TRIMMED MEAN PLOT YANNICK ROEY

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 22 Apr 2009 11:00:21 -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/Apr/22/t1240419683ursort586qlxs2u.htm/, Retrieved Wed, 22 Apr 2009 19:01:30 +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/Apr/22/t1240419683ursort586qlxs2u.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:

» Textbox « » Textfile « » CSV «

3.594 3.617 3.647 3.761 3.767 3.692 3.709 3.716 3.755 3.702 3.698 3.765 3.809 3.777 3.747 3.695 3.719 3.714 3.740 3.632 3.643 3.615 3.747 3.687 3.700 3.578 3.608 3.711 3.599 3.721 3.683 3.668 3.715 3.673 3.701 3.846 3.853 3.807 3.860 3.854 3.842 3.826 3.863 3.763 3.789 3.822 3.877 3.867 3.940 3.864 3.859 3.868 3.887 3.908 3.936 3.891 3.962 3.947 3.909 3.897 3.878 3.841 3.841 3.842 3.836 3.821 3.815 3.805 3.815 3.803 3.722 3.745 3.681 3.684 3.676 3.725 3.734 3.747 3.683 3.715 3.717 3.772 3.655 3.615 3.634 3.540 3.580 3.598 3.577 3.568 3.493 3.446 3.376 3.345 3.336 3.341 3.196 3.191 3.157 3.111 3.054 3.109 3.041 3.017 3.045 3.037 3.043 2.992 2.946 2.883 2.988 2.950 3.054 3.083 3.125 3.175 3.066 3.054 2.969 3.007 3.021 2.982 2.987 2.964 3.084 3.060 3.026 3.083 3.089 3.090 3.065 3.072 3.070 3.057 3.009 2.990 2.984 3.014 2.987 3.025 3.030 3.097 3.118 3.153 3.189 3.173 3. 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 2.93124409448819 0.0475453900021472 61.6514891213598 Geometric Mean 2.82546799055594 Harmonic Mean 2.71531923203185 Quadratic Mean 3.02722887496425 Winsorized Mean ( 1 / 84 ) 2.93125590551181 0.0475335414020144 61.6671053545274 Winsorized Mean ( 2 / 84 ) 2.93138188976378 0.0475117626305202 61.6980243936634 Winsorized Mean ( 3 / 84 ) 2.93144094488189 0.0474978831438748 61.7172966635655 Winsorized Mean ( 4 / 84 ) 2.93109448818898 0.0474554869789588 61.7651334921205 Winsorized Mean ( 5 / 84 ) 2.93107480314961 0.0474538844133357 61.7668045384689 Winsorized Mean ( 6 / 84 ) 2.93116929133858 0.0474002295778814 61.8387150746285 Winsorized Mean ( 7 / 84 ) 2.93103149606299 0.0473844300122749 61.8564261573625 Winsorized Mean ( 8 / 84 ) 2.931 0.0473657322237123 61.8801792434379 Winsorized Mean ( 9 / 84 ) 2.93071653543307 0.0473371692622762 61.9115291663334 Winsorized Mean ( 10 / 84 ) 2.93083464566929 0.047319724037159 61.9368499141664 Winsorized Mean ( 11 / 84 ) 2.93057480314961 0.0472772556453196 61.9869906395409 Winsorized Mean ( 12 / 84 ) 2.93057480314961 0.0472692724320398 61.997459498937 Winsorized Mean ( 13 / 84 ) 2.93047244094488 0.0472526303509614 62.0171283414121 Winsorized Mean ( 14 / 84 ) 2.93069291338583 0.0472234215167363 62.0601561525391 Winsorized Mean ( 15 / 84 ) 2.93098818897638 0.0471671246904057 62.1404889149957 Winsorized Mean ( 16 / 84 ) 2.93092519685039 0.0471622229413533 62.1456117642086 Winsorized Mean ( 17 / 84 ) 2.93059055118110 0.047136252457609 62.1727523590609 Winsorized Mean ( 18 / 84 ) 2.93066141732283 0.0471180644000681 62.1982556931731 Winsorized Mean ( 19 / 84 ) 2.93028740157480 0.0470642814757262 62.2613861232775 Winsorized Mean ( 20 / 84 ) 2.93028740157480 0.0470119584966756 62.3306812836146 Winsorized Mean ( 21 / 84 ) 2.93037007874016 