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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 02 Jun 2009 10:48:33 -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/2009/Jun/02/t12439617217cizvujfs14idx0.htm/, Retrieved Fri, 10 May 2024 07:47:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41322, Retrieved Fri, 10 May 2024 07:47:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5_maandeli...] [2009-06-02 16:48:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41322&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41322&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41322&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.983333333333330.047469617991278183.9133218654765
Geometric Mean3.9634202090647
Harmonic Mean3.94377783005191
Quadratic Mean4.00336525105234
Winsorized Mean ( 1 / 24 )3.983333333333330.047469617991278183.9133218654765
Winsorized Mean ( 2 / 24 )3.983333333333330.047366483134909284.0960330955541
Winsorized Mean ( 3 / 24 )3.981250.046375659349762385.8478360377297
Winsorized Mean ( 4 / 24 )3.977916666666670.045098977178717888.2041437636826
Winsorized Mean ( 5 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 6 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 7 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 8 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 9 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 10 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 11 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 12 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 13 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 14 / 24 )3.987777777777780.042996261357207292.747081999708
Winsorized Mean ( 15 / 24 )3.991944444444440.042446983819849294.0454205506521
Winsorized Mean ( 16 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 17 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 18 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 19 / 24 )3.997222222222220.041151853516187797.13346740627
Winsorized Mean ( 20 / 24 )4.011111111111110.0394571713471472101.657340710540
Winsorized Mean ( 21 / 24 )4.011111111111110.038668445177021103.730860983641
Winsorized Mean ( 22 / 24 )3.995833333333330.0363654669033493109.879885330589
Winsorized Mean ( 23 / 24 )3.947916666666670.0295433009573304133.631535364605
Winsorized Mean ( 24 / 24 )3.937916666666670.0282163682809666139.561428581261
Trimmed Mean ( 1 / 24 )3.981428571428570.047102938114935684.526119404983
Trimmed Mean ( 2 / 24 )3.979411764705880.046645075337551885.3125809296795
Trimmed Mean ( 3 / 24 )3.977272727272730.046141843462963586.1966585809505
Trimmed Mean ( 4 / 24 )3.975781250.045949422617309286.525162309707
Trimmed Mean ( 5 / 24 )3.975161290322580.04611205509794786.2065523186704
Trimmed Mean ( 6 / 24 )3.974666666666670.046333028491457485.7847370671979
Trimmed Mean ( 7 / 24 )3.974137931034480.046528640285022985.4127244357432
Trimmed Mean ( 8 / 24 )3.973571428571430.046692158864668285.1014715359031
Trimmed Mean ( 9 / 24 )3.973148148148150.046851106078148484.8037214216644
Trimmed Mean ( 10 / 24 )3.972692307692310.046964505856048684.5892495892334
Trimmed Mean ( 11 / 24 )3.97220.047020004427121684.4789371757013
Trimmed Mean ( 12 / 24 )3.971666666666670.047001710144431884.5004714607641
Trimmed Mean ( 13 / 24 )3.971086956521740.046888940901112184.6913340375227
Trimmed Mean ( 14 / 24 )3.970454545454550.046654406789509585.1035265193281
Trimmed Mean ( 15 / 24 )3.968333333333330.046576048570331385.201159289866
Trimmed Mean ( 16 / 24 )3.96550.046461936447607785.3494344660311
Trimmed Mean ( 17 / 24 )3.962368421052630.04631273832572585.5567725921248
Trimmed Mean ( 18 / 24 )3.958888888888890.045972348103218186.114567826736
Trimmed Mean ( 19 / 24 )3.9550.045366894099264887.1781081452542
Trimmed Mean ( 20 / 24 )3.950.044536139728713488.692015609367
Trimmed Mean ( 21 / 24 )3.942666666666670.04358881363755590.4513414714679
Trimmed Mean ( 22 / 24 )3.934285714285710.042252793562911293.1130318857582
Trimmed Mean ( 23 / 24 )3.926538461538460.040946277402666395.8948825292426
Trimmed Mean ( 24 / 24 )3.923750.04130047416999895.0049625059836
Median3.805
Midrange4.05
Midmean - Weighted Average at Xnp3.9655
Midmean - Weighted Average at X(n+1)p3.9655
Midmean - Empirical Distribution Function3.9655
Midmean - Empirical Distribution Function - Averaging3.9655
Midmean - Empirical Distribution Function - Interpolation3.9655
Midmean - Closest Observation3.9655
Midmean - True Basic - Statistics Graphics Toolkit3.9655
Midmean - MS Excel (old versions)3.9655
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.98333333333333 & 0.0474696179912781 & 83.9133218654765 \tabularnewline
Geometric Mean & 3.9634202090647 &  &  \tabularnewline
Harmonic Mean & 3.94377783005191 &  &  \tabularnewline
