median

*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: Tue, 20 Oct 2009 09:50:54 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6.htm/, Retrieved Tue, 20 Oct 2009 17:52:55 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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10.505 10.505 10.315 10.145 10.815 13.945 13.915 13.525 12.775 12.165 11.635 11.045 10.295 10.045 9.625 9.245 8.885 8.545 8.225 7.895 7.165 6.055 5.175 4.415 3.705 2.085 -7.305 -8.005 -6.715 -2.825 -0.975 1.015 4.795 6.295 7.565 8.325 8.475 7.485 6.855 9.665 8.525 7.325 6.585 5.705 4.805 3.695 2.565 5.355 4.915 3.925 3.105 2.385 1.605 0.645 -0.305 -1.315 -2.295 1.495 3.925 3.135 1.975 1.005 4.365 4.305 3.255 2.135 1.235 0.125 -0.805 5.155 3.495 1.895 0.645 -0.615 -2.075 -0.385 -0.735 -2.125 -3.485 -4.985 -2.385 -1.865 -2.235 -3.695 -4.025 -5.455 -6.395 -6.425 -6.765 -7.415 -9.005 -7.515 -6.975 -8.395 -9.155 -8.385 -9.825 -11.565 -10.135 -13.325 -16.115 -14.435 -16.455 -18.135 -16.315 -18.185 -14.905 -14.925 -9.335 0.285 14.965 16.375 17.375 16.335 14.735 13.185 11.385 10.205 11.255 9.465 7.875 6.455 4.925 3.475 2.025 0.735 -0.575 -1.735 -2.775 -1.285 0.365 -0.625 -0.505 1.415 - etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.763166666666667 0.993560981023033 0.768112558004102 Geometric Mean NaN Harmonic Mean -35.691635702792 Quadratic Mean 18.8407561478361 Winsorized Mean ( 1 / 120 ) 0.766555555555556 0.99319454144667 0.771808063341753 Winsorized Mean ( 2 / 120 ) 0.687777777777778 0.973042432546294 0.70683225599728 Winsorized Mean ( 3 / 120 ) 0.605361111111111 0.955044856652947 0.633856207793906 Winsorized Mean ( 4 / 120 ) 0.443694444444445 0.924609648060975 0.47987217673418 Winsorized Mean ( 5 / 120 ) 0.352444444444444 0.909725896869446 0.387418282426914 Winsorized Mean ( 6 / 120 ) 0.333444444444444 0.905989502540267 0.368044490040462 Winsorized Mean ( 7 / 120 ) 0.267527777777778 0.896283439210147 0.298485686641201 Winsorized Mean ( 8 / 120 ) 0.202416666666667 0.88561668803013 0.228560131490860 Winsorized Mean ( 9 / 120 ) 0.205416666666667 0.884119772360002 0.232340315292738 Winsorized Mean ( 10 / 120 ) 0.147361111111111 0.876301225032592 0.168162621369872 Winsorized Mean ( 11 / 120 ) 0.0880833333333333 0.868738956463745 0.101392176185907 Winsorized Mean ( 12 / 120 ) 0.0590833333333334 0.863359864768634 0.068434190358347 Winsorized Mean ( 13 / 120 ) 0.0500555555555555 0.86218105581302 0.0580568956115071 Winsorized Mean ( 14 / 120 ) 0.0309999999999998 0.858033680555072 0.0361291178919055 Winsorized Mean ( 15 / 120 ) 0.00433333333333334 0.853804611040914 0.00507532200845152 Winsorized Mean ( 16 / 120 ) -0.0281111111111111 0.849553612808801 -0.0330892726336245 Winsorized Mean ( 17 / 120 ) -0.0172499999999998 0.847797381369426 -0.0203468427469501 Winsorized Mean ( 18 / 120 ) -0.09725 0.83873642120631 -0.115948225856379 Winsorized Mean ( 19 / 120 ) -0.104111111111111 0.83627207138107 -0.124494305948991 Winsorized Mean ( 20 / 120 ) -0.133 0.832342300033991 -0.159790028687198 Winsorized Mean ( 21 / 120 ) -0.131250000000000 0.831729941405851 -0.157803625270664 Winsorized Mean ( 22 / 120 ) -0.183194444444445 0.824516820731613 -0.222183998965469 Winsorized Mean ( 23 / 120 ) -0.194055555555556 0.816656487529123 -0.237622009399191 Winsorized Mean ( 24 / 120 ) -0.205388888888889 0.81555133105194 -0.251840541568325 Winsorized Mean ( 25 / 120 ) -0.225527777777778 0.813077536566036 -0.277375487127926 Winsorized Mean ( 26 / 120 ) -0.245750000000000 0.811131884598025 -0.302971692601859 Winsorized Mean ( 27 / 120 ) -0.32225 0.79766859864512 -0.403989828040564 Winsorized Mean ( 28 / 120 ) -0.353361111111111 0.793949437803454 -0.445067524814581 Winsorized Mean ( 29 / 120 ) -0.348527777777778 0.78882457943024 -0.441831792347946 Winsorized Mean ( 30 / 120 ) -0.282694444444444 0.782650864255735 -0.361201216730622 Winsorized Mean ( 31 / 120 ) -0.270638888888889 0.77650787831817 -0.348533345823951 Winsorized Mean ( 32 / 120 ) -0.34975 0.757250506810145 -0.461868294381595 Winsorized Mean ( 33 / 120 ) -0.375416666666667 0.754857678510186 -0.497334368258136 Winsorized Mean ( 34 / 120 ) -0.359361111111111 0.75167843477487 -0.47807825060026 Winsorized Mean ( 35 / 120 ) -0.403111111111111 0.746746624268885 -0.539823144839501 Winsorized Mean ( 36 / 120 ) -0.408111111111111 0.746148739300877 -0.54695677901098 Winsorized Mean ( 37 / 120 ) -0.50575 0.737239165366731 -0.686005334169164 Winsorized Mean ( 38 / 120 ) -0.504694444444445 0.732865862790889 -0.688658689221073 Winsorized Mean ( 39 / 120 ) -0.557777777777778 0.725254082107508 -0.769079129009433 Winsorized Mean ( 40 / 120 ) -0.611111111111111 0.719305581529136 -0.849584831264593 Winsorized Mean ( 41 / 120 ) -0.615666666666667 0.710294828738455 -0.86677621989751 Winsorized Mean ( 42 / 120 ) -0.655333333333333 0.69920593507719 -0.937253676573821 Winsorized Mean ( 43 / 120 ) -0.635027777777778 0.694585948750852 -0.914253705995371 Winsorized Mean ( 44 / 120 ) -0.685138888888889 0.687817299633067 -0.996105927045442 Winsorized Mean ( 45 / 120 ) -0.685138888888889 0.681634744260152 -1.00514079521070 Winsorized Mean ( 46 / 120 ) -0.678750000000001 0.680489556952096 -0.99744366840854 Winsorized Mean ( 47 / 120 ) -0.665694444444445 0.678982503620495 -0.980429452739658 Winsorized Mean ( 48 / 120 ) -0.688361111111111 0.675599264192375 -1.01888966965349 Winsorized Mean ( 49 / 120 ) -0.74825 0.67052950118423 -1.11590914147477 Winsorized Mean ( 50 / 120 ) -0.787138888888888 0.66638641192081 -1.18120489074802 Winsorized Mean ( 51 / 120 ) -0.767305555555555 0.661630003652437 -1.15972001166778 Winsorized Mean ( 52 / 120 ) -0.693638888888889 0.654403588220279 -1.05995581530247 Winsorized Mean ( 53 / 120 ) -0.646527777777777 0.64963361730725 -0.995219090504666 Winsorized Mean ( 54 / 120 ) -0.753027777777778 0.62691939195975 -1.20115566280988 Winsorized Mean ( 55 / 120 ) -0.769833333333333 0.625748110543662 -1.23026073968404 Winsorized Mean ( 56 / 120 ) -0.713833333333333 0.619123056382654 -1.15297488273824 Winsorized Mean ( 57 / 120 ) -0.686916666666667 0.616256688088322 -1.11465997845401 Winsorized Mean ( 58 / 120 ) -0.665972222222223 0.614586949281793 -1.08360944370927 Winsorized Mean ( 59 / 120 ) -0.66761111111111 0.613493788213614 -1.08821168842651 