0.047004583937679 62.3422192743028 Winsorized Mean ( 22 / 84 ) 2.93054330708661 0.0469748010004791 62.3854331401367 Winsorized Mean ( 23 / 84 ) 2.93063385826772 0.0469667461539967 62.3980602926722 Winsorized Mean ( 24 / 84 ) 2.93016141732283 0.046930626933682 62.4360169205382 Winsorized Mean ( 25 / 84 ) 2.92927559055118 0.0468470934207477 62.52843830123 Winsorized Mean ( 26 / 84 ) 2.92927559055118 0.0467797842084137 62.6184075048455 Winsorized Mean ( 27 / 84 ) 2.92916929133858 0.0467717694859521 62.6268649557584 Winsorized Mean ( 28 / 84 ) 2.92883858267717 0.0466927094805774 62.7258219807412 Winsorized Mean ( 29 / 84 ) 2.92906692913386 0.0466724871687128 62.7578924291264 Winsorized Mean ( 30 / 84 ) 2.92835826771654 0.0466194468405193 62.8140929628396 Winsorized Mean ( 31 / 84 ) 2.92811417322835 0.0466012363667929 62.8334010321422 Winsorized Mean ( 32 / 84 ) 2.92798818897638 0.0465713130114914 62.8710680382556 Winsorized Mean ( 33 / 84 ) 2.92785826771654 0.046540488158443 62.9099174411085 Winsorized Mean ( 34 / 84 ) 2.92611811023622 0.0463901086247784 63.0763366799552 Winsorized Mean ( 35 / 84 ) 2.92446456692913 0.046269111178349 63.2055488521594 Winsorized Mean ( 36 / 84 ) 2.9246062992126 0.0461423281550982 63.3822872868946 Winsorized Mean ( 37 / 84 ) 2.92402362204724 0.0460766874087638 63.459935739458 Winsorized Mean ( 38 / 84 ) 2.92387401574803 0.046041849639406 63.504703626102 Winsorized Mean ( 39 / 84 ) 2.92372047244094 0.0460061316136362 63.5506696584408 Winsorized Mean ( 40 / 84 ) 2.92356299212598 0.0459695345087972 63.5978376410686 Winsorized Mean ( 41 / 84 ) 2.92291732283465 0.0458714571743278 63.7197399621845 Winsorized Mean ( 42 / 84 ) 2.92159448818898 0.0457768964447538 63.8224675566402 Winsorized Mean ( 43 / 84 ) 2.92244094488189 0.0457022493919726 63.9452321004402 Winsorized Mean ( 44 / 84 ) 2.92313385826772 0.0456412759357432 64.0458400502014 Winsorized Mean ( 45 / 84 ) 2.9241968503937 0.0454916239441775 64.2798958766995 Winsorized Mean ( 46 / 84 ) 2.92383464566929 0.0453795777413987 64.4306269734623 Winsorized Mean ( 47 / 84 ) 2.92457480314961 0.0451391394224046 64.790220650463 Winsorized Mean ( 48 / 84 ) 2.92514173228346 0.0448216323455043 65.2618295945856 Winsorized Mean ( 49 / 84 ) 2.93073622047244 0.0442488076461016 66.2331117238736 Winsorized Mean ( 50 / 84 ) 2.93073622047244 0.0442180603777525 66.2791672776987 Winsorized Mean ( 51 / 84 ) 2.93053543307087 0.0441725411864597 66.3429215154407 Winsorized Mean ( 52 / 84 ) 2.93074015748032 0.0440911832793584 66.4699819669471 Winsorized Mean ( 53 / 84 ) 2.93094881889764 0.0440408489508695 66.5506884794002 Winsorized Mean ( 54 / 84 ) 2.93116141732283 0.0439895971724297 66.6330588532856 Winsorized Mean ( 55 / 84 ) 2.93137795275591 0.0439711338260556 66.6659623641291 Winsorized Mean ( 56 / 84 ) 2.93292125984252 0.0438054669221176 66.9533157826397 Winsorized Mean ( 57 / 84 ) 2.93471653543307 0.0435486406853909 67.3893946916595 Winsorized Mean ( 58 / 84 ) 2.93448818897638 0.0434971516466537 67.4639160930468 Winsorized Mean ( 59 / 84 ) 2.93402362204724 0.0432846607234693 67.7843737944882 Winsorized Mean ( 60 / 84 ) 2.93945669291339 