819803004681
Trimmed Mean ( 1 / 163 )42.26087352342160.107857497005754391.821381884721
Trimmed Mean ( 2 / 163 )42.26129325153370.107511548710596393.086080131676
Trimmed Mean ( 3 / 163 )42.26247092783510.107186675756168394.288475033737
Trimmed Mean ( 4 / 163 )42.26247092783510.106859142028689395.497007794511
Trimmed Mean ( 5 / 163 )42.2637270270270.106533566182355396.717471699799
Trimmed Mean ( 6 / 163 )42.26442881002090.106214579134026397.915513619742
Trimmed Mean ( 7 / 163 )42.26561404612160.105930770523749398.992793473979
Trimmed Mean ( 8 / 163 )42.26561404612160.105675373851197399.957080877105
Trimmed Mean ( 9 / 163 )42.26786131078220.105433261967338400.896837696973
Trimmed Mean ( 10 / 163 )42.26920615711250.105203103394248401.786684929903
Trimmed Mean ( 11 / 163 )42.27057377398720.104975665342171402.67021538949
Trimmed Mean ( 12 / 163 )42.27214368308350.104755953538284403.529749434572
Trimmed Mean ( 13 / 163 )42.27374989247310.104538576744761404.384211157646
Trimmed Mean ( 14 / 163 )42.27536868250540.10431530260538405.265264315355
Trimmed Mean ( 15 / 163 )42.27701344902390.104088234195592406.16515186127
Trimmed Mean ( 16 / 163 )42.27701344902390.103858634047917407.063060636043
Trimmed Mean ( 17 / 163 )42.2803155361050.103628444141083407.999134663676
Trimmed Mean ( 18 / 163 )42.28207516483520.103397071786545408.929135363942
Trimmed Mean ( 19 / 163 )42.28388896247240.10317184521735409.839417656957
Trimmed Mean ( 20 / 163 )42.28588093126390.102951705012575410.735120181824
Trimmed Mean ( 21 / 163 )42.28782583518930.102734382590794411.622913076997
Trimmed Mean ( 22 / 163 )42.28977606263980.102512388104364412.533322505239
Trimmed Mean ( 23 / 163 )42.29160876404490.102301950059168413.399830008956
Trimmed Mean ( 24 / 163 )42.2934444695260.10209178757907414.268820954573
Trimmed Mean ( 25 / 163 )42.29532131519270.101886662745178415.12127471458
Trimmed Mean ( 26 / 163 )42.29718154897490.101680302334019415.982059239251
Trimmed Mean ( 27 / 163 )42.2990713958810.101470820352317416.859460177955
Trimmed Mean ( 28 / 163 )42.30096482758620.101261853255775417.73840264151
Trimmed Mean ( 29 / 163 )42.30282840646650.101057964112687418.599649991918
Trimmed Mean ( 30 / 163 )42.30470696055680.10086025575708419.438822983425
Trimmed Mean ( 31 / 163 )42.30660536130540.100656322931806420.307479242688
Trimmed Mean ( 32 / 163 )42.30660536130540.100457631547239421.138789653935
Trimmed Mean ( 33 / 163 )42.31023929411770.1002565284484422.019792116518
Trimmed Mean ( 34 / 163 )42.31200354609930.100056404615287422.88151077172
Trimmed Mean ( 35 / 163 )42.31373016627080.0998554762427034423.749720680569
Trimmed Mean ( 36 / 163 )42.31546396181380.0996495928425085424.642617744474
Trimmed Mean ( 37 / 163 )42.31719280575540.0994468461491664425.525740075068
Trimmed Mean ( 38 / 163 )42.31894891566270.0992457187386533426.405788113666
Trimmed Mean ( 39 / 163 )42.32068474576270.0990439168173976427.292115514649
Trimmed Mean ( 40 / 163 )42.32248491484190.0988525164402313428.137658391641
Trimmed Mean ( 41 / 163 )42.32413887530560.0986730744777873428.933010340459
Trimmed Mean ( 42 / 163 )42.32572628992630.0985079946614315429.667931373472
Trimmed Mean ( 43 / 163 )42.32736814814810.098343244664031430.404429839088
Trimmed Mean ( 44 / 163 )42.32903870967740.0981747437340616431.160165025126
Trimmed Mean ( 45 / 163 )42.33072967581050.0980044021085213431.926819255907
