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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 computationFri, 30 Nov 2007 07:59:20 -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/Nov/30/t1196434165x39674hn61lv32f.htm/, Retrieved Sat, 27 Apr 2024 14:40:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7723, Retrieved Sat, 27 Apr 2024 14:40:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-30 14:59:20] [48e0b7671e607713e2c1c3706de6df4e] [Current]
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Dataseries X:
0.0737989090370497 
-1.73056884000632 
-4.26690966722568 
-1.87190665644042 
8.09310693639853 
2.28202560313572 
-1.52423810324954 
9.65087813151564 
8.57883542347068 
-3.83936856455255 
2.57757413153932 
1.05265031865835 
9.78560469516523 
0.218777577238443 
-3.16626703543187 
-5.52530239562368 
1.59942714200415 
2.02274856038333 
0.39587125331722 
-1.51165850054888 
-3.65982260227440 
-4.779430209703 
10.7899207854783 
-5.36351054351817 
-3.39694257559186 
0.587311205102004 
-5.98292980269166 
6.71836779857355 
8.59068300592714 
6.90794529857334 
-0.386628320548454 
7.8413230983498 
-6.91392196403692 
7.32085705000419 
2.30336714831568 
-4.20375035425027 
-4.00125362105022 
5.55650085960689 
12.4928206247253 
8.1394288444998 
-2.88913368828725 
2.34474807086669 
-4.04319517674926 
-1.34850973559181 
-5.25685880781531 
1.06449150194289 
2.72129740577611 
4.34194294374565 
2.18749463671286 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 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=7723&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]4 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=7723&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7723&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.236279424385230.7435462919222031.66267983287123
Geometric MeanNaN
Harmonic Mean2.4019108423453
Quadratic Mean5.29770884914023
Winsorized Mean ( 1 / 16 )1.220526206468870.7291811938719931.67383116394954
Winsorized Mean ( 2 / 16 )1.198212382662950.7146884664051081.67655200690445
Winsorized Mean ( 3 / 16 )1.199869441139840.7107106721158661.68826709407317
Winsorized Mean ( 4 / 16 )1.122029164414480.6885188378988651.62962740110140
Winsorized Mean ( 5 / 16 )1.169537431318140.6790960285116461.72219742454006
Winsorized Mean ( 6 / 16 )1.178490161543420.6558702178337381.79683438811391
Winsorized Mean ( 7 / 16 )1.180895505096870.6528532625586491.80882224662358
Winsorized Mean ( 8 / 16 )1.166001029905400.6393712177668161.82366831271822
Winsorized Mean ( 9 / 16 )1.078108776153990.6175896498687511.74567170350590
Winsorized Mean ( 10 / 16 )1.026878838412530.5943797197240081.72764783914455
Winsorized Mean ( 11 / 16 )1.024626860556650.5787960255099261.77027279973794
Winsorized Mean ( 12 / 16 )0.8044668004054350.5110435154742951.57416497039164
Winsorized Mean ( 13 / 16 )0.5434367823622460.4400887213747781.23483460486018
Winsorized Mean ( 14 / 16 )0.1595761564122690.3481008159684070.458419369021967
Winsorized Mean ( 15 / 16 )0.426975265884730.2866405314967511.48958440613822
Winsorized Mean ( 16 / 16 )0.3971015534803120.2672372279807571.48595147644963
Trimmed Mean ( 1 / 16 )1.236279424385230.7155561262046121.72771831462417
Trimmed Mean ( 2 / 16 )1.170187087961450.6974509539702911.67780555937313
Trimmed Mean ( 3 / 16 )1.068174415159530.683526954846331.56273927104993
Trimmed Mean ( 4 / 16 )1.068174415159530.6665516492014481.602538102545
Trimmed Mean ( 5 / 16 )0.98231559142950.6529640598096951.50439457834141
Trimmed Mean ( 6 / 16 )0.9327271041076430.6372288718973871.46372386004795
Trimmed Mean ( 7 / 16 )0.8753823907059620.622940235452341.40524297659199
Trimmed Mean ( 8 / 16 )0.8753823907059620.6028288495930521.45212424935685
Trimmed Mean ( 9 / 16 )0.7403515861599960.5779178363800061.28106720290457
Trimmed Mean ( 10 / 16 )0.6769412324829620.5489660191164011.23312046449167
Trimmed Mean ( 11 / 16 )0.6134340373327820.5138757750038541.19373994099679
Trimmed Mean ( 12 / 16 )0.5401669524674380.4649566555768731.16175765200576
Trimmed Mean ( 13 / 16 )0.4932441533769970.4193815732308231.17612261687406
Trimmed Mean ( 14 / 16 )0.4842352199693880.3804431266802631.27281894719669
Trimmed Mean ( 15 / 16 )0.5440408369404360.3600580929780861.51098072102923
Trimmed Mean ( 16 / 16 )0.5440408369404360.3554038901103231.5307678167832
