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*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Thu, 18 Mar 2010 14:41:16 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/18/t1268945099c8nmt3ftwk1p1xi.htm/, Retrieved Thu, 18 Mar 2010 21:45:02 +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/Mar/18/t1268945099c8nmt3ftwk1p1xi.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:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
93.2 96 95.2 77.1 70.9 64.8 70.1 77.3 79.5 100.6 100.7 107.1 95.9 82.8 83.3 80 80.4 67.5 75.7 71.1 89.3 101.1 105.2 114.1 96.3 84.4 91.2 81.9 80.5 70.4 74.8 75.9 86.3 98.7 100.9 113.8 89.8 84.4 87.2 85.6 72 69.2 77.5 78.1 94.3 97.7 100.2 116.4 97.1 93 96 80.5 76.1 69.9 73.6 92.6 94.2 93.5 108.5 109.4 105.1 92.5 97.1 81.4 79.1 72.1 78.7 87.1 91.4 109.9 116.3 113 100 84.8 94.3 87.1 90.3 72.4 84.9 92.7 92.2 114.9 112.5 118.3 106 91.2 96.6 96.3 88.2 70.2 86.5 88.2 102.8 119.1 119.2 125.1 106.1 102.1 105.2 101 84.3 87.5 92.7 94.4 113 113.9 122.9 132.7 106.9 96.6 127.3 98.2 100.2 89.4 95.3 104.2 106.4 116.2 135.9 134 104.6 107.1 123.5 98.8 98.6 90.6 89.1 105.2 114 122.1 138 142.2 116.4 112.6 123.8 103.6 113.9 98.6 95 116 113.9 127.5 131.4 145.9 131.5 131 130.5 118.9 114.3 85.7 104.6 105.1 117.3 142.5 140 159.8 131.2 125.4 126.5 119.4 113.5 98.7 114.5 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean136.3953781512611.5464119058447588.2011950604792
Geometric Mean131.941570667006
Harmonic Mean127.205573038972
Quadratic Mean140.497720009013
Winsorized Mean ( 1 / 158 )136.3957983193281.5452959415879588.2651630982523
Winsorized Mean ( 2 / 158 )136.3840336134451.5426568846783488.4085339831631
Winsorized Mean ( 3 / 158 )136.3865546218491.5420627465026188.4442315535945
Winsorized Mean ( 4 / 158 )136.3857142857141.5416558053279888.4670325336975
Winsorized Mean ( 5 / 158 )136.3699579831931.5398838540427188.5585998094442
Winsorized Mean ( 6 / 158 )136.367436974791.5391594420422888.5986423822646
Winsorized Mean ( 7 / 158 )136.3306722689081.5342455717719688.8584427272967
Winsorized Mean ( 8 / 158 )136.3306722689081.5336269276548788.8942870071906
Winsorized Mean ( 9 / 158 )136.3212184873951.5296386239044489.1198851526326
Winsorized Mean ( 10 / 158 )136.3170168067231.5288702922330189.16192400313
Winsorized Mean ( 11 / 158 )136.2939075630251.5255105544411589.3431429669491
Winsorized Mean ( 12 / 158 )136.3115546218491.5217245426125889.5770231764951
Winsorized Mean ( 13 / 158 )136.3142857142861.5162118506965389.9045114649809
Winsorized Mean ( 14 / 158 )136.3054621848741.5108467414511590.2179277654292
Winsorized Mean ( 15 / 158 )136.2928571428571.5086645457805490.3400676605302
Winsorized Mean ( 16 / 158 )136.2928571428571.5075149151617590.4089609808161
Winsorized Mean ( 17 / 158 )136.3214285714291.5039143110167290.64441210036
Winsorized Mean ( 18 / 158 )136.2949579831931.5003570972537890.8416791127023
Winsorized Mean ( 19 / 158 )136.2909663865551.4986738810820490.9410433497062
Winsorized Mean ( 20 / 158 )136.2027310924371.4870926704710491.5899417682521
Winsorized Mean ( 21 / 158 )136.2203781512601.4841990594243691.7803964948561
Winsorized Mean ( 22 / 158 )136.2296218487391.4819365450741991.9267577964479
Winsorized Mean ( 23 / 158 )136.1571428571431.4729448094982792.4387268138867
Winsorized Mean ( 24 / 158 )136.1823529411761.4709104609386292.5837136641722
