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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 04 Nov 2007 04:37:24 -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/2007/Nov/04/ypym0q1m5gvzdx81194176150.htm/, Retrieved Sun, 05 May 2024 19:05:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=384, Retrieved Sun, 05 May 2024 19:05:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsFinaciële situatie
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper WS2 Q3] [2007-11-04 11:37:24] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
22
27
24
24
22
23
25
23
21
21
22
20
22
22
20
21
20
21
21
21
19
21
21
22
19
24
22
22
22
24
22
23
24
21
20
22
23
23
22
20
21
21
20
20
17
18
19
19
20
21
20
21
19
22
20
18
16
17
18
19




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=384&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=384&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.06666666666670.26453953883736679.6352286665853
Geometric Mean20.9676630607978
Harmonic Mean20.8672311079985
Quadratic Mean21.1644355779532
Winsorized Mean ( 1 / 20 )21.050.24864037061246784.6604272192334
Winsorized Mean ( 2 / 20 )21.01666666666670.24063436251260087.3385930721601
Winsorized Mean ( 3 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 4 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 5 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 6 / 20 )21.16666666666670.207441594348658102.036752721302
Winsorized Mean ( 7 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 8 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 9 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 10 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 11 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 12 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 13 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 14 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 15 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 16 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 17 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 18 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 19 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 20 / 20 )21.050.115041137324160182.978024119198
Trimmed Mean ( 1 / 20 )21.05172413793100.23773280536600188.5520368361484
Trimmed Mean ( 2 / 20 )21.05357142857140.22421528797515493.8989112593628
Trimmed Mean ( 3 / 20 )21.07407407407410.21288319230328098.993602294592
Trimmed Mean ( 4 / 20 )21.07692307692310.205222451953820102.702812856294
Trimmed Mean ( 5 / 20 )21.080.195542155797356107.802841356856
Trimmed Mean ( 6 / 20 )21.08333333333330.183139807593258115.121521696463
Trimmed Mean ( 7 / 20 )21.06521739130430.174184570643566120.936184608510
Trimmed Mean ( 8 / 20 )21.06818181818180.170181246723892123.798492629235
Trimmed Mean ( 9 / 20 )21.07142857142860.164831442228431127.83622036278
Trimmed Mean ( 10 / 20 )21.0750.157657125531227133.676165469766
Trimmed Mean ( 11 / 20 )21.07894736842110.147918603137507142.503694067647
Trimmed Mean ( 12 / 20 )21.08333333333330.134370962471643156.903939255349
Trimmed Mean ( 13 / 20 )21.08823529411760.135943570255467155.124918776875
Trimmed Mean ( 14 / 20 )21.093750.137367054497395153.557562089242
Trimmed Mean ( 15 / 20 )21.10.138547473087208152.294369069573
Trimmed Mean ( 16 / 20 )21.10714285714290.139341665603805151.477612713182
Trimmed Mean ( 17 / 20 )21.11538461538460.139525824209362151.336748842282
Trimmed Mean ( 18 / 20 )21.1250.138737840569172152.265596129611
Trimmed Mean ( 19 / 20 )21.13636363636360.136363636363636155
Trimmed Mean ( 20 / 20 )21.150.131289154560699161.094799267838
Median21
Midrange21.5
Midmean - Weighted Average at Xnp21.0833333333333
Midmean - Weighted Average at X(n+1)p21.0833333333333
Midmean - Empirical Distribution Function21.0833333333333
Midmean - Empirical Distribution Function - Averaging21.0833333333333
Midmean - Empirical Distribution Function - Interpolation21.0833333333333
Midmean - Closest Observation21.0833333333333
Midmean - True Basic - Statistics Graphics Toolkit21.0833333333333
Midmean - MS Excel (old versions)21.0833333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.0666666666667 & 0.264539538837366 & 79.6352286665853 \tabularnewline
Geometric Mean & 20.9676630607978 &  &  \tabularnewline
Harmonic Mean & 20.8672311079985 &  &  \tabularnewline
Quadratic Mean & 21.1644355779532 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 21.05 & 0.248640370612467 & 84.6604272192334 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 21.0166666666667 & 0.240634362512600 & 87.3385930721601 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 21.0666666666667 & 0.227820261528883 & 92.4705578217233 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 21.0666666666667 & 0.227820261528883 & 92.4705578217233 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 21.0666666666667 & 0.227820261528883 & 92.4705578217233 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 21.1666666666667 & 0.207441594348658 & 102.036752721302 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 21.05 & 0.183230582402839 & 114.88256885917 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 21.05 & 0.183230582402839 & 114.88256885917 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 21.05 & 0.183230582402839 & 114.88256885917 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 21.05 & 0.183230582402839 & 114.88256885917 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 21.05 & 0.183230582402839 & 114.88256885917 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 21.05 & 0.115041137324160 & 182.978024119198 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 21.0517241379310 & 0.237732805366001 & 88.5520368361484 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 21.0535714285714 & 0.224215287975154 & 93.8989112593628 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 21.0740740740741 & 0.212883192303280 & 98.993602294592 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 21.0769230769231 & 0.205222451953820 & 102.702812856294 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 21.08 & 0.195542155797356 & 107.802841356856 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 21.0833333333333 & 0.183139807593258 & 115.121521696463 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 21.0652173913043 & 0.174184570643566 & 120.936184608510 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 21.0681818181818 & 0.170181246723892 & 123.798492629235 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 21.0714285714286 & 0.164831442228431 & 127.83622036278 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 21.075 & 0.157657125531227 & 133.676165469766 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 21.0789473684211 & 0.147918603137507 & 142.503694067647 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 21.0833333333333 & 0.134370962471643 & 156.903939255349 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 21.0882352941176 & 0.135943570255467 & 155.124918776875 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 21.09375 & 0.137367054497395 & 153.557562089242 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 21.1 & 0.138547473087208 & 152.294369069573 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 21.1071428571429 & 0.139341665603805 & 151.477612713182 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 21.1153846153846 & 0.139525824209362 & 151.336748842282 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 21.125 & 0.138737840569172 & 152.265596129611 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 21.1363636363636 & 0.136363636363636 & 155 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 21.15 & 0.131289154560699 & 161.094799267838 \tabularnewline
Median & 21 &  &  \tabularnewline
Midrange & 21.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.0833333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.0833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.0833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.0833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.0833333333333 &  &  \tabularnewline
Midmean - Closest Observation & 21.0833333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.0833333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.0833333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=384&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]21.0666666666667[/C][C]0.264539538837366[/C][C]79.6352286665853[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.9676630607978[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.8672311079985[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.1644355779532[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]21.05[/C][C]0.248640370612467[/C][C]84.6604272192334[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]21.0166666666667[/C][C]0.240634362512600[/C][C]87.3385930721601[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]21.0666666666667[/C][C]0.227820261528883[/C][C]92.4705578217233[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]21.0666666666667[/C][C]0.227820261528883[/C][C]92.4705578217233[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]21.0666666666667[/C][C]0.227820261528883[/C][C]92.4705578217233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]21.1666666666667[/C][C]0.207441594348658[/C][C]102.036752721302[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]21.05[/C][C]0.183230582402839[/C][C]114.88256885917[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]21.05[/C][C]0.183230582402839[/C][C]114.88256885917[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]21.05[/C][C]0.183230582402839[/C][C]114.88256885917[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]21.05[/C][C]0.183230582402839[/C][C]114.88256885917[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]21.05[/C][C]0.183230582402839[/C][C]114.88256885917[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]21.05[/C][C]0.115041137324160[/C][C]182.978024119198[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]21.0517241379310[/C][C]0.237732805366001[/C][C]88.5520368361484[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]21.0535714285714[/C][C]0.224215287975154[/C][C]93.8989112593628[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]21.0740740740741[/C][C]0.212883192303280[/C][C]98.993602294592[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]21.0769230769231[/C][C]0.205222451953820[/C][C]102.702812856294[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]21.08[/C][C]0.195542155797356[/C][C]107.802841356856[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