Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 14 Nov 2009 08:18:12 -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/2009/Nov/14/t1258212037rcgptepmd4w1y1v.htm/, Retrieved Sat, 27 Apr 2024 22:24:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57236, Retrieved Sat, 27 Apr 2024 22:24:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [workshop 3] [2009-10-16 16:14:51] [b5908418e3090fddbd22f5f0f774653d]
-  M D          [Central Tendency] [ws 2] [2009-11-14 15:18:12] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
Feedback Forum

Post a new message
Dataseries X:
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57236&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57236&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57236&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.861666666666670.091413620944375486.0010421362746
Geometric Mean7.82931079421107
Harmonic Mean7.7959156854323
Quadratic Mean7.89296099910125
Winsorized Mean ( 1 / 20 )7.866666666666670.089904741385204487.5000199707074
Winsorized Mean ( 2 / 20 )7.850.0845560022359492.8378801317478
Winsorized Mean ( 3 / 20 )7.8550.083240343597680394.3653000516795
Winsorized Mean ( 4 / 20 )7.868333333333330.080024419531044498.3241537950915
Winsorized Mean ( 5 / 20 )7.876666666666670.078198886906215100.726071409600
Winsorized Mean ( 6 / 20 )7.876666666666670.078198886906215100.726071409600
Winsorized Mean ( 7 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 8 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 9 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 10 / 20 )7.876666666666670.0677885823872396116.194591910353
Winsorized Mean ( 11 / 20 )7.8950.0643272442304385122.731823731137
Winsorized Mean ( 12 / 20 )7.8950.0643272442304385122.731823731137
Winsorized Mean ( 13 / 20 )7.916666666666670.0604674197500117130.924499497353
Winsorized Mean ( 14 / 20 )7.916666666666670.0604674197500117130.924499497353
Winsorized Mean ( 15 / 20 )7.891666666666670.0565131686401955139.642969179641
Winsorized Mean ( 16 / 20 )7.891666666666670.0478516815534762164.919317576069
Winsorized Mean ( 17 / 20 )7.920.0430346070172593184.037930143608
Winsorized Mean ( 18 / 20 )7.890.0387444182238271203.642237042233
Winsorized Mean ( 19 / 20 )7.953333333333330.0284700920153008279.357486061476
Winsorized Mean ( 20 / 20 )7.953333333333330.0284700920153008279.357486061476
Trimmed Mean ( 1 / 20 )7.867241379310340.085923611984118591.5608782922728
Trimmed Mean ( 2 / 20 )7.867857142857140.08098850098180797.1478302163483
Trimmed Mean ( 3 / 20 )7.877777777777780.0784932649287826100.362467848997
Trimmed Mean ( 4 / 20 )7.886538461538460.0760065114973634103.761352891614
Trimmed Mean ( 5 / 20 )7.8920.0741669380106631106.408599460657
Trimmed Mean ( 6 / 20 )7.895833333333330.0724420980163594108.995094696874
Trimmed Mean ( 7 / 20 )7.90.0701964118163034112.541364944315
Trimmed Mean ( 8 / 20 )7.904545454545450.0685823331572746115.256292555964
Trimmed Mean ( 9 / 20 )7.909523809523810.0664173203248596119.088270511921
Trimmed Mean ( 10 / 20 )7.9150.0635034826422324124.638833504483
Trimmed Mean ( 11 / 20 )7.921052631578950.0612991051727219129.219710618285
Trimmed Mean ( 12 / 20 )7.9250.0592780641459291133.691950204218
Trimmed Mean ( 13 / 20 )7.929411764705880.0564122544816182140.561866168452
Trimmed Mean ( 14 / 20 )7.931250.0535884669525317148.002927701318
Trimmed Mean ( 15 / 20 )7.933333333333330.0494413232473044160.459567266252
Trimmed Mean ( 16 / 20 )7.939285714285710.0446441798745841177.834730900848
Trimmed Mean ( 17 / 20 )7.946153846153850.0408489786072361194.525153800204
Trimmed Mean ( 18 / 20 )7.950.0371054119260640214.254460126763
Trimmed Mean ( 19 / 20 )7.959090909090910.0326725131103754243.602041942817
Trimmed Mean ( 20 / 20 )7.960.0311194642086199255.788465593027
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.89375
Midmean - Weighted Average at X(n+1)p7.89375
Midmean - Empirical Distribution Function7.89375
Midmean - Empirical Distribution Function - Averaging7.89375
Midmean - Empirical Distribution Function - Interpolation7.89375
Midmean - Closest Observation7.89375
Midmean - True Basic - Statistics Graphics Toolkit7.89375
Midmean - MS Excel (old versions)7.97567567567568
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.86166666666667 & 0.0914136209443754 & 86.0010421362746 \tabularnewline
Geometric Mean & 7.82931079421107 &  &  \tabularnewline
Harmonic Mean & 7.7959156854323 &  &  \tabularnewline