Winsorized Mean ( 25 / 158 )136.1981092436971.4688062534771392.7270761009314
Winsorized Mean ( 26 / 158 )136.0997899159661.4601931827065293.2067013651579
Winsorized Mean ( 27 / 158 )136.0997899159661.4601931827065293.2067013651579
Winsorized Mean ( 28 / 158 )136.1527310924371.4559755419085693.513061980397
Winsorized Mean ( 29 / 158 )136.1344537815131.4497948351215493.8991162636474
Winsorized Mean ( 30 / 158 )136.1407563025211.4414849482178694.4447990739233
Winsorized Mean ( 31 / 158 )136.1472689075631.4369723233177994.7459228673352
Winsorized Mean ( 32 / 158 )136.1338235294121.4257147240274395.4846164068883
Winsorized Mean ( 33 / 158 )136.1407563025211.4251844691198795.5250069393442
Winsorized Mean ( 34 / 158 )136.1050420168071.4225216161231995.6787162136314
Winsorized Mean ( 35 / 158 )136.0756302521011.4159288390561196.1034386041687
Winsorized Mean ( 36 / 158 )136.0378151260501.4120319506537796.3418816855133
Winsorized Mean ( 37 / 158 )136.0222689075631.4028320756934396.9626167410851
Winsorized Mean ( 38 / 158 )136.0063025210081.4005074601442497.1121585507306
Winsorized Mean ( 39 / 158 )136.0390756302521.3956304674098097.474997004567
Winsorized Mean ( 40 / 158 )136.0222689075631.3919706310568597.719208920585
Winsorized Mean ( 41 / 158 )136.0394957983191.3856659854595598.1762540365762
Winsorized Mean ( 42 / 158 )136.0042016806721.3831714475844398.327797264894
Winsorized Mean ( 43 / 158 )136.0042016806721.3818632365064098.4208842725385
Winsorized Mean ( 44 / 158 )136.0226890756301.3791549101054798.627563937127
Winsorized Mean ( 45 / 158 )136.0888655462181.3742766518185999.025815046869
Winsorized Mean ( 46 / 158 )136.0792016806721.3735959967876899.0678496434975
Winsorized Mean ( 47 / 158 )136.1680672268911.3671147422081699.6025154457426
Winsorized Mean ( 48 / 158 )136.1781512605041.3649432964216199.7683578633001
Winsorized Mean ( 49 / 158 )136.157563025211.3620256442876199.9669599440072
Winsorized Mean ( 50 / 158 )136.0735294117651.35020840770261100.779649004923
Winsorized Mean ( 51 / 158 )136.0521008403361.34119097215537101.441259048809
Winsorized Mean ( 52 / 158 )136.0848739495801.33884212501062101.643704965214
Winsorized Mean ( 53 / 158 )136.1182773109241.33179299550349102.206782713604
Winsorized Mean ( 54 / 158 )135.8686974789921.31499591534528103.322524346637
Winsorized Mean ( 55 / 158 )135.8802521008401.31258103411479103.521419683226
Winsorized Mean ( 56 / 158 )135.9626050420171.30512336186803104.176056466733
Winsorized Mean ( 57 / 158 )135.8907563025211.29550046225859104.894409736920
Winsorized Mean ( 58 / 158 )135.8907563025211.29384601191765105.028538984414
Winsorized Mean ( 59 / 158 )135.8907563025211.29216490206713105.165181382911
Winsorized Mean ( 60 / 158 )135.8529411764711.28970565314283105.336392722957
Winsorized Mean ( 61 / 158 )135.8401260504201.28368361558106105.82056544278
Winsorized Mean ( 62 / 158 )135.7619747899161.27516640733785106.466084746810
Winsorized Mean ( 63 / 158 )135.7619747899161.26985207366981106.911645541177
Winsorized Mean ( 64 / 158 )135.8023109243701.25987121815071107.790628889598
Winsorized Mean ( 65 / 158 )135.6111344537821.24610247921681108.828235811724
Winsorized Mean ( 66 / 158 )135.5972689075631.24524607986662108.891946017680
Winsorized Mean ( 67 / 158 )135.6113445378151.24426397096989108.989207838356