Median0.587311205102004
Midrange2.78944933034419
Midmean - Weighted Average at Xnp0.331153039669961
Midmean - Weighted Average at X(n+1)p0.540166952467438
Midmean - Empirical Distribution Function0.540166952467438
Midmean - Empirical Distribution Function - Averaging0.540166952467438
Midmean - Empirical Distribution Function - Interpolation0.540166952467438
Midmean - Closest Observation0.378628892669675
Midmean - True Basic - Statistics Graphics Toolkit0.540166952467438
Midmean - MS Excel (old versions)0.540166952467438
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.23627942438523 & 0.743546291922203 & 1.66267983287123 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2.4019108423453 &  &  \tabularnewline
Quadratic Mean & 5.29770884914023 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 1.22052620646887 & 0.729181193871993 & 1.67383116394954 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 1.19821238266295 & 0.714688466405108 & 1.67655200690445 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 1.19986944113984 & 0.710710672115866 & 1.68826709407317 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 1.12202916441448 & 0.688518837898865 & 1.62962740110140 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 1.16953743131814 & 0.679096028511646 & 1.72219742454006 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 1.17849016154342 & 0.655870217833738 & 1.79683438811391 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 1.18089550509687 & 0.652853262558649 & 1.80882224662358 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 1.16600102990540 & 0.639371217766816 & 1.82366831271822 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 1.07810877615399 & 0.617589649868751 & 1.74567170350590 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 1.02687883841253 & 0.594379719724008 & 1.72764783914455 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 1.02462686055665 & 0.578796025509926 & 1.77027279973794 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.804466800405435 & 0.511043515474295 & 1.57416497039164 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.543436782362246 & 0.440088721374778 & 1.23483460486018 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.159576156412269 & 0.348100815968407 & 0.458419369021967 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.42697526588473 & 0.286640531496751 & 1.48958440613822 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.397101553480312 & 0.267237227980757 & 1.48595147644963 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 1.23627942438523 & 0.715556126204612 & 1.72771831462417 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 1.17018708796145 & 0.697450953970291 & 1.67780555937313 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 1.06817441515953 & 0.68352695484633 & 1.56273927104993 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 1.06817441515953 & 0.666551649201448 & 1.602538102545 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.9823155914295 & 0.652964059809695 & 1.50439457834141 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.932727104107643 & 0.637228871897387 & 1.46372386004795 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.875382390705962 & 0.62294023545234 & 1.40524297659199 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.875382390705962 & 0.602828849593052 & 1.45212424935685 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.740351586159996 & 0.577917836380006 & 1.28106720290457 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.676941232482962 & 0.548966019116401 & 1.23312046449167 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.613434037332782 & 0.513875775003854 & 1.19373994099679 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.540166952467438 & 0.464956655576873 & 1.16175765200576 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.493244153376997 & 0.419381573230823 & 1.17612261687406 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.484235219969388 & 0.380443126680263 & 1.27281894719669 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.544040836940436 & 0.360058092978086 & 1.51098072102923 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.544040836940436 & 0.355403890110323 & 1.5307678167832 \tabularnewline
Median & 0.587311205102004 &  &  \tabularnewline