Quadratic Mean & 7.89296099910125 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.86666666666667 & 0.0899047413852044 & 87.5000199707074 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.85 & 0.08455600223594 & 92.8378801317478 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.855 & 0.0832403435976803 & 94.3653000516795 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.86833333333333 & 0.0800244195310444 & 98.3241537950915 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.87666666666667 & 0.078198886906215 & 100.726071409600 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.87666666666667 & 0.078198886906215 & 100.726071409600 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.87666666666667 & 0.0737749925732982 & 106.766078747360 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.87666666666667 & 0.0737749925732982 & 106.766078747360 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.87666666666667 & 0.0737749925732982 & 106.766078747360 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.87666666666667 & 0.0677885823872396 & 116.194591910353 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.895 & 0.0643272442304385 & 122.731823731137 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.895 & 0.0643272442304385 & 122.731823731137 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.91666666666667 & 0.0604674197500117 & 130.924499497353 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.91666666666667 & 0.0604674197500117 & 130.924499497353 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.89166666666667 & 0.0565131686401955 & 139.642969179641 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.89166666666667 & 0.0478516815534762 & 164.919317576069 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.92 & 0.0430346070172593 & 184.037930143608 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.89 & 0.0387444182238271 & 203.642237042233 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.95333333333333 & 0.0284700920153008 & 279.357486061476 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.95333333333333 & 0.0284700920153008 & 279.357486061476 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.86724137931034 & 0.0859236119841185 & 91.5608782922728 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.86785714285714 & 0.080988500981807 & 97.1478302163483 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.87777777777778 & 0.0784932649287826 & 100.362467848997 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.88653846153846 & 0.0760065114973634 & 103.761352891614 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.892 & 0.0741669380106631 & 106.408599460657 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.89583333333333 & 0.0724420980163594 & 108.995094696874 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.9 & 0.0701964118163034 & 112.541364944315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.90454545454545 & 0.0685823331572746 & 115.256292555964 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.90952380952381 & 0.0664173203248596 & 119.088270511921 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.915 & 0.0635034826422324 & 124.638833504483 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.92105263157895 & 0.0612991051727219 & 129.219710618285 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.925 & 0.0592780641459291 & 133.691950204218 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.92941176470588 & 0.0564122544816182 & 140.561866168452 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.93125 & 0.0535884669525317 & 148.002927701318 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.93333333333333 & 0.0494413232473044 & 160.459567266252 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.93928571428571 & 0.0446441798745841 & 177.834730900848 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.94615384615385 & 0.0408489786072361 & 194.525153800204 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.95 & 0.0371054119260640 & 214.254460126763 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.95909090909091 & 0.0326725131103754 & 243.602041942817 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.96 & 0.0311194642086199 & 255.788465593027 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.89375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.89375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.89375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.89375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.89375 &  &  \tabularnewline