Winsorized Mean ( 68 / 158 )135.6827731092441.23742688388667109.649123415739
Winsorized Mean ( 69 / 158 )135.5233193277311.22389440699947110.731218765828
Winsorized Mean ( 70 / 158 )135.4350840336131.21668084119665111.315210569444
Winsorized Mean ( 71 / 158 )135.4649159663871.20692441244594112.239767933648
Winsorized Mean ( 72 / 158 )135.4497899159661.20408226824769112.492139023929
Winsorized Mean ( 73 / 158 )135.4497899159661.20408226824769112.492139023929
Winsorized Mean ( 74 / 158 )135.4031512605041.19535605400914113.274325926883
Winsorized Mean ( 75 / 158 )135.3873949579831.19443010079192113.348947643081
Winsorized Mean ( 76 / 158 )135.3554621848741.18646311289429114.083160878625
Winsorized Mean ( 77 / 158 )135.3231092436971.18458092100879114.237116978430
Winsorized Mean ( 78 / 158 )135.4050420168071.17895944326326114.851314683071
Winsorized Mean ( 79 / 158 )135.3884453781511.17799428194886114.931326452762
Winsorized Mean ( 80 / 158 )135.4052521008401.16624414998772116.103692440615
Winsorized Mean ( 81 / 158 )135.3882352941181.15459126970459117.260747458066
Winsorized Mean ( 82 / 158 )135.4399159663871.14894252015698117.882238310652
Winsorized Mean ( 83 / 158 )135.4224789915971.14794462685239117.969522069125
Winsorized Mean ( 84 / 158 )135.4224789915971.14574502620823118.195999889931
Winsorized Mean ( 85 / 158 )135.3689075630251.14269396193039118.46470890101
Winsorized Mean ( 86 / 158 )135.3689075630251.14269396193039118.46470890101
Winsorized Mean ( 87 / 158 )135.3689075630251.14042210702203118.700704528178
Winsorized Mean ( 88 / 158 )135.4983193277311.12029695835637120.948573783978
Winsorized Mean ( 89 / 158 )135.5170168067231.11674756825255121.349730824823
Winsorized Mean ( 90 / 158 )135.4602941176471.11354985310927121.647265041087
Winsorized Mean ( 91 / 158 )135.4220588235291.10203578731601122.883540064835
Winsorized Mean ( 92 / 158 )135.4027310924371.09859893574759123.250375261192
Winsorized Mean ( 93 / 158 )135.4418067226891.09600330994082123.577917597715
Winsorized Mean ( 94 / 158 )135.4023109243701.09140546489439124.062335474444
Winsorized Mean ( 95 / 158 )135.4023109243701.08897739698962124.338954416021
Winsorized Mean ( 96 / 158 )135.4628151260501.06788040614154126.852046677684
Winsorized Mean ( 97 / 158 )135.5850840336131.05741417698664128.223251573944
Winsorized Mean ( 98 / 158 )135.7086134453781.0444439778386129.933836878659
Winsorized Mean ( 99 / 158 )135.7918067226891.03410493285064131.313372955645
Winsorized Mean ( 100 / 158 )135.7497899159661.02180575297417132.852833839347
Winsorized Mean ( 101 / 158 )135.5800420168071.01262407662587133.889806835887
Winsorized Mean ( 102 / 158 )135.6443277310921.00344130270033135.179135407386
Winsorized Mean ( 103 / 158 )135.6226890756301.00228221432029135.313873815076
Winsorized Mean ( 104 / 158 )135.5571428571430.996220734991722136.071392710240
Winsorized Mean ( 105 / 158 )135.4909663865550.992714752178423136.485295588921
Winsorized Mean ( 106 / 158 )135.4686974789920.991539538897902136.624604632071
Winsorized Mean ( 107 / 158 )135.6260504201680.978844639728541138.557279588087
Winsorized Mean ( 108 / 158 )135.6260504201680.976201053128454138.932497548045
Winsorized Mean ( 109 / 158 )135.6718487394960.970624585804611139.777881916136