Quadratic Mean & 4.00336525105234 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.98333333333333 & 0.0474696179912781 & 83.9133218654765 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.98333333333333 & 0.0473664831349092 & 84.0960330955541 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.98125 & 0.0463756593497623 & 85.8478360377297 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.97791666666667 & 0.0450989771787178 & 88.2041437636826 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.97722222222222 & 0.0447839633499133 & 88.8090719248483 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.97722222222222 & 0.0447839633499133 & 88.8090719248483 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.97722222222222 & 0.0447839633499133 & 88.8090719248483 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.97611111111111 & 0.0446164999074207 & 89.1175040480886 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.98777777777778 & 0.0429962613572072 & 92.747081999708 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.99194444444444 & 0.0424469838198492 & 94.0454205506521 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.99194444444444 & 0.0418230113188676 & 95.4485178986516 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.99194444444444 & 0.0418230113188676 & 95.4485178986516 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.99194444444444 & 0.0418230113188676 & 95.4485178986516 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.99722222222222 & 0.0411518535161877 & 97.13346740627 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.01111111111111 & 0.0394571713471472 & 101.657340710540 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.01111111111111 & 0.038668445177021 & 103.730860983641 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.99583333333333 & 0.0363654669033493 & 109.879885330589 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.94791666666667 & 0.0295433009573304 & 133.631535364605 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.93791666666667 & 0.0282163682809666 & 139.561428581261 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.98142857142857 & 0.0471029381149356 & 84.526119404983 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.97941176470588 & 0.0466450753375518 & 85.3125809296795 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.97727272727273 & 0.0461418434629635 & 86.1966585809505 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.97578125 & 0.0459494226173092 & 86.525162309707 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.97516129032258 & 0.046112055097947 & 86.2065523186704 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.97466666666667 & 0.0463330284914574 & 85.7847370671979 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.97413793103448 & 0.0465286402850229 & 85.4127244357432 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.97357142857143 & 0.0466921588646682 & 85.1014715359031 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.97314814814815 & 0.0468511060781484 & 84.8037214216644 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.97269230769231 & 0.0469645058560486 & 84.5892495892334 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.9722 & 0.0470200044271216 & 84.4789371757013 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.97166666666667 & 0.0470017101444318 & 84.5004714607641 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.97108695652174 & 0.0468889409011121 & 84.6913340375227 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.97045454545455 & 0.0466544067895095 & 85.1035265193281 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.96833333333333 & 0.0465760485703313 & 85.201159289866 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.9655 & 0.0464619364476077 & 85.3494344660311 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.96236842105263 & 0.046312738325725 & 85.5567725921248 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.95888888888889 & 0.0459723481032181 & 86.114567826736 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.955 & 0.0453668940992648 & 87.1781081452542 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.95 & 0.0445361397287134 & 88.692015609367 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.94266666666667 & 0.043588813637555 & 90.4513414714679 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.93428571428571 & 0.0422527935629112 & 93.1130318857582 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.92653846153846 & 0.0409462774026663 & 95.8948825292426 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.92375 & 0.041300474169998 & 95.0049625059836 \tabularnewline
Median & 3.805 &  &  \tabularnewline
Midrange & 4.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.9655 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.9655 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.9655 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.9655 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.9655 &  &  \tabularnewline
