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Classical Decomposition of Time Series by Moving Averages

*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: Fri, 17 Dec 2010 19:46:13 +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/17/t1292615768tchkr8kbc85d7q7.htm/, Retrieved Fri, 17 Dec 2010 20:56:09 +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/17/t1292615768tchkr8kbc85d7q7.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:
Yen
 
Dataseries X:
» Textbox « » Textfile « » CSV «
126,64 126,81 125,84 126,77 124,34 124,4 120,48 118,54 117,66 116,97 120,11 119,16 116,9 116,11 114,98 113,65 115,82 117,59 118,57 118,07 114,98 114,04 115,02 114,28 115,04 116,7 119,21 118,39 116,5 115,46 117,59 117,33 116,2 116,83 118,99 118,62 121,09 122,4 123,76 125,33 123,23 122,52 123,64 124,67 124,71 122,53 124,4 125,45 125,35 124,3 127,03 128,51 128,1 128,94 129,67 129,87 131,12 132,68 132,24 133,63 129,91 127,93 131,17 130,86 133,48 134,08 136,02 132,8 132,37 133,05 132,57 130,7 130,5 129,67 127,8 126,82 126,85 128,28 128,3 126,82 125,08 128,53 130,34 131,52 132,59 131,17 132,72 133,36 132,82 132,9 130,9 129,41 128,67 129,28 130,91 131,06 130,84 131,41 133,22 132,06 132,48 134,38 135,22 134,89 136,09 136,33 136,32 137,48 136,53 136,8 138,03 137,39 137,55 136,08 134,78 133,28 133,57 134,84 133,02 133,49 133,77 134,34 134,5 134,03 135,51 136,53 135,95 134,32 132,44 133,61 13 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean123.876171079430.423092271409042292.787600839126
Geometric Mean123.516097052934
Harmonic Mean123.150898919683
Quadratic Mean124.229703475706
Winsorized Mean ( 1 / 163 )123.876496945010.423045921179583292.820449845265
Winsorized Mean ( 2 / 163 )123.8766191446030.423023225744185292.836448700135
Winsorized Mean ( 3 / 163 )123.8765580448070.422991195572732292.858478713906
Winsorized Mean ( 4 / 163 )123.8759877800410.422524969968645293.180277107016
Winsorized Mean ( 5 / 163 )123.8758859470470.422488064685363293.205646032392
Winsorized Mean ( 6 / 163 )123.8775967413440.422275997440882293.356945438716
Winsorized Mean ( 7 / 163 )123.8767413441960.42215713585215293.437516090171
Winsorized Mean ( 8 / 163 )123.8778818737270.422040824975108293.521087399622
Winsorized Mean ( 9 / 163 )123.8837474541750.421385165676603293.991714813358
Winsorized Mean ( 10 / 163 )123.8756008146640.420862838087594294.337227248565
Winsorized Mean ( 11 / 163 )123.8787372708760.420583593490596294.540108525764
Winsorized Mean ( 12 / 163 )123.8797148676170.420472296740073294.620396701657
Winsorized Mean ( 13 / 163 )123.8791853360490.420177370042402294.825933446981
Winsorized Mean ( 14 / 163 )123.8863136456210.419306788540017295.455063050566
Winsorized Mean ( 15 / 163 )123.8832586558040.418736379352951295.850240782122
Winsorized Mean ( 16 / 163 )123.8858655804480.418537941540291295.996738371023
Winsorized Mean ( 17 / 163 )123.8813645621180.417930240545723296.416369393028
Winsorized Mean ( 18 / 163 )123.8824643584520.417797084021808296.513472918317
Winsorized Mean ( 19 / 163 )123.8832382892060.417213156594241296.930325257427
Winsorized Mean ( 20 / 163 )123.8881262729120.416135788981978297.710818326846
Winsorized Mean ( 21 / 163 )123.8966802443990.415449042821747298.223530382662
Winsorized Mean ( 22 / 163 )123.90832993890.414248524162956299.115923681981
Winsorized Mean ( 23 / 163 )123.9130142566190.413483682532862299.680542403922
Winsorized Mean ( 24 / 163 )123.9091038696540.413188374475199299.885261842214