Trimmed Mean ( 46 / 163 )42.33242882205510.0978312523125129432.70864699583
Trimmed Mean ( 47 / 163 )42.33407959697730.097659553418729433.486311528213
Trimmed Mean ( 48 / 163 )42.33572430379750.097487515495488434.268163350177
Trimmed Mean ( 49 / 163 )42.33744427480920.0973175817670943435.044146248244
Trimmed Mean ( 50 / 163 )42.33919590792840.0971465723883827435.827995440337
Trimmed Mean ( 51 / 163 )42.34096786632390.0969734567785938436.624301874638
Trimmed Mean ( 52 / 163 )42.34275348837210.0968006325684069437.422280876619
Trimmed Mean ( 53 / 163 )42.34453792207790.0966249572106927438.236032847547
Trimmed Mean ( 54 / 163 )42.34631618798960.0964472539481622439.061916793915
Trimmed Mean ( 55 / 163 )42.34816062992130.0962693024428176439.892671447114
Trimmed Mean ( 56 / 163 )42.35002427440630.096088258714181440.74088594298
Trimmed Mean ( 57 / 163 )42.3518241379310.0959105421973703441.576318594644
Trimmed Mean ( 58 / 163 )42.35363253333330.0957336279022335442.41123481277
Trimmed Mean ( 59 / 163 )42.35543056300270.0955566119640831443.24960557332
Trimmed Mean ( 60 / 163 )42.35726307277630.095384166361981444.070171059956
Trimmed Mean ( 61 / 163 )42.35912818428180.0952063748359645444.919032546553
Trimmed Mean ( 62 / 163 )42.36102152588560.0950265200327592445.781046294047
Trimmed Mean ( 63 / 163 )42.36298575342470.094845515964564446.652488761327
Trimmed Mean ( 64 / 163 )42.36298575342470.094659884055689447.528392581827
Trimmed Mean ( 65 / 163 )42.36698891966760.0944755194341807448.444096136289
Trimmed Mean ( 66 / 163 )42.3689910863510.0942873417151104449.360331043896
Trimmed Mean ( 67 / 163 )42.37100084033610.0940946502757034450.301911067062
Trimmed Mean ( 68 / 163 )42.37304056338030.0938955059605883451.278686129728
Trimmed Mean ( 69 / 163 )42.37510679886690.0936938371932288452.272081796318
Trimmed Mean ( 70 / 163 )42.37722336182340.0934871342275723453.294709608555
Trimmed Mean ( 71 / 163 )42.37935931232090.0932769981281014454.338799090849
Trimmed Mean ( 72 / 163 )42.38151815561960.0930601137204759455.420872178608
Trimmed Mean ( 73 / 163 )42.38369652173910.0928413382366561456.517509621646
Trimmed Mean ( 74 / 163 )42.38590699708450.0926156746258138457.65370892489
Trimmed Mean ( 75 / 163 )42.38819824046920.0923874694504744458.808954207713
Trimmed Mean ( 76 / 163 )42.39053274336280.0921527486392177460.002912222659
Trimmed Mean ( 77 / 163 )42.39292017804150.09191061987942461.24071661858
Trimmed Mean ( 78 / 163 )42.39533761194030.091662404870176462.516095579055
Trimmed Mean ( 79 / 163 )42.39782342342340.0914133072999893463.803626361393
Trimmed Mean ( 80 / 163 )42.40033172205440.0911549677250708465.145595245412
Trimmed Mean ( 81 / 163 )42.40287112462010.0908916041696776466.521319675047
Trimmed Mean ( 82 / 163 )42.40543761467890.0906232587901446467.931060754246
Trimmed Mean ( 83 / 163 )42.40805630769230.0903487041064182469.382009704771
Trimmed Mean ( 84 / 163 )42.41068544891640.0900679918676107470.874109320158
Trimmed Mean ( 85 / 163 )42.41326728971960.0897856062475392472.383815873406
Trimmed Mean ( 86 / 163 )42.415858307210.0895036699359053473.900772310058
Trimmed Mean ( 87 / 163 )42.41854447949530.0892150670589952475.463908483588
Trimmed Mean ( 88 / 163 )42.4212209523810.0889191792164758477.076164289658
Trimmed Mean ( 89 / 163 )42.42421533546330.0886376097793462478.625443996897
