WS 6(1) Mini- tutorial H2

*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, 16 Nov 2010 14:22:48 +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/Nov/16/t1289925628dmgqvrwwfyktofn.htm/, Retrieved Tue, 16 Nov 2010 17:40:30 +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/Nov/16/t1289925628dmgqvrwwfyktofn.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

87.28 87.28 87.09 86.92 87.59 90.72 90.69 90.3 89.55 88.94 88.41 87.82 87.07 86.82 86.4 86.02 85.66 85.32 85 84.67 83.94 82.83 81.95 81.19 80.48 78.86 69.47 68.77 70.06 73.95 75.8 77.79 81.57 83.07 84.34 85.1 85.25 84.26 83.63 86.44 85.3 84.1 83.36 82.48 81.58 80.47 79.34 82.13 81.69 80.7 79.88 79.16 78.38 77.42 76.47 75.46 74.48 78.27 80.7 79.91 78.75 77.78 81.14 81.08 80.03 78.91 78.01 76.9 75.97 81.93 80.27 78.67 77.42 76.16 74.7 76.39 76.04 74.65 73.29 71.79 74.39 74.91 74.54 73.08 72.75 71.32 70.38 70.35 70.01 69.36 67.77 69.26 69.8 68.38 67.62 68.39 66.95 65.21 66.64 63.45 60.66 62.34 60.32 58.64 60.46 58.59 61.87 61.85 67.44 77.06 91.74 93.15 94.15 93.11 91.51 89.96 88.16 86.98 88.03 86.24 84.65 83.23 81.7 80.25 78.8 77.51 76.2 75.04 74 75.49 77.14 76.15 76.27 78.19 76.49 77.31 76.65 74.99 73.51 72.07 70.59 71.96 76.29 74.86 74.93 71.9 71.01 77.47 75.78 76 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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 77.5381666666667 0.993560981023033 78.0406720348745 Geometric Mean 75.4064875707584 Harmonic Mean 73.3492143886423 Quadratic Mean 79.7907197541725 Winsorized Mean ( 1 / 120 ) 77.5415555555555 0.99319454144667 78.072877286065 Winsorized Mean ( 2 / 120 ) 77.4627777777778 0.973042432546294 79.6088384091023 Winsorized Mean ( 3 / 120 ) 77.3803611111111 0.955044856652947 81.0227504729972 Winsorized Mean ( 4 / 120 ) 77.2186944444444 0.924609648060975 83.5149131380815 Winsorized Mean ( 5 / 120 ) 77.1274444444444 0.909725896869446 84.7809705207424 Winsorized Mean ( 6 / 120 ) 77.1084444444445 0.905989502540267 85.1096444586204 Winsorized Mean ( 7 / 120 ) 77.0425277777778 0.896283439210147 85.9577722931841 Winsorized Mean ( 8 / 120 ) 76.9774166666667 0.88561668803013 86.9195643070897 Winsorized Mean ( 9 / 120 ) 76.9804166666667 0.884119772360002 87.0701222541161 Winsorized Mean ( 10 / 120 ) 76.9223611111111 0.876301225032592 87.780729860614 Winsorized Mean ( 11 / 120 ) 76.8630833333333 0.868738956463745 88.4766163200615 Winsorized Mean ( 12 / 120 ) 76.8340833333333 0.863359864768634 88.994272804103 Winsorized Mean ( 13 / 120 ) 76.8250555555556 0.86218105581302 89.1054785274898 Winsorized Mean ( 14 / 120 ) 76.806 0.858033680555072 89.513968671152 Winsorized Mean ( 15 / 120 ) 76.7793333333333 0.853804611040914 89.926116983285 Winsorized Mean ( 16 / 120 ) 76.7468888888889 0.849553612808801 90.3378994942387 Winsorized Mean ( 17 / 120 ) 76.75775 0.847797381369426 90.5378474701292 Winsorized Mean ( 18 / 120 ) 76.67775 0.83873642120631 91.4205560427654 Winsorized Mean ( 19 / 120 ) 76.6708888888889 0.83627207138107 91.6817522822087 Winsorized Mean ( 20 / 120 ) 