Winsorized Mean ( 110 / 158 )135.7642857142860.962087497221196141.114281296051
Winsorized Mean ( 111 / 158 )135.7876050420170.957913239674958141.753552845864
Winsorized Mean ( 112 / 158 )135.7876050420170.957913239674958141.753552845864
Winsorized Mean ( 113 / 158 )136.0962184873950.935861511000492145.423459441023
Winsorized Mean ( 114 / 158 )136.2878151260500.9212748827988147.933931197617
Winsorized Mean ( 115 / 158 )136.2394957983190.918705600290096148.295053121805
Winsorized Mean ( 116 / 158 )136.3613445378150.911233808222974149.644738054372
Winsorized Mean ( 117 / 158 )136.9758403361340.871474402673485157.177124096731
Winsorized Mean ( 118 / 158 )136.9758403361340.868673214849326157.683969062973
Winsorized Mean ( 119 / 158 )136.9508403361340.856064944978779159.977161942461
Winsorized Mean ( 120 / 158 )136.9256302521010.854717810538678160.199809298235
Winsorized Mean ( 121 / 158 )137.0273109243700.845893598196125161.991190400993
Winsorized Mean ( 122 / 158 )137.0785714285710.840029857277156163.182975272919
Winsorized Mean ( 123 / 158 )137.0785714285710.840029857277156163.182975272919
Winsorized Mean ( 124 / 158 )137.1046218487390.8385111113283163.509606487563
Winsorized Mean ( 125 / 158 )137.0258403361340.83431028373903164.238465001345
Winsorized Mean ( 126 / 158 )137.0258403361340.83431028373903164.238465001345
Winsorized Mean ( 127 / 158 )136.9991596638660.829920091387566165.075121190057
Winsorized Mean ( 128 / 158 )136.9991596638660.826926923316309165.672631765869
Winsorized Mean ( 129 / 158 )137.0262605042020.822335434721754166.630616556814
Winsorized Mean ( 130 / 158 )137.0535714285710.81771551531808167.605443288256
Winsorized Mean ( 131 / 158 )136.9159663865550.807424577180347169.571214768674
Winsorized Mean ( 132 / 158 )136.9991596638660.802592933229538170.695696400661
Winsorized Mean ( 133 / 158 )137.2506302521010.781954337870494175.522563920903
Winsorized Mean ( 134 / 158 )137.2506302521010.775775623948461176.920524459814
Winsorized Mean ( 135 / 158 )137.1371848739500.769840077787664178.137237629988
Winsorized Mean ( 136 / 158 )137.0514705882350.76538395625275179.062377083558
Winsorized Mean ( 137 / 158 )136.965126050420.757783848090287180.744319630974
Winsorized Mean ( 138 / 158 )136.8491596638660.748686450089645182.785677031392
Winsorized Mean ( 139 / 158 )136.6739495798320.73979573598456184.745522218966
Winsorized Mean ( 140 / 158 )136.8504201680670.720144126306356190.031988277094
Winsorized Mean ( 141 / 158 )136.9689075630250.71020893149028192.857202282170
Winsorized Mean ( 142 / 158 )136.9390756302520.705506907430402194.100262078244
Winsorized Mean ( 143 / 158 )137.0292016806720.697183200029614196.546907147005
Winsorized Mean ( 144 / 158 )137.0594537815130.689014729822486198.920934269176
Winsorized Mean ( 145 / 158 )137.1203781512600.682338618259837200.9564964987
Winsorized Mean ( 146 / 158 )137.1203781512600.679075366926952201.922179524457
Winsorized Mean ( 147 / 158 )137.1512605042020.677341595889314202.484627160878
Winsorized Mean ( 148 / 158 )137.1512605042020.674038142948841203.477001915916
Winsorized Mean ( 149 / 158 )137.182563025210.668962722881208205.067574519500
Winsorized Mean ( 150 / 158 )137.2140756302520.663860873336893206.691011838891
Winsorized Mean ( 151 / 158 )137.3409663865550.656790243496068209.109327896673