Winsorized Mean ( 25 / 163 )123.9085947046840.412959694672626300.050092789111
Winsorized Mean ( 26 / 163 )123.9075356415480.412691312140239300.242655942905
Winsorized Mean ( 27 / 163 )123.9031364562120.412220880303187300.574624859084
Winsorized Mean ( 28 / 163 )123.9042769857430.411772847273714300.904437497749
Winsorized Mean ( 29 / 163 )123.9113645621180.411274166393181301.286525358021
Winsorized Mean ( 30 / 163 )123.9131975560080.411067516468861301.442445806576
Winsorized Mean ( 31 / 163 )123.9125661914460.410869423163113301.586244207453
Winsorized Mean ( 32 / 163 )123.9112627291240.410627610831828301.760669425301
Winsorized Mean ( 33 / 163 )123.9112627291240.410456216588746301.88667565797
Winsorized Mean ( 34 / 163 )123.9112627291240.410015622967448302.21107633004
Winsorized Mean ( 35 / 163 )123.901995926680.409485382622855302.57977741002
Winsorized Mean ( 36 / 163 )123.89832993890.408721814790926303.136082918104
Winsorized Mean ( 37 / 163 )123.8915478615070.408339647615879303.403180623917
Winsorized Mean ( 38 / 163 )123.9101221995930.406864286594853304.549026007239
Winsorized Mean ( 39 / 163 )123.9252138492870.405638581354156305.506476813877
Winsorized Mean ( 40 / 163 )123.9301018329940.404905297558955306.071821189125
Winsorized Mean ( 41 / 163 )123.9301018329940.403979999449924306.772864997629
Winsorized Mean ( 42 / 163 )123.9335234215890.403331429171695307.274649228566
Winsorized Mean ( 43 / 163 )123.9335234215890.403010122292569307.519629324888
Winsorized Mean ( 44 / 163 )123.9317311608960.402582717433796307.841657860726
Winsorized Mean ( 45 / 163 )123.9408961303460.401639760090537308.587217815307
Winsorized Mean ( 46 / 163 )123.9408961303460.401298865901069308.849355584526
Winsorized Mean ( 47 / 163 )123.9475967413440.400625566385114309.385139495056
Winsorized Mean ( 48 / 163 )123.9524847250510.400304603505457309.645414116156
Winsorized Mean ( 49 / 163 )123.9554786150710.39998813608557309.897888042743
Winsorized Mean ( 50 / 163 )123.9615885947050.398488850096743311.079189705333
Winsorized Mean ( 51 / 163 )123.9553564154790.397280651126763312.009548071163
Winsorized Mean ( 52 / 163 )123.9532382892060.397165671846006312.09454158784
Winsorized Mean ( 53 / 163 )123.952158859470.397107138171849312.137826154689
Winsorized Mean ( 54 / 163 )123.9609572301430.39575629629088313.225483440019
Winsorized Mean ( 55 / 163 )123.9553564154790.395321821434506313.55556332732
Winsorized Mean ( 56 / 163 )123.9576374745420.395175227051379313.677652315046
Winsorized Mean ( 57 / 163 )123.9587983706720.39455319023171314.175126293808
Winsorized Mean ( 58 / 163 )123.9635234215890.39397289123879314.649881193103
Winsorized Mean ( 59 / 163 )123.9755397148680.393207178848567315.293174651355
Winsorized Mean ( 60 / 163 )123.9804276985740.392896838316071315.554658647664
Winsorized Mean ( 61 / 163 )123.9878818737270.392134333324687316.187263743277
Winsorized Mean ( 62 / 163 )123.9904073319760.391974882149536316.322328237027
Winsorized Mean ( 63 / 163 )123.9891242362530.391008600530225317.100759594847
Winsorized Mean ( 64 / 163 )123.9891242362530.391008600530225317.100759594847
Winsorized Mean ( 65 / 163 )123.9851527494910.390642613146021317.387680138074
Winsorized Mean ( 66 / 163 )123.987841140530.390161330157764317.786083747445
Winsorized Mean ( 67 / 163 )123.9919348268840.389271935821134318.522666077466
Winsorized Mean ( 68 / 163 )123.9933197556010.389025011073871318.728401069452
Winsorized Mean ( 69 / 163 )123.9933197556010.38886249500512318.861606218847
