*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 09 Dec 2008 03:37:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/09/t1228819103zhpe4lc87xgixx2.htm/, Retrieved Tue, 09 Dec 2008 10:38:25 +0000

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/2008/Dec/09/t1228819103zhpe4lc87xgixx2.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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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 -0.00948065551169261 0.0280014425907807 -0.338577395823673 Geometric Mean NaN Harmonic Mean -0.751278795264501 Quadratic Mean 0.530636302396557 Winsorized Mean ( 1 / 120 ) -0.00905189826948639 0.0278669979306895 -0.324825023922568 Winsorized Mean ( 2 / 120 ) -0.00928599149553578 0.0276119675433526 -0.336303143952207 Winsorized Mean ( 3 / 120 ) -0.0090182777269467 0.0275675795211737 -0.327133461971881 Winsorized Mean ( 4 / 120 ) -0.0097766744096928 0.0273268701571515 -0.357767807051047 Winsorized Mean ( 5 / 120 ) -0.0116178063995618 0.0270629157909504 -0.42928879095307 Winsorized Mean ( 6 / 120 ) -0.0120271139509668 0.0270016486921658 -0.44542146622537 Winsorized Mean ( 7 / 120 ) -0.0129586257064455 0.0268643780896859 -0.482372071416788 Winsorized Mean ( 8 / 120 ) -0.0123825848532920 0.0265037520371457 -0.467201203661182 Winsorized Mean ( 9 / 120 ) -0.0124793978048427 0.0263052228975236 -0.474407605419589 Winsorized Mean ( 10 / 120 ) -0.0131618037171278 0.0261280608095049 -0.503742080711163 Winsorized Mean ( 11 / 120 ) -0.0138891792983648 0.0260020221680433 -0.534157659300621 Winsorized Mean ( 12 / 120 ) -0.0138287664815781 0.0259130560222570 -0.533660193135865 Winsorized Mean ( 13 / 120 ) -0.0126401657621609 0.0257888464232875 -0.490140797874028 Winsorized Mean ( 14 / 120 ) -0.0152457479867797 0.0254947204869302 -0.597996279056887 Winsorized Mean ( 15 / 120 ) -0.0140777883948075 0.0253379303827815 -0.555601352680885 Winsorized Mean ( 16 / 120 ) -0.0150539171286081 0.0251119691471584 -0.599471791335468 Winsorized Mean ( 17 / 120 ) -0.015072085518921 0.0250172816900135 -0.602466954870541 Winsorized Mean ( 18 / 120 ) -0.0156043596768871 0.0249471166822128 -0.625497522445666 Winsorized Mean ( 19 / 120 ) -0.0151052086690066 0.0248891741023612 -0.606898750713211 Winsorized Mean ( 20 / 120 ) -0.0154288190876244 0.0248131852177143 -0.621799214903278 Winsorized Mean ( 21 / 120 ) -0.0141261119481453 0.0246537732792038 -0.572979713416163 Winsorized Mean ( 22 / 120 ) -0.0136501755633154 0.0245378222931010 -0.556291238899112 Winsorized Mean ( 23 / 120 ) -0.0149896064739968 0.0244053789416984 -0.614192736355587 Winsorized Mean ( 24 / 120 ) -0.0127275430529922 0.0241493538966538 -0.527034516428852 Winsorized Mean ( 25 / 120 ) -0.0123311432539549 0.0241054827869936 -0.511549316930018 Winsorized Mean ( 26 / 120 ) -0.0100596101980799 0.0238925535523234 -0.421035373052524 Winsorized Mean ( 27 / 120 ) -0.0100284840693151 0.0237701781360217 -0.421893517664379 Winsorized Mean ( 28 / 120 ) -0.0112879227693335 0.0236118994847501 -0.478060766632685 Winsorized Mean ( 29 / 120 ) -0.0136928577493112 0.0233387890141473 -0.586699581585443 Winsorized Mean ( 30 / 120 ) -0.0155733389676953 0.0229782555268688 -0.677742439998772 Winsorized Mean ( 31 / 120 ) -0.0153581665633090 0.0229439413949482 -0.66937786751367 Winsorized Mean ( 32 / 120 ) -0.0169890115222246 0.0227971780638838 -0.745224320072285 Winsorized Mean ( 33 / 120 ) -0.0168778492513383 0.0227150088069937 -0.743026313339654 Winsorized Mean ( 34 / 120 ) -0.0149909730826164 0.0225190684895963 -0.665701296194477 Winsorized Mean ( 35 / 120 ) -0.0144743441521291 0.022153656437537 -0.653361407537397 Winsorized Mean ( 36 / 120 ) -0.0117796316008824 0.0216665934418535 -0.543677142071057 Winsorized Mean ( 37 / 120 ) -0.0117262912821723 0.0216480467084443 -0.541678953307052 Winsorized Mean ( 38 / 120 ) -0.0119552062424549 0.0215534369474850 -0.554677487009789 Winsorized Mean ( 39 / 120 ) -0.0130040376965518 0.0214012749065144 -0.607629113375552 Winsorized Mean ( 40 / 120 ) -0.0125927512597236 0.0210475266937750 -0.598300762029586 Winsorized Mean ( 41 / 120 ) -0.0132741580626055 0.0208999951342218 -0.635127327894459 Winsorized Mean ( 42 / 120 ) -0.0131631459751712 0.0208321116040611 -0.63186806145015 Winsorized Mean ( 43 / 120 ) -0.0133945528194732 0.0207192325133539 -0.646479198051384 Winsorized Mean ( 44 / 120 ) -0.0138669452888885 0.0206467361560593 -0.671628928857062 Winsorized Mean ( 45 / 120 ) -0.0140256074080692 0.0205347853618933 -0.683016995838522 Winsorized Mean ( 46 / 120 ) -0.0137844482521926 0.0205075293062804 -0.672165234842362 Winsorized Mean ( 47 / 120 ) -0.0144336471164702 0.0203924459461933 -0.707793815148723 Winsorized Mean ( 48 / 120 ) -0.0140075384101256 0.0203582589296260 -0.68805188393303 Winsorized Mean ( 49 / 120 ) -0.0140980199626572 0.0201629118881704 -0.699205553287596 Winsorized Mean ( 50 / 120 ) -0.0151910122642812 0.0198420118452079 -0.765598387038061 Winsorized Mean ( 51 / 120 ) -0.0134421700369045 0.0197149328800383 -0.681826822272111 Winsorized Mean ( 52 / 120 ) -0.0136550847316955 0.0196278797326641 -0.695698410509984 Winsorized Mean ( 53 / 120 ) -0.0130452534740404 0.0195557781910034 -0.667079230835307 Winsorized Mean ( 54 / 120 ) -0.0132274469779503 0.0193787708461421 -0.68257409528033 Winsorized Mean ( 55 / 120 ) -0.0139020735740186 0.0192919816930317 -0.72061407662646 Winsorized Mean ( 56 / 120 ) -0.0121838617347731 0.0191499913704459 -0.636233275466451 Winsorized Mean ( 57 / 120 ) -0.0119685715249250 0.0189897219131914 -0.630265760585513 Winsorized Mean ( 58 / 120 ) -0.0139322689958128 0.0188172364568802 -0.740399315687966 Winsorized Mean ( 59 / 120 ) -0.0142424069714128 0.0186486612978232 -0.763722754355309 Winsorized Mean ( 60 / 120 ) -0.0152075407078641 0.0185035136910791 -0.821873129707033 Winsorized Mean ( 61 / 120 ) -0.0152480650084462 0.0184793243648984 -0.825141910350901 Winsorized Mean ( 62 / 120 ) -0.0153215939348947 0.0183713221103404 -0.833995171543529 Winsorized Mean ( 63 / 120 ) -0.0160239311806008 0.0180779618078894 -0.886379302649474 Winsorized Mean ( 64 / 120 ) -0.0192521443963382 0.0178147443645796 -1.08068597574807 Winsorized Mean ( 65 / 120 ) -0.0165966223852509 0.0175998801783308 -0.942996328218467 Winsorized Mean ( 66 / 120 ) -0.0156708297439905 