Midrange & 2.78944933034419 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.331153039669961 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.540166952467438 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.540166952467438 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.540166952467438 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.540166952467438 &  &  \tabularnewline
Midmean - Closest Observation & 0.378628892669675 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.540166952467438 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.540166952467438 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7723&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]1.23627942438523[/C][C]0.743546291922203[/C][C]1.66267983287123[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.4019108423453[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.29770884914023[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]1.22052620646887[/C][C]0.729181193871993[/C][C]1.67383116394954[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]1.19821238266295[/C][C]0.714688466405108[/C][C]1.67655200690445[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]1.19986944113984[/C][C]0.710710672115866[/C][C]1.68826709407317[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]1.12202916441448[/C][C]0.688518837898865[/C][C]1.62962740110140[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]1.16953743131814[/C][C]0.679096028511646[/C][C]1.72219742454006[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]1.17849016154342[/C][C]0.655870217833738[/C][C]1.79683438811391[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]1.18089550509687[/C][C]0.652853262558649[/C][C]1.80882224662358[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]1.16600102990540[/C][C]0.639371217766816[/C][C]1.82366831271822[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]1.07810877615399[/C][C]0.617589649868751[/C][C]1.74567170350590[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]1.02687883841253[/C][C]0.594379719724008[/C][C]1.72764783914455[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]1.02462686055665[/C][C]0.578796025509926[/C][C]1.77027279973794[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.804466800405435[/C][C]0.511043515474295[/C][C]1.57416497039164[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.543436782362246[/C][C]0.440088721374778[/C][C]1.23483460486018[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.159576156412269[/C][C]0.348100815968407[/C][C]0.458419369021967[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.42697526588473[/C][C]0.286640531496751[/C][C]1.48958440613822[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.397101553480312[/C][C]0.267237227980757[/C][C]1.48595147644963[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]1.23627942438523[/C][C]0.715556126204612[/C][C]1.72771831462417[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]1.17018708796145[/C][C]0.697450953970291[/C][C]1.67780555937313[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]1.06817441515953[/C][C]0.68352695484633[/C][C]1.56273927104993[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]1.06817441515953[/C][C]0.666551649201448[/C][C]1.602538102545[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.9823155914295[/C][C]0.652964059809695[/C][C]1.50439457834141[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.932727104107643[/C][C]0.637228871897387[/C][C]1.46372386004795[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.875382390705962[/C][C]0.62294023545234[/C][C]1.40524297659199[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.875382390705962[/C][C]0.602828849593052[/C][C]1.45212424935685[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.740351586159996[/C][C]0.577917836380006[/C][C]1.28106720290457[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.676941232482962[/C][C]0.548966019116401[/C][C]1.23312046449167[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.613434037332782[/C][C]0.513875775003854[/C][C]1.19373994099679[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.540166952467438[/C][C]0.464956655576873[/C][C]1.16175765200576[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.493244153376997[/C][C]0.419381573230823[/C][C]1.17612261687406[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.484235219969388[/C][C]0.380443126680263[/C][C]1.27281894719669[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.544040836940436[/C][C]0.360058092978086[/C][C]1.51098072102923[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.544040836940436[/C][C]0.355403890110323[/C][C]1.5307678167832[/C][/ROW]