Winsorized Mean ( 60 / 120 ) -0.782611111111111 0.604343645807639 -1.29497698294691 Winsorized Mean ( 61 / 120 ) -0.763972222222223 0.602104334417477 -1.26883694162632 Winsorized Mean ( 62 / 120 ) -0.774305555555555 0.596838805138381 -1.29734452399761 Winsorized Mean ( 63 / 120 ) -0.755055555555556 0.595053027755498 -1.26888784753113 Winsorized Mean ( 64 / 120 ) -0.763944444444445 0.592108264976506 -1.29021074292006 Winsorized Mean ( 65 / 120 ) -0.55811111111111 0.575772991889226 -0.96932492314347 Winsorized Mean ( 66 / 120 ) -0.589277777777779 0.569949114645801 -1.03391296281597 Winsorized Mean ( 67 / 120 ) -0.555777777777778 0.566844583887636 -0.980476471991744 Winsorized Mean ( 68 / 120 ) -0.580333333333333 0.55760913523203 -1.04075291573523 Winsorized Mean ( 69 / 120 ) -0.494083333333333 0.551076628342768 -0.896578275909054 Winsorized Mean ( 70 / 120 ) -0.429916666666667 0.542686868673236 -0.792200238265816 Winsorized Mean ( 71 / 120 ) -0.443722222222223 0.541761563091016 -0.81903599747935 Winsorized Mean ( 72 / 120 ) -0.455722222222222 0.540394145651254 -0.843314506438647 Winsorized Mean ( 73 / 120 ) -0.427333333333334 0.528876227256766 -0.808002536907121 Winsorized Mean ( 74 / 120 ) -0.530111111111111 0.521265827083413 -1.01696885459994 Winsorized Mean ( 75 / 120 ) -0.494694444444444 0.518646047195635 -0.95381898140225 Winsorized Mean ( 76 / 120 ) -0.370138888888889 0.507780550872865 -0.728934749967535 Winsorized Mean ( 77 / 120 ) -0.355166666666666 0.501102533954626 -0.708770446367022 Winsorized Mean ( 78 / 120 ) -0.112499999999999 0.480084930956597 -0.234333537142765 Winsorized Mean ( 79 / 120 ) -0.138833333333333 0.478352125567853 -0.290232500103400 Winsorized Mean ( 80 / 120 ) -0.132166666666667 0.475489264953848 -0.277959307198019 Winsorized Mean ( 81 / 120 ) -0.0444166666666667 0.46914369613728 -0.094676038562116 Winsorized Mean ( 82 / 120 ) -0.0763055555555556 0.464305286086242 -0.164343499508171 Winsorized Mean ( 83 / 120 ) 0.0297500000000001 0.453740460255789 0.0655661167691085 Winsorized Mean ( 84 / 120 ) 0.0297500000000001 0.45064876011655 0.066015936651653 Winsorized Mean ( 85 / 120 ) 0.0321111111111106 0.449553717933252 0.0714288634042136 Winsorized Mean ( 86 / 120 ) 0.0798888888888892 0.444164428541761 0.179863320327503 Winsorized Mean ( 87 / 120 ) 0.0871388888888889 0.443683873439305 0.196398593920970 Winsorized Mean ( 88 / 120 ) 0.106694444444444 0.436294722290048 0.244546722647527 Winsorized Mean ( 89 / 120 ) 0.116583333333333 0.434997783655332 0.268009028353366 Winsorized Mean ( 90 / 120 ) 0.171583333333334 0.428468424855271 0.400457357835158 Winsorized Mean ( 91 / 120 ) 0.222138888888889 0.424866592503677 0.522843859244985 Winsorized Mean ( 92 / 120 ) 0.232361111111111 0.422549979215991 0.549902076772643 Winsorized Mean ( 93 / 120 ) 0.237527777777778 0.418872585956862 0.56706451016644 Winsorized Mean ( 94 / 120 ) 0.232305555555555 0.416170368180146 0.558198212360468 Winsorized Mean ( 95 / 120 ) 0.166333333333333 0.41053730485223 0.405160094752422 Winsorized Mean ( 96 / 120 ) 0.193000000000000 0.407458435504251 0.473667945446148 Winsorized Mean ( 97 / 120 ) 