Midmean - Closest Observation & 3.9655 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.9655 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.9655 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41322&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]3.98333333333333[/C][C]0.0474696179912781[/C][C]83.9133218654765[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.9634202090647[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.94377783005191[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.00336525105234[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.98333333333333[/C][C]0.0474696179912781[/C][C]83.9133218654765[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.98333333333333[/C][C]0.0473664831349092[/C][C]84.0960330955541[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.98125[/C][C]0.0463756593497623[/C][C]85.8478360377297[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.97791666666667[/C][C]0.0450989771787178[/C][C]88.2041437636826[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.97722222222222[/C][C]0.0447839633499133[/C][C]88.8090719248483[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.97722222222222[/C][C]0.0447839633499133[/C][C]88.8090719248483[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.97722222222222[/C][C]0.0447839633499133[/C][C]88.8090719248483[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.97611111111111[/C][C]0.0446164999074207[/C][C]89.1175040480886[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.98777777777778[/C][C]0.0429962613572072[/C][C]92.747081999708[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.99194444444444[/C][C]0.0424469838198492[/C][C]94.0454205506521[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.99194444444444[/C][C]0.0418230113188676[/C][C]95.4485178986516[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.99194444444444[/C][C]0.0418230113188676[/C][C]95.4485178986516[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.99194444444444[/C][C]0.0418230113188676[/C][C]95.4485178986516[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.99722222222222[/C][C]0.0411518535161877[/C][C]97.13346740627[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.01111111111111[/C][C]0.0394571713471472[/C][C]101.657340710540[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.01111111111111[/C][C]0.038668445177021[/C][C]103.730860983641[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.99583333333333[/C][C]0.0363654669033493[/C][C]109.879885330589[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.94791666666667[/C][C]0.0295433009573304[/C][C]133.631535364605[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.93791666666667[/C][C]0.0282163682809666[/C][C]139.561428581261[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.98142857142857[/C][C]0.0471029381149356[/C][C]84.526119404983[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.97941176470588[/C][C]0.0466450753375518[/C][C]85.3125809296795[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.97727272727273[/C][C]0.0461418434629635[/C][C]86.1966585809505[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.97578125[/C][C]0.0459494226173092[/C][C]86.525162309707[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.97516129032258[/C][C]0.046112055097947[/C][C]86.2065523186704[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.97466666666667[/C][C]0.0463330284914574[/C][C]85.7847370671979[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.97413793103448[/C][C]0.0465286402850229[/C][C]85.4127244357432[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.97357142857143[/C][C]0.0466921588646682[/C][C]85.1014715359031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.97314814814815[/C][C]0.0468511060781484[/C][C]84.8037214216644[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.97269230769231[/C][C]0.0469645058560486[/C][C]84.5892495892334[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.9722[/C][C]0.0470200044271216[/C][C]84.4789371757013[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.97166666666667[/C][C]0.0470017101444318[/C][C]84.5004714607641[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.97108695652174[/C][C]0.0468889409011121[/C][C]84.6913340375227[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.97045454545455[/C][C]0.0466544067895095[/C][C]85.1035265193281[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.96833333333333[/C][C]0.0465760485703313[/C][C]85.201159289866[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.9655[/C][C]0.0464619364476077[/C][C]85.3494344660311[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.96236842105263[/C][C]0.046312738325725[/C][C]85.5567725921248[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.95888888888889[/C][C]0.0459723481032181[/C][C]86.114567826736[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.955[/C][C]0.0453668940992648[/C][C]87.1781081452542[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.95[/C][C]0.0445361397287134[/C][C]88.692015609367[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.94266666666667[/C][C]0.043588813637555[/C][C]90.4513414714679[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.93428571428571[/C][C]0.0422527935629112[/C][C]93.1130318857582[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.92653846153846[/C][C]0.0409462774026663[/C][C]95.8948825292426[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.92375[/C][C]0.041300474169998[/C][C]95.0049625059836[/C][/ROW]