Winsorized Mean ( 70 / 163 )123.9975967413440.388430601631463319.227157233588
Winsorized Mean ( 71 / 163 )123.9990427698570.388006635746337319.579696185719
Winsorized Mean ( 72 / 163 )124.0210386965380.386472246200518320.905420546526
Winsorized Mean ( 73 / 163 )124.0225254582480.385697775853473321.553644388566
Winsorized Mean ( 74 / 163 )124.0315682281060.384968032572531322.186669369066
Winsorized Mean ( 75 / 163 )124.0178207739310.384067794614552322.906066358399
Winsorized Mean ( 76 / 163 )124.0193686354380.383443072893966323.436195363824
Winsorized Mean ( 77 / 163 )124.0162321792260.383099835193852323.717790472222
Winsorized Mean ( 78 / 163 )124.0146435845210.383016557624106323.784027389828
Winsorized Mean ( 79 / 163 )124.0017718940940.382343721847496324.320146529185
Winsorized Mean ( 80 / 163 )123.9805906313650.381059488966723325.357573347797
Winsorized Mean ( 81 / 163 )123.9789409368640.38097426219987325.426028049686
Winsorized Mean ( 82 / 163 )123.9839511201630.38047760688222325.86399009428
Winsorized Mean ( 83 / 163 )123.9890224032590.380166526253191326.143975970893
Winsorized Mean ( 84 / 163 )123.9856008146640.379603821172706326.618421362663
Winsorized Mean ( 85 / 163 )123.9856008146640.379603821172706326.618421362663
Winsorized Mean ( 86 / 163 )123.9803462321790.378741455557896327.348232977436
Winsorized Mean ( 87 / 163 )123.9785743380860.378650497625114327.42218778445
Winsorized Mean ( 88 / 163 )124.0054582484730.376808971393054329.09369909646
Winsorized Mean ( 89 / 163 )124.0036456211810.376715887677753329.170204064383
Winsorized Mean ( 90 / 163 )123.9981466395110.375202964115846330.482854610995
Winsorized Mean ( 91 / 163 )124.0055600814660.374753416974041330.89907780629
Winsorized Mean ( 92 / 163 )124.0018126272910.374352878539176331.243112410887
Winsorized Mean ( 93 / 163 )124.007494908350.374008881685012331.562968102958
Winsorized Mean ( 94 / 163 )124.0170672097760.372790760880335332.672051520035
Winsorized Mean ( 95 / 163 )124.019002036660.371598697699325333.744447449621
Winsorized Mean ( 96 / 163 )124.0229124236250.370929532792498334.357071786476
Winsorized Mean ( 97 / 163 )124.0248879837070.370810832677284334.469430378388
Winsorized Mean ( 98 / 163 )124.0208961303460.370608059527226334.641659678303
Winsorized Mean ( 99 / 163 )124.0229124236250.370040181326717335.160662766302
Winsorized Mean ( 100 / 163 )124.0127291242360.369524411976935335.600910534639
Winsorized Mean ( 101 / 163 )124.0147861507130.369173444577877335.925533030998
Winsorized Mean ( 102 / 163 )124.0064765784110.368295053078307336.704160270231
Winsorized Mean ( 103 / 163 )124.0022810590630.368083765978928336.886036604401
Winsorized Mean ( 104 / 163 )124.000162932790.367510059030742337.40617402371
Winsorized Mean ( 105 / 163 )123.9980244399190.367166990507187337.715610732418
Winsorized Mean ( 106 / 163 )123.9958655804480.367058641997411337.809416243966
Winsorized Mean ( 107 / 163 )123.9980448065170.366927981117386337.935647286731
Winsorized Mean ( 108 / 163 )124.0002443991850.366796147497256338.063104657098
Winsorized Mean ( 109 / 163 )124.0024643584520.365930309696561338.869071712803
Winsorized Mean ( 110 / 163 )124.0024643584520.364945422135597339.78358635878
Winsorized Mean ( 111 / 163 )124.0092464358450.364291969237698340.411694211491
Winsorized Mean ( 112 / 163 )124.0297759674130.362068561795314342.558810829675
Winsorized Mean ( 113 / 163 )124.025173116090.361838557730903342.763838917151