76.642 0.832342300033991 92.0799051025883 Winsorized Mean ( 21 / 120 ) 76.64375 0.831729941405852 92.1498026997213 Winsorized Mean ( 22 / 120 ) 76.5918055555556 0.824516820731613 92.8929569776319 Winsorized Mean ( 23 / 120 ) 76.5809444444444 0.816656487529123 93.77375385353 Winsorized Mean ( 24 / 120 ) 76.5696111111111 0.81555133105194 93.8869304674516 Winsorized Mean ( 25 / 120 ) 76.5494722222222 0.813077536566036 94.1478134367387 Winsorized Mean ( 26 / 120 ) 76.52925 0.811131884598025 94.348713758091 Winsorized Mean ( 27 / 120 ) 76.45275 0.79766859864512 95.8452546958208 Winsorized Mean ( 28 / 120 ) 76.4216388888889 0.793949437803454 96.2550450319828 Winsorized Mean ( 29 / 120 ) 76.4264722222222 0.78882457943024 96.8865248562923 Winsorized Mean ( 30 / 120 ) 76.4923055555556 0.782650864255735 97.7349020476663 Winsorized Mean ( 31 / 120 ) 76.5043611111111 0.77650787831817 98.5236122482249 Winsorized Mean ( 32 / 120 ) 76.42525 0.757250506810145 100.924660086310 Winsorized Mean ( 33 / 120 ) 76.3995833333333 0.754857678510186 101.210579832901 Winsorized Mean ( 34 / 120 ) 76.4156388888889 0.75167843477487 101.660012252148 Winsorized Mean ( 35 / 120 ) 76.3718888888889 0.746746624268885 102.272827766261 Winsorized Mean ( 36 / 120 ) 76.3668888888889 0.746148739300877 102.348077355787 Winsorized Mean ( 37 / 120 ) 76.26925 0.737239165366731 103.452520678362 Winsorized Mean ( 38 / 120 ) 76.2703055555556 0.732865862790889 104.071303396646 Winsorized Mean ( 39 / 120 ) 76.2172222222222 0.725254082107508 105.090373294754 Winsorized Mean ( 40 / 120 ) 76.1638888888889 0.719305581529136 105.885302220199 Winsorized Mean ( 41 / 120 ) 76.1593333333333 0.710294828738455 107.222142484972 Winsorized Mean ( 42 / 120 ) 76.1196666666666 0.69920593507719 108.865876057335 Winsorized Mean ( 43 / 120 ) 76.1399722222222 0.694585948750852 109.619223307285 Winsorized Mean ( 44 / 120 ) 76.0898611111111 0.687817299633067 110.625105172119 Winsorized Mean ( 45 / 120 ) 76.0898611111111 0.681634744260152 111.628495688991 Winsorized Mean ( 46 / 120 ) 76.09625 0.680489556952096 111.825742544579 Winsorized Mean ( 47 / 120 ) 76.1093055555556 0.678982503620495 112.093176406937 Winsorized Mean ( 48 / 120 ) 76.0866388888889 0.675599264192376 112.620961746967 Winsorized Mean ( 49 / 120 ) 76.02675 0.67052950118423 113.383154455886 Winsorized Mean ( 50 / 120 ) 75.9878611111111 0.66638641192081 114.029727725212 Winsorized Mean ( 51 / 120 ) 76.0076944444444 0.661630003652437 114.879455322241 Winsorized Mean ( 52 / 120 ) 76.0813611111111 0.654403588220279 116.260611158968 Winsorized Mean ( 53 / 120 ) 76.1284722222222 0.64963361730725 117.186780662271 Winsorized Mean ( 54 / 120 ) 76.0219722222222 0.62691939195975 121.26275434642 Winsorized Mean ( 55 / 120 ) 76.0051666666667 0.625748110543662 121.462878410663 Winsorized Mean ( 56 / 120 ) 76.0611666666667 0.619123056382654 122.853067548588 Winsorized Mean ( 57 / 120 ) 76.0880833333333 0.616256688088322 123.46816643786 Winsorized Mean ( 58 / 120 ) 76.1090277777778 0.614586949281793 