0.0174771700533101 -0.896645721028644 Winsorized Mean ( 67 / 120 ) -0.0155853345344856 0.0173064284737394 -0.90055175498137 Winsorized Mean ( 68 / 120 ) -0.0153367844491022 0.0172571036778441 -0.88872297086519 Winsorized Mean ( 69 / 120 ) -0.0178766273043696 0.0170575105817515 -1.04802088315832 Winsorized Mean ( 70 / 120 ) -0.0221319888033926 0.0166960960635564 -1.32557866935742 Winsorized Mean ( 71 / 120 ) -0.0225631264882653 0.0165736747930724 -1.36138344513049 Winsorized Mean ( 72 / 120 ) -0.0231092661127777 0.0164493597613886 -1.40487328674164 Winsorized Mean ( 73 / 120 ) -0.0221605604487345 0.0163501083348350 -1.35537697946135 Winsorized Mean ( 74 / 120 ) -0.0266186192917238 0.0159443068353953 -1.66947485184068 Winsorized Mean ( 75 / 120 ) -0.0261000555452565 0.0158907852908164 -1.64246480382189 Winsorized Mean ( 76 / 120 ) -0.0264333207093683 0.0157738990726207 -1.67576327119080 Winsorized Mean ( 77 / 120 ) -0.026065302881534 0.0156994177215034 -1.66027195045792 Winsorized Mean ( 78 / 120 ) -0.0269370234288360 0.0155215052543158 -1.73546463358288 Winsorized Mean ( 79 / 120 ) -0.0266399221573712 0.0153717764286281 -1.73304121882475 Winsorized Mean ( 80 / 120 ) -0.0251722030597081 0.0152633351258664 -1.64919415397290 Winsorized Mean ( 81 / 120 ) -0.0275081769686876 0.0150949861103314 -1.82233867375739 Winsorized Mean ( 82 / 120 ) -0.0271921717596334 0.0150335181453797 -1.80876967697614 Winsorized Mean ( 83 / 120 ) -0.0284390761974296 0.0149052479148225 -1.90799082041088 Winsorized Mean ( 84 / 120 ) -0.0282089055949748 0.0148611245906505 -1.89816762674352 Winsorized Mean ( 85 / 120 ) -0.0280400252075302 0.0148450892164536 -1.88884181150302 Winsorized Mean ( 86 / 120 ) -0.0273710382247224 0.0146801310800445 -1.86449549227319 Winsorized Mean ( 87 / 120 ) -0.0278655979895117 0.0146416033898658 -1.90317940238696 Winsorized Mean ( 88 / 120 ) -0.0286640367030704 0.0145492767883451 -1.97013481288857 Winsorized Mean ( 89 / 120 ) -0.0284198480881850 0.0145188353195201 -1.95744682426251 Winsorized Mean ( 90 / 120 ) -0.0291367664159075 0.0144582335376748 -2.01523694716811 Winsorized Mean ( 91 / 120 ) -0.0286569895214192 0.0143947583296122 -1.9907933752849 Winsorized Mean ( 92 / 120 ) -0.0282598262019861 0.0142935622492582 -1.97710169859531 Winsorized Mean ( 93 / 120 ) -0.025569983800935 0.0141174037725035 -1.81123839857423 Winsorized Mean ( 94 / 120 ) -0.0263612295336399 0.0140061726479744 -1.88211513567573 Winsorized Mean ( 95 / 120 ) -0.0255421698612935 0.0139334802341463 -1.83315075860933 Winsorized Mean ( 96 / 120 ) -0.0258163943703007 0.0138796949775632 -1.86001165097889 Winsorized Mean ( 97 / 120 ) -0.0261391776849673 0.0138094764768050 -1.89284349257351 Winsorized Mean ( 98 / 120 ) -0.0257979993379993 0.0136624186446947 -1.88824541312214 Winsorized Mean ( 99 / 120 ) -0.0233720585137946 0.0135138210982073 -1.72949296456907 Winsorized Mean ( 100 / 120 ) -0.0239459262828015 0.0132693257573936 -1.80460761312299 Winsorized Mean ( 101 / 120 ) -0.0234541596903999 0.0131568689905507 -1.78265510641208 Winsorized Mean ( 102 / 120 ) -0.0233006671778432 0.0131474120024354 -1.77226264557063 Winsorized Mean ( 