0.149888888888889 0.404686420202919 0.370382798646248 Winsorized Mean ( 98 / 120 ) 0.130833333333333 0.398245173381078 0.328524592583422 Winsorized Mean ( 99 / 120 ) 0.0895833333333333 0.388280228948572 0.230718245881118 Winsorized Mean ( 100 / 120 ) 0.18125 0.380017586594581 0.47695161064576 Winsorized Mean ( 101 / 120 ) 0.108305555555556 0.375070736817405 0.288760345513923 Winsorized Mean ( 102 / 120 ) 0.116805555555555 0.373822804363409 0.312462359685269 Winsorized Mean ( 103 / 120 ) 0.108222222222222 0.372566849611932 0.290477325975049 Winsorized Mean ( 104 / 120 ) 0.128444444444445 0.370570331020731 0.346612865877973 Winsorized Mean ( 105 / 120 ) 0.128444444444444 0.369108178566174 0.347985907392774 Winsorized Mean ( 106 / 120 ) 0.152000000000000 0.364318527496121 0.417217320910527 Winsorized Mean ( 107 / 120 ) 0.125249999999999 0.362278640057109 0.345728359751641 Winsorized Mean ( 108 / 120 ) 0.0532499999999999 0.354455834187868 0.150230282207110 Winsorized Mean ( 109 / 120 ) 0.168305555555556 0.346549433859355 0.485661031620272 Winsorized Mean ( 110 / 120 ) 0.153027777777778 0.341830081849195 0.447672062534534 Winsorized Mean ( 111 / 120 ) 0.168444444444444 0.338600419308836 0.497472639839843 Winsorized Mean ( 112 / 120 ) 0.177777777777778 0.334200698607936 0.531949150669897 Winsorized Mean ( 113 / 120 ) 0.19975 0.329775595665591 0.605714924407433 Winsorized Mean ( 114 / 120 ) 0.158583333333333 0.326085655181052 0.486324163034045 Winsorized Mean ( 115 / 120 ) 0.142611111111111 0.324327754448249 0.439712942093787 Winsorized Mean ( 116 / 120 ) 0.1555 0.320000617914716 0.485936561664524 Winsorized Mean ( 117 / 120 ) 0.06775 0.313486202775661 0.216117964363758 Winsorized Mean ( 118 / 120 ) 0.0808611111111115 0.312286658009560 0.258932327197392 Winsorized Mean ( 119 / 120 ) 0.0478055555555553 0.308287796411395 0.155067946613628 Winsorized Mean ( 120 / 120 ) 0.0111388888888889 0.305682842846175 0.0364393656679454 Trimmed Mean ( 1 / 120 ) 0.591536312849162 0.959119157088214 0.616749554502701 Trimmed Mean ( 2 / 120 ) 0.414550561797753 0.922845871913721 0.44920888136834 Trimmed Mean ( 3 / 120 ) 0.275621468926554 0.89564947342803 0.307733635873902 Trimmed Mean ( 4 / 120 ) 0.163210227272727 0.873850527828105 0.186771332253326 Trimmed Mean ( 5 / 120 ) 0.0910857142857143 0.859808183053018 0.105937249820403 Trimmed Mean ( 6 / 120 ) 0.0370114942528735 0.848626317557062 0.0436134179286572 Trimmed Mean ( 7 / 120 ) -0.0143930635838150 0.837725363493644 -0.0171811242813400 Trimmed Mean ( 8 / 120 ) -0.0565406976744186 0.828048959721277 -0.0682818292452784 Trimmed Mean ( 9 / 120 ) -0.0906140350877193 0.819608716915409 -0.110557676141787 Trimmed Mean ( 10 / 120 ) -0.125441176470588 0.811047446016324 -0.154665645131769 Trimmed Mean ( 11 / 120 ) -0.154497041420118 0.803134488558204 -0.192367584285259 Trimmed Mean ( 12 / 120 ) -0.178125 0.795790452999308 -0.223834049941983 Trimmed Mean ( 13 / 120 ) -0.178125 0.78874206681106 -0.225834284102751 Trimmed Mean ( 14 / 120 ) -0.220240963855422 0.781544424043551 -0.281802232963214 Trimmed Mean ( 15 / 120 ) -0.239818181818182 0.774464146005729 -0.309656919632801 