123.837689470495 Winsorized Mean ( 59 / 120 ) 76.1073888888889 0.613493788213614 124.055679700523 Winsorized Mean ( 60 / 120 ) 75.9923888888889 0.604343645807638 125.743671528694 Winsorized Mean ( 61 / 120 ) 76.0110277777778 0.602104334417477 126.242286316236 Winsorized Mean ( 62 / 120 ) 76.0006944444444 0.596838805138381 127.338728296702 Winsorized Mean ( 63 / 120 ) 76.0199444444444 0.595053027755498 127.753226853054 Winsorized Mean ( 64 / 120 ) 76.0110555555556 0.592108264976506 128.373576340083 Winsorized Mean ( 65 / 120 ) 76.2168888888889 0.575772991889226 132.373157411927 Winsorized Mean ( 66 / 120 ) 76.1857222222222 0.569949114645801 133.671094953044 Winsorized Mean ( 67 / 120 ) 76.2192222222222 0.566844583887636 134.462292467332 Winsorized Mean ( 68 / 120 ) 76.1946666666667 0.55760913523203 136.645298386227 Winsorized Mean ( 69 / 120 ) 76.2809166666667 0.551076628342768 138.421614605692 Winsorized Mean ( 70 / 120 ) 76.3450833333333 0.542686868673236 140.679805870340 Winsorized Mean ( 71 / 120 ) 76.3312777777778 0.541761563091016 140.894598247743 Winsorized Mean ( 72 / 120 ) 76.3192777777778 0.540394145651254 141.228912992390 Winsorized Mean ( 73 / 120 ) 76.3476666666667 0.528876227256766 144.358287878953 Winsorized Mean ( 74 / 120 ) 76.2448888888889 0.521265827083413 146.268726871075 Winsorized Mean ( 75 / 120 ) 76.2803055555556 0.518646047195635 147.075844823285 Winsorized Mean ( 76 / 120 ) 76.4048611111111 0.507780550872865 150.468270160747 Winsorized Mean ( 77 / 120 ) 76.4198333333333 0.501102533954626 152.503386343389 Winsorized Mean ( 78 / 120 ) 76.6625 0.480084930956597 159.685287032954 Winsorized Mean ( 79 / 120 ) 76.6361666666667 0.478352125567853 160.208688475444 Winsorized Mean ( 80 / 120 ) 76.6428333333333 0.475489264953848 161.187305334375 Winsorized Mean ( 81 / 120 ) 76.7305833333333 0.46914369613728 163.554544087662 Winsorized Mean ( 82 / 120 ) 76.6986944444444 0.464305286086242 165.190224498539 Winsorized Mean ( 83 / 120 ) 76.80475 0.453740460255789 169.270225442762 Winsorized Mean ( 84 / 120 ) 76.80475 0.45064876011655 170.431512959530 Winsorized Mean ( 85 / 120 ) 76.8071111111111 0.449553717933252 170.851909454156 Winsorized Mean ( 86 / 120 ) 76.8548888888889 0.444164428541761 173.032516676790 Winsorized Mean ( 87 / 120 ) 76.8621388888889 0.443683873439305 173.236269087440 Winsorized Mean ( 88 / 120 ) 76.8816944444444 0.436294722290048 176.215045739961 Winsorized Mean ( 89 / 120 ) 76.8915833333333 0.434997783655332 176.763161152697 Winsorized Mean ( 90 / 120 ) 76.9465833333333 0.428468424855271 179.585189642211 Winsorized Mean ( 91 / 120 ) 76.9971388888889 0.424866592503677 181.226625598299 Winsorized Mean ( 92 / 120 ) 77.0073611111111 0.422549979215991 182.244385040540 Winsorized Mean ( 93 / 120 ) 77.0125277777778 0.418872585956862 183.856691413338 Winsorized Mean ( 94 / 120 ) 77.0073055555555 0.416170368180146 185.037935046403 Winsorized Mean ( 95 / 120 ) 76.9413333333333 0.41053730485223 187.416179781830 Winsorized Mean ( 96 / 120 ) 76.968 0.407458435504251 