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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 15 Mar 2012 09:56:28 -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/2012/Mar/15/t13318198267xefq74ziod45ve.htm/, Retrieved Sun, 28 Apr 2024 11:38:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164020, Retrieved Sun, 28 Apr 2024 11:38:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave5 Oefening2...] [2012-03-15 13:56:28] [8c2ac70842cc3f093ee1ba38f92d16ef] [Current]
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Dataseries X:
1.26
1.26
1.28
1.34
1.39
1.47
1.57
1.63
1.72
1.43
1.35
1.41
1.44
1.43
1.43
1.42
1.45
1.51
1.48
1.48
1.45
1.38
1.46
1.45
1.41
1.45
1.47
1.47
1.53
1.56
1.66
1.79
1.78
1.46
1.41
1.43
1.43
1.45
1.35
1.35
1.29
1.29
1.26
1.3
1.3
1.16
1.24
1.15
1.21
1.22
1.17
1.13
1.15
1.2
1.23
1.25
1.38
1.28
1.26
1.25




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=164020&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=164020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164020&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 Mean1.386833333333330.019356150085679771.6482010727616
Geometric Mean1.37907313449182
Harmonic Mean1.37150306952698
Quadratic Mean1.39478014994001
Winsorized Mean ( 1 / 20 )1.3870.019225542097078972.1436094231505
Winsorized Mean ( 2 / 20 )1.3850.018572654705907374.5719996376977
Winsorized Mean ( 3 / 20 )1.38250.017604610656989378.5305637788205
Winsorized Mean ( 4 / 20 )1.381166666666670.016946395491391681.5020909531036
Winsorized Mean ( 5 / 20 )1.378666666666670.015276115300747590.2498206857082
Winsorized Mean ( 6 / 20 )1.378666666666670.014871325053646892.7063769834405
Winsorized Mean ( 7 / 20 )1.376333333333330.013959114363847698.5974681100022
Winsorized Mean ( 8 / 20 )1.3750.013228756555323103.940230077537
Winsorized Mean ( 9 / 20 )1.3720.0122238999019772112.239138981993
Winsorized Mean ( 10 / 20 )1.373666666666670.0119248273191412115.193841378459
Winsorized Mean ( 11 / 20 )1.371833333333330.0116553415573001117.69996842985
Winsorized Mean ( 12 / 20 )1.373833333333330.011307443842547121.498134544251
Winsorized Mean ( 13 / 20 )1.373833333333330.011307443842547121.498134544251
Winsorized Mean ( 14 / 20 )1.37150.0109797579547895124.911678895593
Winsorized Mean ( 15 / 20 )1.37150.0109797579547895124.911678895593
Winsorized Mean ( 16 / 20 )1.374166666666670.00972297548870966141.331906910837
Winsorized Mean ( 17 / 20 )1.374166666666670.00972297548870966141.331906910837
Winsorized Mean ( 18 / 20 )1.377166666666670.00923666137578931149.097884033773
Winsorized Mean ( 19 / 20 )1.377166666666670.00923666137578931149.097884033773
Winsorized Mean ( 20 / 20 )1.38050.00870880131470359158.517797124298
Trimmed Mean ( 1 / 20 )1.384310344827590.018219459473504975.9797702473381
Trimmed Mean ( 2 / 20 )1.381428571428570.016955688183647381.4728695447982
Trimmed Mean ( 3 / 20 )1.379444444444440.015828873181062487.1473558897929
Trimmed Mean ( 4 / 20 )1.378269230769230.014917372103897492.3935677926234
Trimmed Mean ( 5 / 20 )1.37740.014046017664978898.0633822947761
Trimmed Mean ( 6 / 20 )1.377083333333330.0135595558324571101.558144702428
Trimmed Mean ( 7 / 20 )1.376739130434780.0130663647843939105.365122828893
Trimmed Mean ( 8 / 20 )1.376818181818180.0127040334494627108.376460696143
Trimmed Mean ( 9 / 20 )1.377142857142860.0124299931102457110.79192441448
Trimmed Mean ( 10 / 20 )1.3780.0123163431136156111.883859298839
Trimmed Mean ( 11 / 20 )1.378684210526320.0122164630929888112.854612667521
Trimmed Mean ( 12 / 20 )1.379722222222220.0121137866565535113.896856642741
Trimmed Mean ( 13 / 20 )1.380588235294120.0120304217506791114.758091104843
Trimmed Mean ( 14 / 20 )1.38156250.0118722142318158116.369404478704
Trimmed Mean ( 15 / 20 )1.3830.0116870101778236118.33651027568
Trimmed Mean ( 16 / 20 )1.384642857142860.0113678529248463121.803375386437
Trimmed Mean ( 17 / 20 )1.386153846153850.0112602353176248123.101676568358
Trimmed Mean ( 18 / 20 )1.387916666666670.0110167719085503125.982155043936
Trimmed Mean ( 19 / 20 )1.389545454545450.0107606239203247129.132424368152
Trimmed Mean ( 20 / 20 )1.39150.0102411707801095135.87313695643
Median1.41
Midrange1.46
Midmean - Weighted Average at Xnp1.37441176470588
Midmean - Weighted Average at X(n+1)p1.37441176470588
Midmean - Empirical Distribution Function1.37441176470588
Midmean - Empirical Distribution Function - Averaging1.37441176470588
Midmean - Empirical Distribution Function - Interpolation1.37441176470588
Midmean - Closest Observation1.37441176470588
Midmean - True Basic - Statistics Graphics Toolkit1.37441176470588
Midmean - MS Excel (old versions)1.37441176470588