Winsorized Mean ( 114 / 163 )124.0182077393080.360729659563491343.798200262708
Winsorized Mean ( 115 / 163 )124.0158655804480.360357282534718344.146966333336
Winsorized Mean ( 116 / 163 )124.0347657841140.358205250503506346.267302363007
Winsorized Mean ( 117 / 163 )124.0276171079430.357590791032245346.842313108559
Winsorized Mean ( 118 / 163 )124.0204073319760.357233414870682347.169111760922
Winsorized Mean ( 119 / 163 )124.0204073319760.356969832504302347.425457389262
Winsorized Mean ( 120 / 163 )124.0106313645620.356220851790473348.128501577736
Winsorized Mean ( 121 / 163 )124.0106313645620.355953205727961348.390264138646
Winsorized Mean ( 122 / 163 )124.0156008146640.355119611504697349.22205588475
Winsorized Mean ( 123 / 163 )124.0181059063140.354699682467992349.64256252895
Winsorized Mean ( 124 / 163 )124.0307331975560.353953520431589350.415311723191
Winsorized Mean ( 125 / 163 )124.0409164969450.352801083066476351.588820019503
Winsorized Mean ( 126 / 163 )124.0717107942970.350989036590928353.491698770355
Winsorized Mean ( 127 / 163 )124.0768839103870.350126084730022354.3777208318
Winsorized Mean ( 128 / 163 )124.0820977596740.349538614735106354.988240294161
Winsorized Mean ( 129 / 163 )124.0820977596740.348120650940022356.434177129734
Winsorized Mean ( 130 / 163 )124.0820977596740.347835091920465356.726795662257
Winsorized Mean ( 131 / 163 )124.0981059063140.346610834167677358.032968600975
Winsorized Mean ( 132 / 163 )124.1034826883910.345717533922677358.973643252205
Winsorized Mean ( 133 / 163 )124.1061914460290.345267760708501359.449116220288
Winsorized Mean ( 134 / 163 )124.1089205702650.345108466128164359.622938152361
Winsorized Mean ( 135 / 163 )124.106171079430.344381440903436360.374155918085
Winsorized Mean ( 136 / 163 )124.1006313645620.343513456930562361.268616587698
Winsorized Mean ( 137 / 163 )124.0950509164970.343239428240446361.540780884782
Winsorized Mean ( 138 / 163 )124.1175356415480.340420554164531364.600592188567
Winsorized Mean ( 139 / 163 )124.1090427698570.339397412054005365.674688026522
Winsorized Mean ( 140 / 163 )124.2116904276990.333145916715863372.844703162421
Winsorized Mean ( 141 / 163 )124.2231771894090.328197041917236378.501818492123
Winsorized Mean ( 142 / 163 )124.2116089613030.327630962497215379.120483651967
Winsorized Mean ( 143 / 163 )124.2116089613030.327630962497215379.120483651967
Winsorized Mean ( 144 / 163 )124.2204073319760.326813290425654380.095947659246
Winsorized Mean ( 145 / 163 )124.1731568228110.323885134439031383.386403447872
Winsorized Mean ( 146 / 163 )124.1880244399190.322714849029385384.82277717754
Winsorized Mean ( 147 / 163 )124.1640733197560.31997111432193388.047757319842
Winsorized Mean ( 148 / 163 )124.185173116090.315576260713719393.518741984038
Winsorized Mean ( 149 / 163 )124.2094501018330.312267479322139397.766204702018
Winsorized Mean ( 150 / 163 )124.230835030550.310402775483263400.224626977436
Winsorized Mean ( 151 / 163 )124.3046435845210.305233323713892407.244668020053
Winsorized Mean ( 152 / 163 )124.3603665987780.298512811658095416.599763031999
Winsorized Mean ( 153 / 163 )124.3884114052950.296932714243978418.911104901329
Winsorized Mean ( 154 / 163 )124.4197759674130.288630638853552431.069190927242
Winsorized Mean ( 155 / 163 )124.4702851323830.284496655920707437.510538496713
Winsorized Mean ( 156 / 163 )124.5115885947050.282198273973388441.220234417331
Winsorized Mean ( 157 / 163 )124.5275763747450.280647859984349443.714683524363