103 / 120 ) -0.0254613886327794 0.0129768358623999 -1.96206447417227 Winsorized Mean ( 104 / 120 ) -0.0264696100605655 0.0129072818695309 -2.05075013687042 Winsorized Mean ( 105 / 120 ) -0.0267984324796268 0.0128270661408397 -2.08920981504134 Winsorized Mean ( 106 / 120 ) -0.027853184909355 0.0126253769215576 -2.20612699980434 Winsorized Mean ( 107 / 120 ) -0.0281542432362148 0.0125805821078181 -2.23791260173236 Winsorized Mean ( 108 / 120 ) -0.0237817965687193 0.0121201137786842 -1.96217601608201 Winsorized Mean ( 109 / 120 ) -0.0254519385893212 0.0120010435751949 -2.12081044701214 Winsorized Mean ( 110 / 120 ) -0.0329441078575590 0.0115120385897179 -2.86170929682111 Winsorized Mean ( 111 / 120 ) -0.0397838245912781 0.0110446918293439 -3.60207647311437 Winsorized Mean ( 112 / 120 ) -0.0407278537772378 0.0108242910354426 -3.76263476692195 Winsorized Mean ( 113 / 120 ) -0.0407600293154675 0.0106797204852519 -3.81658203243753 Winsorized Mean ( 114 / 120 ) -0.0413336995746145 0.0105653172357428 -3.91220619810462 Winsorized Mean ( 115 / 120 ) -0.0450629275907294 0.0103157000786235 -4.36838287729109 Winsorized Mean ( 116 / 120 ) -0.0449910170095247 0.0102714161362091 -4.38021558204822 Winsorized Mean ( 117 / 120 ) -0.0448708352073836 0.0102199325687840 -4.39052165025413 Winsorized Mean ( 118 / 120 ) -0.0475466235666028 0.0100259764374826 -4.74234343787679 Winsorized Mean ( 119 / 120 ) -0.0484495591736582 0.0099338023123208 -4.87724213250818 Winsorized Mean ( 120 / 120 ) -0.0481536253613849 0.00990504927212141 -4.86152305137111 Trimmed Mean ( 1 / 120 ) -0.0100749496699398 0.027363394959602 -0.368190777672651 Trimmed Mean ( 2 / 120 ) -0.0111094960299488 0.0268376295664438 -0.413952208500538 Trimmed Mean ( 3 / 120 ) -0.012036701725413 0.0264268626990128 -0.455472216377112 Trimmed Mean ( 4 / 120 ) -0.0130657099067083 0.0260153953408259 -0.502229919458665 Trimmed Mean ( 5 / 120 ) -0.0139114618916552 0.0256549325590540 -0.542252912169346 Trimmed Mean ( 6 / 120 ) -0.0143860113038124 0.0253407343203152 -0.567703016099237 Trimmed Mean ( 7 / 120 ) -0.0147950686482365 0.0250262162111494 -0.591182803001804 Trimmed Mean ( 8 / 120 ) -0.0150696199186039 0.0247227587048563 -0.609544432258032 Trimmed Mean ( 9 / 120 ) -0.0154231771640397 0.0244619054568711 -0.630497783225938 Trimmed Mean ( 10 / 120 ) -0.0157695041474747 0.0242180690140059 -0.651146222201067 Trimmed Mean ( 11 / 120 ) -0.0160472473885767 0.023986982826584 -0.668998160568657 Trimmed Mean ( 12 / 120 ) -0.0162574488259350 0.0237616129260187 -0.684189616106964 Trimmed Mean ( 13 / 120 ) -0.0162574488259350 0.0235371991193252 -0.69071297496 Trimmed Mean ( 14 / 120 ) -0.0167955091798711 0.0233166414836746 -0.720322830010948 Trimmed Mean ( 15 / 120 ) -0.0169162697923198 0.0231154713157894 -0.731815915030247 Trimmed Mean ( 16 / 120 ) -0.0171239635531134 0.0229205961410895 -0.747099396878927 Trimmed Mean ( 17 / 120 ) -0.0172668348554182 0.0227374336582833 -0.759401219808634 Trimmed Mean ( 18 / 120 ) -0.0174102825244703 0.0225549361426268 -0.771905644705704 Trimmed Mean ( 19 / 120 ) -0.0175224516454382 0.0223708943514918 -0.783270054836665 Trimmed Mean ( 20 / 