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.38683333333333 & 0.0193561500856797 & 71.6482010727616 \tabularnewline
Geometric Mean & 1.37907313449182 &  &  \tabularnewline
Harmonic Mean & 1.37150306952698 &  &  \tabularnewline
Quadratic Mean & 1.39478014994001 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.387 & 0.0192255420970789 & 72.1436094231505 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.385 & 0.0185726547059073 & 74.5719996376977 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.3825 & 0.0176046106569893 & 78.5305637788205 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.38116666666667 & 0.0169463954913916 & 81.5020909531036 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.37866666666667 & 0.0152761153007475 & 90.2498206857082 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.37866666666667 & 0.0148713250536468 & 92.7063769834405 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.37633333333333 & 0.0139591143638476 & 98.5974681100022 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.375 & 0.013228756555323 & 103.940230077537 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.372 & 0.0122238999019772 & 112.239138981993 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.37366666666667 & 0.0119248273191412 & 115.193841378459 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.37183333333333 & 0.0116553415573001 & 117.69996842985 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.37383333333333 & 0.011307443842547 & 121.498134544251 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.37383333333333 & 0.011307443842547 & 121.498134544251 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.3715 & 0.0109797579547895 & 124.911678895593 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.3715 & 0.0109797579547895 & 124.911678895593 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.37416666666667 & 0.00972297548870966 & 141.331906910837 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.37416666666667 & 0.00972297548870966 & 141.331906910837 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.37716666666667 & 0.00923666137578931 & 149.097884033773 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.37716666666667 & 0.00923666137578931 & 149.097884033773 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.3805 & 0.00870880131470359 & 158.517797124298 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.38431034482759 & 0.0182194594735049 & 75.9797702473381 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.38142857142857 & 0.0169556881836473 & 81.4728695447982 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.37944444444444 & 0.0158288731810624 & 87.1473558897929 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.37826923076923 & 0.0149173721038974 & 92.3935677926234 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.3774 & 0.0140460176649788 & 98.0633822947761 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.37708333333333 & 0.0135595558324571 & 101.558144702428 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.37673913043478 & 0.0130663647843939 & 105.365122828893 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.37681818181818 & 0.0127040334494627 & 108.376460696143 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.37714285714286 & 0.0124299931102457 & 110.79192441448 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.378 & 0.0123163431136156 & 111.883859298839 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.37868421052632 & 0.0122164630929888 & 112.854612667521 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.37972222222222 & 0.0121137866565535 & 113.896856642741 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.38058823529412 & 0.0120304217506791 & 114.758091104843 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.3815625 & 0.0118722142318158 & 116.369404478704 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.383 & 0.0116870101778236 & 118.33651027568 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.38464285714286 & 0.0113678529248463 & 121.803375386437 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.38615384615385 & 0.0112602353176248 & 123.101676568358 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.38791666666667 & 0.0110167719085503 & 125.982155043936 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.38954545454545 & 0.0107606239203247 & 129.132424368152 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.3915 & 0.0102411707801095 & 135.87313695643 \tabularnewline
Median & 1.41 &  &  \tabularnewline