Winsorized Mean ( 158 / 163 )124.543665987780.279089459631676446.249980748626
Winsorized Mean ( 159 / 163 )124.5469042769860.278574892322721447.085892194123
Winsorized Mean ( 160 / 163 )124.6576985743380.272467247594337457.514434028176
Winsorized Mean ( 161 / 163 )124.6576985743380.270774696680156460.374252478939
Winsorized Mean ( 162 / 163 )124.7236863543790.266824455452319467.437237501143
Winsorized Mean ( 163 / 163 )124.7104073319760.26618148956707468.516452946485
Trimmed Mean ( 1 / 163 )123.876171079430.422277516373851293.352514107712
Trimmed Mean ( 2 / 163 )123.883271983640.421487611468978293.919129798096
Trimmed Mean ( 3 / 163 )123.8969278350520.420687363401207294.510695147484
Trimmed Mean ( 4 / 163 )123.8969278350520.419875866533589295.079897918211
Trimmed Mean ( 5 / 163 )123.9109355509360.419164155456448295.614340916158
Trimmed Mean ( 6 / 163 )123.9181210855950.418439490181567296.143466363141
Trimmed Mean ( 7 / 163 )123.9250733752620.417731612602521296.66194665803
Trimmed Mean ( 8 / 163 )123.9250733752620.41702117175294297.167342498093
Trimmed Mean ( 9 / 163 )123.9392600422830.416305593344708297.712214353218
Trimmed Mean ( 10 / 163 )123.9456900212310.415649304750596298.197756148307
Trimmed Mean ( 11 / 163 )123.953027718550.415030672106975298.659920938569
Trimmed Mean ( 12 / 163 )123.9601284796570.414421136887664299.116327440748
Trimmed Mean ( 13 / 163 )123.9672043010750.413802726374742299.580443529533
Trimmed Mean ( 14 / 163 )123.9743844492440.413190543967538300.041678734506
Trimmed Mean ( 15 / 163 )123.9810845986980.412630721488181300.464987559705
Trimmed Mean ( 16 / 163 )123.9810845986980.412096339759066300.854612470435
Trimmed Mean ( 17 / 163 )123.9949234135670.411558324697035301.281534044645
Trimmed Mean ( 18 / 163 )124.0021318681320.411044022602975301.676037235322
Trimmed Mean ( 19 / 163 )124.0093377483440.410520495362751302.078310703501
Trimmed Mean ( 20 / 163 )124.0165631929050.410015688851603302.467848340774
Trimmed Mean ( 21 / 163 )124.0235857461020.409558502285095302.822637191327
Trimmed Mean ( 22 / 163 )124.0302237136470.409124510666644303.16009058354
Trimmed Mean ( 23 / 163 )124.0363370786520.408741539812443303.459093332103
Trimmed Mean ( 24 / 163 )124.0422799097070.408384252021074303.739136109748
Trimmed Mean ( 25 / 163 )124.0484580498870.408026815347016304.020356957144
Trimmed Mean ( 26 / 163 )124.0547152619590.407665372002503304.305255687003
Trimmed Mean ( 27 / 163 )124.0610755148740.407301326379646304.592859094293
Trimmed Mean ( 28 / 163 )124.067678160920.40694367886427304.876779281048
Trimmed Mean ( 29 / 163 )124.0742956120090.406590999875767305.157506314502
Trimmed Mean ( 30 / 163 )124.0806960556840.406245273853583305.432958957708
Trimmed Mean ( 31 / 163 )124.0870862470860.405892877015024305.713879877949
Trimmed Mean ( 32 / 163 )124.0870862470860.405532891634911305.985257439483
Trimmed Mean ( 33 / 163 )124.1001411764710.405166680267171306.294044452613
Trimmed Mean ( 34 / 163 )124.1067848699760.404790916000843306.594787492014
Trimmed Mean ( 35 / 163 )124.1134916864610.404416066386887306.89555139416
Trimmed Mean ( 36 / 163 )124.1205727923630.404044856375435307.195032516466
Trimmed Mean ( 37 / 163 )124.1278417266190.403686152295527307.486003720406
Trimmed Mean ( 38 / 163 )124.1353975903610.403324773739656307.78024478727
Trimmed Mean ( 39 / 163 )124.1424455205810.40300255366973308.043818556839
Trimmed Mean ( 40 / 163 )124.1490997566910.402709796145608308.284280504074
