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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 27 Oct 2008 12:16:35 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/27/t12251314393rcmvgjg0pdfwsc.htm/, Retrieved Sun, 19 May 2024 12:58:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19364, Retrieved Sun, 19 May 2024 12:58:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Harrell-Davis Quantiles] [Q5 Distributions] [2007-10-22 09:17:45] [b731da8b544846036771bbf9bf2f34ce]
-   PD  [Harrell-Davis Quantiles] [Reproduce Q5] [2008-10-27 10:38:50] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F   P     [Harrell-Davis Quantiles] [Reproduce 2 Q5] [2008-10-27 10:41:32] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F    D      [Harrell-Davis Quantiles] [Q9 Harrell Davis ...] [2008-10-27 18:14:20] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
- RM            [Central Tendency] [Q9 Central Tenden...] [2008-10-27 18:16:35] [5e9e099b83e50415d7642e10d74756e4] [Current]
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Dataseries X:
0.533479702
0.527755967
0.528426364
0.526282111
0.524451163
0.523287701
0.52320954
0.523797873
0.525131274
0.530389407
0.532850909
0.532795864
0.532164678
0.537001655
0.534327891
0.533272092
0.530979158
0.529839034
0.529391131
0.528616297
0.529232222
0.534305869
0.537227641
0.536979793
0.534726025
0.529197849
0.527250405
0.526651159
0.527829082
0.524790195
0.522531084
0.520700795
0.521012614
0.526459921
0.532250749
0.535439727
0.528484504
0.526048075
0.523058214
0.522925886
0.520075779
0.518677098
0.52000948
0.518266121
0.518515257
0.527992909
0.534436998
0.537730853
0.529844533
0.524459749
0.522557792
0.519492162
0.519190516
0.51722256
0.518738505
0.516392891
0.519440426
0.52502408
0.530764849
0.534599599
0.523175241




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19364&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19364&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5270681806229510.000748143996262312704.500982773578
Geometric Mean0.527036328153348
Harmonic Mean0.527004482724048
Quadratic Mean0.527100038125151
Winsorized Mean ( 1 / 20 )0.5270735323770490.000743104529342391709.285856248894
Winsorized Mean ( 2 / 20 )0.5271003381147540.000734215526708773717.90954963532
Winsorized Mean ( 3 / 20 )0.527111515524590.000731545419258625720.545165956728
Winsorized Mean ( 4 / 20 )0.5270211401147540.000708084152370343744.29167543226
Winsorized Mean ( 5 / 20 )0.5269676733114750.000695859390807035757.290453032926
Winsorized Mean ( 6 / 20 )0.5269996980655740.000684947269412279769.401852667823
Winsorized Mean ( 7 / 20 )0.5270097171311480.000676113213853839779.4696307253
Winsorized Mean ( 8 / 20 )0.5270021930655740.000672239152230491783.950460661179
Winsorized Mean ( 9 / 20 )0.527075269524590.000657704654612583801.385950104094
Winsorized Mean ( 10 / 20 )0.5269507010.000631657153428048834.235309677412
Winsorized Mean ( 11 / 20 )0.5270259709344260.000605164140032712870.881032220346
Winsorized Mean ( 12 / 20 )0.5270044567049180.000580458672045195907.910385502665
Winsorized Mean ( 13 / 20 )0.5273163341639350.0005259200645674021002.65490839883
Winsorized Mean ( 14 / 20 )0.5271973555081970.0005036531008821971046.74696648300
Winsorized Mean ( 15 / 20 )0.5272667054262290.0004864241543088451083.96489104333
Winsorized Mean ( 16 / 20 )0.5269904583442620.0004310064424573971222.69740410285
Winsorized Mean ( 17 / 20 )0.5269633469672130.0004169118151527051263.96836888443
Winsorized Mean ( 18 / 20 )0.5268626818196720.0003987845810421131321.17114569190
Winsorized Mean ( 19 / 20 )0.5267173121967210.000370586108212471421.30884165452
Winsorized Mean ( 20 / 20 )0.5268827787540980.0003449491644037721527.42152503772
Trimmed Mean ( 1 / 20 )0.5270683944745760.000729466381792922722.539664102298
Trimmed Mean ( 2 / 20 )0.5270628960175440.000712572004026576739.662648882128
Trimmed Mean ( 3 / 20 )0.5270421326727270.000697417166638604755.705706547135
Trimmed Mean ( 4 / 20 )0.527015514094340.000679654072248024775.417283017496
Trimmed Mean ( 5 / 20 )0.5270138318039220.000666445486895696790.78310554514
Trimmed Mean ( 6 / 20 )0.527025324326530.000653553869601568806.399210286714
Trimmed Mean ( 7 / 20 )0.5270308675957450.000640110389877516823.343716849513
Trimmed Mean ( 8 / 20 )0.52703496340.000624982581087206843.27944385775
Trimmed Mean ( 9 / 20 )0.5270407744186050.000606038408900716869.649128962957
Trimmed Mean ( 10 / 20 )0.527035071975610.000584917263860516901.042086699788
Trimmed Mean ( 11 / 20 )0.5270482684615390.000563820619790358934.7800523108
Trimmed Mean ( 12 / 20 )0.5270516103513510.000542552386380654971.42989982459
Trimmed Mean ( 13 / 20 )0.5270584588571430.0005201718003056571013.23920010166
Trimmed Mean ( 14 / 20 )0.5270217912727270.00050427091217241045.11638199062
Trimmed Mean ( 15 / 20 )0.5269971151935480.0004877435215616831080.47998978271
Trimmed Mean ( 16 / 20 )0.5269593105862070.0004680968725537811125.74841124507
Trimmed Mean ( 17 / 20 )0.5269549124074070.0004568922516136361153.34613477538
Trimmed Mean ( 18 / 20 )0.52695370180.0004429847671225421189.55264584579
Trimmed Mean ( 19 / 20 )0.5269671129565220.0004262028961047771236.42311624972
Trimmed Mean ( 20 / 20 )0.5270053030476190.0004084409999338191290.28501823522
Median0.527250405
Midrange0.527061872