Trimmed Mean ( 90 / 163 )42.42731511254020.0883508944736196480.213758619143
Trimmed Mean ( 91 / 163 )42.43046245954690.0880542696097625481.867178588722
Trimmed Mean ( 92 / 163 )42.43380358306190.087758476061087483.529403513394
Trimmed Mean ( 93 / 163 )42.43718918032790.0874580741509447485.228946467368
Trimmed Mean ( 94 / 163 )42.44061287128710.0871451057627105487.010859644255
Trimmed Mean ( 95 / 163 )42.44413521594680.0868251681266979488.845989379613
Trimmed Mean ( 96 / 163 )42.44766755852840.0865049215763435490.69656136347
Trimmed Mean ( 97 / 163 )42.45124006734010.0861723554886077492.631770672118
Trimmed Mean ( 98 / 163 )42.45486711864410.0858270773698998494.655864089033
Trimmed Mean ( 99 / 163 )42.45855563139930.0854795629857904496.710022236044
Trimmed Mean ( 100 / 163 )42.4623893470790.0851275179040398498.809202858996
Trimmed Mean ( 101 / 163 )42.4662927335640.0847623269872982501.004328726459
Trimmed Mean ( 102 / 163 )42.47032439024390.0843946587243767503.23474295864
Trimmed Mean ( 103 / 163 )42.47448456140350.084025745405396505.493695491524
Trimmed Mean ( 104 / 163 )42.4787388692580.0836439555964862507.851865282211
Trimmed Mean ( 105 / 163 )42.48317935943060.0832573468425298510.263429842196
Trimmed Mean ( 106 / 163 )42.48785913978490.08287128566366512.69699509943
Trimmed Mean ( 107 / 163 )42.49255018050540.0824798521471086515.187031430621
Trimmed Mean ( 108 / 163 )42.49741418181820.082087957968631517.705827181839
Trimmed Mean ( 109 / 163 )42.50241062271060.0816889743622947520.295559523251
Trimmed Mean ( 110 / 163 )42.50747601476020.0812792845331469522.980440328864
Trimmed Mean ( 111 / 163 )42.51262267657990.0808667157911683525.712244656569
Trimmed Mean ( 112 / 163 )42.51786891385770.0804452989599135528.531430221232
Trimmed Mean ( 113 / 163 )42.52318415094340.0800071324841343531.492416121474
Trimmed Mean ( 114 / 163 )42.52857908745250.0795568152865997534.568646749436
Trimmed Mean ( 115 / 163 )42.53407969348660.079091500260985537.783194820344
Trimmed Mean ( 116 / 163 )42.53961312741310.0786120153713918541.133730339319
Trimmed Mean ( 117 / 163 )42.54516848249030.0781176687683451544.629264458164
Trimmed Mean ( 118 / 163 )42.55078745098040.0776100950587167548.263565697067
Trimmed Mean ( 119 / 163 )42.55636482213440.0770976464343505551.980077087977
Trimmed Mean ( 120 / 163 )42.56202310756970.076564411202103555.898261859822
Trimmed Mean ( 121 / 163 )42.5677622489960.0760229013206943559.933408347946
Trimmed Mean ( 122 / 163 )42.57356396761130.075469651425279564.11502058894
Trimmed Mean ( 123 / 163 )42.57356396761130.0749099601875217568.329817036842
Trimmed Mean ( 124 / 163 )42.58539423868310.0743307940542304572.917251598491
Trimmed Mean ( 125 / 163 )42.5915551867220.0737467715771347577.537894552764
Trimmed Mean ( 126 / 163 )42.59736527196650.0732159144641927581.804728981421
Trimmed Mean ( 127 / 163 )42.60298523206750.0727018543968322585.995853689309
Trimmed Mean ( 128 / 163 )42.60298523206750.0721754207297234590.269994983523
Trimmed Mean ( 129 / 163 )42.61415536480690.0716519183611689594.738512791881
Trimmed Mean ( 130 / 163 )42.61980822510820.0711029117397107599.410167351912
Trimmed Mean ( 131 / 163 )42.62496157205240.0706286978005126603.507680297952
Trimmed Mean ( 132 / 163 )42.63010660792950.0701474849141567607.721098769233
Trimmed Mean ( 133 / 163 )42.63486977777780.0697247071645078611.474346922469