[ROW][C]Median[/C][C]3.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.9655[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41322&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41322&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 Mean3.983333333333330.047469617991278183.9133218654765
Geometric Mean3.9634202090647
Harmonic Mean3.94377783005191
Quadratic Mean4.00336525105234
Winsorized Mean ( 1 / 24 )3.983333333333330.047469617991278183.9133218654765
Winsorized Mean ( 2 / 24 )3.983333333333330.047366483134909284.0960330955541
Winsorized Mean ( 3 / 24 )3.981250.046375659349762385.8478360377297
Winsorized Mean ( 4 / 24 )3.977916666666670.045098977178717888.2041437636826
Winsorized Mean ( 5 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 6 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 7 / 24 )3.977222222222220.044783963349913388.8090719248483
Winsorized Mean ( 8 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 9 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 10 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 11 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 12 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 13 / 24 )3.976111111111110.044616499907420789.1175040480886
Winsorized Mean ( 14 / 24 )3.987777777777780.042996261357207292.747081999708
Winsorized Mean ( 15 / 24 )3.991944444444440.042446983819849294.0454205506521
Winsorized Mean ( 16 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 17 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 18 / 24 )3.991944444444440.041823011318867695.4485178986516
Winsorized Mean ( 19 / 24 )3.997222222222220.041151853516187797.13346740627
Winsorized Mean ( 20 / 24 )4.011111111111110.0394571713471472101.657340710540
Winsorized Mean ( 21 / 24 )4.011111111111110.038668445177021103.730860983641
Winsorized Mean ( 22 / 24 )3.995833333333330.0363654669033493109.879885330589
Winsorized Mean ( 23 / 24 )3.947916666666670.0295433009573304133.631535364605
Winsorized Mean ( 24 / 24 )3.937916666666670.0282163682809666139.561428581261
Trimmed Mean ( 1 / 24 )3.981428571428570.047102938114935684.526119404983
Trimmed Mean ( 2 / 24 )3.979411764705880.046645075337551885.3125809296795
Trimmed Mean ( 3 / 24 )3.977272727272730.046141843462963586.1966585809505
Trimmed Mean ( 4 / 24 )3.975781250.045949422617309286.525162309707
Trimmed Mean ( 5 / 24 )3.975161290322580.04611205509794786.2065523186704
Trimmed Mean ( 6 / 24 )3.974666666666670.046333028491457485.7847370671979
Trimmed Mean ( 7 / 24 )3.974137931034480.046528640285022985.4127244357432
Trimmed Mean ( 8 / 24 )3.973571428571430.046692158864668285.1014715359031
Trimmed Mean ( 9 / 24 )3.973148148148150.046851106078148484.8037214216644
Trimmed Mean ( 10 / 24 )3.972692307692310.046964505856048684.5892495892334
Trimmed Mean ( 11 / 24 )3.97220.047020004427121684.4789371757013
Trimmed Mean ( 12 / 24 )3.971666666666670.047001710144431884.5004714607641
Trimmed Mean ( 13 / 24 )3.971086956521740.046888940901112184.6913340375227
Trimmed Mean ( 14 / 24 )3.970454545454550.046654406789509585.1035265193281
Trimmed Mean ( 15 / 24 )3.968333333333330.046576048570331385.201159289866
Trimmed Mean ( 16 / 24 )3.96550.046461936447607785.3494344660311
Trimmed Mean ( 17 / 24 )3.962368421052630.04631273832572585.5567725921248
Trimmed Mean ( 18 / 24 )3.958888888888890.045972348103218186.114567826736
Trimmed Mean ( 19 / 24 )3.9550.045366894099264887.1781081452542
Trimmed Mean ( 20 / 24 )3.950.044536139728713488.692015609367
Trimmed Mean ( 21 / 24 )3.942666666666670.04358881363755590.4513414714679
Trimmed Mean ( 22 / 24 )3.934285714285710.042252793562911293.1130318857582
Trimmed Mean ( 23 / 24 )3.926538461538460.040946277402666395.8948825292426
Trimmed Mean ( 24 / 24 )3.923750.04130047416999895.0049625059836
Median3.805
Midrange4.05
Midmean - Weighted Average at Xnp3.9655
Midmean - Weighted Average at X(n+1)p3.9655
Midmean - Empirical Distribution Function3.9655
Midmean - Empirical Distribution Function - Averaging3.9655
Midmean - Empirical Distribution Function - Interpolation3.9655
Midmean - Closest Observation3.9655
Midmean - True Basic - Statistics Graphics Toolkit3.9655
Midmean - MS Excel (old versions)3.9655
Number of observations72



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')