Midmean - Weighted Average at Xnp0.5268248631
Midmean - Weighted Average at X(n+1)p0.526997115193548
Midmean - Empirical Distribution Function0.526997115193548
Midmean - Empirical Distribution Function - Averaging0.526997115193548
Midmean - Empirical Distribution Function - Interpolation0.526997115193548
Midmean - Closest Observation0.52685838634375
Midmean - True Basic - Statistics Graphics Toolkit0.526997115193548
Midmean - MS Excel (old versions)0.526997115193548
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.527068180622951 & 0.000748143996262312 & 704.500982773578 \tabularnewline
Geometric Mean & 0.527036328153348 &  &  \tabularnewline
Harmonic Mean & 0.527004482724048 &  &  \tabularnewline
Quadratic Mean & 0.527100038125151 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.527073532377049 & 0.000743104529342391 & 709.285856248894 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.527100338114754 & 0.000734215526708773 & 717.90954963532 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.52711151552459 & 0.000731545419258625 & 720.545165956728 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.527021140114754 & 0.000708084152370343 & 744.29167543226 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.526967673311475 & 0.000695859390807035 & 757.290453032926 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.526999698065574 & 0.000684947269412279 & 769.401852667823 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.527009717131148 & 0.000676113213853839 & 779.4696307253 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.527002193065574 & 0.000672239152230491 & 783.950460661179 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.52707526952459 & 0.000657704654612583 & 801.385950104094 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.526950701 & 0.000631657153428048 & 834.235309677412 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.527025970934426 & 0.000605164140032712 & 870.881032220346 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.527004456704918 & 0.000580458672045195 & 907.910385502665 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.527316334163935 & 0.000525920064567402 & 1002.65490839883 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.527197355508197 & 0.000503653100882197 & 1046.74696648300 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.527266705426229 & 0.000486424154308845 & 1083.96489104333 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.526990458344262 & 0.000431006442457397 & 1222.69740410285 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.526963346967213 & 0.000416911815152705 & 1263.96836888443 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.526862681819672 & 0.000398784581042113 & 1321.17114569190 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.526717312196721 & 0.00037058610821247 & 1421.30884165452 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.526882778754098 & 0.000344949164403772 & 1527.42152503772 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.527068394474576 & 0.000729466381792922 & 722.539664102298 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.527062896017544 & 0.000712572004026576 & 739.662648882128 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.527042132672727 & 0.000697417166638604 & 755.705706547135 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.52701551409434 & 0.000679654072248024 & 775.417283017496 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.527013831803922 & 0.000666445486895696 & 790.78310554514 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.52702532432653 & 0.000653553869601568 & 806.399210286714 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.527030867595745 & 0.000640110389877516 & 823.343716849513 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.5270349634 & 0.000624982581087206 & 843.27944385775 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.527040774418605 & 0.000606038408900716 & 869.649128962957 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.52703507197561 & 0.000584917263860516 & 901.042086699788 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.527048268461539 & 0.000563820619790358 & 934.7800523108 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.527051610351351 & 0.000542552386380654 & 971.42989982459 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.527058458857143 & 0.000520171800305657 & 1013.23920010166 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.527021791272727 & 0.0005042709121724 & 1045.11638199062 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.526997115193548 & 0.000487743521561683 & 1080.47998978271 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.526959310586207 & 0.000468096872553781 & 1125.74841124507 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.526954912407407 & 0.000456892251613636 & 1153.34613477538 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.5269537018 & 0.000442984767122542 & 1189.55264584579 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.526967112956522 & 0.000426202896104777 & 1236.42311624972 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.527005303047619 & 0.000408440999933819 & 1290.28501823522 \tabularnewline
Median & 0.527250405 &  &  \tabularnewline