Trimmed Mean ( 16 / 120 ) -0.257682926829268 0.767492480974379 -0.335746516372543 Trimmed Mean ( 17 / 120 ) -0.273527607361963 0.760616892112443 -0.359612848726383 Trimmed Mean ( 18 / 120 ) -0.290277777777778 0.753617633463439 -0.385179121199346 Trimmed Mean ( 19 / 120 ) -0.302267080745342 0.74706030948403 -0.404608673366823 Trimmed Mean ( 20 / 120 ) -0.314 0.740433440532594 -0.424075930139163 Trimmed Mean ( 21 / 120 ) -0.324245283018868 0.733834035941838 -0.44185097329632 Trimmed Mean ( 22 / 120 ) -0.334715189873418 0.727017028713808 -0.460395254380182 Trimmed Mean ( 23 / 120 ) -0.342611464968153 0.72042553649169 -0.475568185209805 Trimmed Mean ( 24 / 120 ) -0.350064102564103 0.714093804227907 -0.490221453388185 Trimmed Mean ( 25 / 120 ) -0.357064516129032 0.707580161186524 -0.504627653113224 Trimmed Mean ( 26 / 120 ) -0.357064516129032 0.700960352376692 -0.509393312928986 Trimmed Mean ( 27 / 120 ) -0.368529411764706 0.694191700535534 -0.530875565755689 Trimmed Mean ( 28 / 120 ) -0.370559210526316 0.687963469128034 -0.538632103527219 Trimmed Mean ( 29 / 120 ) -0.371291390728477 0.68169979760143 -0.544655274997691 Trimmed Mean ( 30 / 120 ) -0.372233333333333 0.675474890577047 -0.55106909009651 Trimmed Mean ( 31 / 120 ) -0.375838926174497 0.669342414247238 -0.56150472191005 Trimmed Mean ( 32 / 120 ) -0.379966216216216 0.663297254494715 -0.572844548415425 Trimmed Mean ( 33 / 120 ) -0.381122448979592 0.658051260744696 -0.579168328844606 Trimmed Mean ( 34 / 120 ) -0.381335616438356 0.652712987442241 -0.584231697200756 Trimmed Mean ( 35 / 120 ) -0.382137931034483 0.647316643495638 -0.590341581472187 Trimmed Mean ( 36 / 120 ) -0.381388888888889 0.641947387615581 -0.59411237781573 Trimmed Mean ( 37 / 120 ) -0.380454545454545 0.636378472056591 -0.597843205199929 Trimmed Mean ( 38 / 120 ) -0.376161971830986 0.63102184164364 -0.596115612814901 Trimmed Mean ( 39 / 120 ) -0.371843971631206 0.625652380462062 -0.594329987774663 Trimmed Mean ( 40 / 120 ) -0.365714285714286 0.620425052681766 -0.589457637362479 Trimmed Mean ( 41 / 120 ) -0.357769784172662 0.615257601163317 -0.58149591893899 Trimmed Mean ( 42 / 120 ) -0.349565217391304 0.610298424246716 -0.572777519166576 Trimmed Mean ( 43 / 120 ) -0.34 0.605646172752605 -0.561383882696281 Trimmed Mean ( 44 / 120 ) -0.330919117647059 0.60100416308521 -0.550610358418002 Trimmed Mean ( 45 / 120 ) -0.320185185185185 0.596465745591069 -0.536803978354024 Trimmed Mean ( 46 / 120 ) -0.309291044776119 0.592006914092867 -0.522444987403646 Trimmed Mean ( 47 / 120 ) -0.298421052631579 0.587396063275608 -0.5080406071628 Trimmed Mean ( 48 / 120 ) -0.287765151515152 0.582641658817966 -0.493897316060363 Trimmed Mean ( 49 / 120 ) -0.287765151515152 0.577819035516275 -0.498019507540171 Trimmed Mean ( 50 / 120 ) -0.262961538461538 0.572996658861515 -0.458923336453681 Trimmed Mean ( 51 / 120 ) -0.248333333333333 0.568130496392898 -0.437106148869001 Trimmed Mean ( 52 / 120 ) -0.248333333333333 0.563249841386019 -0.440893747474915 Trimmed Mean ( 53 / 120 ) -0.221496062992126 0.558469004047475 -0.396612992640316 Trimmed Mean ( 54 / 120 ) -0.210039682539683 