Central Tendency - Fortis - Caroline Thys

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 10 Mar 2009 16:03:25 -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/Mar/10/t1236722650rzh9bz0wholptrm.htm/, Retrieved Tue, 10 Mar 2009 23:04:12 +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/2009/Mar/10/t1236722650rzh9bz0wholptrm.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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18,09 18,13 18 17,72 17,62 17,13 17,39 17,09 17,14 17,38 16,8 16,51 16,01 15,05 13,56 15,22 14,91 15,13 15,25 14,61 14,87 15,1 15,22 15,46 14,96 14 14,2 13,9 13,63 13,32 13,8 14,5 14,12 13,88 14,11 14,26 14,71 14,52 14,32 14,69 15,25 15,04 14,82 14,5 14,72 14,6 14,58 14 14,75 14,41 15,19 14,96 14,83 14,25 14,32 14,93 14,65 15,65 15,65 15,61 15,95 15,83 15,77 16,7 16,69 16,4 16,77 16,78 16,84 16,68 16,67 16,3 16,37 16,6 16,72 16,82 17,5 17,2 17,29 17,2 17,2 17,32 17,16 17,41 17,31 17,3 17,34 17,19 17,05 17,07 17,07 16,81 16,81 16,96 17,05 17 16,77 16,66 16,2 16,26 15,84 15,85 15,71 15,84 15,73 15,77 15,3 15,41 15,4 15,61 15 14,12 14,01 13,46 13,85 13,92 13,59 13,67 13,05 12,87 12,28 11,88 12,49 11,9 10,8 10,99 10,15 10,07 10,05 10,31 9,94 9,65 9,74 9,85 9,96 9,63 9,43 8,77 9,53 9,5 9,78 9,9 9,93 10,35 9,79 9,63 9,02 9,25 9,11 8,95 9,3 9,13 9,75 9,65 9,27 9,5 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9.70054945054945 0.3763103948508 25.7780533923214 Geometric Mean 6.12726763930763 Harmonic Mean 2.80594451629474 Quadratic Mean 11.5160083037808 Winsorized Mean ( 1 / 91 ) 9.70043956043956 0.376295090867769 25.7788097582393 Winsorized Mean ( 2 / 91 ) 9.69992673992674 0.37622828717403 25.7820240279804 Winsorized Mean ( 3 / 91 ) 9.69684981684982 0.3759828084115 25.7906734029098 Winsorized Mean ( 4 / 91 ) 9.69567765567766 0.375842505056886 25.7971823974783 Winsorized Mean ( 5 / 91 ) 9.69347985347985 0.375673370043236 25.8029464594848 Winsorized Mean ( 6 / 91 ) 9.69172161172161 0.375503567137403 25.8099322081147 Winsorized Mean ( 7 / 91 ) 9.6914652014652 0.375442122727017 25.8134732753784 Winsorized Mean ( 8 / 91 ) 9.69175824175824 0.37536814788328 25.8193410826426 Winsorized Mean ( 9 / 91 ) 9.6910989010989 0.375210812508994 25.8284105308575 Winsorized Mean ( 10 / 91 ) 9.6907326007326 0.375123642862296 25.8334359487172 Winsorized Mean ( 11 / 91 ) 9.69113553113553 0.375022511498147 25.8414768020757 Winsorized Mean ( 12 / 91 ) 9.69113553113553 0.374951015761894 25.8464042601493 Winsorized Mean ( 13 / 91 ) 9.69113553113553 0.374873640062345 25.8517390807308 Winsorized Mean ( 14 / 91 ) 9.68754578754579 0.374441371883778 25.8719962989364 Winsorized Mean ( 15 / 91 ) 9.68864468864469 0.374345028795076 25.8815903601820 Winsorized Mean ( 16 / 91 ) 9.68923076923077 0.374293717175501 25.8867042769185 Winsorized Mean ( 17 / 91 ) 9.69234432234432 0.373921715189276 25.9207848290869 Winsorized Mean ( 18 / 91 ) 9.6903663003663 0.373776142727073 25.9255880529595 Winsorized Mean ( 19 / 91 ) 9.68967032967033 0.373613422141076 25.9350166654653 Winsorized Mean ( 20 / 91 ) 9.68893772893773 0.373559742145205 25.9367823558771 Winsorized Mean ( 21 / 91 ) 9.68663003663004 0.373267997992285 25.9508719974174 Winsorized Mean ( 22 / 91 ) 9.68663003663004 0.3730105834023 25.9687806932352 Winsorized Mean ( 23 / 91 ) 9.68747252747253 0.372937486061048 25.9761297524453 Winsorized Mean ( 24 / 91 ) 