Midrange & 0.527061872 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.5268248631 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.526997115193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.526997115193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.526997115193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.526997115193548 &  &  \tabularnewline
Midmean - Closest Observation & 0.52685838634375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.526997115193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.526997115193548 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19364&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.527068180622951[/C][C]0.000748143996262312[/C][C]704.500982773578[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.527036328153348[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.527004482724048[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.527100038125151[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.527073532377049[/C][C]0.000743104529342391[/C][C]709.285856248894[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.527100338114754[/C][C]0.000734215526708773[/C][C]717.90954963532[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.52711151552459[/C][C]0.000731545419258625[/C][C]720.545165956728[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.527021140114754[/C][C]0.000708084152370343[/C][C]744.29167543226[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.526967673311475[/C][C]0.000695859390807035[/C][C]757.290453032926[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.526999698065574[/C][C]0.000684947269412279[/C][C]769.401852667823[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.527009717131148[/C][C]0.000676113213853839[/C][C]779.4696307253[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.527002193065574[/C][C]0.000672239152230491[/C][C]783.950460661179[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.52707526952459[/C][C]0.000657704654612583[/C][C]801.385950104094[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.526950701[/C][C]0.000631657153428048[/C][C]834.235309677412[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.527025970934426[/C][C]0.000605164140032712[/C][C]870.881032220346[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.527004456704918[/C][C]0.000580458672045195[/C][C]907.910385502665[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.527316334163935[/C][C]0.000525920064567402[/C][C]1002.65490839883[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.527197355508197[/C][C]0.000503653100882197[/C][C]1046.74696648300[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.527266705426229[/C][C]0.000486424154308845[/C][C]1083.96489104333[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.526990458344262[/C][C]0.000431006442457397[/C][C]1222.69740410285[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.526963346967213[/C][C]0.000416911815152705[/C][C]1263.96836888443[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.526862681819672[/C][C]0.000398784581042113[/C][C]1321.17114569190[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.526717312196721[/C][C]0.00037058610821247[/C][C]1421.30884165452[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.526882778754098[/C][C]0.000344949164403772[/C][C]1527.42152503772[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.527068394474576[/C][C]0.000729466381792922[/C][C]722.539664102298[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.527062896017544[/C][C]0.000712572004026576[/C][C]739.662648882128[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.527042132672727[/C][C]0.000697417166638604[/C][C]755.705706547135[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.52701551409434[/C][C]0.000679654072248024[/C][C]775.417283017496[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.527013831803922[/C][C]0.000666445486895696[/C][C]790.78310554514[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.52702532432653[/C][C]0.000653553869601568[/C][C]806.399210286714[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.527030867595745[/C][C]0.000640110389877516[/C][C]823.343716849513[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.5270349634[/C][C]0.000624982581087206[/C][C]843.27944385775[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.527040774418605[/C][C]0.000606038408900716[/C][C]869.649128962957[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.52703507197561[/C][C]0.000584917263860516[/C][C]901.042086699788[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.527048268461539[/C][C]0.000563820619790358[/C][C]934.7800523108[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.527051610351351[/C][C]0.000542552386380654[/C][C]971.42989982459[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.527058458857143[/C][C]0.000520171800305657[/C][C]1013.23920010166[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.527021791272727[/C][C]0.0005042709121724[/C][C]1045.11638199062[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.526997115193548[/C][C]0.000487743521561683[/C][C]1080.47998978271[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.526959310586207[/C][C]0.000468096872553781[/C][C]1125.74841124507[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.526954912407407[/C][C]0.000456892251613636[/C][C]1153.34613477538[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.5269537018[/C][C]0.000442984767122542[/C][C]1189.55264584579[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.526967112956522[/C][C]0.000426202896104777[/C][C]1236.42311624972[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.527005303047619[/C][C]0.000408440999933819[/C][C]1290.28501823522[/C][/ROW]