0.0427907543815251 68.6937338543977 Winsorized Mean ( 61 / 84 ) 2.93945669291339 0.04275373666781 68.7532113450695 Winsorized Mean ( 62 / 84 ) 2.93896850393701 0.0427194314856942 68.7969947568522 Winsorized Mean ( 63 / 84 ) 2.93996062992126 0.0425218011125977 69.1400776306781 Winsorized Mean ( 64 / 84 ) 2.93970866141732 0.0424266347238529 69.2892255195668 Winsorized Mean ( 65 / 84 ) 2.94098818897638 0.042123267049354 69.8186155772427 Winsorized Mean ( 66 / 84 ) 2.94488582677165 0.0416795553022675 70.6554042003285 Winsorized Mean ( 67 / 84 ) 2.94699606299213 0.0414643593577406 71.0729915676842 Winsorized Mean ( 68 / 84 ) 2.95020866141732 0.0411990415076242 71.6086722763044 Winsorized Mean ( 69 / 84 ) 2.95075196850394 0.0410713232022859 71.8445800728356 Winsorized Mean ( 70 / 84 ) 2.95764173228346 0.0402962687493281 73.3974093403569 Winsorized Mean ( 71 / 84 ) 2.95820078740157 0.0401231113990772 73.7281004451118 Winsorized Mean ( 72 / 84 ) 2.95735039370079 0.0399771595753399 73.976000924414 Winsorized Mean ( 73 / 84 ) 2.96022440944882 0.0391767242936474 75.5607943956872 Winsorized Mean ( 74 / 84 ) 2.95993307086614 0.0388479490125593 76.1927758376436 Winsorized Mean ( 75 / 84 ) 2.96052362204724 0.0386216555392262 76.6544981232195 Winsorized Mean ( 76 / 84 ) 2.95842913385827 0.0383853861155179 77.0717565522228 Winsorized Mean ( 77 / 84 ) 2.95812598425197 0.0383186135291753 77.1981476312991 Winsorized Mean ( 78 / 84 ) 2.95720472440945 0.0377000403219649 78.4403597225468 Winsorized Mean ( 79 / 84 ) 2.96249212598425 0.0371782168862468 79.6835452073592 Winsorized Mean ( 80 / 84 ) 2.97414566929134 0.0362398756380308 82.068318859522 Winsorized Mean ( 81 / 84 ) 2.97478346456693 0.0358539082973834 82.9695730767523 Winsorized Mean ( 82 / 84 ) 3.00609842519685 0.0329380603828191 91.265192614829 Winsorized Mean ( 83 / 84 ) 3.01426771653543 0.0322521050297054 93.4595653139284 Winsorized Mean ( 84 / 84 ) 3.03377952755905 0.0305505140529102 99.3037145726868 Trimmed Mean ( 1 / 84 ) 2.93178571428571 0.0475218050695644 61.6934838648078 Trimmed Mean ( 2 / 84 ) 2.932324 0.0475066075735638 61.724550536666 Trimmed Mean ( 3 / 84 ) 2.9328064516129 0.0474992202993542 61.7443072355606 Trimmed Mean ( 4 / 84 ) 2.93327642276423 0.0474933532508217 61.7618302770289 Trimmed Mean ( 5 / 84 ) 2.93384426229508 0.047495531463912 61.7709534322039 Trimmed Mean ( 6 / 84 ) 2.93442561983471 0.0474948476810084 61.7840831818919 Trimmed Mean ( 7 / 84 ) 2.935 0.0475008078181327 61.788422867192 Trimmed Mean ( 8 / 84 ) 2.93560504201681 0.0475061283617681 61.7942388329696 Trimmed Mean ( 9 / 84 ) 2.93622457627119 0.0475108693881249 61.8011123367294 Trimmed Mean ( 10 / 84 ) 2.93688888888889 0.0475159620200951 61.8084694917225 Trimmed Mean ( 11 / 84 ) 2.93755172413793 0.0475197355665071 61.8175099065235 Trimmed Mean ( 12 / 84 ) 2.93825217391304 0.0475246615651372 61.8258410927532 Trimmed Mean ( 13 / 84 ) 2.9389649122807 0.0475268639828915 61.8379725903787 Trimmed Mean ( 14 / 84 ) 2.93969911504425 0.0475269589779496 61.8532971235997 Trimmed Mean ( 15 / 84 ) 2.94042857142857 0.0475258836674974 61.8700452157927 Trimmed Mean ( 16 / 84 ) 