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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 15:55:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1255989666ptxejtnsty8jyjc.htm/, Retrieved Thu, 02 May 2024 19:20:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48281, Retrieved Thu, 02 May 2024 19:20:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS3P2ST3AMLDG
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 3: part ...] [2009-10-19 21:13:54] [7c2a5b25a196bd646844b8f5223c9b3e]
- RMP     [Central Tendency] [Workshop 3: part ...] [2009-10-19 21:55:53] [3d2053c5f7c50d3c075d87ce0bd87294] [Current]
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Dataseries X:
0.88
0.86
0.87
0.88
0.88
0.89
0.89
0.89
0.89
0.87
0.86
0.86
0.87
0.89
0.90
0.90
0.89
0.91
0.91
0.92
0.92
0.90
0.88
0.87
0.89
0.90
0.91
0.91
0.92
0.93
0.92
0.93
0.93
0.89
0.87
0.86
0.89
0.91
0.91
0.92
0.93
0.93
0.93
0.94
0.93
0.90
0.88
0.87
0.91
0.94
0.96
0.98
1.00
1.02
1.04
1.04
1.04
1.03
1.00
0.98
1.02




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48281&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48281&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9186885245901640.00632660878192784145.210262915960
Geometric Mean0.917430772364169
Harmonic Mean0.91622082930188
Quadratic Mean0.919994654296657
Winsorized Mean ( 1 / 20 )0.9186885245901640.00632660878192784145.210262915960
Winsorized Mean ( 2 / 20 )0.9186885245901640.00632660878192784145.210262915960
Winsorized Mean ( 3 / 20 )0.9181967213114750.00617375104831974148.725906523454
Winsorized Mean ( 4 / 20 )0.9181967213114750.00588370072718406156.057686120777
Winsorized Mean ( 5 / 20 )0.9181967213114750.00588370072718406156.057686120777
Winsorized Mean ( 6 / 20 )0.9162295081967210.00534168029081694171.524587454596
Winsorized Mean ( 7 / 20 )0.9162295081967210.00534168029081694171.524587454596
Winsorized Mean ( 8 / 20 )0.913606557377050.00468711049025171194.918929109347
Winsorized Mean ( 9 / 20 )0.913606557377050.00468711049025171194.918929109347
Winsorized Mean ( 10 / 20 )0.9119672131147540.0036947730923411246.826311203027
Winsorized Mean ( 11 / 20 )0.9083606557377050.00297696372136073305.129904412307
Winsorized Mean ( 12 / 20 )0.9083606557377050.00297696372136073305.129904412307
Winsorized Mean ( 13 / 20 )0.9062295081967210.00262568163854781345.140665529402
Winsorized Mean ( 14 / 20 )0.9062295081967210.00262568163854781345.140665529402
Winsorized Mean ( 15 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 16 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 17 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 18 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 19 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 20 / 20 )0.9054098360655740.00175825563226869514.947780885149
Trimmed Mean ( 1 / 20 )0.9176271186440680.00612235931959835149.881290976608
Trimmed Mean ( 2 / 20 )0.9164912280701750.00586764645677808156.194009782488
Trimmed Mean ( 3 / 20 )0.9152727272727270.00554658596395341165.015512825542
Trimmed Mean ( 4 / 20 )0.9141509433962260.00521965945888948175.136127288794
Trimmed Mean ( 5 / 20 )0.9129411764705880.00492527787727726185.358308549948
Trimmed Mean ( 6 / 20 )0.9116326530612250.00453957408674801200.818983376101
Trimmed Mean ( 7 / 20 )0.910638297872340.00424072427749095214.736502136170
Trimmed Mean ( 8 / 20 )0.9095555555555560.00383965954345591236.884428231599
Trimmed Mean ( 9 / 20 )0.9088372093023260.00354076563733241256.678160147035
Trimmed Mean ( 10 / 20 )0.9080487804878050.00312775755787889290.319426517062
Trimmed Mean ( 11 / 20 )0.9074358974358970.00290928869153292311.909883703485
Trimmed Mean ( 12 / 20 )0.9072972972972970.00283819531567989319.674016895470
Trimmed Mean ( 13 / 20 )0.9071428571428570.00273696846868199331.440740923004
Trimmed Mean ( 14 / 20 )0.9072727272727270.00269232661271468336.984644800551
Trimmed Mean ( 15 / 20 )0.907419354838710.00262198078023696346.081619544405
Trimmed Mean ( 16 / 20 )0.9072413793103450.00262127294519971346.107177038454
Trimmed Mean ( 17 / 20 )0.9070370370370370.00260477398742929348.221013191326
Trimmed Mean ( 18 / 20 )0.90680.00256385126973726353.686662991543
Trimmed Mean ( 19 / 20 )0.9065217391304350.00248383673412885364.968327698228
Trimmed Mean ( 20 / 20 )0.9061904761904760.00233770242069211387.641501402982
Median0.91
Midrange0.95
Midmean - Weighted Average at Xnp0.908787878787879
Midmean - Weighted Average at X(n+1)p0.908787878787879
Midmean - Empirical Distribution Function0.908787878787879
Midmean - Empirical Distribution Function - Averaging0.908787878787879
Midmean - Empirical Distribution Function - Interpolation0.908787878787879
Midmean - Closest Observation0.905
Midmean - True Basic - Statistics Graphics Toolkit0.908787878787879
Midmean - MS Excel (old versions)0.908787878787879