Midrange & 1.46 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.37441176470588 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.37441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.37441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.37441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.37441176470588 &  &  \tabularnewline
Midmean - Closest Observation & 1.37441176470588 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.37441176470588 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.37441176470588 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164020&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.38683333333333[/C][C]0.0193561500856797[/C][C]71.6482010727616[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.37907313449182[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.37150306952698[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.39478014994001[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.387[/C][C]0.0192255420970789[/C][C]72.1436094231505[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.385[/C][C]0.0185726547059073[/C][C]74.5719996376977[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.3825[/C][C]0.0176046106569893[/C][C]78.5305637788205[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.38116666666667[/C][C]0.0169463954913916[/C][C]81.5020909531036[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.37866666666667[/C][C]0.0152761153007475[/C][C]90.2498206857082[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.37866666666667[/C][C]0.0148713250536468[/C][C]92.7063769834405[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.37633333333333[/C][C]0.0139591143638476[/C][C]98.5974681100022[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.375[/C][C]0.013228756555323[/C][C]103.940230077537[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.372[/C][C]0.0122238999019772[/C][C]112.239138981993[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.37366666666667[/C][C]0.0119248273191412[/C][C]115.193841378459[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.37183333333333[/C][C]0.0116553415573001[/C][C]117.69996842985[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.37383333333333[/C][C]0.011307443842547[/C][C]121.498134544251[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.37383333333333[/C][C]0.011307443842547[/C][C]121.498134544251[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.3715[/C][C]0.0109797579547895[/C][C]124.911678895593[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.3715[/C][C]0.0109797579547895[/C][C]124.911678895593[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.37416666666667[/C][C]0.00972297548870966[/C][C]141.331906910837[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.37416666666667[/C][C]0.00972297548870966[/C][C]141.331906910837[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.37716666666667[/C][C]0.00923666137578931[/C][C]149.097884033773[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.37716666666667[/C][C]0.00923666137578931[/C][C]149.097884033773[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.3805[/C][C]0.00870880131470359[/C][C]158.517797124298[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.38431034482759[/C][C]0.0182194594735049[/C][C]75.9797702473381[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.38142857142857[/C][C]0.0169556881836473[/C][C]81.4728695447982[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.37944444444444[/C][C]0.0158288731810624[/C][C]87.1473558897929[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.37826923076923[/C][C]0.0149173721038974[/C][C]92.3935677926234[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.3774[/C][C]0.0140460176649788[/C][C]98.0633822947761[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.37708333333333[/C][C]0.0135595558324571[/C][C]101.558144702428[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.37673913043478[/C][C]0.0130663647843939[/C][C]105.365122828893[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.37681818181818[/C][C]0.0127040334494627[/C][C]108.376460696143[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.37714285714286[/C][C]0.0124299931102457[/C][C]110.79192441448[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.378[/C][C]0.0123163431136156[/C][C]111.883859298839[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.37868421052632[/C][C]0.0122164630929888[/C][C]112.854612667521[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.37972222222222[/C][C]0.0121137866565535[/C][C]113.896856642741[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.38058823529412[/C][C]0.0120304217506791[/C][C]114.758091104843[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.3815625[/C][C]0.0118