Trimmed Mean ( 134 / 163 )42.63972062780270.0692833337638722615.439793545806
Trimmed Mean ( 135 / 163 )42.64460678733030.0688314281788355619.551386853873
Trimmed Mean ( 136 / 163 )42.64952785388130.0683608736004897623.887987493123
Trimmed Mean ( 137 / 163 )42.65447511520740.0678835541440612628.347700014157
Trimmed Mean ( 138 / 163 )42.65911953488370.0674494650919167632.460457273457
Trimmed Mean ( 139 / 163 )42.66350093896710.0670567174357654636.230083583127
Trimmed Mean ( 140 / 163 )42.66785639810430.0666633121959375640.050051409004
Trimmed Mean ( 141 / 163 )42.67226937799040.0662511044699324644.098988528666
Trimmed Mean ( 142 / 163 )42.67666038647340.0658327137549892648.259170133923
Trimmed Mean ( 143 / 163 )42.68113024390240.0653900542765488652.715932355625
Trimmed Mean ( 144 / 163 )42.68553103448280.0649508732547734657.197184509689
Trimmed Mean ( 145 / 163 )42.6899840796020.0644890197158154661.972910547012
Trimmed Mean ( 146 / 163 )42.69446080402010.0640183610585153666.909619335548
Trimmed Mean ( 147 / 163 )42.6989832487310.0635338753498224672.066405734376
Trimmed Mean ( 148 / 163 )42.70331641025640.0630665779073377677.114849532496
Trimmed Mean ( 149 / 163 )42.70771347150260.062578638844593682.464723746427
Trimmed Mean ( 150 / 163 )42.71227853403140.0620645934738554688.190740377988
Trimmed Mean ( 151 / 163 )42.71681058201060.0615460241802098694.062876538274
Trimmed Mean ( 152 / 163 )42.72119946524060.0610422643706936699.862626422343
Trimmed Mean ( 153 / 163 )42.72566864864870.060519333592571705.983792489965
Trimmed Mean ( 154 / 163 )42.73028524590160.0599663528001228712.57102109125
Trimmed Mean ( 155 / 163 )42.73487734806630.0593973425287875719.474567862265
Trimmed Mean ( 156 / 163 )42.73940726256980.0588320128875251726.465153321864
Trimmed Mean ( 157 / 163 )42.74355593220340.0583291835332217732.798804013065
Trimmed Mean ( 158 / 163 )42.74704971428570.0579210190449725738.02309453663
Trimmed Mean ( 159 / 163 )42.75034855491330.0575291709823618743.107328419879
Trimmed Mean ( 160 / 163 )42.75370409356730.0571251930561637748.421174726415
Trimmed Mean ( 161 / 163 )42.75724792899410.0567130517567747753.922538190453
Trimmed Mean ( 162 / 163 )42.76092035928140.0562745924343603759.861928971917
Trimmed Mean ( 163 / 163 )42.76456181818180.0558328599364784765.93894467945
Median42.9278
Midrange42.15825
Midmean - Weighted Average at Xnp42.5675743902439
Midmean - Weighted Average at X(n+1)p42.5735639676114
Midmean - Empirical Distribution Function42.5735639676114
Midmean - Empirical Distribution Function - Averaging42.5735639676114
Midmean - Empirical Distribution Function - Interpolation42.5794114285715
Midmean - Closest Observation42.5675743902439
Midmean - True Basic - Statistics Graphics Toolkit42.5735639676114
Midmean - MS Excel (old versions)42.5735639676114
Number of observations491
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/06/t12916690616ghlhv7l54tsw2m/1vg0e1291668922.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/06/t12916690616ghlhv7l54tsw2m/1vg0e1291668922.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/06/t12916690616ghlhv7l54tsw2m/2vg0e1291668922.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/06/t12916690616ghlhv7l54tsw2m/2vg0e1291668922.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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