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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Dec 2007 14:41:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t119680377335yhgb539vxsqui.htm/, Retrieved Thu, 02 May 2024 03:29:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2455, Retrieved Thu, 02 May 2024 03:29:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Variance reductio...] [2007-11-30 14:45:44] [6c50c82828af94f83a614a64264ea782]
- RMPD    [Central Tendency] [Residuals - niet ...] [2007-12-04 21:41:41] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
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Dataseries X:
0.108397535296452 
6.88213944030765 
1.13142671384286 
0.568429643989868 
7.82742281451333 
-15.2979948018352 
0.659568031942231 
-2.48486689008790 
3.73313678733907 
3.18702415540184 
7.32489610404771 
-0.826443362738051 
3.58457657151601 
-2.42080838535725 
-3.95682304806516 
4.70539387134873 
3.53848256216961 
3.77975438112004 
-3.10333309031763 
-3.27846831327734 
0.537515719740319 
6.68876613008393 
-3.16186838952486 
-8.81909606143759 
-0.462228463730614 
4.14441902897876 
-0.24601163222917 
1.8364073572271 
-5.42672265668867 
-3.24644815524683 
4.87556642116095 
12.7968770579264 
-4.87312764178992 
8.62556294682243 
-1.57473735930230 
-0.453717351025394 
1.19829356320731 
-3.92351593729743 
4.25933700214477 
4.24932490944296 
-0.959648967110727 
-1.33019447782621 
-5.69289271381884 
-0.470982235059333 
-2.06183336497025 
5.0823465628746 
-1.73006651968059 
0.187291309316967 
-1.47555961388836 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2455&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2455&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.4945911671317610.6921074862537180.71461612098565
Geometric MeanNaN
Harmonic Mean7.90789351218751
Quadratic Mean4.82050137475034
Winsorized Mean ( 1 / 16 )0.5416847309948960.6112031010730010.886259788348487
Winsorized Mean ( 2 / 16 )0.6367077193748820.5670028218145391.12293571544718
Winsorized Mean ( 3 / 16 )0.6222369038645480.5553235991876771.12049425735688
Winsorized Mean ( 4 / 16 )0.6312849325305640.536426232571931.17683456587093
Winsorized Mean ( 5 / 16 )0.7050534308469960.5127577407452291.37502250053269
Winsorized Mean ( 6 / 16 )0.5124274157725150.4678660126643841.09524394143179
Winsorized Mean ( 7 / 16 )0.5750370561020060.4444385494634171.29385053748435
Winsorized Mean ( 8 / 16 )0.5524815635662170.4379488275959751.26152081876539
Winsorized Mean ( 9 / 16 )0.4860878098654430.4193569386377171.15912666532835
Winsorized Mean ( 10 / 16 )0.4959905050706310.4168167265700231.18994865957546
Winsorized Mean ( 11 / 16 )0.6112795564465660.3883228749770021.57415283990872
Winsorized Mean ( 12 / 16 )0.5376617254764270.3690667705724651.45681423619485
Winsorized Mean ( 13 / 16 )0.6205320631474140.3512559489689771.76660940538895
Winsorized Mean ( 14 / 16 )0.6728768144235860.3286503405341032.04739424073033
Winsorized Mean ( 15 / 16 )0.7063161463721230.3188769049860292.21501192255698
Winsorized Mean ( 16 / 16 )0.623938787562710.2929635669649162.12974873984051
Trimmed Mean ( 1 / 16 )0.4945911671317610.5793337410748440.853724083486215
Trimmed Mean ( 2 / 16 )0.5688528709226610.5377390429566181.05786045922009
Trimmed Mean ( 3 / 16 )0.5766299522624590.5159063335495781.11770279751188
Trimmed Mean ( 4 / 16 )0.5766299522624590.4933032662001621.16891573961014
Trimmed Mean ( 5 / 16 )0.5355872487540760.4715806217226551.13572785666554
Trimmed Mean ( 6 / 16 )0.490701611334870.4514420752480141.08696472535328
Trimmed Mean ( 7 / 16 )0.4856322569660870.4404849413570881.10249457216382
Trimmed Mean ( 8 / 16 )0.4856322569660870.432400219104441.12310825829806
Trimmed Mean ( 9 / 16 )0.4497124248331460.4220754223742561.06547882438505
Trimmed Mean ( 10 / 16 )0.4428833295588830.4124288533388521.07384176924937
Trimmed Mean ( 11 / 16 )0.4332453606697140.3977358669170571.08927908369919
Trimmed Mean ( 12 / 16 )0.4015229039676570.3845749050605441.04406943532742
Trimmed Mean ( 13 / 16 )0.3773533305838540.3702025854727181.01931576221167
Trimmed Mean ( 14 / 16 )0.3337058657647530.3521916260118260.947512209599067
Trimmed Mean ( 15 / 16 )0.2712270068012840.3297831559788020.822440448773914
Trimmed Mean ( 16 / 16 )0.2712270068012840.2907489010176390.932856515886984
Median0.108397535296452
Midrange-1.2505588719544
Midmean - Weighted Average at Xnp0.260763259086308
Midmean - Weighted Average at X(n+1)p0.401522903967657
Midmean - Empirical Distribution Function0.401522903967657
Midmean - Empirical Distribution Function - Averaging0.401522903967657
Midmean - Empirical Distribution Function - Interpolation0.401522903967657
Midmean - Closest Observation0.290507911888597
Midmean - True Basic - Statistics Graphics Toolkit0.401522903967657
Midmean - MS Excel (old versions)0.401522903967657
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.494591167131761 & 0.692107486253718 & 0.71461612098565 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 7.90789351218751 &  &  \tabularnewline