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.918688524590164 & 0.00632660878192784 & 145.210262915960 \tabularnewline
Geometric Mean & 0.917430772364169 &  &  \tabularnewline
Harmonic Mean & 0.91622082930188 &  &  \tabularnewline
Quadratic Mean & 0.919994654296657 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.918688524590164 & 0.00632660878192784 & 145.210262915960 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.918688524590164 & 0.00632660878192784 & 145.210262915960 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.918196721311475 & 0.00617375104831974 & 148.725906523454 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.918196721311475 & 0.00588370072718406 & 156.057686120777 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.918196721311475 & 0.00588370072718406 & 156.057686120777 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.916229508196721 & 0.00534168029081694 & 171.524587454596 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.916229508196721 & 0.00534168029081694 & 171.524587454596 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.91360655737705 & 0.00468711049025171 & 194.918929109347 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.91360655737705 & 0.00468711049025171 & 194.918929109347 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.911967213114754 & 0.0036947730923411 & 246.826311203027 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.908360655737705 & 0.00297696372136073 & 305.129904412307 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.908360655737705 & 0.00297696372136073 & 305.129904412307 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.906229508196721 & 0.00262568163854781 & 345.140665529402 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.906229508196721 & 0.00262568163854781 & 345.140665529402 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.908688524590164 & 0.00224795486697087 & 404.228989621409 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.908688524590164 & 0.00224795486697087 & 404.228989621409 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.908688524590164 & 0.00224795486697087 & 404.228989621409 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.908688524590164 & 0.00224795486697087 & 404.228989621409 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.908688524590164 & 0.00224795486697087 & 404.228989621409 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.905409836065574 & 0.00175825563226869 & 514.947780885149 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.917627118644068 & 0.00612235931959835 & 149.881290976608 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.916491228070175 & 0.00586764645677808 & 156.194009782488 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.915272727272727 & 0.00554658596395341 & 165.015512825542 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.914150943396226 & 0.00521965945888948 & 175.136127288794 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.912941176470588 & 0.00492527787727726 & 185.358308549948 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.911632653061225 & 0.00453957408674801 & 200.818983376101 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.91063829787234 & 0.00424072427749095 & 214.736502136170 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.909555555555556 & 0.00383965954345591 & 236.884428231599 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.908837209302326 & 0.00354076563733241 & 256.678160147035 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.908048780487805 & 0.00312775755787889 & 290.319426517062 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.907435897435897 & 0.00290928869153292 & 311.909883703485 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.907297297297297 & 0.00283819531567989 & 319.674016895470 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.907142857142857 & 0.00273696846868199 & 331.440740923004 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.907272727272727 & 0.00269232661271468 & 336.984644800551 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.90741935483871 & 0.00262198078023696 & 346.081619544405 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.907241379310345 & 0.00262127294519971 & 346.107177038454 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.907037037037037 & 0.00260477398742929 & 348.221013191326 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.9068 & 0.00256385126973726 & 353.686662991543 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.906521739130435 & 0.00248383673412885 & 364.968327698228 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.906190476190476 & 0.00233770242069211 & 387.641501402982 \tabularnewline
Median & 0.91 &  &  \tabularnewline