Midmean - Closest Observation & 7.89375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.89375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.97567567567568 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57236&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]7.86166666666667[/C][C]0.0914136209443754[/C][C]86.0010421362746[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.82931079421107[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.7959156854323[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.89296099910125[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.86666666666667[/C][C]0.0899047413852044[/C][C]87.5000199707074[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.85[/C][C]0.08455600223594[/C][C]92.8378801317478[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.855[/C][C]0.0832403435976803[/C][C]94.3653000516795[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.86833333333333[/C][C]0.0800244195310444[/C][C]98.3241537950915[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.87666666666667[/C][C]0.078198886906215[/C][C]100.726071409600[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.87666666666667[/C][C]0.078198886906215[/C][C]100.726071409600[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.87666666666667[/C][C]0.0737749925732982[/C][C]106.766078747360[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.87666666666667[/C][C]0.0737749925732982[/C][C]106.766078747360[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.87666666666667[/C][C]0.0737749925732982[/C][C]106.766078747360[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.87666666666667[/C][C]0.0677885823872396[/C][C]116.194591910353[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.895[/C][C]0.0643272442304385[/C][C]122.731823731137[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.895[/C][C]0.0643272442304385[/C][C]122.731823731137[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.91666666666667[/C][C]0.0604674197500117[/C][C]130.924499497353[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.91666666666667[/C][C]0.0604674197500117[/C][C]130.924499497353[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.89166666666667[/C][C]0.0565131686401955[/C][C]139.642969179641[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.89166666666667[/C][C]0.0478516815534762[/C][C]164.919317576069[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.92[/C][C]0.0430346070172593[/C][C]184.037930143608[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.89[/C][C]0.0387444182238271[/C][C]203.642237042233[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.95333333333333[/C][C]0.0284700920153008[/C][C]279.357486061476[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.95333333333333[/C][C]0.0284700920153008[/C][C]279.357486061476[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.86724137931034[/C][C]0.0859236119841185[/C][C]91.5608782922728[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.86785714285714[/C][C]0.080988500981807[/C][C]97.1478302163483[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.87777777777778[/C][C]0.0784932649287826[/C][C]100.362467848997[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.88653846153846[/C][C]0.0760065114973634[/C][C]103.761352891614[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.892[/C][C]0.0741669380106631[/C][C]106.408599460657[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.89583333333333[/C][C]0.0724420980163594[/C][C]108.995094696874[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.9[/C][C]0.0701964118163034[/C][C]112.541364944315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.90454545454545[/C][C]0.0685823331572746[/C][C]115.256292555964[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.90952380952381[/C][C]0.0664173203248596[/C][C]119.088270511921[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.915[/C][C]0.0635034826422324[/C][C]124.638833504483[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.92105263157895[/C][C]0.0612991051727219[/C][C]129.219710618285[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.925[/C][C]0.0592780641459291[/C][C]133.691950204218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.92941176470588[/C][C]0.0564122544816182[/C][C]140.561866168452[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.93125[/C][C]0.0535884669525317[/C][C]148.002