Quadratic Mean & 4.82050137475034 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.541684730994896 & 0.611203101073001 & 0.886259788348487 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.636707719374882 & 0.567002821814539 & 1.12293571544718 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.622236903864548 & 0.555323599187677 & 1.12049425735688 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.631284932530564 & 0.53642623257193 & 1.17683456587093 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.705053430846996 & 0.512757740745229 & 1.37502250053269 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.512427415772515 & 0.467866012664384 & 1.09524394143179 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.575037056102006 & 0.444438549463417 & 1.29385053748435 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.552481563566217 & 0.437948827595975 & 1.26152081876539 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.486087809865443 & 0.419356938637717 & 1.15912666532835 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.495990505070631 & 0.416816726570023 & 1.18994865957546 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.611279556446566 & 0.388322874977002 & 1.57415283990872 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.537661725476427 & 0.369066770572465 & 1.45681423619485 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.620532063147414 & 0.351255948968977 & 1.76660940538895 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.672876814423586 & 0.328650340534103 & 2.04739424073033 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.706316146372123 & 0.318876904986029 & 2.21501192255698 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.62393878756271 & 0.292963566964916 & 2.12974873984051 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.494591167131761 & 0.579333741074844 & 0.853724083486215 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.568852870922661 & 0.537739042956618 & 1.05786045922009 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.576629952262459 & 0.515906333549578 & 1.11770279751188 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.576629952262459 & 0.493303266200162 & 1.16891573961014 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.535587248754076 & 0.471580621722655 & 1.13572785666554 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.49070161133487 & 0.451442075248014 & 1.08696472535328 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.485632256966087 & 0.440484941357088 & 1.10249457216382 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.485632256966087 & 0.43240021910444 & 1.12310825829806 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.449712424833146 & 0.422075422374256 & 1.06547882438505 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.442883329558883 & 0.412428853338852 & 1.07384176924937 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.433245360669714 & 0.397735866917057 & 1.08927908369919 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.401522903967657 & 0.384574905060544 & 1.04406943532742 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.377353330583854 & 0.370202585472718 & 1.01931576221167 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.333705865764753 & 0.352191626011826 & 0.947512209599067 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.271227006801284 & 0.329783155978802 & 0.822440448773914 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.271227006801284 & 0.290748901017639 & 0.932856515886984 \tabularnewline
Median & 0.108397535296452 &  &  \tabularnewline
Midrange & -1.2505588719544 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.260763259086308 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.401522903967657 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.401522903967657 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.401522903967657 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.401522903967657 &  &  \tabularnewline
Midmean - Closest Observation & 0.290507911888597 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.401522903967657 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.401522903967657 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2455&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]0.494591167131761[/C][C]0.692107486253718[/C][C]0.71461612098565[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.90789351218751[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.82050137475034[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.541684730994896[/C][C]0.611203101073001[/C][C]0.886259788348487[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.636707719374882[/C][C]0.567002821814539[/C][C]1.12293571544718[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.622236903864548[/C][C]0.555323599187677[/C][C]1.12049425735688[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.631284932530564[/C][C]0.53642623257193[/C][C]1.17683456587093[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.705053430846996[/C][C]0.512757740745229[/C][C]1.37502250053269[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.512427415772515[/C][C]0.467866012664384[/C][C]1.09524394143179[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.575037056102006[/C][C]0.444438549463417[/C][C]1.29385053748435[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.552481563566217[/C][C]0.437948827595975[/C][C]1.26152081876539[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.486087809865443[/C][C]0.419356938637717[/C][C]1.15912666532835[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.495990505070631[/C][C]0.416816726570023[/C][C]1.18994865957546[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.611279556446566[/C][C]0.388322874977002[/C][C]1.57415283990872[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.537661725476427[/C][C]0.369066770572465[/C][C]1.45681423619485[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.620532063147414[/C][C]0.351255948968977[/C][C]1.76660940538895[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.672876814423586[/C][C]0.328650340534103[/C][C]2.04739424073033[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.706316146372123[/C][C]0.318876904986029[/C][C]2.21501192255698[