Trimmed Mean ( 41 / 163 )124.1556723716380.402427945842013308.516527379487
Trimmed Mean ( 42 / 163 )124.162309582310.402163347427711308.736015791762
Trimmed Mean ( 43 / 163 )124.1689135802470.401906147060422308.950023502824
Trimmed Mean ( 44 / 163 )124.1755831265510.401644574678915309.167833838712
Trimmed Mean ( 45 / 163 )124.1823690773070.401381815611823309.387132767877
Trimmed Mean ( 46 / 163 )124.1889724310780.401135390024762309.593657202401
Trimmed Mean ( 47 / 163 )124.195642317380.400884677367198309.80391451485
Trimmed Mean ( 48 / 163 )124.2022025316460.400640550729241310.009064997475
Trimmed Mean ( 49 / 163 )124.2087022900760.400391236445181310.218333929699
Trimmed Mean ( 50 / 163 )124.2151918158570.400136162481273310.432306456856
Trimmed Mean ( 51 / 163 )124.2215938303340.399912736053973310.621749774854
Trimmed Mean ( 52 / 163 )124.2282170542640.39971125884957310.794890821468
Trimmed Mean ( 53 / 163 )124.2349610389610.39949783502141310.977808008154
Trimmed Mean ( 54 / 163 )124.241801566580.399270332055459311.172134746346
Trimmed Mean ( 55 / 163 )124.2485039370080.399068237601661311.346512275
Trimmed Mean ( 56 / 163 )124.2554089709760.398863188321772311.523882396328
Trimmed Mean ( 57 / 163 )124.2623342175070.398646578989051311.710524476668
Trimmed Mean ( 58 / 163 )124.2693066666670.398432101983697311.895818755467
Trimmed Mean ( 59 / 163 )124.2762466487940.39821845313318312.080582079984
Trimmed Mean ( 60 / 163 )124.2829919137470.398011173389332312.260057564197
Trimmed Mean ( 61 / 163 )124.2897018970190.397796497025676312.445440888326
Trimmed Mean ( 62 / 163 )124.2963215258860.397587277351497312.626506446278
Trimmed Mean ( 63 / 163 )124.302958904110.397365755839341312.817491385359
Trimmed Mean ( 64 / 163 )124.302958904110.397154397561053312.983967110678
Trimmed Mean ( 65 / 163 )124.3165096952910.396925652805605313.198476381105
Trimmed Mean ( 66 / 163 )124.323481894150.396689132106114313.402792847105
Trimmed Mean ( 67 / 163 )124.3304761904760.396448015521399313.611044381089
Trimmed Mean ( 68 / 163 )124.3374647887320.396213500786755313.814306029041
Trimmed Mean ( 69 / 163 )124.3445042492920.395967352244216314.027162958126
Trimmed Mean ( 70 / 163 )124.3516239316240.395706663743544314.252033956688
Trimmed Mean ( 71 / 163 )124.3587392550140.395438602001672314.483054070904
Trimmed Mean ( 72 / 163 )124.365907780980.395162399981142314.721005305451
Trimmed Mean ( 73 / 163 )124.3727246376810.394909360175174314.939925917461
Trimmed Mean ( 74 / 163 )124.3795918367350.3946577462764315.158116140523
Trimmed Mean ( 75 / 163 )124.3863636363640.394406501749961315.376047515616
Trimmed Mean ( 76 / 163 )124.3934808259590.394158843191286315.592261786678
Trimmed Mean ( 77 / 163 )124.4006528189910.393907879078226315.81153723073
Trimmed Mean ( 78 / 163 )124.4079701492540.393645376744174316.040724720883
Trimmed Mean ( 79 / 163 )124.4154054054050.393363839777135316.285821990894
Trimmed Mean ( 80 / 163 )124.4231722054380.39307787844426316.535676588785
Trimmed Mean ( 81 / 163 )124.4314285714290.392803066793634316.778149384462
Trimmed Mean ( 82 / 163 )124.4398165137610.392508183536329317.037508345973
Trimmed Mean ( 83 / 163 )124.4482153846150.392204042639666317.304774695938
Trimmed Mean ( 84 / 163 )124.4566253869970.391885160005699317.584430564268
Trimmed Mean ( 85 / 163 )124.4652024922120.391557135027105317.872390407586
Trimmed Mean ( 86 / 163 )124.4738871473350.391204477729497318.181141150957