9.6865934065934 0.372733438490978 25.9879914337974 Winsorized Mean ( 25 / 91 ) 9.6865934065934 0.372733438490978 25.9879914337974 Winsorized Mean ( 26 / 91 ) 9.68373626373626 0.372223478130340 26.0159200928894 Winsorized Mean ( 27 / 91 ) 9.67978021978022 0.371938196934804 26.025238331402 Winsorized Mean ( 28 / 91 ) 9.66849816849817 0.37096915888305 26.0628085569405 Winsorized Mean ( 29 / 91 ) 9.66637362637363 0.370818319251792 26.0676809222308 Winsorized Mean ( 30 / 91 ) 9.66637362637363 0.370645265758403 26.0798518675116 Winsorized Mean ( 31 / 91 ) 9.66637362637363 0.370645265758403 26.0798518675116 Winsorized Mean ( 32 / 91 ) 9.66637362637363 0.370460818915099 26.0928366316356 Winsorized Mean ( 33 / 91 ) 9.66395604395604 0.370289838976995 26.0983560085116 Winsorized Mean ( 34 / 91 ) 9.66395604395604 0.370094167820484 26.1121543764602 Winsorized Mean ( 35 / 91 ) 9.66652014652015 0.369872620891189 26.1347274724719 Winsorized Mean ( 36 / 91 ) 9.66124542124542 0.369294333110791 26.1613692792491 Winsorized Mean ( 37 / 91 ) 9.6585347985348 0.369104034629333 26.1675134714641 Winsorized Mean ( 38 / 91 ) 9.6585347985348 0.368886298238072 26.1829589352255 Winsorized Mean ( 39 / 91 ) 9.65710622710623 0.368786233632993 26.1861895764709 Winsorized Mean ( 40 / 91 ) 9.65564102564103 0.368683700024732 26.1894980032839 Winsorized Mean ( 41 / 91 ) 9.65564102564103 0.368449099854569 26.2061734699643 Winsorized Mean ( 42 / 91 ) 9.64641025641026 0.367805727444772 26.2269169200437 Winsorized Mean ( 43 / 91 ) 9.6369597069597 0.366416520920451 26.3005600368437 Winsorized Mean ( 44 / 91 ) 9.6208424908425 0.365060941165647 26.3540724464331 Winsorized Mean ( 45 / 91 ) 9.61589743589744 0.364723801489099 26.3648750003085 Winsorized Mean ( 46 / 91 ) 9.60578754578755 0.363777792278029 26.4056458357030 Winsorized Mean ( 47 / 91 ) 9.5989010989011 0.363312750661573 26.4204905592276 Winsorized Mean ( 48 / 91 ) 9.5901098901099 0.362451612368824 26.4590073897952 Winsorized Mean ( 49 / 91 ) 9.56139194139194 0.359719005272194 26.5801689687121 Winsorized Mean ( 50 / 91 ) 9.55040293040293 0.358996776170135 26.6030325739661 Winsorized Mean ( 51 / 91 ) 9.53172161172161 0.357778150315637 26.6414301804417 Winsorized Mean ( 52 / 91 ) 9.52981684981685 0.357654540357965 26.6453120943991 Winsorized Mean ( 53 / 91 ) 9.53369963369963 0.357318247559398 26.6812559918727 Winsorized Mean ( 54 / 91 ) 9.53567765567765 0.356847609315078 26.7219883411301 Winsorized Mean ( 55 / 91 ) 9.5256043956044 0.355891504912131 26.7654728031687 Winsorized Mean ( 56 / 91 ) 9.5256043956044 0.355891504912131 26.7654728031687 Winsorized Mean ( 57 / 91 ) 9.51725274725275 0.355353727728442 26.7824761768807 Winsorized Mean ( 58 / 91 ) 9.52150183150183 0.354345622891418 26.8706630374252 Winsorized Mean ( 59 / 91 ) 9.5323076923077 0.35146332073634 27.1217709783679 Winsorized Mean ( 60 / 91 ) 9.5323076923077 0.35146332073634 27.1217709783679 Winsorized Mean ( 61 / 91 ) 9.53454212454212 0.349930707114097 27.2469432682092 Winsorized Mean ( 62 / 91 ) 9.53454212454213 0.349930707114097 27.2469432682092 Winsorized Mean ( 63 / 91 ) 9.50223443223443 0.347536477699346 27.3416894109597 Winsorized Mean ( 64 / 91 ) 9.49520146520146 0.34639533040083 27.4114591966761 Winsorized Mean ( 65 / 91 ) 9.49520146520146 0.346040859934529 27.4395384030601 Winsorized Mean ( 66 / 91 ) 9.48069597069597 