[ROW][C]Median[/C][C]0.587311205102004[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.78944933034419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.331153039669961[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.540166952467438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.540166952467438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.540166952467438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.540166952467438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.378628892669675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.540166952467438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.540166952467438[/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=7723&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7723&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 Mean1.236279424385230.7435462919222031.66267983287123
Geometric MeanNaN
Harmonic Mean2.4019108423453
Quadratic Mean5.29770884914023
Winsorized Mean ( 1 / 16 )1.220526206468870.7291811938719931.67383116394954
Winsorized Mean ( 2 / 16 )1.198212382662950.7146884664051081.67655200690445
Winsorized Mean ( 3 / 16 )1.199869441139840.7107106721158661.68826709407317
Winsorized Mean ( 4 / 16 )1.122029164414480.6885188378988651.62962740110140
Winsorized Mean ( 5 / 16 )1.169537431318140.6790960285116461.72219742454006
Winsorized Mean ( 6 / 16 )1.178490161543420.6558702178337381.79683438811391
Winsorized Mean ( 7 / 16 )1.180895505096870.6528532625586491.80882224662358
Winsorized Mean ( 8 / 16 )1.166001029905400.6393712177668161.82366831271822
Winsorized Mean ( 9 / 16 )1.078108776153990.6175896498687511.74567170350590
Winsorized Mean ( 10 / 16 )1.026878838412530.5943797197240081.72764783914455
Winsorized Mean ( 11 / 16 )1.024626860556650.5787960255099261.77027279973794
Winsorized Mean ( 12 / 16 )0.8044668004054350.5110435154742951.57416497039164
Winsorized Mean ( 13 / 16 )0.5434367823622460.4400887213747781.23483460486018
Winsorized Mean ( 14 / 16 )0.1595761564122690.3481008159684070.458419369021967
Winsorized Mean ( 15 / 16 )0.426975265884730.2866405314967511.48958440613822
Winsorized Mean ( 16 / 16 )0.3971015534803120.2672372279807571.48595147644963
Trimmed Mean ( 1 / 16 )1.236279424385230.7155561262046121.72771831462417
Trimmed Mean ( 2 / 16 )1.170187087961450.6974509539702911.67780555937313
Trimmed Mean ( 3 / 16 )1.068174415159530.683526954846331.56273927104993
Trimmed Mean ( 4 / 16 )1.068174415159530.6665516492014481.602538102545
Trimmed Mean ( 5 / 16 )0.98231559142950.6529640598096951.50439457834141
Trimmed Mean ( 6 / 16 )0.9327271041076430.6372288718973871.46372386004795
Trimmed Mean ( 7 / 16 )0.8753823907059620.622940235452341.40524297659199
Trimmed Mean ( 8 / 16 )0.8753823907059620.6028288495930521.45212424935685
Trimmed Mean ( 9 / 16 )0.7403515861599960.5779178363800061.28106720290457
Trimmed Mean ( 10 / 16 )0.6769412324829620.5489660191164011.23312046449167
Trimmed Mean ( 11 / 16 )0.6134340373327820.5138757750038541.19373994099679
Trimmed Mean ( 12 / 16 )0.5401669524674380.4649566555768731.16175765200576
Trimmed Mean ( 13 / 16 )0.4932441533769970.4193815732308231.17612261687406
Trimmed Mean ( 14 / 16 )0.4842352199693880.3804431266802631.27281894719669
Trimmed Mean ( 15 / 16 )0.5440408369404360.3600580929780861.51098072102923
Trimmed Mean ( 16 / 16 )0.5440408369404360.3554038901103231.5307678167832
Median0.587311205102004
Midrange2.78944933034419
Midmean - Weighted Average at Xnp0.331153039669961
Midmean - Weighted Average at X(n+1)p0.540166952467438
Midmean - Empirical Distribution Function0.540166952467438
Midmean - Empirical Distribution Function - Averaging0.540166952467438
Midmean - Empirical Distribution Function - Interpolation0.540166952467438
Midmean - Closest Observation0.378628892669675
Midmean - True Basic - Statistics Graphics Toolkit0.540166952467438
Midmean - MS Excel (old versions)0.540166952467438
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')