0.553675597237758 -0.379355137895824 Trimmed Mean ( 55 / 120 ) -0.19556 0.549651039667196 -0.355789375234164 Trimmed Mean ( 56 / 120 ) -0.180403225806452 0.545476102016566 -0.330726176893031 Trimmed Mean ( 57 / 120 ) -0.166463414634146 0.541390026073028 -0.307474106683473 Trimmed Mean ( 58 / 120 ) -0.152991803278689 0.537226586254322 -0.284780774431484 Trimmed Mean ( 59 / 120 ) -0.139834710743802 0.532927234481041 -0.262389875570858 Trimmed Mean ( 60 / 120 ) -0.126416666666667 0.528455753336589 -0.239219018562086 Trimmed Mean ( 61 / 120 ) -0.109873949579832 0.524144706552887 -0.209625220299245 Trimmed Mean ( 62 / 120 ) -0.0935169491525424 0.519709813565343 -0.179940702891470 Trimmed Mean ( 63 / 120 ) -0.0935169491525424 0.515273513072799 -0.181489920944821 Trimmed Mean ( 64 / 120 ) -0.0599137931034483 0.510683321454534 -0.117320833844350 Trimmed Mean ( 65 / 120 ) -0.0426956521739131 0.505977354181655 -0.084382535742073 Trimmed Mean ( 66 / 120 ) -0.0301754385964912 0.501774394090386 -0.0601374620783372 Trimmed Mean ( 67 / 120 ) -0.0166814159292035 0.497596819829531 -0.033523960090658 Trimmed Mean ( 68 / 120 ) -0.00375000000000000 0.493331456415312 -0.00760138027128571 Trimmed Mean ( 69 / 120 ) 0.00999999999999998 0.489237379276313 0.0204399754057880 Trimmed Mean ( 70 / 120 ) 0.0219545454545454 0.485214443772572 0.0452470979302420 Trimmed Mean ( 71 / 120 ) 0.0326146788990826 0.481343192278728 0.067757640332839 Trimmed Mean ( 72 / 120 ) 0.0437962962962963 0.477290445087174 0.0917602620104771 Trimmed Mean ( 73 / 120 ) 0.0554672897196262 0.473064351801941 0.117251045250708 Trimmed Mean ( 74 / 120 ) 0.0666981132075472 0.469115664878895 0.142178396930671 Trimmed Mean ( 75 / 120 ) 0.0805238095238095 0.465263001259857 0.173071594572885 Trimmed Mean ( 76 / 120 ) 0.093798076923077 0.461304009171525 0.203332455513519 Trimmed Mean ( 77 / 120 ) 0.104466019417476 0.457614443560102 0.228283920858707 Trimmed Mean ( 78 / 120 ) 0.115 0.454003356396236 0.253302092109717 Trimmed Mean ( 79 / 120 ) 0.120198019801980 0.451125953511553 0.266440045992393 Trimmed Mean ( 80 / 120 ) 0.1261 0.448140915730486 0.281384706403012 Trimmed Mean ( 81 / 120 ) 0.131969696969697 0.445093310110218 0.296498945214471 Trimmed Mean ( 82 / 120 ) 0.135969387755102 0.442138324694538 0.307526808152267 Trimmed Mean ( 83 / 120 ) 0.140773195876289 0.43920576294788 0.320517642872992 Trimmed Mean ( 84 / 120 ) 0.14328125 0.436556647278521 0.328207692846301 Trimmed Mean ( 85 / 120 ) 0.145842105263158 0.433866347377725 0.336145234919978 Trimmed Mean ( 86 / 120 ) 0.148404255319149 0.431041902843514 0.34429194549335 Trimmed Mean ( 87 / 120 ) 0.149946236559140 0.428270857099177 0.350120102905848 Trimmed Mean ( 88 / 120 ) 0.151358695652174 0.425329434335582 0.355862264478862 Trimmed Mean ( 89 / 120 ) 0.152362637362637 0.422526498911457 0.360599010370154 Trimmed Mean ( 90 / 120 ) 0.153166666666667 0.419585215914513 0.365043049319147 Trimmed Mean ( 91 / 120 ) 0.152752808988764 0.416742555183588 0.366539982751394 Trimmed Mean ( 92 / 120 ) 0.151193181818182 0.413863964939035 0.365320962023001 Trimmed Mean ( 93 / 120 ) 0.149367816091954 0.410885318649921 