120 ) -0.0176655778743059 0.0221840719824488 -0.796318092020357 Trimmed Mean ( 21 / 120 ) -0.0177921868622313 0.0219954845596499 -0.808901791364514 Trimmed Mean ( 22 / 120 ) -0.0179910697689629 0.0218106433344375 -0.824875703714628 Trimmed Mean ( 23 / 120 ) -0.0182172889227025 0.0216263798649146 -0.842364234628891 Trimmed Mean ( 24 / 120 ) -0.0183792127913666 0.0214435964827632 -0.857095627878478 Trimmed Mean ( 25 / 120 ) -0.0186526806819332 0.0212698720992462 -0.876953119177159 Trimmed Mean ( 26 / 120 ) -0.0186526806819332 0.0210919173086229 -0.884352067619165 Trimmed Mean ( 27 / 120 ) -0.0193504332116196 0.0209196544437346 -0.924988185807006 Trimmed Mean ( 28 / 120 ) -0.0197592906301417 0.020747694003921 -0.952360808213553 Trimmed Mean ( 29 / 120 ) -0.0201199448910086 0.0205780333721446 -0.977738957224353 Trimmed Mean ( 30 / 120 ) -0.0203858933244582 0.0204171320275716 -0.998469975946123 Trimmed Mean ( 31 / 120 ) -0.0205796874596299 0.0202697368176697 -1.01529130075779 Trimmed Mean ( 32 / 120 ) -0.0207845422463207 0.0201181200329547 -1.03312547157858 Trimmed Mean ( 33 / 120 ) -0.0209297793913754 0.0199681279003398 -1.04815932148648 Trimmed Mean ( 34 / 120 ) -0.021081159097728 0.0198162035392559 -1.06383440480747 Trimmed Mean ( 35 / 120 ) -0.0213035188305313 0.0196680281892048 -1.08315478428204 Trimmed Mean ( 36 / 120 ) -0.0215474179261885 0.0195322144091354 -1.10317332560667 Trimmed Mean ( 37 / 120 ) -0.0218889489165838 0.0194146759061997 -1.12744343620972 Trimmed Mean ( 38 / 120 ) -0.0222371176212268 0.0192929574966825 -1.15260284096155 Trimmed Mean ( 39 / 120 ) -0.0225825345768406 0.0191705369023304 -1.17798133103385 Trimmed Mean ( 40 / 120 ) -0.0228983091992677 0.0190501012706510 -1.20200459167875 Trimmed Mean ( 41 / 120 ) -0.0232319423699724 0.0189409656105826 -1.22654477325023 Trimmed Mean ( 42 / 120 ) -0.0235487329629957 0.0188338200566407 -1.25034288806919 Trimmed Mean ( 43 / 120 ) -0.0238736209813844 0.0187249486777853 -1.27496322645238 Trimmed Mean ( 44 / 120 ) -0.0241961641190629 0.0186162891193705 -1.29973078758679 Trimmed Mean ( 45 / 120 ) -0.0245091707502803 0.0185059685826054 -1.32439275690317 Trimmed Mean ( 46 / 120 ) -0.0248221129396000 0.0183956114344461 -1.34934970919859 Trimmed Mean ( 47 / 120 ) -0.0251468562615571 0.0182813390798890 -1.37554782785145 Trimmed Mean ( 48 / 120 ) -0.0254576843798865 0.01816691213152 -1.40132149016766 Trimmed Mean ( 49 / 120 ) -0.0254576843798865 0.0180485974936996 -1.41050762469346 Trimmed Mean ( 50 / 120 ) -0.0261157129457313 0.0179333394097087 -1.45626602770886 Trimmed Mean ( 51 / 120 ) -0.0264205883135857 0.0178266985347068 -1.48207971667595 Trimmed Mean ( 52 / 120 ) -0.0264205883135857 0.0177202737713501 -1.49098081973780 Trimmed Mean ( 53 / 120 ) -0.0271361422655616 0.0176124289184106 -1.54073821340994 Trimmed Mean ( 54 / 120 ) -0.0275159505887832 0.0175023374583299 -1.57213004573212 Trimmed Mean ( 55 / 120 ) -0.0278969773517388 0.0173944249527689 -1.60378842229550 Trimmed Mean ( 56 / 120 ) -0.0282663443136141 0.0172848969697433 -1.63532038189718 Trimmed Mean ( 57 / 120 ) -0.0286866182486012 0.0171757681412935 -1.67017963986331 Trimmed