Midrange & 0.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.908787878787879 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.908787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.908787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.908787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.908787878787879 &  &  \tabularnewline
Midmean - Closest Observation & 0.905 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.908787878787879 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.908787878787879 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48281&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]0.918688524590164[/C][C]0.00632660878192784[/C][C]145.210262915960[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.917430772364169[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.91622082930188[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.919994654296657[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.918688524590164[/C][C]0.00632660878192784[/C][C]145.210262915960[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.918688524590164[/C][C]0.00632660878192784[/C][C]145.210262915960[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.918196721311475[/C][C]0.00617375104831974[/C][C]148.725906523454[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.918196721311475[/C][C]0.00588370072718406[/C][C]156.057686120777[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.918196721311475[/C][C]0.00588370072718406[/C][C]156.057686120777[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.916229508196721[/C][C]0.00534168029081694[/C][C]171.524587454596[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.916229508196721[/C][C]0.00534168029081694[/C][C]171.524587454596[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.91360655737705[/C][C]0.00468711049025171[/C][C]194.918929109347[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.91360655737705[/C][C]0.00468711049025171[/C][C]194.918929109347[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.911967213114754[/C][C]0.0036947730923411[/C][C]246.826311203027[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.908360655737705[/C][C]0.00297696372136073[/C][C]305.129904412307[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.908360655737705[/C][C]0.00297696372136073[/C][C]305.129904412307[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.906229508196721[/C][C]0.00262568163854781[/C][C]345.140665529402[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.906229508196721[/C][C]0.00262568163854781[/C][C]345.140665529402[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.908688524590164[/C][C]0.00224795486697087[/C][C]404.228989621409[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.908688524590164[/C][C]0.00224795486697087[/C][C]404.228989621409[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.908688524590164[/C][C]0.00224795486697087[/C][C]404.228989621409[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.908688524590164[/C][C]0.00224795486697087[/C][C]404.228989621409[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.908688524590164[/C][C]0.00224795486697087[/C][C]404.228989621409[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.905409836065574[/C][C]0.00175825563226869[/C][C]514.947780885149[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.917627118644068[/C][C]0.00612235931959835[/C][C]149.881290976608[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.916491228070175[/C][C]0.00586764645677808[/C][C]156.194009782488[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.915272727272727[/C][C]0.00554658596395341[/C][C]165.015512825542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.914150943396226[/C][C]0.00521965945888948[/C][C]175.136127288794[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.912941176470588[/C][C]0.00492527787727726[/C][C]185.358308549948[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.911632653061225[/C][C]0.00453957408674801[/C][C]200.818983376101[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.91063829787234[/C][C]0.00424072427749095[/C][C]214.736502136170[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.909555555555556[/C][C]0.00383965954345591[/C][C]236.884428231599[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.908837209302326[/C][C]0.00354076563733241[/C][C]256.678160147035[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.908048780487805[/C][C]0.00312775755787889[/C][C]290.319426517062[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.907435897435897[/C][C]0.00290928869153292[/C][C]311.909883703485[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.907297297297297[/C][C]0.00283819531567989[/C][C]319.674016895470[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.907142857142857[/C][C]0.00273696846868