Trimmed Mean ( 87 / 163 )124.4827760252370.390849243296802318.49307158747
Trimmed Mean ( 88 / 163 )124.491809523810.390470435164758318.825187036966
Trimmed Mean ( 89 / 163 )124.5004792332270.390116716577222319.1364890117
Trimmed Mean ( 90 / 163 )124.5092926045020.389739045570874319.468357146833
Trimmed Mean ( 91 / 163 )124.5183171521040.389374693697732319.790472178878
Trimmed Mean ( 92 / 163 )124.5273289902280.388995892917729320.125048252283
Trimmed Mean ( 93 / 163 )124.5365245901640.388599783864697320.475022789836
Trimmed Mean ( 94 / 163 )124.5457425742570.388184800271203320.841368562716
Trimmed Mean ( 95 / 163 )124.5549169435220.387774296486713321.204675173176
Trimmed Mean ( 96 / 163 )124.5641806020070.387366807320529321.566479749865
Trimmed Mean ( 97 / 163 )124.5735016835020.386948021675852321.938593054386
Trimmed Mean ( 98 / 163 )124.5829152542370.386502087488411322.334391681579
Trimmed Mean ( 99 / 163 )124.592525597270.386029685124356322.753742518878
Trimmed Mean ( 100 / 163 )124.6022336769760.38554030317414323.18860739365
Trimmed Mean ( 101 / 163 )124.6122491349480.385030578901887323.642474035034
Trimmed Mean ( 102 / 163 )124.6223693379790.384496074005683324.118704359351
Trimmed Mean ( 103 / 163 )124.6327719298250.383949452387712324.607239715426
Trimmed Mean ( 104 / 163 )124.6433922261480.383371654952348325.124172890772
Trimmed Mean ( 105 / 163 )124.6541992882560.382771746640117325.661965342119
Trimmed Mean ( 106 / 163 )124.6651971326160.382142120884168326.227312613896
Trimmed Mean ( 107 / 163 )124.6763898916970.381474721699637326.827395891945
Trimmed Mean ( 108 / 163 )124.6877090909090.380768992047594327.462875641207
Trimmed Mean ( 109 / 163 )124.6991575091580.380023270599008328.135583151531
Trimmed Mean ( 110 / 163 )124.710738007380.379257160261191328.828961123616
Trimmed Mean ( 111 / 163 )124.722490706320.378472844970118329.541451556893
Trimmed Mean ( 112 / 163 )124.7343071161050.37766040607346330.281663394288
Trimmed Mean ( 113 / 163 )124.7459622641510.376866575788539331.008293858743
Trimmed Mean ( 114 / 163 )124.7578707224330.376029555593561331.776768252974
Trimmed Mean ( 115 / 163 )124.7700766283520.375173303082091332.566511538407
Trimmed Mean ( 116 / 163 )124.782509652510.374275129107589333.397813394755
Trimmed Mean ( 117 / 163 )124.7948249027240.373389782579721334.221317039063
Trimmed Mean ( 118 / 163 )124.8074509803920.372467203744608335.083061610895
Trimmed Mean ( 119 / 163 )124.8203952569170.371497575486935335.992489569577
Trimmed Mean ( 120 / 163 )124.8335458167330.370476659570376336.953874399258
Trimmed Mean ( 121 / 163 )124.8470682730920.369415667792827337.958238260507
Trimmed Mean ( 122 / 163 )124.8608097165990.368298762922927339.020442875418
Trimmed Mean ( 123 / 163 )124.8608097165990.367141980107228340.088620974731
Trimmed Mean ( 124 / 163 )124.8887654320990.365929545164704341.291833584759
Trimmed Mean ( 125 / 163 )124.9028630705390.364670897988283342.508447368764
Trimmed Mean ( 126 / 163 )124.9170292887030.363376630642325343.76737179794
Trimmed Mean ( 127 / 163 )124.9309282700420.362070164926511345.046182679534
Trimmed Mean ( 128 / 163 )124.9309282700420.360714755759472346.342716163648
Trimmed Mean ( 129 / 163 )124.9591845493560.359298493524566347.786552967588
Trimmed Mean ( 130 / 163 )124.9736363636360.357845592153025349.238998898145
Trimmed Mean ( 131 / 163 )124.9883406113540.356314850820018350.780609687492
Trimmed Mean ( 132 / 163 )125.0030396475770.354737838700829352.38146600143