0.343697298515671 27.5844355240508 Winsorized Mean ( 67 / 91 ) 9.47333333333333 0.342512223555907 27.6583802907316 Winsorized Mean ( 68 / 91 ) 9.47582417582417 0.342297742547979 27.6829876390317 Winsorized Mean ( 69 / 91 ) 9.47076923076923 0.341610425572942 27.723888153838 Winsorized Mean ( 70 / 91 ) 9.47846153846154 0.340948356114921 27.800285199987 Winsorized Mean ( 71 / 91 ) 9.47065934065934 0.340465903386463 27.8167629899467 Winsorized Mean ( 72 / 91 ) 9.4601098901099 0.3390367106918 27.9029072421292 Winsorized Mean ( 73 / 91 ) 9.47882783882784 0.336243539817031 28.1903641746866 Winsorized Mean ( 74 / 91 ) 9.46798534798535 0.335179150480285 28.2475366812598 Winsorized Mean ( 75 / 91 ) 9.4707326007326 0.334538668362435 28.3098293153727 Winsorized Mean ( 76 / 91 ) 9.52919413919414 0.327888622730426 29.0622896880096 Winsorized Mean ( 77 / 91 ) 9.52637362637363 0.326473593733596 29.1796145514519 Winsorized Mean ( 78 / 91 ) 10.1035164835165 0.278226203667902 36.314036385934 Winsorized Mean ( 79 / 91 ) 10.3726373626374 0.255431824994738 40.6082419951039 Winsorized Mean ( 80 / 91 ) 10.4371062271062 0.249542249910518 41.8250065103156 Winsorized Mean ( 81 / 91 ) 10.5884249084249 0.23618748232866 44.8305930696652 Winsorized Mean ( 82 / 91 ) 10.6665201465201 0.228573998883678 46.6655008820509 Winsorized Mean ( 83 / 91 ) 10.8458974358974 0.214890614638093 50.471713034855 Winsorized Mean ( 84 / 91 ) 10.8489743589744 0.211643221661910 51.2606747987661 Winsorized Mean ( 85 / 91 ) 10.9454945054945 0.203418166921020 53.8078514380884 Winsorized Mean ( 86 / 91 ) 11.1030036630037 0.192001050452236 57.8278276960039 Winsorized Mean ( 87 / 91 ) 11.1030036630037 0.191125222543103 58.0928226806888 Winsorized Mean ( 88 / 91 ) 11.1384615384615 0.186947928675518 59.5805560263487 Winsorized Mean ( 89 / 91 ) 11.2558241758242 0.177366628834262 63.460777541992 Winsorized Mean ( 90 / 91 ) 11.2854945054945 0.174990378896490 64.49208566015 Winsorized Mean ( 91 / 91 ) 11.2788278388278 0.174526455714279 64.6253187957514 Trimmed Mean ( 1 / 91 ) 9.70313653136531 0.376298837369243 25.7857201983436 Trimmed Mean ( 2 / 91 ) 9.70587360594796 0.376281743368702 25.7941656139229 Trimmed Mean ( 3 / 91 ) 9.7089138576779 0.37627776143029 25.8025183863453 Trimmed Mean ( 4 / 91 ) 9.71305660377359 0.376338704910949 25.8093480075932 Trimmed Mean ( 5 / 91 ) 9.71756653992395 0.376417173214886 25.8159489826902 Trimmed Mean ( 6 / 91 ) 9.72260536398468 0.376512468698786 25.8227978414252 Trimmed Mean ( 7 / 91 ) 9.72803088803089 0.376619162538533 25.8298882681934 Trimmed Mean ( 8 / 91 ) 9.73357976653696 0.376715831909854 25.8379896517494 Trimmed Mean ( 9 / 91 ) 9.73917647058824 0.376802530631908 25.8468977218793 Trimmed Mean ( 10 / 91 ) 9.74494071146245 0.376888234447964 25.8563144740670 Trimmed Mean ( 11 / 91 ) 9.75083665338645 0.376962536828471 25.8668586417737 Trimmed Mean ( 12 / 91 ) 9.75678714859438 0.377025467267969 25.8783238683974 Trimmed Mean ( 13 / 91 ) 9.76283400809717 0.377072479139112 25.8911337957799 Trimmed Mean ( 14 / 91 ) 9.76897959183673 0.377102750619630 25.9053522568717 Trimmed Mean ( 15 / 91 ) 9.77551440329218 0.377146414444623 25.9196800735528 Trimmed Mean ( 16 / 91 ) 9.78207468879668 0.377173245380287 25.9352295227988 Trimmed Mean ( 17 / 91 ) 9.7887029288703 0.377178169442912 25.9524641718477 Trimmed Mean ( 18 / 91 ) 9.79523206751055 0.377184843939711 