199[/C][C]331.440740923004[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.907272727272727[/C][C]0.00269232661271468[/C][C]336.984644800551[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.90741935483871[/C][C]0.00262198078023696[/C][C]346.081619544405[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.907241379310345[/C][C]0.00262127294519971[/C][C]346.107177038454[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.907037037037037[/C][C]0.00260477398742929[/C][C]348.221013191326[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.9068[/C][C]0.00256385126973726[/C][C]353.686662991543[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.906521739130435[/C][C]0.00248383673412885[/C][C]364.968327698228[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.906190476190476[/C][C]0.00233770242069211[/C][C]387.641501402982[/C][/ROW]
[ROW][C]Median[/C][C]0.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.908787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48281&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 Mean0.9186885245901640.00632660878192784145.210262915960
Geometric Mean0.917430772364169
Harmonic Mean0.91622082930188
Quadratic Mean0.919994654296657
Winsorized Mean ( 1 / 20 )0.9186885245901640.00632660878192784145.210262915960
Winsorized Mean ( 2 / 20 )0.9186885245901640.00632660878192784145.210262915960
Winsorized Mean ( 3 / 20 )0.9181967213114750.00617375104831974148.725906523454
Winsorized Mean ( 4 / 20 )0.9181967213114750.00588370072718406156.057686120777
Winsorized Mean ( 5 / 20 )0.9181967213114750.00588370072718406156.057686120777
Winsorized Mean ( 6 / 20 )0.9162295081967210.00534168029081694171.524587454596
Winsorized Mean ( 7 / 20 )0.9162295081967210.00534168029081694171.524587454596
Winsorized Mean ( 8 / 20 )0.913606557377050.00468711049025171194.918929109347
Winsorized Mean ( 9 / 20 )0.913606557377050.00468711049025171194.918929109347
Winsorized Mean ( 10 / 20 )0.9119672131147540.0036947730923411246.826311203027
Winsorized Mean ( 11 / 20 )0.9083606557377050.00297696372136073305.129904412307
Winsorized Mean ( 12 / 20 )0.9083606557377050.00297696372136073305.129904412307
Winsorized Mean ( 13 / 20 )0.9062295081967210.00262568163854781345.140665529402
Winsorized Mean ( 14 / 20 )0.9062295081967210.00262568163854781345.140665529402
Winsorized Mean ( 15 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 16 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 17 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 18 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 19 / 20 )0.9086885245901640.00224795486697087404.228989621409
Winsorized Mean ( 20 / 20 )0.9054098360655740.00175825563226869514.947780885149
Trimmed Mean ( 1 / 20 )0.9176271186440680.00612235931959835149.881290976608
Trimmed Mean ( 2 / 20 )0.9164912280701750.00586764645677808156.194009782488
Trimmed Mean ( 3 / 20 )0.9152727272727270.00554658596395341165.015512825542
Trimmed Mean ( 4 / 20 )0.9141509433962260.00521965945888948175.136127288794
Trimmed Mean ( 5 / 20 )0.9129411764705880.00492527787727726185.358308549948
Trimmed Mean ( 6 / 20 )0.9116326530612250.00453957408674801200.818983376101
Trimmed Mean ( 7 / 20 )0.910638297872340.00424072427749095214.736502136170
Trimmed Mean ( 8 / 20 )0.9095555555555560.00383965954345591236.884428231599
Trimmed Mean ( 9 / 20 )0.9088372093023260.00354076563733241256.678160147035
Trimmed Mean ( 10 / 20 )0.9080487804878050.00312775755787889290.319426517062
Trimmed Mean ( 11 / 20 )0.9074358974358970.00290928869153292311.909883703485
Trimmed Mean ( 12 / 20 )0.9072972972972970.00283819531567989319.674016895470
Trimmed Mean ( 13 / 20 )0.9071428571428570.00273696846868199331.440740923004
Trimmed Mean ( 14 / 20 )0.9072727272727270.00269232661271468336.984644800551
Trimmed Mean ( 15 / 20 )0.907419354838710.00262198078023696346.081619544405
Trimmed Mean ( 16 / 20 )0.9072413793103450.00262127294519971346.107177038454
Trimmed Mean ( 17 / 20 )0.9070370370370370.00260477398742929348.221013191326
Trimmed Mean ( 18 / 20 )0.90680.00256385126973726353.686662991543
Trimmed Mean ( 19 / 20 )0.9065217391304350.00248383673412885364.968327698228
Trimmed Mean ( 20 / 20 )0.9061904761904760.00233770242069211387.641501402982
Median0.91
Midrange0.95
Midmean - Weighted Average at Xnp0.908787878787879
Midmean - Weighted Average at X(n+1)p0.908787878787879
Midmean - Empirical Distribution Function0.908787878787879
Midmean - Empirical Distribution Function - Averaging0.908787878787879
Midmean - Empirical Distribution Function - Interpolation0.908787878787879
Midmean - Closest Observation0.905
Midmean - True Basic - Statistics Graphics Toolkit0.908787878787879
Midmean - MS Excel (old versions)0.908787878787879
Number of observations61



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')