Mean ( 58 / 120 ) -0.0291193545744945 0.0170679075114463 -1.70608813968356 Trimmed Mean ( 59 / 120 ) -0.029508878000565 0.0169620483571323 -1.73970014583510 Trimmed Mean ( 60 / 120 ) -0.0298970086199502 0.0168578816829145 -1.77347362986009 Trimmed Mean ( 61 / 120 ) -0.0302673313404230 0.0167544952380256 -1.80652003599184 Trimmed Mean ( 62 / 120 ) -0.0306429173281634 0.0166466697395208 -1.84078364067104 Trimmed Mean ( 63 / 120 ) -0.0306429173281634 0.0165377197533795 -1.85291066635117 Trimmed Mean ( 64 / 120 ) -0.0313925366823340 0.016435457596267 -1.91004944635458 Trimmed Mean ( 65 / 120 ) -0.031689448450198 0.0163390170936824 -1.93949539733642 Trimmed Mean ( 66 / 120 ) -0.0320560758040024 0.0162460093101393 -1.97316615988863 Trimmed Mean ( 67 / 120 ) -0.0324515362881539 0.0161528155797226 -2.00903279852287 Trimmed Mean ( 68 / 120 ) -0.0328561093579381 0.0160614706226663 -2.04564763276228 Trimmed Mean ( 69 / 120 ) -0.0332738993001201 0.0159669185478210 -2.08392741532843 Trimmed Mean ( 70 / 120 ) -0.0336390519956715 0.0158755924107358 -2.11891632925291 Trimmed Mean ( 71 / 120 ) -0.0339105161338904 0.015794415887445 -2.14699399936948 Trimmed Mean ( 72 / 120 ) -0.0341768867828488 0.0157134804401353 -2.17500425275322 Trimmed Mean ( 73 / 120 ) -0.0344354760508411 0.0156328482862451 -2.20276404019989 Trimmed Mean ( 74 / 120 ) -0.0347210129865324 0.0155513302772551 -2.23267157005303 Trimmed Mean ( 75 / 120 ) -0.0349087132265666 0.0154819523360450 -2.25480045855020 Trimmed Mean ( 76 / 120 ) -0.0351119899422891 0.0154102663636637 -2.27848040479563 Trimmed Mean ( 77 / 120 ) -0.0353115505531636 0.0153388081014005 -2.30210524310162 Trimmed Mean ( 78 / 120 ) -0.0355234584447976 0.0152657431597375 -2.32700485479728 Trimmed Mean ( 79 / 120 ) -0.0357196450788257 0.0151953697485577 -2.35069272218375 Trimmed Mean ( 80 / 120 ) -0.035926524841593 0.0151265160108019 -2.37506936930736 Trimmed Mean ( 81 / 120 ) -0.0361709412457267 0.0150573912252303 -2.40220505030900 Trimmed Mean ( 82 / 120 ) -0.0363673758098319 0.0149907655897251 -2.42598522351378 Trimmed Mean ( 83 / 120 ) -0.0365750118079506 0.0149220070899183 -2.45107857056720 Trimmed Mean ( 84 / 120 ) -0.0367588055340919 0.0148539347872625 -2.47468472566698 Trimmed Mean ( 85 / 120 ) -0.0369516604199366 0.0147828368372140 -2.49963256896101 Trimmed Mean ( 86 / 120 ) -0.0371524231656479 0.0147072901471165 -2.52612294950419 Trimmed Mean ( 87 / 120 ) -0.0373725593608675 0.0146335156346834 -2.55390162513576 Trimmed Mean ( 88 / 120 ) -0.0375863590918575 0.0145560779466867 -2.58217627231194 Trimmed Mean ( 89 / 120 ) -0.0377869107939032 0.0144771671335172 -2.61010392747486 Trimmed Mean ( 90 / 120 ) -0.0379974065850429 0.0143937793047716 -2.63984918626942 Trimmed Mean ( 91 / 120 ) -0.0381965220944617 0.0143070715766060 -2.66976521994328 Trimmed Mean ( 92 / 120 ) -0.0384109471522973 0.0142168428505367 -2.70179163940377 Trimmed Mean ( 93 / 120 ) -0.0386392332306402 0.0141246263706195 -2.73559329760490 Trimmed Mean ( 94 / 120 ) -0.0389333648757198 0.0140335765074814 -2.77430096703888 Trimmed Mean ( 95 / 120 ) -0.0392165919547654 0.0139410055435291 -2.81303897572642 Trimmed