927701318[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.93333333333333[/C][C]0.0494413232473044[/C][C]160.459567266252[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.93928571428571[/C][C]0.0446441798745841[/C][C]177.834730900848[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.94615384615385[/C][C]0.0408489786072361[/C][C]194.525153800204[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.95[/C][C]0.0371054119260640[/C][C]214.254460126763[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.95909090909091[/C][C]0.0326725131103754[/C][C]243.602041942817[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.96[/C][C]0.0311194642086199[/C][C]255.788465593027[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.89375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.97567567567568[/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=57236&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57236&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 Mean7.861666666666670.091413620944375486.0010421362746
Geometric Mean7.82931079421107
Harmonic Mean7.7959156854323
Quadratic Mean7.89296099910125
Winsorized Mean ( 1 / 20 )7.866666666666670.089904741385204487.5000199707074
Winsorized Mean ( 2 / 20 )7.850.0845560022359492.8378801317478
Winsorized Mean ( 3 / 20 )7.8550.083240343597680394.3653000516795
Winsorized Mean ( 4 / 20 )7.868333333333330.080024419531044498.3241537950915
Winsorized Mean ( 5 / 20 )7.876666666666670.078198886906215100.726071409600
Winsorized Mean ( 6 / 20 )7.876666666666670.078198886906215100.726071409600
Winsorized Mean ( 7 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 8 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 9 / 20 )7.876666666666670.0737749925732982106.766078747360
Winsorized Mean ( 10 / 20 )7.876666666666670.0677885823872396116.194591910353
Winsorized Mean ( 11 / 20 )7.8950.0643272442304385122.731823731137
Winsorized Mean ( 12 / 20 )7.8950.0643272442304385122.731823731137
Winsorized Mean ( 13 / 20 )7.916666666666670.0604674197500117130.924499497353
Winsorized Mean ( 14 / 20 )7.916666666666670.0604674197500117130.924499497353
Winsorized Mean ( 15 / 20 )7.891666666666670.0565131686401955139.642969179641
Winsorized Mean ( 16 / 20 )7.891666666666670.0478516815534762164.919317576069
Winsorized Mean ( 17 / 20 )7.920.0430346070172593184.037930143608
Winsorized Mean ( 18 / 20 )7.890.0387444182238271203.642237042233
Winsorized Mean ( 19 / 20 )7.953333333333330.0284700920153008279.357486061476
Winsorized Mean ( 20 / 20 )7.953333333333330.0284700920153008279.357486061476
Trimmed Mean ( 1 / 20 )7.867241379310340.085923611984118591.5608782922728
Trimmed Mean ( 2 / 20 )7.867857142857140.08098850098180797.1478302163483
Trimmed Mean ( 3 / 20 )7.877777777777780.0784932649287826100.362467848997
Trimmed Mean ( 4 / 20 )7.886538461538460.0760065114973634103.761352891614
Trimmed Mean ( 5 / 20 )7.8920.0741669380106631106.408599460657
Trimmed Mean ( 6 / 20 )7.895833333333330.0724420980163594108.995094696874
Trimmed Mean ( 7 / 20 )7.90.0701964118163034112.541364944315
Trimmed Mean ( 8 / 20 )7.904545454545450.0685823331572746115.256292555964
Trimmed Mean ( 9 / 20 )7.909523809523810.0664173203248596119.088270511921
Trimmed Mean ( 10 / 20 )7.9150.0635034826422324124.638833504483
Trimmed Mean ( 11 / 20 )7.921052631578950.0612991051727219129.219710618285
Trimmed Mean ( 12 / 20 )7.9250.0592780641459291133.691950204218
Trimmed Mean ( 13 / 20 )7.929411764705880.0564122544816182140.561866168452
Trimmed Mean ( 14 / 20 )7.931250.0535884669525317148.002927701318
Trimmed Mean ( 15 / 20 )7.933333333333330.0494413232473044160.459567266252
Trimmed Mean ( 16 / 20 )7.939285714285710.0446441798745841177.834730900848
Trimmed Mean ( 17 / 20 )7.946153846153850.0408489786072361194.525153800204
Trimmed Mean ( 18 / 20 )7.950.0371054119260640214.254460126763
Trimmed Mean ( 19 / 20 )7.959090909090910.0326725131103754243.602041942817
Trimmed Mean ( 20 / 20 )7.960.0311194642086199255.788465593027
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.89375
Midmean - Weighted Average at X(n+1)p7.89375
Midmean - Empirical Distribution Function7.89375
Midmean - Empirical Distribution Function - Averaging7.89375
Midmean - Empirical Distribution Function - Interpolation7.89375
Midmean - Closest Observation7.89375
Midmean - True Basic - Statistics Graphics Toolkit7.89375
Midmean - MS Excel (old versions)7.97567567567568
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')