188.8977949487 Winsorized Mean ( 97 / 120 ) 76.9248888888889 0.404686420202919 190.085174714578 Winsorized Mean ( 98 / 120 ) 76.9058333333333 0.398245173381078 193.111777552525 Winsorized Mean ( 99 / 120 ) 76.8645833333333 0.388280228948572 197.961620506601 Winsorized Mean ( 100 / 120 ) 76.95625 0.380017586594581 202.507075237284 Winsorized Mean ( 101 / 120 ) 76.8833055555556 0.375070736817405 204.983481803819 Winsorized Mean ( 102 / 120 ) 76.8918055555556 0.373822804363409 205.690516089558 Winsorized Mean ( 103 / 120 ) 76.8832222222222 0.372566849611933 206.360878060687 Winsorized Mean ( 104 / 120 ) 76.9034444444444 0.370570331020731 207.527257329573 Winsorized Mean ( 105 / 120 ) 76.9034444444444 0.369108178566174 208.349337430509 Winsorized Mean ( 106 / 120 ) 76.927 0.364318527496121 211.153137142659 Winsorized Mean ( 107 / 120 ) 76.90025 0.362278640057109 212.268241892146 Winsorized Mean ( 108 / 120 ) 76.82825 0.354455834187868 216.749853126355 Winsorized Mean ( 109 / 120 ) 76.9433055555555 0.346549433859355 222.026926140593 Winsorized Mean ( 110 / 120 ) 76.9280277777778 0.341830081849195 225.047565625649 Winsorized Mean ( 111 / 120 ) 76.9434444444444 0.338600419308836 227.239660841249 Winsorized Mean ( 112 / 120 ) 76.9527777777778 0.334200698607936 230.259176890752 Winsorized Mean ( 113 / 120 ) 76.97475 0.329775595665591 233.415543817427 Winsorized Mean ( 114 / 120 ) 76.9335833333333 0.326085655181052 235.930597102217 Winsorized Mean ( 115 / 120 ) 76.9176111111111 0.324327754448249 237.160126002674 Winsorized Mean ( 116 / 120 ) 76.9305 0.320000617914716 240.407348277380 Winsorized Mean ( 117 / 120 ) 76.84275 0.313486202775661 245.123228134511 Winsorized Mean ( 118 / 120 ) 76.8558611111111 0.312286658009559 246.106771262570 Winsorized Mean ( 119 / 120 ) 76.8228055555555 0.308287796411395 249.191847519774 Winsorized Mean ( 120 / 120 ) 76.7861388888889 0.305682842846176 251.195448766252 Trimmed Mean ( 1 / 120 ) 77.3665363128492 0.959119157088214 80.664154960397 Trimmed Mean ( 2 / 120 ) 77.1895505617978 0.922845871913721 83.642949392761 Trimmed Mean ( 3 / 120 ) 77.0506214689266 0.89564947342803 86.027652284572 Trimmed Mean ( 4 / 120 ) 76.9382102272727 0.873850527828105 88.0450463519172 Trimmed Mean ( 5 / 120 ) 76.8660857142857 0.859808183053018 89.3991092773141 Trimmed Mean ( 6 / 120 ) 76.8120114942529 0.848626317557062 90.513350699954 Trimmed Mean ( 7 / 120 ) 76.7606069364162 0.837725363493644 91.6297993130998 Trimmed Mean ( 8 / 120 ) 76.7184593023256 0.828048959721277 92.6496657011068 Trimmed Mean ( 9 / 120 ) 76.6843859649123 0.819608716915409 93.562189349954 Trimmed Mean ( 10 / 120 ) 76.6495588235294 0.811047446016324 94.5068740429603 Trimmed Mean ( 11 / 120 ) 76.6205029585799 0.803134488558204 95.4018337528125 Trimmed Mean ( 12 / 120 ) 76.596875 0.795790452999308 96.2525683882094 Trimmed Mean ( 13 / 120 ) 76.596875 0.78874206681106 97.1127041691671 Trimmed Mean ( 14 / 120 ) 76.5547590361446 0.781544424043551 97.9531766602158 Trimmed Mean ( 15 / 120 ) 76.5351818181818 0.774464146005729 