]21.0833333333333[/C][C]0.183139807593258[/C][C]115.121521696463[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]21.0652173913043[/C][C]0.174184570643566[/C][C]120.936184608510[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]21.0681818181818[/C][C]0.170181246723892[/C][C]123.798492629235[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]21.0714285714286[/C][C]0.164831442228431[/C][C]127.83622036278[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]21.075[/C][C]0.157657125531227[/C][C]133.676165469766[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]21.0789473684211[/C][C]0.147918603137507[/C][C]142.503694067647[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]21.0833333333333[/C][C]0.134370962471643[/C][C]156.903939255349[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]21.0882352941176[/C][C]0.135943570255467[/C][C]155.124918776875[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]21.09375[/C][C]0.137367054497395[/C][C]153.557562089242[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]21.1[/C][C]0.138547473087208[/C][C]152.294369069573[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]21.1071428571429[/C][C]0.139341665603805[/C][C]151.477612713182[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]21.1153846153846[/C][C]0.139525824209362[/C][C]151.336748842282[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]21.125[/C][C]0.138737840569172[/C][C]152.265596129611[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]21.1363636363636[/C][C]0.136363636363636[/C][C]155[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]21.15[/C][C]0.131289154560699[/C][C]161.094799267838[/C][/ROW]
[ROW][C]Median[/C][C]21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.0833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.0833333333333[/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=384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=384&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 Mean21.06666666666670.26453953883736679.6352286665853
Geometric Mean20.9676630607978
Harmonic Mean20.8672311079985
Quadratic Mean21.1644355779532
Winsorized Mean ( 1 / 20 )21.050.24864037061246784.6604272192334
Winsorized Mean ( 2 / 20 )21.01666666666670.24063436251260087.3385930721601
Winsorized Mean ( 3 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 4 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 5 / 20 )21.06666666666670.22782026152888392.4705578217233
Winsorized Mean ( 6 / 20 )21.16666666666670.207441594348658102.036752721302
Winsorized Mean ( 7 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 8 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 9 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 10 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 11 / 20 )21.050.183230582402839114.88256885917
Winsorized Mean ( 12 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 13 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 14 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 15 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 16 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 17 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 18 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 19 / 20 )21.050.115041137324160182.978024119198
Winsorized Mean ( 20 / 20 )21.050.115041137324160182.978024119198
Trimmed Mean ( 1 / 20 )21.05172413793100.23773280536600188.5520368361484
Trimmed Mean ( 2 / 20 )21.05357142857140.22421528797515493.8989112593628
Trimmed Mean ( 3 / 20 )21.07407407407410.21288319230328098.993602294592
Trimmed Mean ( 4 / 20 )21.07692307692310.205222451953820102.702812856294
Trimmed Mean ( 5 / 20 )21.080.195542155797356107.802841356856
Trimmed Mean ( 6 / 20 )21.08333333333330.183139807593258115.121521696463
Trimmed Mean ( 7 / 20 )21.06521739130430.174184570643566120.936184608510
Trimmed Mean ( 8 / 20 )21.06818181818180.170181246723892123.798492629235
Trimmed Mean ( 9 / 20 )21.07142857142860.164831442228431127.83622036278
Trimmed Mean ( 10 / 20 )21.0750.157657125531227133.676165469766
Trimmed Mean ( 11 / 20 )21.07894736842110.147918603137507142.503694067647
Trimmed Mean ( 12 / 20 )21.08333333333330.134370962471643156.903939255349
Trimmed Mean ( 13 / 20 )21.08823529411760.135943570255467155.124918776875
Trimmed Mean ( 14 / 20 )21.093750.137367054497395153.557562089242
Trimmed Mean ( 15 / 20 )21.10.138547473087208152.294369069573
Trimmed Mean ( 16 / 20 )21.10714285714290.139341665603805151.477612713182
Trimmed Mean ( 17 / 20 )21.11538461538460.139525824209362151.336748842282
Trimmed Mean ( 18 / 20 )21.1250.138737840569172152.265596129611
Trimmed Mean ( 19 / 20 )21.13636363636360.136363636363636155
Trimmed Mean ( 20 / 20 )21.150.131289154560699161.094799267838
Median21
Midrange21.5
Midmean - Weighted Average at Xnp21.0833333333333
Midmean - Weighted Average at X(n+1)p21.0833333333333
Midmean - Empirical Distribution Function21.0833333333333
Midmean - Empirical Distribution Function - Averaging21.0833333333333
Midmean - Empirical Distribution Function - Interpolation21.0833333333333
Midmean - Closest Observation21.0833333333333
Midmean - True Basic - Statistics Graphics Toolkit21.0833333333333
Midmean - MS Excel (old versions)21.0833333333333
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')