[ROW][C]Median[/C][C]0.527250405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.527061872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.5268248631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.52685838634375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.526997115193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19364&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5270681806229510.000748143996262312704.500982773578
Geometric Mean0.527036328153348
Harmonic Mean0.527004482724048
Quadratic Mean0.527100038125151
Winsorized Mean ( 1 / 20 )0.5270735323770490.000743104529342391709.285856248894
Winsorized Mean ( 2 / 20 )0.5271003381147540.000734215526708773717.90954963532
Winsorized Mean ( 3 / 20 )0.527111515524590.000731545419258625720.545165956728
Winsorized Mean ( 4 / 20 )0.5270211401147540.000708084152370343744.29167543226
Winsorized Mean ( 5 / 20 )0.5269676733114750.000695859390807035757.290453032926
Winsorized Mean ( 6 / 20 )0.5269996980655740.000684947269412279769.401852667823
Winsorized Mean ( 7 / 20 )0.5270097171311480.000676113213853839779.4696307253
Winsorized Mean ( 8 / 20 )0.5270021930655740.000672239152230491783.950460661179
Winsorized Mean ( 9 / 20 )0.527075269524590.000657704654612583801.385950104094
Winsorized Mean ( 10 / 20 )0.5269507010.000631657153428048834.235309677412
Winsorized Mean ( 11 / 20 )0.5270259709344260.000605164140032712870.881032220346
Winsorized Mean ( 12 / 20 )0.5270044567049180.000580458672045195907.910385502665
Winsorized Mean ( 13 / 20 )0.5273163341639350.0005259200645674021002.65490839883
Winsorized Mean ( 14 / 20 )0.5271973555081970.0005036531008821971046.74696648300
Winsorized Mean ( 15 / 20 )0.5272667054262290.0004864241543088451083.96489104333
Winsorized Mean ( 16 / 20 )0.5269904583442620.0004310064424573971222.69740410285
Winsorized Mean ( 17 / 20 )0.5269633469672130.0004169118151527051263.96836888443
Winsorized Mean ( 18 / 20 )0.5268626818196720.0003987845810421131321.17114569190
Winsorized Mean ( 19 / 20 )0.5267173121967210.000370586108212471421.30884165452
Winsorized Mean ( 20 / 20 )0.5268827787540980.0003449491644037721527.42152503772
Trimmed Mean ( 1 / 20 )0.5270683944745760.000729466381792922722.539664102298
Trimmed Mean ( 2 / 20 )0.5270628960175440.000712572004026576739.662648882128
Trimmed Mean ( 3 / 20 )0.5270421326727270.000697417166638604755.705706547135
Trimmed Mean ( 4 / 20 )0.527015514094340.000679654072248024775.417283017496
Trimmed Mean ( 5 / 20 )0.5270138318039220.000666445486895696790.78310554514
Trimmed Mean ( 6 / 20 )0.527025324326530.000653553869601568806.399210286714
Trimmed Mean ( 7 / 20 )0.5270308675957450.000640110389877516823.343716849513
Trimmed Mean ( 8 / 20 )0.52703496340.000624982581087206843.27944385775
Trimmed Mean ( 9 / 20 )0.5270407744186050.000606038408900716869.649128962957
Trimmed Mean ( 10 / 20 )0.527035071975610.000584917263860516901.042086699788
Trimmed Mean ( 11 / 20 )0.5270482684615390.000563820619790358934.7800523108
Trimmed Mean ( 12 / 20 )0.5270516103513510.000542552386380654971.42989982459
Trimmed Mean ( 13 / 20 )0.5270584588571430.0005201718003056571013.23920010166
Trimmed Mean ( 14 / 20 )0.5270217912727270.00050427091217241045.11638199062
Trimmed Mean ( 15 / 20 )0.5269971151935480.0004877435215616831080.47998978271
Trimmed Mean ( 16 / 20 )0.5269593105862070.0004680968725537811125.74841124507
Trimmed Mean ( 17 / 20 )0.5269549124074070.0004568922516136361153.34613477538
Trimmed Mean ( 18 / 20 )0.52695370180.0004429847671225421189.55264584579
Trimmed Mean ( 19 / 20 )0.5269671129565220.0004262028961047771236.42311624972
Trimmed Mean ( 20 / 20 )0.5270053030476190.0004084409999338191290.28501823522
Median0.527250405
Midrange0.527061872
Midmean - Weighted Average at Xnp0.5268248631
Midmean - Weighted Average at X(n+1)p0.526997115193548
Midmean - Empirical Distribution Function0.526997115193548
Midmean - Empirical Distribution Function - Averaging0.526997115193548
Midmean - Empirical Distribution Function - Interpolation0.526997115193548
Midmean - Closest Observation0.52685838634375
Midmean - True Basic - Statistics Graphics Toolkit0.526997115193548
Midmean - MS Excel (old versions)0.526997115193548
Number of observations61



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
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('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('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('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('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('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('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('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('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('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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')