Mean ( 96 / 120 ) -0.0395250375658964 0.0138447068273446 -2.85488440158449 Trimmed Mean ( 97 / 120 ) -0.0398347207706161 0.0137436052396657 -2.89841857911113 Trimmed Mean ( 98 / 120 ) -0.0398347207706161 0.0136381723797032 -2.92082543478477 Trimmed Mean ( 99 / 120 ) -0.0404699735336531 0.0135319110715563 -2.99070643604212 Trimmed Mean ( 100 / 120 ) -0.0408585625113771 0.0134244500081865 -3.04359303259803 Trimmed Mean ( 101 / 120 ) -0.0412439137165852 0.0133211889842135 -3.09611355003385 Trimmed Mean ( 102 / 120 ) -0.0416503818207631 0.0132152315260728 -3.15169520402194 Trimmed Mean ( 103 / 120 ) -0.0420709253190729 0.0131008831296014 -3.21130452831944 Trimmed Mean ( 104 / 120 ) -0.0420709253190729 0.0129867700039044 -3.23952186004868 Trimmed Mean ( 105 / 120 ) -0.0428216953318482 0.0128670424249093 -3.3280138448094 Trimmed Mean ( 106 / 120 ) -0.043192890610278 0.0127416992861267 -3.38988463315149 Trimmed Mean ( 107 / 120 ) -0.043549720156177 0.0126174451220768 -3.4515482124014 Trimmed Mean ( 108 / 120 ) -0.043909427560849 0.0124849876305588 -3.51697805878272 Trimmed Mean ( 109 / 120 ) -0.043909427560849 0.0123672198326614 -3.55046875166605 Trimmed Mean ( 110 / 120 ) -0.0448284857124565 0.0122462778534908 -3.66058048402667 Trimmed Mean ( 111 / 120 ) -0.0451103286655371 0.0121453013964584 -3.71422060210802 Trimmed Mean ( 112 / 120 ) -0.0452373518151617 0.0120632693067231 -3.75000761940631 Trimmed Mean ( 113 / 120 ) -0.0453455220772655 0.0119859933972416 -3.78320933229455 Trimmed Mean ( 114 / 120 ) -0.0454561936644368 0.0119092340246616 -3.81688642361938 Trimmed Mean ( 115 / 120 ) -0.0454561936644368 0.0118312314194673 -3.8420509288359 Trimmed Mean ( 116 / 120 ) -0.0455684022557172 0.0117602278195649 -3.87478907338064 Trimmed Mean ( 117 / 120 ) -0.0455826235671998 0.0116839044173820 -3.90131773924708 Trimmed Mean ( 118 / 120 ) -0.0456002858093789 0.0116022094559553 -3.93031051391446 Trimmed Mean ( 119 / 120 ) -0.0455516138454583 0.0115238572349683 -3.95280962933445 Trimmed Mean ( 120 / 120 ) -0.0454785564002096 0.0114423989596039 -3.97456482340517 Median -0.0416614371759786 Midrange 0.096897998814545 Midmean - Weighted Average at Xnp -0.0397576650988843 Midmean - Weighted Average at X(n+1)p -0.037997406585043 Midmean - Empirical Distribution Function -0.0397576650988843 Midmean - Empirical Distribution Function - Averaging -0.037997406585043 Midmean - Empirical Distribution Function - Interpolation -0.037997406585043 Midmean - Closest Observation -0.0397576650988843 Midmean - True Basic - Statistics Graphics Toolkit -0.037997406585043 Midmean - MS Excel (old versions) -0.0377869107939032 Number of observations 360

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228819103zhpe4lc87xgixx2/1at3e1228819022.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228819103zhpe4lc87xgixx2/1at3e1228819022.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228819103zhpe4lc87xgixx2/2gnkl1228819022.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/09/t1228819103zhpe4lc87xgixx2/2gnkl1228819022.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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