98.8234022361258 Trimmed Mean ( 16 / 120 ) 76.5173170731707 0.767492480974379 99.6978067798492 Trimmed Mean ( 17 / 120 ) 76.501472392638 0.760616892112443 100.578192761631 Trimmed Mean ( 18 / 120 ) 76.4847222222222 0.753617633463439 101.490091030272 Trimmed Mean ( 19 / 120 ) 76.4727329192547 0.747060309484031 102.364871949993 Trimmed Mean ( 20 / 120 ) 76.461 0.740433440532594 103.265190109460 Trimmed Mean ( 21 / 120 ) 76.4507547169811 0.733834035941838 104.179897596138 Trimmed Mean ( 22 / 120 ) 76.4402848101266 0.727017028713808 105.14235814443 Trimmed Mean ( 23 / 120 ) 76.4323885350318 0.72042553649169 106.093391563048 Trimmed Mean ( 24 / 120 ) 76.4249358974359 0.714093804227907 107.023664741172 Trimmed Mean ( 25 / 120 ) 76.417935483871 0.707580161186524 107.998979727933 Trimmed Mean ( 26 / 120 ) 76.417935483871 0.700960352376692 109.018912731322 Trimmed Mean ( 27 / 120 ) 76.4064705882353 0.694191700535534 110.065376075933 Trimmed Mean ( 28 / 120 ) 76.4044407894737 0.687963469128034 111.058863178176 Trimmed Mean ( 29 / 120 ) 76.4037086092715 0.68169979760143 112.078232791177 Trimmed Mean ( 30 / 120 ) 76.4027666666667 0.675474890577047 113.109706567178 Trimmed Mean ( 31 / 120 ) 76.3991610738255 0.669342414247238 114.140624361518 Trimmed Mean ( 32 / 120 ) 76.3950337837838 0.663297254494715 115.174657012533 Trimmed Mean ( 33 / 120 ) 76.3938775510204 0.658051260744696 116.091073915074 Trimmed Mean ( 34 / 120 ) 76.3936643835616 0.652712987442241 117.040208871777 Trimmed Mean ( 35 / 120 ) 76.3928620689655 0.647316643495638 118.014673091717 Trimmed Mean ( 36 / 120 ) 76.3936111111111 0.641947387615581 119.00291610324 Trimmed Mean ( 37 / 120 ) 76.3945454545455 0.636378472056591 120.045772773646 Trimmed Mean ( 38 / 120 ) 76.398838028169 0.63102184164364 121.071622226532 Trimmed Mean ( 39 / 120 ) 76.4031560283688 0.625652380462062 122.117582245820 Trimmed Mean ( 40 / 120 ) 76.4092857142857 0.620425052681766 123.156351253079 Trimmed Mean ( 41 / 120 ) 76.4172302158273 0.615257601163317 124.203634496086 Trimmed Mean ( 42 / 120 ) 76.4254347826087 0.610298424246716 125.226334767191 Trimmed Mean ( 43 / 120 ) 76.435 0.605646172752605 126.204050217324 Trimmed Mean ( 44 / 120 ) 76.444080882353 0.60100416308521 127.193929056885 Trimmed Mean ( 45 / 120 ) 76.4548148148148 0.596465745591069 128.179724284169 Trimmed Mean ( 46 / 120 ) 76.4657089552239 0.592006914092867 129.163540382619 Trimmed Mean ( 47 / 120 ) 76.4765789473684 0.587396063275608 130.195933763835 Trimmed Mean ( 48 / 120 ) 76.4872348484848 0.582641658817966 131.276632370672 Trimmed Mean ( 49 / 120 ) 76.4872348484848 0.577819035516275 132.372300230892 Trimmed Mean ( 50 / 120 ) 76.5120384615385 0.572996658861515 133.529641540249 Trimmed Mean ( 51 / 120 ) 76.5266666666667 0.568130496392898 134.699100211202 Trimmed Mean ( 52 / 120 ) 76.5266666666667 0.563249841386019 135.86629066482 Trimmed Mean ( 53 / 120 ) 76.5535039370079 0.558469004047475 137.077444553217 Trimmed Mean ( 54 / 120 ) 76.5649603174603 0.553675597237758 138.284874210524 