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.62393878756271[/C][C]0.292963566964916[/C][C]2.12974873984051[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.494591167131761[/C][C]0.579333741074844[/C][C]0.853724083486215[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.568852870922661[/C][C]0.537739042956618[/C][C]1.05786045922009[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.576629952262459[/C][C]0.515906333549578[/C][C]1.11770279751188[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.576629952262459[/C][C]0.493303266200162[/C][C]1.16891573961014[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.535587248754076[/C][C]0.471580621722655[/C][C]1.13572785666554[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.49070161133487[/C][C]0.451442075248014[/C][C]1.08696472535328[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.485632256966087[/C][C]0.440484941357088[/C][C]1.10249457216382[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.485632256966087[/C][C]0.43240021910444[/C][C]1.12310825829806[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.449712424833146[/C][C]0.422075422374256[/C][C]1.06547882438505[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.442883329558883[/C][C]0.412428853338852[/C][C]1.07384176924937[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.433245360669714[/C][C]0.397735866917057[/C][C]1.08927908369919[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.401522903967657[/C][C]0.384574905060544[/C][C]1.04406943532742[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.377353330583854[/C][C]0.370202585472718[/C][C]1.01931576221167[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.333705865764753[/C][C]0.352191626011826[/C][C]0.947512209599067[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.271227006801284[/C][C]0.329783155978802[/C][C]0.822440448773914[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.271227006801284[/C][C]0.290748901017639[/C][C]0.932856515886984[/C][/ROW]
[ROW][C]Median[/C][C]0.108397535296452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.2505588719544[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.260763259086308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.290507911888597[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.401522903967657[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2455&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 Mean0.4945911671317610.6921074862537180.71461612098565
Geometric MeanNaN
Harmonic Mean7.90789351218751
Quadratic Mean4.82050137475034
Winsorized Mean ( 1 / 16 )0.5416847309948960.6112031010730010.886259788348487
Winsorized Mean ( 2 / 16 )0.6367077193748820.5670028218145391.12293571544718
Winsorized Mean ( 3 / 16 )0.6222369038645480.5553235991876771.12049425735688
Winsorized Mean ( 4 / 16 )0.6312849325305640.536426232571931.17683456587093
Winsorized Mean ( 5 / 16 )0.7050534308469960.5127577407452291.37502250053269
Winsorized Mean ( 6 / 16 )0.5124274157725150.4678660126643841.09524394143179
Winsorized Mean ( 7 / 16 )0.5750370561020060.4444385494634171.29385053748435
Winsorized Mean ( 8 / 16 )0.5524815635662170.4379488275959751.26152081876539
Winsorized Mean ( 9 / 16 )0.4860878098654430.4193569386377171.15912666532835
Winsorized Mean ( 10 / 16 )0.4959905050706310.4168167265700231.18994865957546
Winsorized Mean ( 11 / 16 )0.6112795564465660.3883228749770021.57415283990872
Winsorized Mean ( 12 / 16 )0.5376617254764270.3690667705724651.45681423619485
Winsorized Mean ( 13 / 16 )0.6205320631474140.3512559489689771.76660940538895
Winsorized Mean ( 14 / 16 )0.6728768144235860.3286503405341032.04739424073033
Winsorized Mean ( 15 / 16 )0.7063161463721230.3188769049860292.21501192255698
Winsorized Mean ( 16 / 16 )0.623938787562710.2929635669649162.12974873984051
Trimmed Mean ( 1 / 16 )0.4945911671317610.5793337410748440.853724083486215
Trimmed Mean ( 2 / 16 )0.5688528709226610.5377390429566181.05786045922009
Trimmed Mean ( 3 / 16 )0.5766299522624590.5159063335495781.11770279751188
Trimmed Mean ( 4 / 16 )0.5766299522624590.4933032662001621.16891573961014
Trimmed Mean ( 5 / 16 )0.5355872487540760.4715806217226551.13572785666554
Trimmed Mean ( 6 / 16 )0.490701611334870.4514420752480141.08696472535328
Trimmed Mean ( 7 / 16 )0.4856322569660870.4404849413570881.10249457216382
Trimmed Mean ( 8 / 16 )0.4856322569660870.432400219104441.12310825829806
Trimmed Mean ( 9 / 16 )0.4497124248331460.4220754223742561.06547882438505
Trimmed Mean ( 10 / 16 )0.4428833295588830.4124288533388521.07384176924937
Trimmed Mean ( 11 / 16 )0.4332453606697140.3977358669170571.08927908369919
Trimmed Mean ( 12 / 16 )0.4015229039676570.3845749050605441.04406943532742
Trimmed Mean ( 13 / 16 )0.3773533305838540.3702025854727181.01931576221167
Trimmed Mean ( 14 / 16 )0.3337058657647530.3521916260118260.947512209599067
Trimmed Mean ( 15 / 16 )0.2712270068012840.3297831559788020.822440448773914
Trimmed Mean ( 16 / 16 )0.2712270068012840.2907489010176390.932856515886984
Median0.108397535296452
Midrange-1.2505588719544
Midmean - Weighted Average at Xnp0.260763259086308
Midmean - Weighted Average at X(n+1)p0.401522903967657
Midmean - Empirical Distribution Function0.401522903967657
Midmean - Empirical Distribution Function - Averaging0.401522903967657
Midmean - Empirical Distribution Function - Interpolation0.401522903967657
Midmean - Closest Observation0.290507911888597
Midmean - True Basic - Statistics Graphics Toolkit0.401522903967657
Midmean - MS Excel (old versions)0.401522903967657
Number of observations49



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('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')