2.94114864864865 0.0475257461714598 61.8853755191512 Trimmed Mean ( 17 / 84 ) 2.94188636363636 0.0475220073462225 61.9057680413875 Trimmed Mean ( 18 / 84 ) 2.94266055045872 0.0475160892320197 61.9297715367481 Trimmed Mean ( 19 / 84 ) 2.94344444444444 0.0475071877542196 61.9578759254805 Trimmed Mean ( 20 / 84 ) 2.94426635514019 0.0474976403575651 61.9876341851 Trimmed Mean ( 21 / 84 ) 2.94510377358491 0.0474871316212056 62.0189864714793 Trimmed Mean ( 22 / 84 ) 2.94595238095238 0.047472330208503 62.05619922202 Trimmed Mean ( 23 / 84 ) 2.94680769230769 0.0474544771757609 62.0975694536338 Trimmed Mean ( 24 / 84 ) 2.94767475728155 0.0474318772465506 62.1454373808474 Trimmed Mean ( 25 / 84 ) 2.94858333333333 0.0474059709213388 62.198564358611 Trimmed Mean ( 26 / 84 ) 2.94955445544554 0.0473793895994302 62.2539564224571 Trimmed Mean ( 27 / 84 ) 2.950545 0.0473509806309071 62.3122258649509 Trimmed Mean ( 28 / 84 ) 2.95156060606061 0.0473168949718831 62.3785776267546 Trimmed Mean ( 29 / 84 ) 2.95261224489796 0.0472809561616262 62.4482346508537 Trimmed Mean ( 30 / 84 ) 2.95367525773196 0.0472395172757722 62.525517364819 Trimmed Mean ( 31 / 84 ) 2.95479166666667 0.0471939754108662 62.6095098143891 Trimmed Mean ( 32 / 84 ) 2.95594210526316 0.0471420435928092 62.7028843041935 Trimmed Mean ( 33 / 84 ) 2.95712234042553 0.0470839596291229 62.8053027765418 Trimmed Mean ( 34 / 84 ) 2.95833333333333 0.0470193296346809 62.9173864518754 Trimmed Mean ( 35 / 84 ) 2.95964130434783 0.0469540717264163 63.0326869540206 Trimmed Mean ( 36 / 84 ) 2.96104395604396 0.046886277110157 63.1537443053355 Trimmed Mean ( 37 / 84 ) 2.96247222222222 0.0468162078807376 63.2787736625102 Trimmed Mean ( 38 / 84 ) 2.96395505617978 0.0467400864037302 63.4135553489954 Trimmed Mean ( 39 / 84 ) 2.96547727272727 0.0466558225334115 63.560711433254 Trimmed Mean ( 40 / 84 ) 2.96704022988506 0.0465628573545192 63.7211803239367 Trimmed Mean ( 41 / 84 ) 2.96864534883721 0.046460586885708 63.895993310201 Trimmed Mean ( 42 / 84 ) 2.97031176470588 0.0463515255618396 64.082287016488 Trimmed Mean ( 43 / 84 ) 2.97206547619048 0.0462347233071028 64.282107982982 Trimmed Mean ( 44 / 84 ) 2.97383132530120 0.0461089449438769 64.4957573616335 Trimmed Mean ( 45 / 84 ) 2.97561585365854 0.0459726971385506 64.7257184996293 Trimmed Mean ( 46 / 84 ) 2.97740740740741 0.0458300768908659 64.96623198991 Trimmed Mean ( 47 / 84 ) 2.97925625 0.0456780702779142 65.22290087724 Trimmed Mean ( 48 / 84 ) 2.98112658227848 0.0455231876863105 65.4858926580607 Trimmed Mean ( 49 / 84 ) 2.98302564102564 0.0453691794510623 65.7500461132055 Trimmed Mean ( 50 / 84 ) 2.98478571428571 0.0452311551308713 65.9895973394792 Trimmed Mean ( 51 / 84 ) 2.98659210526316 0.0450785963591285 66.2529969094383 Trimmed Mean ( 52 / 84 ) 2.98845333333333 0.0449110665690858 66.5415800966618 Trimmed Mean ( 53 / 84 ) 2.99035810810811 0.044729429068527 66.8543768695723 Trimmed Mean ( 54 / 84 ) 2.99230821917808 0.044530707365229 67.1965121648746 Trimmed Mean ( 55 / 84 ) 2.99430555555556 0.0443134784282789 67.5709888223246 Trimmed Mean ( 56 / 84 ) 2.99635211267606 0.0440742093541687 67.984251029852 Trimmed