0.363526778184103 Trimmed Mean ( 94 / 120 ) 0.147383720930233 0.407865535362539 0.361353701531137 Trimmed Mean ( 95 / 120 ) 0.145470588235294 0.404753643702255 0.359405259220607 Trimmed Mean ( 96 / 120 ) 0.145 0.401689607680064 0.360975233682144 Trimmed Mean ( 97 / 120 ) 0.143915662650602 0.398546208277207 0.361101572820642 Trimmed Mean ( 98 / 120 ) 0.143915662650602 0.395302449383711 0.36406468736779 Trimmed Mean ( 99 / 120 ) 0.144074074074074 0.392139503391394 0.36740515257468 Trimmed Mean ( 100 / 120 ) 0.1453125 0.389242455098642 0.373321301663188 Trimmed Mean ( 101 / 120 ) 0.144493670886076 0.386538061466049 0.373814858847392 Trimmed Mean ( 102 / 120 ) 0.145320512820513 0.383865298738306 0.378571632544422 Trimmed Mean ( 103 / 120 ) 0.145974025974026 0.381031560695428 0.383102191607451 Trimmed Mean ( 104 / 120 ) 0.145974025974026 0.378023957465234 0.386150197867951 Trimmed Mean ( 105 / 120 ) 0.147266666666667 0.374869166100343 0.392848172066643 Trimmed Mean ( 106 / 120 ) 0.147702702702703 0.371524707816399 0.397558223168552 Trimmed Mean ( 107 / 120 ) 0.147602739726027 0.368164901835762 0.400914750401364 Trimmed Mean ( 108 / 120 ) 0.148125 0.364628440016867 0.406235454352239 Trimmed Mean ( 109 / 120 ) 0.148125 0.361240021082387 0.410045928898386 Trimmed Mean ( 110 / 120 ) 0.149928571428571 0.358018563546746 0.41877317741094 Trimmed Mean ( 111 / 120 ) 0.149855072463768 0.354783264945283 0.422384839619986 Trimmed Mean ( 112 / 120 ) 0.149411764705882 0.35144178239492 0.425139446106002 Trimmed Mean ( 113 / 120 ) 0.148731343283582 0.348057592773596 0.427318197825751 Trimmed Mean ( 114 / 120 ) 0.1475 0.344628192356518 0.427997486193501 Trimmed Mean ( 115 / 120 ) 0.1475 0.341103356602257 0.432420253700383 Trimmed Mean ( 116 / 120 ) 0.14734375 0.337345774115623 0.436773664606509 Trimmed Mean ( 117 / 120 ) 0.147142857142857 0.333507356614663 0.441198235134787 Trimmed Mean ( 118 / 120 ) 0.149112903225806 0.32973001958112 0.452227259790405 Trimmed Mean ( 119 / 120 ) 0.150819672131148 0.32564714347501 0.463138323652212 Trimmed Mean ( 120 / 120 ) 0.153416666666667 0.321428272551474 0.477296740105829 Median 0 Midrange 31.485 Midmean - Weighted Average at Xnp 0.0963259668508295 Midmean - Weighted Average at X(n+1)p 0.153166666666668 Midmean - Empirical Distribution Function 0.0963259668508295 Midmean - Empirical Distribution Function - Averaging 0.153166666666668 Midmean - Empirical Distribution Function - Interpolation 0.153166666666668 Midmean - Closest Observation 0.0963259668508295 Midmean - True Basic - Statistics Graphics Toolkit 0.153166666666668 Midmean - MS Excel (old versions) 0.152362637362638 Number of observations 360

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6/1hgln1256053851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6/1hgln1256053851.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6/2fte81256053851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053972rqacyjvorfufgd6/2fte81256053851.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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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