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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 13:46:19 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318873722zxh13kyizitx59t.htm/, Retrieved Wed, 15 May 2024 12:31:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130817, Retrieved Wed, 15 May 2024 12:31:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - We...] [2011-10-17 17:46:19] [05aa4144f69b92f9bd7d460fd0e9a776] [Current]
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Dataseries X:
102,43
102,43
102,43
102,43
104,2
104,2
104,2
104,2
104,2
104,2
104,2
104,2
104,2
104,2
104,2
104,2
108,1
109,2
109,2
109,2
109,2
109,2
109,2
109,2
109,2
109,2
109,2
109,2
112,1
112,1
112,1
112,1
112,1
112,1
112,1
112,1
112,1
112,1
112,1
112,1
114,81
114,81
114,81
114,81
114,81
114,81
114,81
114,81
114,81
114,81
114,81
114,81
115,57
115,57
115,57
115,57
115,57
115,57
115,57
115,57




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130817&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130817&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.2816666666670.586462591303244188.04552635079
Geometric Mean110.188519590422
Harmonic Mean110.094286515649
Quadratic Mean110.373630757834
Winsorized Mean ( 1 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 2 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 3 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 4 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 5 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 6 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 7 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 8 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 9 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 10 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 11 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 12 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 13 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 14 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 15 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 16 / 20 )111.3383333333330.366917158915458303.442699879258
Winsorized Mean ( 17 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 18 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 19 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 20 / 20 )110.7466666666670.188353956173015587.971014343541
Trimmed Mean ( 1 / 20 )110.3258620689660.58407309593613188.890505035401
Trimmed Mean ( 2 / 20 )110.3732142857140.580484074031391190.139952538553
Trimmed Mean ( 3 / 20 )110.4240740740740.575410801421583191.904764042082
Trimmed Mean ( 4 / 20 )110.4788461538460.568484639509222194.339193138488
Trimmed Mean ( 5 / 20 )110.50260.568452091568114194.39210733691
Trimmed Mean ( 6 / 20 )110.5283333333330.567381094280178194.804399454934
Trimmed Mean ( 7 / 20 )110.5563043478260.564981412091798195.681312662129
Trimmed Mean ( 8 / 20 )110.5868181818180.560867812633356197.170912095306
Trimmed Mean ( 9 / 20 )110.6383333333330.558137657045425198.227680818048
Trimmed Mean ( 10 / 20 )110.6950.553224811724576200.09044723596
Trimmed Mean ( 11 / 20 )110.7576315789470.545368894455766203.087548088848
Trimmed Mean ( 12 / 20 )110.8272222222220.533470311444076207.747685006535
Trimmed Mean ( 13 / 20 )110.9050.515876156219833214.98376822196
Trimmed Mean ( 14 / 20 )110.99250.489964613600457226.531665591893
Trimmed Mean ( 15 / 20 )111.0916666666670.451228739642021246.198118397335
Trimmed Mean ( 16 / 20 )111.2050.390796398904628284.559940449039
Trimmed Mean ( 17 / 20 )111.1857692307690.377870622171917294.24295699861
Trimmed Mean ( 18 / 20 )111.11750.370127401685231300.214195150291
Trimmed Mean ( 19 / 20 )111.0368181818180.3548253557144312.93371906373
Trimmed Mean ( 20 / 20 )110.940.325931862430429340.377891172516
Median112.1
Midrange109
Midmean - Weighted Average at Xnp110.054583333333
Midmean - Weighted Average at X(n+1)p110.054583333333
Midmean - Empirical Distribution Function110.054583333333
Midmean - Empirical Distribution Function - Averaging110.054583333333
Midmean - Empirical Distribution Function - Interpolation110.054583333333
Midmean - Closest Observation110.054583333333
Midmean - True Basic - Statistics Graphics Toolkit110.054583333333
Midmean - MS Excel (old versions)110.054583333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.281666666667 & 0.586462591303244 & 188.04552635079 \tabularnewline
Geometric Mean & 110.188519590422 &  &  \tabularnewline
Harmonic Mean & 110.094286515649 &  &  \tabularnewline
Quadratic Mean & 110.373630757834 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 110.281666666667 & 0.586462591303244 & 188.04552635079 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 110.281666666667 & 0.586462591303244 & 188.04552635079 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 110.281666666667 & 0.586462591303244 & 188.04552635079 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 110.399666666667 & 0.561992619463503 & 196.443267835186 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 110.399666666667 & 0.561992619463503 & 196.443267835186 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 110.399666666667 & 0.561992619463503 & 196.443267835186 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 110.399666666667 & 0.561992619463503 & 196.443267835186 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 110.298333333333 & 0.54699792740013 & 201.643055317557 