Mean ( 57 / 84 ) 2.99840714285714 0.0438200983237679 68.4253860113047 Trimmed Mean ( 58 / 84 ) 3.00046376811594 0.0435553105324258 68.8885862926445 Trimmed Mean ( 59 / 84 ) 3.00258823529412 0.0432656213940983 69.3989393552011 Trimmed Mean ( 60 / 84 ) 3.00479104477612 0.04295850403165 69.9463613202713 Trimmed Mean ( 61 / 84 ) 3.00688636363636 0.0426521438167379 70.4978951715993 Trimmed Mean ( 62 / 84 ) 3.00904615384615 0.0423153900082347 71.1099709410827 Trimmed Mean ( 63 / 84 ) 3.0112890625 0.0419448048344649 71.7917051797964 Trimmed Mean ( 64 / 84 ) 3.01357142857143 0.0415483996652005 72.5315885294012 Trimmed Mean ( 65 / 84 ) 3.01593548387097 0.0411159531406801 73.3519535240205 Trimmed Mean ( 66 / 84 ) 3.01833606557377 0.0406588081704233 74.2357240999852 Trimmed Mean ( 67 / 84 ) 3.02069166666667 0.0401855967268172 75.16851590388 Trimmed Mean ( 68 / 84 ) 3.0230593220339 0.0396771161581581 76.1915082231177 Trimmed Mean ( 69 / 84 ) 3.02540517241379 0.0391337287056324 77.3094022082888 Trimmed Mean ( 70 / 84 ) 3.02781578947368 0.0385393589320685 78.5642489489944 Trimmed Mean ( 71 / 84 ) 3.03008928571429 0.0379425909937766 79.859841048053 Trimmed Mean ( 72 / 84 ) 3.03242727272727 0.0372909920971738 81.317956487328 Trimmed Mean ( 73 / 84 ) 3.03487962962963 0.0365742006889948 82.9787000797757 Trimmed Mean ( 74 / 84 ) 3.03733018867925 0.0358427801877862 84.7403625713791 Trimmed Mean ( 75 / 84 ) 3.03988461538462 0.0350506230180436 86.7284046226432 Trimmed Mean ( 76 / 84 ) 3.04251960784314 0.034180007378094 89.0145977497094 Trimmed Mean ( 77 / 84 ) 3.04533 0.0332174015944485 91.6787543222212 Trimmed Mean ( 78 / 84 ) 3.04826530612245 0.0321312188094346 94.8692710413898 Trimmed Mean ( 79 / 84 ) 3.05135416666667 0.030958871908021 98.5615424144736 Trimmed Mean ( 80 / 84 ) 3.05439361702128 0.0296805080754494 102.909074509670 Trimmed Mean ( 81 / 84 ) 3.05716304347826 0.0283341870038832 107.896621246245 Trimmed Mean ( 82 / 84 ) 3.06003333333333 0.0268215374077225 114.088662660041 Trimmed Mean ( 83 / 84 ) 3.06193181818182 0.0254865598375869 120.139078702421 Trimmed Mean ( 84 / 84 ) 3.06362790697674 0.024028084608116 127.501961015317 Median 3.0525 Midrange 2.863 Midmean - Weighted Average at Xnp 3.00590551181102 Midmean - Weighted Average at X(n+1)p 3.0112890625 Midmean - Empirical Distribution Function 3.0112890625 Midmean - Empirical Distribution Function - Averaging 3.0112890625 Midmean - Empirical Distribution Function - Interpolation 3.01357142857143 Midmean - Closest Observation 3.0112890625 Midmean - True Basic - Statistics Graphics Toolkit 3.0112890625 Midmean - MS Excel (old versions) 3.0112890625 Number of observations 254

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240419683ursort586qlxs2u/1ehjx1240419618.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240419683ursort586qlxs2u/1ehjx1240419618.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240419683ursort586qlxs2u/2fcp51240419618.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240419683ursort586qlxs2u/2fcp51240419618.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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