Trimmed Mean ( 55 / 120 ) 76.57944 0.549651039667196 139.323742653826 Trimmed Mean ( 56 / 120 ) 76.5945967741935 0.545476102016566 140.417878053744 Trimmed Mean ( 57 / 120 ) 76.6085365853659 0.541390026073028 141.503413243583 Trimmed Mean ( 58 / 120 ) 76.6220081967213 0.537226586254322 142.625123471549 Trimmed Mean ( 59 / 120 ) 76.6351652892562 0.532927234481041 143.800429647553 Trimmed Mean ( 60 / 120 ) 76.6485833333333 0.528455753336589 145.042575181339 Trimmed Mean ( 61 / 120 ) 76.6651260504202 0.524144706552887 146.26709969966 Trimmed Mean ( 62 / 120 ) 76.6814830508475 0.519709813565343 147.546729057881 Trimmed Mean ( 63 / 120 ) 76.6814830508475 0.515273513072799 148.817047850107 Trimmed Mean ( 64 / 120 ) 76.7150862068966 0.510683321454534 150.220465372544 Trimmed Mean ( 65 / 120 ) 76.7323043478261 0.505977354181655 151.651657359111 Trimmed Mean ( 66 / 120 ) 76.7448245614035 0.501774394090386 152.946873067379 Trimmed Mean ( 67 / 120 ) 76.7583185840708 0.497596819829531 154.258056975458 Trimmed Mean ( 68 / 120 ) 76.77125 0.493331456415312 155.617990707185 Trimmed Mean ( 69 / 120 ) 76.785 0.489237379276313 156.948351153343 Trimmed Mean ( 70 / 120 ) 76.7969545454545 0.485214443772572 158.274254880695 Trimmed Mean ( 71 / 120 ) 76.8076146788991 0.481343192278728 159.569338282908 Trimmed Mean ( 72 / 120 ) 76.8187962962963 0.477290445087174 160.947693562702 Trimmed Mean ( 73 / 120 ) 76.8304672897196 0.473064351801941 162.410181610739 Trimmed Mean ( 74 / 120 ) 76.8416981132075 0.469115664878895 163.801177121307 Trimmed Mean ( 75 / 120 ) 76.8555238095238 0.465263001259857 165.187267419527 Trimmed Mean ( 76 / 120 ) 76.8687980769231 0.461304009171525 166.633709112945 Trimmed Mean ( 77 / 120 ) 76.8794660194175 0.457614443560102 168.000523369233 Trimmed Mean ( 78 / 120 ) 76.89 0.454003356396236 169.359981411445 Trimmed Mean ( 79 / 120 ) 76.895198019802 0.451125953511553 170.451727330808 Trimmed Mean ( 80 / 120 ) 76.9011 0.448140915730486 171.600265230521 Trimmed Mean ( 81 / 120 ) 76.9069696969697 0.445093310110218 172.788419753883 Trimmed Mean ( 82 / 120 ) 76.9109693877551 0.442138324694538 173.952279393312 Trimmed Mean ( 83 / 120 ) 76.9157731958763 0.43920576294788 175.124690258228 Trimmed Mean ( 84 / 120 ) 76.91828125 0.436556647278521 176.193128038494 Trimmed Mean ( 85 / 120 ) 76.9208421052632 0.433866347377724 177.291561261136 Trimmed Mean ( 86 / 120 ) 76.9234042553192 0.431041902843514 178.459225768696 Trimmed Mean ( 87 / 120 ) 76.9249462365591 0.428270857099177 179.617512986052 Trimmed Mean ( 88 / 120 ) 76.9263586956522 0.425329434335582 180.863002852885 Trimmed Mean ( 89 / 120 ) 76.9273626373626 0.422526498911457 182.065178954571 Trimmed Mean ( 90 / 120 ) 76.9281666666667 0.419585215914513 183.343368042644 Trimmed Mean ( 91 / 120 ) 76.9277528089888 0.416742555183588 184.592986370446 Trimmed Mean ( 92 / 120 ) 76.9261931818182 0.413863964939035 185.873136341189 Trimmed Mean ( 93 / 120 ) 76.924367816092 0.410885318649921 187.216150893024 Trimmed Mean ( 94 / 120 ) 76.9223837209302 