25.9693151113893 Trimmed Mean ( 19 / 91 ) 9.802 0.377174480142322 25.9879724532300 Trimmed Mean ( 20 / 91 ) 9.8089270386266 0.377146906331142 26.0082394259763 Trimmed Mean ( 21 / 91 ) 9.81601731601732 0.377093053021073 26.0307561684749 Trimmed Mean ( 22 / 91 ) 9.82336244541485 0.37702715729876 26.0547874476604 Trimmed Mean ( 23 / 91 ) 9.83083700440529 0.376945613343199 26.0802531092319 Trimmed Mean ( 24 / 91 ) 9.8384 0.376835229455435 26.1079623957067 Trimmed Mean ( 25 / 91 ) 9.84614349775785 0.376702182723584 26.1377394380078 Trimmed Mean ( 26 / 91 ) 9.85402714932127 0.376532467677195 26.1704580487046 Trimmed Mean ( 27 / 91 ) 9.86219178082192 0.376353957445556 26.2045651061039 Trimmed Mean ( 28 / 91 ) 9.87069124423963 0.376151852087024 26.241240577372 Trimmed Mean ( 29 / 91 ) 9.87986046511628 0.375962261623491 26.2788621987026 Trimmed Mean ( 30 / 91 ) 9.88929577464789 0.375739139115976 26.3195785190625 Trimmed Mean ( 31 / 91 ) 9.89890995260664 0.375481757777974 26.3632247041411 Trimmed Mean ( 32 / 91 ) 9.90870813397129 0.375178424955369 26.4106555038447 Trimmed Mean ( 33 / 91 ) 9.91869565217391 0.37483638529492 26.4614003370295 Trimmed Mean ( 34 / 91 ) 9.9289756097561 0.37445203340334 26.5160146668536 Trimmed Mean ( 35 / 91 ) 9.93945812807882 0.374024235409563 26.5743692175319 Trimmed Mean ( 36 / 91 ) 9.95004975124378 0.373551860556118 26.6363276478689 Trimmed Mean ( 37 / 91 ) 9.9610552763819 0.373049266179421 26.7017152409866 Trimmed Mean ( 38 / 91 ) 9.97238578680203 0.372494238060647 26.7719195838363 Trimmed Mean ( 39 / 91 ) 9.98394871794872 0.37188514123788 26.8468610623042 Trimmed Mean ( 40 / 91 ) 9.99580310880829 0.371212119298364 26.9274697380613 Trimmed Mean ( 41 / 91 ) 10.0079581151832 0.370471138959581 27.0141370345049 Trimmed Mean ( 42 / 91 ) 10.0203703703704 0.369664728559514 27.1066444705642 Trimmed Mean ( 43 / 91 ) 10.0333689839572 0.368807402223745 27.2049013210160 Trimmed Mean ( 44 / 91 ) 10.0469729729730 0.367932727434376 27.3065487895880 Trimmed Mean ( 45 / 91 ) 10.0614207650273 0.367034816951544 27.4127148170677 Trimmed Mean ( 46 / 91 ) 10.0763535911602 0.366061730738379 27.5263780533281 Trimmed Mean ( 47 / 91 ) 10.0919553072626 0.36503748274355 27.6463535509105 Trimmed Mean ( 48 / 91 ) 10.1081355932203 0.36393403300369 27.7746368202884 Trimmed Mean ( 49 / 91 ) 10.1249714285714 0.362764932907017 27.9105572510412 Trimmed Mean ( 50 / 91 ) 10.1431213872832 0.361613839580337 28.0495940062875 Trimmed Mean ( 51 / 91 ) 10.1620467836257 0.360381987057223 28.1979875481739 Trimmed Mean ( 52 / 91 ) 10.1820118343195 0.359085401911032 28.3554045364457 Trimmed Mean ( 53 / 91 ) 10.2025149700599 0.357667441878072 28.5251431231415 Trimmed Mean ( 54 / 91 ) 10.2233939393939 0.356131972027429 28.7067568833908 Trimmed Mean ( 55 / 91 ) 10.2447239263804 0.354476200333562 28.9010204824473 Trimmed Mean ( 56 / 91 ) 10.2668944099379 0.352711394654961 29.1084851964634 Trimmed Mean ( 57 / 91 ) 10.2896226415094 0.350781150727481 29.3334536937629 Trimmed Mean ( 58 / 91 ) 10.3131847133758 0.348697420249403 29.5763149208256 Trimmed Mean ( 59 / 91 ) 10.3372258064516 0.346478599125759 29.8351062158953 Trimmed Mean ( 60 / 91 ) 10.3615686274510 0.344220065818562 30.1015822619491 Trimmed Mean ( 61 / 91 ) 10.3865562913907 0.341750487275185 30.3922208691022 Trimmed Mean ( 62 / 91 ) 10.4121476510067 0.339139840393170 