Trimmed Mean ( 133 / 163 )125.0179111111110.353098313522375354.05977973664
Trimmed Mean ( 134 / 163 )125.0330044843050.351376349932827355.837848814263
Trimmed Mean ( 135 / 163 )125.0483257918550.349556652875288357.734074758031
Trimmed Mean ( 136 / 163 )125.063972602740.347653367316067359.737555739072
Trimmed Mean ( 137 / 163 )125.080.345666211416402361.851971262891
Trimmed Mean ( 138 / 163 )125.0964186046510.3435674655692364.110200008023
Trimmed Mean ( 139 / 163 )125.1127699530520.341455049386218366.410659845119
Trimmed Mean ( 140 / 163 )125.1295734597160.339250799525686368.840909541443
Trimmed Mean ( 141 / 163 )125.1449760765550.337181092425239371.150633555476
Trimmed Mean ( 142 / 163 )125.1604830917870.335179569532746373.413222250588
Trimmed Mean ( 143 / 163 )125.1764878048780.33307015212522375.826194590433
Trimmed Mean ( 144 / 163 )125.1928078817730.330825656900731378.425328478496
Trimmed Mean ( 145 / 163 )125.2093034825870.328473217006707381.185731438281
Trimmed Mean ( 146 / 163 )125.2269346733670.3260792690666384.038319982218
Trimmed Mean ( 147 / 163 )125.2446700507610.323583114354891387.055641949842
Trimmed Mean ( 148 / 163 )125.2631794871790.32103456821971390.185954683396
Trimmed Mean ( 149 / 163 )125.281709844560.318515552463013393.329961051455
Trimmed Mean ( 150 / 163 )125.3002094240840.315980943700909396.543563534281
Trimmed Mean ( 151 / 163 )125.318730158730.313364458744485399.913668132077
Trimmed Mean ( 152 / 163 )125.3363636363640.310826908251219403.235242217393
Trimmed Mean ( 153 / 163 )125.3534054054050.308436866576883406.415117610978
Trimmed Mean ( 154 / 163 )125.3703278688520.305959638966303409.761000805273
Trimmed Mean ( 155 / 163 )125.3870718232040.303700461257109412.864278520319
Trimmed Mean ( 156 / 163 )125.4032960893850.301484419650167415.952825140681
Trimmed Mean ( 157 / 163 )125.4191525423730.299225769310667419.145559659863
Trimmed Mean ( 158 / 163 )125.4350857142860.296878360682486422.513400525139
Trimmed Mean ( 159 / 163 )125.4510982658960.294436372813811426.072013681631
Trimmed Mean ( 160 / 163 )125.4674269005850.291837002765033429.922956005694
Trimmed Mean ( 161 / 163 )125.4821301775150.289385104730144433.616409851256
Trimmed Mean ( 162 / 163 )125.4971856287430.286831035704418437.530008984343
Trimmed Mean ( 163 / 163 )125.5113939393940.284305131786017441.46721218476
Median125.33
Midrange122.14
Midmean - Weighted Average at Xnp124.829349593496
Midmean - Weighted Average at X(n+1)p124.860809716599
Midmean - Empirical Distribution Function124.860809716599
Midmean - Empirical Distribution Function - Averaging124.860809716599
Midmean - Empirical Distribution Function - Interpolation124.874693877551
Midmean - Closest Observation124.829349593496
Midmean - True Basic - Statistics Graphics Toolkit124.860809716599
Midmean - MS Excel (old versions)124.860809716599
Number of observations491
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292615768tchkr8kbc85d7q7/1v3qw1292615166.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292615768tchkr8kbc85d7q7/1v3qw1292615166.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/17/t1292615768tchkr8kbc85d7q7/25u7g1292615166.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/17/t1292615768tchkr8kbc85d7q7/25u7g1292615166.ps (open in new window)


 
Parameters (Session):
par1 = additive ; par2 = 12 ;
 
Parameters (R input):
par1 = additive ; par2 = 12 ;
 
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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