Winsorized Mean ( 152 / 158 )137.4048319327730.649870734897915211.434096896758
Winsorized Mean ( 153 / 158 )137.5655462184870.634221951077527216.904422788847
Winsorized Mean ( 154 / 158 )137.6626050420170.625496085718895220.085478047074
Winsorized Mean ( 155 / 158 )137.7277310924370.618520634334583222.6728155005
Winsorized Mean ( 156 / 158 )137.7932773109240.608089643142588226.600269984559
Winsorized Mean ( 157 / 158 )137.9581932773110.588849123956048234.284450234842
Winsorized Mean ( 158 / 158 )138.0245798319330.585280158048626235.826514761954
Trimmed Mean ( 1 / 158 )136.3746835443041.5359731894161088.7871510284283
Trimmed Mean ( 2 / 158 )136.3533898305081.5264047469026389.3297731857793
Trimmed Mean ( 3 / 158 )136.3378723404261.5179598733111889.8165193543797
Trimmed Mean ( 4 / 158 )136.3213675213681.5095023879894490.3088120999522
Trimmed Mean ( 5 / 158 )136.3049356223181.5009306858589990.8136111190967
Trimmed Mean ( 6 / 158 )136.2915948275861.4925168615394491.3166198249914
Trimmed Mean ( 7 / 158 )136.2785714285711.4840121658940691.8311686120638
Trimmed Mean ( 8 / 158 )136.2708695652171.4760633612982592.3204742683691
Trimmed Mean ( 9 / 158 )136.2631004366811.4679896066131092.8229326848325
Trimmed Mean ( 10 / 158 )136.2563596491231.4602057712311993.3131222555272
Trimmed Mean ( 11 / 158 )136.251.4523015509884593.8166043458861
Trimmed Mean ( 12 / 158 )136.2457964601771.4445419143158594.3176484599993
Trimmed Mean ( 13 / 158 )136.241.4369459833168994.8121930690242
Trimmed Mean ( 14 / 158 )136.2339285714291.4296520286863495.2916694677161
Trimmed Mean ( 15 / 158 )136.2284753363231.4226236876683295.758615941227
Trimmed Mean ( 16 / 158 )136.2238738738741.4155814919562996.2317426781392
Trimmed Mean ( 17 / 158 )136.2192307692311.4084349457140796.7167359655143
Trimmed Mean ( 18 / 158 )136.2127272727271.4013570411860597.2005871947113
Trimmed Mean ( 19 / 158 )136.2077625570781.3943344621913097.6865782568534
Trimmed Mean ( 20 / 158 )136.2029816513761.3872303433603598.1833927604596
Trimmed Mean ( 21 / 158 )136.2029953917051.3806810992074198.6491344524769
Trimmed Mean ( 22 / 158 )136.2020833333331.3741288695731699.1188572987632
Trimmed Mean ( 23 / 158 )136.2006976744191.3675284885598699.596241550954
Trimmed Mean ( 24 / 158 )136.2028037383181.36126600438364100.055979727481
Trimmed Mean ( 25 / 158 )136.2037558685451.35494029721106100.523806214118
Trimmed Mean ( 26 / 158 )136.2040094339621.34854931609883101.000391908530
Trimmed Mean ( 27 / 158 )136.2085308056871.34243420757006101.463840862814
Trimmed Mean ( 28 / 158 )136.2130952380951.33614243658497101.945040819331
Trimmed Mean ( 29 / 158 )136.2155502392341.32988263471846102.426745551175
Trimmed Mean ( 30 / 158 )136.218751.32374657378254102.903949062366
Trimmed Mean ( 31 / 158 )136.2217391304351.31783258313562103.36801569006
Trimmed Mean ( 32 / 158 )136.2245145631071.31195759856501103.833016182921
Trimmed Mean ( 33 / 158 )136.2278048780491.30642833043128104.274992898445
Trimmed Mean ( 34 / 158 )136.2308823529411.30075816738008104.731906183092
Trimmed Mean ( 35 / 158 )136.2352216748771.29503636139693105.197989597699
Trimmed Mean ( 36 / 158 )136.2405940594061.28943005593884105.659545806235
Trimmed Mean ( 37 / 158 )136.2472636815921.28382083657935106.126384460790
Trimmed Mean ( 38 / 158 )136.25451.27842858560666106.579672524565