30.7016351689491 Trimmed Mean ( 63 / 91 ) 10.4384353741497 0.336285086087357 31.0404350534833 Trimmed Mean ( 64 / 91 ) 10.4664137931034 0.333285897139971 31.4037103967464 Trimmed Mean ( 65 / 91 ) 10.4953846153846 0.330066726317322 31.7977662652809 Trimmed Mean ( 66 / 91 ) 10.5251773049645 0.326562126897437 32.2302448387414 Trimmed Mean ( 67 / 91 ) 10.5562589928058 0.32285753117782 32.6963380853944 Trimmed Mean ( 68 / 91 ) 10.5884671532847 0.318862480309943 33.2070024136812 Trimmed Mean ( 69 / 91 ) 10.6215555555556 0.314489765792008 33.7739306994818 Trimmed Mean ( 70 / 91 ) 10.6557894736842 0.309722959769257 34.4042607678254 Trimmed Mean ( 71 / 91 ) 10.6908396946565 0.304526046817777 35.1064869700741 Trimmed Mean ( 72 / 91 ) 10.7272093023256 0.298819888535231 35.8985787556134 Trimmed Mean ( 73 / 91 ) 10.7650393700787 0.292606939549565 36.7901027455135 Trimmed Mean ( 74 / 91 ) 10.80352 0.285957773918661 37.7801234495307 Trimmed Mean ( 75 / 91 ) 10.8435772357724 0.278641272399257 38.9159048205713 Trimmed Mean ( 76 / 91 ) 10.8848760330579 0.270539459949637 40.2339682169993 Trimmed Mean ( 77 / 91 ) 10.9257983193277 0.262133351507100 41.680306059917 Trimmed Mean ( 78 / 91 ) 10.9682051282051 0.252816571672508 43.3840434416343 Trimmed Mean ( 79 / 91 ) 10.9945217391304 0.247366240842896 44.4463306782155 Trimmed Mean ( 80 / 91 ) 11.0135398230089 0.243378068710463 45.2528031032706 Trimmed Mean ( 81 / 91 ) 11.0312612612613 0.239446027222793 46.0699281136839 Trimmed Mean ( 82 / 91 ) 11.0449541284404 0.236219647315803 46.7571358011315 Trimmed Mean ( 83 / 91 ) 11.0567289719626 0.233252544903099 47.4023937297487 Trimmed Mean ( 84 / 91 ) 11.0633333333333 0.231069367297036 47.8788402926278 Trimmed Mean ( 85 / 91 ) 11.0700970873786 0.228853884436294 48.3718994529901 Trimmed Mean ( 86 / 91 ) 11.0740594059406 0.227015861888256 48.780994040811 Trimmed Mean ( 87 / 91 ) 11.0731313131313 0.225816535120438 49.0359632310606 Trimmed Mean ( 88 / 91 ) 11.0721649484536 0.22447936264313 49.3237543891987 Trimmed Mean ( 89 / 91 ) 11.07 0.223247937632881 49.5861243663715 Trimmed Mean ( 90 / 91 ) 11.0638709677419 0.222535856420177 49.7172507195959 Trimmed Mean ( 91 / 91 ) 11.0564835164835 0.221825337665553 49.8431947983933 Median 9.9 Midrange 9.35 Midmean - Weighted Average at Xnp 10.5541911764706 Midmean - Weighted Average at X(n+1)p 10.6222463768116 Midmean - Empirical Distribution Function 10.6222463768116 Midmean - Empirical Distribution Function - Averaging 10.6222463768116 Midmean - Empirical Distribution Function - Interpolation 10.6222463768116 Midmean - Closest Observation 10.5562589928058 Midmean - True Basic - Statistics Graphics Toolkit 10.6222463768116 Midmean - MS Excel (old versions) 10.6222463768116 Number of observations 273

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/10/t1236722650rzh9bz0wholptrm/139kr1236722596.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/10/t1236722650rzh9bz0wholptrm/139kr1236722596.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/10/t1236722650rzh9bz0wholptrm/2skkb1236722596.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/10/t1236722650rzh9bz0wholptrm/2skkb1236722596.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

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Software written by Ed van Stee & Patrick Wessa

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