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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 computationFri, 14 Dec 2007 03:20:42 -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/Dec/14/t11976267968konc8w8eckl9ys.htm/, Retrieved Fri, 03 May 2024 03:38:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3798, Retrieved Fri, 03 May 2024 03:38:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact216
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper6] [2007-12-14 10:20:42] [0608207d88b1eaba866515cf0d1cb34d] [Current]
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Dataseries X:
-0.32
-4.92
-8.24
-2.26
-3.22
-8.32
-1.78
-5.56
-9.16
-1.94
-7.84
-3.666666667
-1.22
-6.92
-2.24
-5.06
-3.42
-0.12
-0.18
-5.26
-1.66
0.76
-0.54
3.033333333
-0.72
-0.72
2.36
-2.66
-2.92
-5.02
-1.78
-4.76
1.54
-5.74
-2.34
1.833333333
-4.42
4.88
4.36
1.74
2.88
5.08
-1.08
7.94
3.14
0.06
3.66
3.933333333
6.68
7.68
3.76
8.24
6.68
8.38
4.82
7.64
6.14
6.86
7.06
0.933333333





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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3798&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3798&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3798&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.1011111110833330.6158379256752020.164184612327140
Geometric MeanNaN
Harmonic Mean-10.9242150359964
Quadratic Mean4.73142136657482
Winsorized Mean ( 1 / 20 )0.112777777750.61188967268710.1843106409277
Winsorized Mean ( 2 / 20 )0.1054444444166670.6090527462786230.173128591999533
Winsorized Mean ( 3 / 20 )0.1124444444166670.6016866744016790.186882058720151
Winsorized Mean ( 4 / 20 )0.1711111110833330.5879700182949380.291020129869106
Winsorized Mean ( 5 / 20 )0.2211111110833330.5587790062436970.395704041513151
Winsorized Mean ( 6 / 20 )0.2191111110833330.5514370307759270.397345660256117
Winsorized Mean ( 7 / 20 )0.2331111110833330.5410522394753610.430847696535501
Winsorized Mean ( 8 / 20 )0.259777777750.5365168631297820.484193127191904
Winsorized Mean ( 9 / 20 )0.184777777750.5194131627982560.355743348425248
Winsorized Mean ( 10 / 20 )0.02477777774999990.4836877093396940.051226808685764
Winsorized Mean ( 11 / 20 )0.01744444441666670.4721827636100150.0369442634527728
Winsorized Mean ( 12 / 20 )0.07344444441666670.4586033956388660.160148060644762
Winsorized Mean ( 13 / 20 )0.13699999990.4149835360889290.330133578770802
Winsorized Mean ( 14 / 20 )0.09499999990000020.3891905622872030.244096360769136
Winsorized Mean ( 15 / 20 )0.1016666666500000.3743921501690350.271551277461609
Winsorized Mean ( 16 / 20 )0.1549999999833330.3581317788148830.432801580737275
Winsorized Mean ( 17 / 20 )0.08133333331666680.3234278037755480.251472917192705
Winsorized Mean ( 18 / 20 )0.1453333332166670.3047553555414510.476885247704529
Winsorized Mean ( 19 / 20 )0.12211111110.2934951826923180.416058314756102
Winsorized Mean ( 20 / 20 )-0.04455555556666680.265434890123825-0.167858699908975
Trimmed Mean ( 1 / 20 )0.1180459769827590.5995165090257850.196901962173791
Trimmed Mean ( 2 / 20 )0.1236904761607140.5841727768199630.211736118266317
Trimmed Mean ( 3 / 20 )0.1338271604629630.5669756725023160.236036865342607
Trimmed Mean ( 4 / 20 )0.1420512820192310.5490607650901670.258716868971512
Trimmed Mean ( 5 / 20 )0.13333333330.5319953966336050.250628735029881
Trimmed Mean ( 6 / 20 )0.1113888888541670.5203734549682750.214055670577888
Trimmed Mean ( 7 / 20 )0.08797101445652180.5075113570577390.17333802137262
Trimmed Mean ( 8 / 20 )0.05969696965909090.4936566353210830.120928121669555
Trimmed Mean ( 9 / 20 )0.02396825392857150.4764982854666020.0503008188268736
Trimmed Mean ( 10 / 20 )-0.002833333374999980.45861061619946-0.00617808065255885
Trimmed Mean ( 11 / 20 )-0.007192982499999980.444734103758858-0.0161736697033249
Trimmed Mean ( 12 / 20 )-0.01092592597222220.428745115529532-0.0254834995816288
Trimmed Mean ( 13 / 20 )-0.02333333338235290.410244457549133-0.0568766572051944
Trimmed Mean ( 14 / 20 )-0.0464583333750.396975176437947-0.117030827448381
Trimmed Mean ( 15 / 20 )-0.06666666670.385210496264294-0.173065550774244
Trimmed Mean ( 16 / 20 )-0.090714285750.371778435474798-0.244000934680756
Trimmed Mean ( 17 / 20 )-0.1261538461923080.356021496139747-0.354343340388607
Trimmed Mean ( 18 / 20 )-0.1566666667083330.343885162261103-0.455578442751712
Trimmed Mean ( 19 / 20 )-0.2024242424545450.329924429212217-0.613547299112975
Trimmed Mean ( 20 / 20 )-0.25366666670.309929052426706-0.818466886901443