Trimmed Mean ( 39 / 158 )136.2623115577891.27296726020995107.043060585325
Trimmed Mean ( 40 / 158 )136.2691919191921.26753771592011107.507011592372
Trimmed Mean ( 41 / 158 )136.2766497461931.26208746133655107.977183769718
Trimmed Mean ( 42 / 158 )136.2836734693881.25671866159177108.444059624905
Trimmed Mean ( 43 / 158 )136.2917948717951.25127925771572108.921964486651
Trimmed Mean ( 44 / 158 )136.31.24571970217510109.414661871376
Trimmed Mean ( 45 / 158 )136.3077720207251.24008921245795109.917714509066
Trimmed Mean ( 46 / 158 )136.3138020833331.23446701549427110.423203190046
Trimmed Mean ( 47 / 158 )136.3201570680631.22869116558820110.947454401858
Trimmed Mean ( 48 / 158 )136.3242105263161.22297401612909111.469425129574
Trimmed Mean ( 49 / 158 )136.3280423280421.21715346370847112.005631494218
Trimmed Mean ( 50 / 158 )136.3324468085111.21125192883183112.554988407732
Trimmed Mean ( 51 / 158 )136.3390374331551.20558843041873113.089205232172
Trimmed Mean ( 52 / 158 )136.3462365591401.20006401667244113.615802711262
Trimmed Mean ( 53 / 158 )136.3527027027031.19444195608021114.155988919018
Trimmed Mean ( 54 / 158 )136.3584239130431.18888432267131114.694441934148
Trimmed Mean ( 55 / 158 )136.3702185792351.18372508235989115.204299217319
Trimmed Mean ( 56 / 158 )136.3818681318681.17847608952139115.727310332835
Trimmed Mean ( 57 / 158 )136.3917127071821.17330866044270116.245381377923
Trimmed Mean ( 58 / 158 )136.4033333333331.16829212936480116.754474249086
Trimmed Mean ( 59 / 158 )136.4150837988831.16315945304511117.279779175377
Trimmed Mean ( 60 / 158 )136.4269662921351.15790669401288117.822072363472
Trimmed Mean ( 61 / 158 )136.4269662921351.15255391839220118.369270291882
Trimmed Mean ( 62 / 158 )136.4531251.14721708338473118.942724072249
Trimmed Mean ( 63 / 158 )136.4682857142861.14197543034672119.501945565371
Trimmed Mean ( 64 / 158 )136.4836206896551.13672561525019120.067339785966
Trimmed Mean ( 65 / 158 )136.4982658959541.13162124088338120.621866190315
Trimmed Mean ( 66 / 158 )136.5171511627911.12677718693917121.157184175545
Trimmed Mean ( 67 / 158 )136.5365497076021.12178478345055121.713676029393
Trimmed Mean ( 68 / 158 )136.5558823529411.11664359685416122.291376351102
Trimmed Mean ( 69 / 158 )136.5739644970411.11154124916057122.869002477579
Trimmed Mean ( 70 / 158 )136.5955357142861.10668095869852123.428106936009
Trimmed Mean ( 71 / 158 )136.6191616766471.10186633267886123.988870178561
Trimmed Mean ( 72 / 158 )136.6424698795181.09718533806295124.539095756381
Trimmed Mean ( 73 / 158 )136.6663636363641.09241676197317125.104601461360
Trimmed Mean ( 74 / 158 )136.6905487804881.08746674336615125.696302543814
Trimmed Mean ( 75 / 158 )136.7159509202451.08260342468136126.284424936569
Trimmed Mean ( 76 / 158 )136.7419753086421.07758124316673126.897137617942
Trimmed Mean ( 77 / 158 )136.7689440993791.07261700572412127.509580185191
Trimmed Mean ( 78 / 158 )136.7968751.06751676990399128.144942409010
Trimmed Mean ( 79 / 158 )136.8235849056601.06240350124818128.786835458384
Trimmed Mean ( 80 / 158 )136.8509493670891.05711853417213129.456579317533
Trimmed Mean ( 81 / 158 )136.8783439490451.05200266077948130.112165160899
Trimmed Mean ( 82 / 158 )136.9064102564101.04705273628077130.754073326540
Trimmed Mean ( 83 / 158 )136.9338709677421.04208746370998131.403433719698