722142318158[/C][C]116.369404478704[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.383[/C][C]0.0116870101778236[/C][C]118.33651027568[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.38464285714286[/C][C]0.0113678529248463[/C][C]121.803375386437[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.38615384615385[/C][C]0.0112602353176248[/C][C]123.101676568358[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.38791666666667[/C][C]0.0110167719085503[/C][C]125.982155043936[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.38954545454545[/C][C]0.0107606239203247[/C][C]129.132424368152[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.3915[/C][C]0.0102411707801095[/C][C]135.87313695643[/C][/ROW]
[ROW][C]Median[/C][C]1.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.37441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.37441176470588[/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=164020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164020&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.386833333333330.019356150085679771.6482010727616
Geometric Mean1.37907313449182
Harmonic Mean1.37150306952698
Quadratic Mean1.39478014994001
Winsorized Mean ( 1 / 20 )1.3870.019225542097078972.1436094231505
Winsorized Mean ( 2 / 20 )1.3850.018572654705907374.5719996376977
Winsorized Mean ( 3 / 20 )1.38250.017604610656989378.5305637788205
Winsorized Mean ( 4 / 20 )1.381166666666670.016946395491391681.5020909531036
Winsorized Mean ( 5 / 20 )1.378666666666670.015276115300747590.2498206857082
Winsorized Mean ( 6 / 20 )1.378666666666670.014871325053646892.7063769834405
Winsorized Mean ( 7 / 20 )1.376333333333330.013959114363847698.5974681100022
Winsorized Mean ( 8 / 20 )1.3750.013228756555323103.940230077537
Winsorized Mean ( 9 / 20 )1.3720.0122238999019772112.239138981993
Winsorized Mean ( 10 / 20 )1.373666666666670.0119248273191412115.193841378459
Winsorized Mean ( 11 / 20 )1.371833333333330.0116553415573001117.69996842985
Winsorized Mean ( 12 / 20 )1.373833333333330.011307443842547121.498134544251
Winsorized Mean ( 13 / 20 )1.373833333333330.011307443842547121.498134544251
Winsorized Mean ( 14 / 20 )1.37150.0109797579547895124.911678895593
Winsorized Mean ( 15 / 20 )1.37150.0109797579547895124.911678895593
Winsorized Mean ( 16 / 20 )1.374166666666670.00972297548870966141.331906910837
Winsorized Mean ( 17 / 20 )1.374166666666670.00972297548870966141.331906910837
Winsorized Mean ( 18 / 20 )1.377166666666670.00923666137578931149.097884033773
Winsorized Mean ( 19 / 20 )1.377166666666670.00923666137578931149.097884033773
Winsorized Mean ( 20 / 20 )1.38050.00870880131470359158.517797124298
Trimmed Mean ( 1 / 20 )1.384310344827590.018219459473504975.9797702473381
Trimmed Mean ( 2 / 20 )1.381428571428570.016955688183647381.4728695447982
Trimmed Mean ( 3 / 20 )1.379444444444440.015828873181062487.1473558897929
Trimmed Mean ( 4 / 20 )1.378269230769230.014917372103897492.3935677926234
Trimmed Mean ( 5 / 20 )1.37740.014046017664978898.0633822947761
Trimmed Mean ( 6 / 20 )1.377083333333330.0135595558324571101.558144702428
Trimmed Mean ( 7 / 20 )1.376739130434780.0130663647843939105.365122828893
Trimmed Mean ( 8 / 20 )1.376818181818180.0127040334494627108.376460696143
Trimmed Mean ( 9 / 20 )1.377142857142860.0124299931102457110.79192441448
Trimmed Mean ( 10 / 20 )1.3780.0123163431136156111.883859298839
Trimmed Mean ( 11 / 20 )1.378684210526320.0122164630929888112.854612667521
Trimmed Mean ( 12 / 20 )1.379722222222220.0121137866565535113.896856642741
Trimmed Mean ( 13 / 20 )1.380588235294120.0120304217506791114.758091104843
Trimmed Mean ( 14 / 20 )1.38156250.0118722142318158116.369404478704
Trimmed Mean ( 15 / 20 )1.3830.0116870101778236118.33651027568
Trimmed Mean ( 16 / 20 )1.384642857142860.0113678529248463121.803375386437
Trimmed Mean ( 17 / 20 )1.386153846153850.0112602353176248123.101676568358
Trimmed Mean ( 18 / 20 )1.387916666666670.0110167719085503125.982155043936
Trimmed Mean ( 19 / 20 )1.389545454545450.0107606239203247129.132424368152
Trimmed Mean ( 20 / 20 )1.39150.0102411707801095135.87313695643
Median1.41
Midrange1.46
Midmean - Weighted Average at Xnp1.37441176470588
Midmean - Weighted Average at X(n+1)p1.37441176470588
Midmean - Empirical Distribution Function1.37441176470588
Midmean - Empirical Distribution Function - Averaging1.37441176470588
Midmean - Empirical Distribution Function - Interpolation1.37441176470588
Midmean - Closest Observation1.37441176470588
Midmean - True Basic - Statistics Graphics Toolkit1.37441176470588
Midmean - MS Excel (old versions)1.37441176470588
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')