0.407865535362539 188.597410302286 Trimmed Mean ( 95 / 120 ) 76.9204705882353 0.404753643702255 190.042688398426 Trimmed Mean ( 96 / 120 ) 76.92 0.401689607680064 191.491137757452 Trimmed Mean ( 97 / 120 ) 76.9189156626506 0.398546208277207 192.998739080087 Trimmed Mean ( 98 / 120 ) 76.9189156626506 0.395302449383711 194.582441324534 Trimmed Mean ( 99 / 120 ) 76.9190740740741 0.392139503391394 196.152321836602 Trimmed Mean ( 100 / 120 ) 76.9203125 0.389242455098642 197.615423221259 Trimmed Mean ( 101 / 120 ) 76.9194936708861 0.386538061466049 198.995910982603 Trimmed Mean ( 102 / 120 ) 76.9203205128205 0.383865298738306 200.383626146055 Trimmed Mean ( 103 / 120 ) 76.920974025974 0.381031560695428 201.875597616072 Trimmed Mean ( 104 / 120 ) 76.920974025974 0.378023957465234 203.481743701517 Trimmed Mean ( 105 / 120 ) 76.9222666666667 0.374869166100343 205.197635929535 Trimmed Mean ( 106 / 120 ) 76.9227027027027 0.371524707816399 207.045994746375 Trimmed Mean ( 107 / 120 ) 76.922602739726 0.368164901835762 208.935187347220 Trimmed Mean ( 108 / 120 ) 76.923125 0.364628440016867 210.963042258694 Trimmed Mean ( 109 / 120 ) 76.923125 0.361240021082387 212.941868316568 Trimmed Mean ( 110 / 120 ) 76.9249285714286 0.358018563546746 214.862960762046 Trimmed Mean ( 111 / 120 ) 76.9248550724638 0.354783264945283 216.822107109048 Trimmed Mean ( 112 / 120 ) 76.9244117647059 0.35144178239492 218.882374316737 Trimmed Mean ( 113 / 120 ) 76.9237313432836 0.348057592773596 221.008628860227 Trimmed Mean ( 114 / 120 ) 76.9225 0.344628192356518 223.204316147251 Trimmed Mean ( 115 / 120 ) 76.9225 0.341103356602257 225.510826883171 Trimmed Mean ( 116 / 120 ) 76.92234375 0.337345774115623 228.022253877813 Trimmed Mean ( 117 / 120 ) 76.9221428571429 0.333507356614663 230.646015242235 Trimmed Mean ( 118 / 120 ) 76.9241129032258 0.32973001958112 233.294235693032 Trimmed Mean ( 119 / 120 ) 76.9258196721311 0.32564714347501 236.224457095643 Trimmed Mean ( 120 / 120 ) 76.9284166666667 0.321428272551474 239.333074393284 Median 76.775 Midrange 108.26 Midmean - Weighted Average at Xnp 76.8713259668508 Midmean - Weighted Average at X(n+1)p 76.9281666666666 Midmean - Empirical Distribution Function 76.8713259668508 Midmean - Empirical Distribution Function - Averaging 76.9281666666666 Midmean - Empirical Distribution Function - Interpolation 76.9281666666666 Midmean - Closest Observation 76.8713259668508 Midmean - True Basic - Statistics Graphics Toolkit 76.9281666666666 Midmean - MS Excel (old versions) 76.9273626373626 Number of observations 360

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289925628dmgqvrwwfyktofn/1cibn1289917365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289925628dmgqvrwwfyktofn/1cibn1289917365.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289925628dmgqvrwwfyktofn/259s81289917365.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289925628dmgqvrwwfyktofn/259s81289917365.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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