Trimmed Mean ( 84 / 158 )136.9620129870131.03695101789382132.081468288831
Trimmed Mean ( 85 / 158 )136.9905228758171.03167587500721132.784458951179
Trimmed Mean ( 86 / 158 )137.0203947368421.02627794117778133.511974913534
Trimmed Mean ( 87 / 158 )137.0506622516561.02065775823205134.276804488362
Trimmed Mean ( 88 / 158 )137.0813333333331.01487924531519135.071570303677
Trimmed Mean ( 89 / 158 )137.1100671140941.00952802597434135.816008655890
Trimmed Mean ( 90 / 158 )137.1388513513511.00406881359110136.583120095990
Trimmed Mean ( 91 / 158 )137.1690476190480.99847721541748137.378245092648
Trimmed Mean ( 92 / 158 )137.2003424657530.993019284275302138.164831880260
Trimmed Mean ( 93 / 158 )137.2324137931030.98743698625165138.978401360114
Trimmed Mean ( 94 / 158 )137.2642361111110.981703269293944139.822531313188
Trimmed Mean ( 95 / 158 )137.2972027972030.975867803720281140.692419889034
Trimmed Mean ( 96 / 158 )137.3306338028170.969857794378547141.598731895343
Trimmed Mean ( 97 / 158 )137.3634751773050.964292275227736142.450042073462
Trimmed Mean ( 98 / 158 )137.3946428571430.95883995801334143.292571099995
Trimmed Mean ( 99 / 158 )137.4241007194240.953585799774388144.112989887159
Trimmed Mean ( 100 / 158 )137.4525362318840.94844403625948144.924245371373
Trimmed Mean ( 101 / 158 )137.4821167883210.943467563964796145.720024767540
Trimmed Mean ( 102 / 158 )137.5150735294120.938541680874818146.519942940876
Trimmed Mean ( 103 / 158 )137.5474074074070.933696108652316147.314962687315
Trimmed Mean ( 104 / 158 )137.5805970149250.928656782542308148.150101955086
Trimmed Mean ( 105 / 158 )137.6154135338350.923571057597931149.003601186628
Trimmed Mean ( 106 / 158 )137.6518939393940.918349378763789149.890550505615
Trimmed Mean ( 107 / 158 )137.6893129770990.912912018866926150.824296461771
Trimmed Mean ( 108 / 158 )137.7246153846150.907668403887553151.734504357251
Trimmed Mean ( 109 / 158 )137.7604651162790.90225853967617152.684024654089
Trimmed Mean ( 110 / 158 )137.796093750.89678206796106153.656165386197
Trimmed Mean ( 111 / 158 )137.8307086614170.891345038117195154.632272315735
Trimmed Mean ( 112 / 158 )137.8654761904760.885785869873231155.641990778434
Trimmed Mean ( 113 / 158 )137.90080.879947240477573156.714850228017
Trimmed Mean ( 114 / 158 )137.9314516129030.87464217461391157.700435236604
Trimmed Mean ( 115 / 158 )137.9593495934960.869605616885483158.645881437152
Trimmed Mean ( 116 / 158 )137.9885245901640.864392536062016159.636413820519
Trimmed Mean ( 117 / 158 )138.0161157024790.859191316053079160.634905315958
Trimmed Mean ( 118 / 158 )138.033750.855184743400622161.408106336313
Trimmed Mean ( 119 / 158 )138.0516806722690.851057003820291162.212025813279
Trimmed Mean ( 120 / 158 )138.0703389830510.847140800855797162.983932356427
Trimmed Mean ( 121 / 158 )138.0897435897440.843050590296535163.797695155129
Trimmed Mean ( 122 / 158 )138.0897435897440.839053505943006164.577994861657
Trimmed Mean ( 123 / 158 )138.1252173913040.835043121175844165.410879855889
Trimmed Mean ( 124 / 158 )138.1429824561400.830803549852968166.276350745719
Trimmed Mean ( 125 / 158 )138.1606194690270.826379714128317167.187815851411
Trimmed Mean ( 126 / 158 )138.1799107142860.821849384570414168.132888225637
Trimmed Mean ( 127 / 158 )138.1995495495500.817057934741698169.142901223081