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.338333333333 & 0.366917158915458 & 303.442699879258 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.65 & 0.323387787365183 & 345.251133042696 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.65 & 0.323387787365183 & 345.251133042696 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.65 & 0.323387787365183 & 345.251133042696 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.746666666667 & 0.188353956173015 & 587.971014343541 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 110.325862068966 & 0.58407309593613 & 188.890505035401 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 110.373214285714 & 0.580484074031391 & 190.139952538553 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 110.424074074074 & 0.575410801421583 & 191.904764042082 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 110.478846153846 & 0.568484639509222 & 194.339193138488 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 110.5026 & 0.568452091568114 & 194.39210733691 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 110.528333333333 & 0.567381094280178 & 194.804399454934 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 110.556304347826 & 0.564981412091798 & 195.681312662129 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 110.586818181818 & 0.560867812633356 & 197.170912095306 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 110.638333333333 & 0.558137657045425 & 198.227680818048 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.695 & 0.553224811724576 & 200.09044723596 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.757631578947 & 0.545368894455766 & 203.087548088848 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.827222222222 & 0.533470311444076 & 207.747685006535 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 110.905 & 0.515876156219833 & 214.98376822196 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 110.9925 & 0.489964613600457 & 226.531665591893 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.091666666667 & 0.451228739642021 & 246.198118397335 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.205 & 0.390796398904628 & 284.559940449039 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.185769230769 & 0.377870622171917 & 294.24295699861 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.1175 & 0.370127401685231 & 300.214195150291 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.036818181818 & 0.3548253557144 & 312.93371906373 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 110.94 & 0.325931862430429 & 340.377891172516 \tabularnewline
Median & 112.1 &  &  \tabularnewline
Midrange & 109 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.054583333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.054583333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.054583333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.054583333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.054583333333 &  &  \tabularnewline
Midmean - Closest Observation & 110.054583333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.054583333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.054583333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130817&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]110.281666666667[/C][C]0.586462591303244[/C][C]188.04552635079[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.188519590422[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.094286515649[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.373630757834[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]110.281666666667[/C][C]0.586462591303244[/C][C]188.04552635079[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]110.281666666667[/C][C]0.586462591303244[/C][C]188.04552635079[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]110.281666666667[/C][C]0.586462591303244[/C][C]188.04552635079[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]110.399666666667[/C][C]0.561992619463503[/C][C]196.443267835186[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]110.399666666667[/C][C]0.561992619463503[/C][C]196.443267835186[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]110.399666666667[/C][C]0.561992619463503[/C][C]196.443267835186[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]110.399666666667[/C][C]0.561992619463503[/C][C]196.443267835186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]110.298333333333[/C][C]0.54699792740013[/C][C]201.643055317557[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.338333333333[/C][C]0.366917158915458[/C][C]303.442699879258[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.65[/C][C]0.323387787365183[/C][C]345.251133042696[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.65[/C][C]0.323387787365183[/C][C]345.251133042696[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.65[/C][C]0.323387787365183[/C][C]345.251133042696[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.746666666667[/C][C]0.188353956173015[/C][C]587.971014343541[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]110.325862068966[/C][C]0.58407309593613[/C][C]188.890505035401[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]110.373214285714[/C][C]0.580484074031391[/C][C]190.139952538553[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]110.424074074074[/C][C]0.575410801421583[/C][C]191.904764042082[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