Trimmed Mean ( 128 / 158 )138.220.812153071189124170.189592212738
Trimmed Mean ( 129 / 158 )138.2408256880730.807077813023509171.285622597144
Trimmed Mean ( 130 / 158 )138.2615740740740.801887457237232172.420172963462
Trimmed Mean ( 131 / 158 )138.2822429906540.796576475894334173.595690025119
Trimmed Mean ( 132 / 158 )138.3056603773580.791339789486115174.774050559460
Trimmed Mean ( 133 / 158 )138.3280952380950.78599330091545175.991443027547
Trimmed Mean ( 134 / 158 )138.3466346153850.781182821626487177.098920746024
Trimmed Mean ( 135 / 158 )138.3655339805830.776322674771874178.231988420591
Trimmed Mean ( 136 / 158 )138.3867647058820.771384880611599179.40041111016
Trimmed Mean ( 137 / 158 )138.4099009900990.766305925939464180.619640674726
Trimmed Mean ( 138 / 158 )138.4350.761205322310326181.8628902644
Trimmed Mean ( 139 / 158 )138.4626262626260.756136146049063183.118644686035
Trimmed Mean ( 140 / 158 )138.4938775510200.751074803788515184.394253212117
Trimmed Mean ( 141 / 158 )138.5226804123710.746544846614499185.551720088293
Trimmed Mean ( 142 / 158 )138.550.74214913616748186.687544656434
Trimmed Mean ( 143 / 158 )138.5784210526320.737643246099477187.866454123194
Trimmed Mean ( 144 / 158 )138.6058510638300.733200045281568189.042338384747
Trimmed Mean ( 145 / 158 )138.6333333333330.728803610782896190.220426027267
Trimmed Mean ( 146 / 158 )138.6603260869570.72439749709511191.414695168047
Trimmed Mean ( 147 / 158 )138.6879120879120.719817007996698192.671068545449
Trimmed Mean ( 148 / 158 )138.7155555555560.714987996418894194.011027108608
Trimmed Mean ( 149 / 158 )138.7438202247190.70995850439392195.425252836660
Trimmed Mean ( 150 / 158 )138.7721590909090.704804789671356196.894460884151
Trimmed Mean ( 151 / 158 )138.8005747126440.699519799378047198.422653420322
Trimmed Mean ( 152 / 158 )138.8273255813950.694212185090142199.978232250949
Trimmed Mean ( 153 / 158 )138.8535294117650.688858246186991201.570541080629
Trimmed Mean ( 154 / 158 )138.8773809523810.683905834291146203.065062453115
Trimmed Mean ( 155 / 158 )138.90.679021158344401204.559163279489
Trimmed Mean ( 156 / 158 )138.9219512195120.674114184132708206.080741941730
Trimmed Mean ( 157 / 158 )138.9432098765430.669358423977329207.576695682625
Trimmed Mean ( 158 / 158 )138.9618750.665226749937604208.893997442277
Median139.15
Midrange141.3
Midmean - Weighted Average at Xnp137.945188284519
Midmean - Weighted Average at X(n+1)p138.051680672269
Midmean - Empirical Distribution Function137.945188284519
Midmean - Empirical Distribution Function - Averaging138.051680672269
Midmean - Empirical Distribution Function - Interpolation138.051680672269
Midmean - Closest Observation137.945188284519
Midmean - True Basic - Statistics Graphics Toolkit138.051680672269
Midmean - MS Excel (old versions)138.03375
Number of observations476
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Mar/18/t1268945099c8nmt3ftwk1p1xi/1i8sz1268944872.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/18/t1268945099c8nmt3ftwk1p1xi/1i8sz1268944872.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Mar/18/t1268945099c8nmt3ftwk1p1xi/219dp1268944872.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/18/t1268945099c8nmt3ftwk1p1xi/219dp1268944872.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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