]110.478846153846[/C][C]0.568484639509222[/C][C]194.339193138488[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]110.5026[/C][C]0.568452091568114[/C][C]194.39210733691[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]110.528333333333[/C][C]0.567381094280178[/C][C]194.804399454934[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]110.556304347826[/C][C]0.564981412091798[/C][C]195.681312662129[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]110.586818181818[/C][C]0.560867812633356[/C][C]197.170912095306[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]110.638333333333[/C][C]0.558137657045425[/C][C]198.227680818048[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.695[/C][C]0.553224811724576[/C][C]200.09044723596[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.757631578947[/C][C]0.545368894455766[/C][C]203.087548088848[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.827222222222[/C][C]0.533470311444076[/C][C]207.747685006535[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]110.905[/C][C]0.515876156219833[/C][C]214.98376822196[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]110.9925[/C][C]0.489964613600457[/C][C]226.531665591893[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.091666666667[/C][C]0.451228739642021[/C][C]246.198118397335[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.205[/C][C]0.390796398904628[/C][C]284.559940449039[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.185769230769[/C][C]0.377870622171917[/C][C]294.24295699861[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.1175[/C][C]0.370127401685231[/C][C]300.214195150291[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.036818181818[/C][C]0.3548253557144[/C][C]312.93371906373[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]110.94[/C][C]0.325931862430429[/C][C]340.377891172516[/C][/ROW]
[ROW][C]Median[/C][C]112.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.054583333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130817&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 Mean110.2816666666670.586462591303244188.04552635079
Geometric Mean110.188519590422
Harmonic Mean110.094286515649
Quadratic Mean110.373630757834
Winsorized Mean ( 1 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 2 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 3 / 20 )110.2816666666670.586462591303244188.04552635079
Winsorized Mean ( 4 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 5 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 6 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 7 / 20 )110.3996666666670.561992619463503196.443267835186
Winsorized Mean ( 8 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 9 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 10 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 11 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 12 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 13 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 14 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 15 / 20 )110.2983333333330.54699792740013201.643055317557
Winsorized Mean ( 16 / 20 )111.3383333333330.366917158915458303.442699879258
Winsorized Mean ( 17 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 18 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 19 / 20 )111.650.323387787365183345.251133042696
Winsorized Mean ( 20 / 20 )110.7466666666670.188353956173015587.971014343541
Trimmed Mean ( 1 / 20 )110.3258620689660.58407309593613188.890505035401
Trimmed Mean ( 2 / 20 )110.3732142857140.580484074031391190.139952538553
Trimmed Mean ( 3 / 20 )110.4240740740740.575410801421583191.904764042082
Trimmed Mean ( 4 / 20 )110.4788461538460.568484639509222194.339193138488
Trimmed Mean ( 5 / 20 )110.50260.568452091568114194.39210733691
Trimmed Mean ( 6 / 20 )110.5283333333330.567381094280178194.804399454934
Trimmed Mean ( 7 / 20 )110.5563043478260.564981412091798195.681312662129
Trimmed Mean ( 8 / 20 )110.5868181818180.560867812633356197.170912095306
Trimmed Mean ( 9 / 20 )110.6383333333330.558137657045425198.227680818048
Trimmed Mean ( 10 / 20 )110.6950.553224811724576200.09044723596
Trimmed Mean ( 11 / 20 )110.7576315789470.545368894455766203.087548088848
Trimmed Mean ( 12 / 20 )110.8272222222220.533470311444076207.747685006535
Trimmed Mean ( 13 / 20 )110.9050.515876156219833214.98376822196
Trimmed Mean ( 14 / 20 )110.99250.489964613600457226.531665591893
Trimmed Mean ( 15 / 20 )111.0916666666670.451228739642021246.198118397335
Trimmed Mean ( 16 / 20 )111.2050.390796398904628284.559940449039
Trimmed Mean ( 17 / 20 )111.1857692307690.377870622171917294.24295699861
Trimmed Mean ( 18 / 20 )111.11750.370127401685231300.214195150291
Trimmed Mean ( 19 / 20 )111.0368181818180.3548253557144312.93371906373
Trimmed Mean ( 20 / 20 )110.940.325931862430429340.377891172516
Median112.1
Midrange109
Midmean - Weighted Average at Xnp110.054583333333
Midmean - Weighted Average at X(n+1)p110.054583333333
Midmean - Empirical Distribution Function110.054583333333
Midmean - Empirical Distribution Function - Averaging110.054583333333
Midmean - Empirical Distribution Function - Interpolation110.054583333333
Midmean - Closest Observation110.054583333333
Midmean - True Basic - Statistics Graphics Toolkit110.054583333333
Midmean - MS Excel (old versions)110.054583333333
Number of observations60



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')