Median-0.43
Midrange-0.39
Midmean - Weighted Average at Xnp-0.174838709709678
Midmean - Weighted Average at X(n+1)p-0.0666666667000001
Midmean - Empirical Distribution Function-0.174838709709678
Midmean - Empirical Distribution Function - Averaging-0.0666666667000001
Midmean - Empirical Distribution Function - Interpolation-0.0666666667000001
Midmean - Closest Observation-0.174838709709678
Midmean - True Basic - Statistics Graphics Toolkit-0.0666666667000001
Midmean - MS Excel (old versions)-0.0464583333750002
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.101111111083333 & 0.615837925675202 & 0.164184612327140 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -10.9242150359964 &  &  \tabularnewline
Quadratic Mean & 4.73142136657482 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.11277777775 & 0.6118896726871 & 0.1843106409277 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.105444444416667 & 0.609052746278623 & 0.173128591999533 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.112444444416667 & 0.601686674401679 & 0.186882058720151 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.171111111083333 & 0.587970018294938 & 0.291020129869106 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.221111111083333 & 0.558779006243697 & 0.395704041513151 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.219111111083333 & 0.551437030775927 & 0.397345660256117 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.233111111083333 & 0.541052239475361 & 0.430847696535501 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.25977777775 & 0.536516863129782 & 0.484193127191904 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.18477777775 & 0.519413162798256 & 0.355743348425248 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.0247777777499999 & 0.483687709339694 & 0.051226808685764 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.0174444444166667 & 0.472182763610015 & 0.0369442634527728 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.0734444444166667 & 0.458603395638866 & 0.160148060644762 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.1369999999 & 0.414983536088929 & 0.330133578770802 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.0949999999000002 & 0.389190562287203 & 0.244096360769136 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.101666666650000 & 0.374392150169035 & 0.271551277461609 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.154999999983333 & 0.358131778814883 & 0.432801580737275 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.0813333333166668 & 0.323427803775548 & 0.251472917192705 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.145333333216667 & 0.304755355541451 & 0.476885247704529 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.1221111111 & 0.293495182692318 & 0.416058314756102 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -0.0445555555666668 & 0.265434890123825 & -0.167858699908975 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.118045976982759 & 0.599516509025785 & 0.196901962173791 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.123690476160714 & 0.584172776819963 & 0.211736118266317 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.133827160462963 & 0.566975672502316 & 0.236036865342607 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.142051282019231 & 0.549060765090167 & 0.258716868971512 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.1333333333 & 0.531995396633605 & 0.250628735029881 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.111388888854167 & 0.520373454968275 & 0.214055670577888 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.0879710144565218 & 0.507511357057739 & 0.17333802137262 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.0596969696590909 & 0.493656635321083 & 0.120928121669555 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.0239682539285715 & 0.476498285466602 & 0.0503008188268736 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -0.00283333337499998 & 0.45861061619946 & -0.00617808065255885 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -0.00719298249999998 & 0.444734103758858 & -0.0161736697033249 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -0.0109259259722222 & 0.428745115529532 & -0.0254834995816288 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -0.0233333333823529 & 0.410244457549133 & -0.0568766572051944 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -0.046458333375 & 0.396975176437947 & -0.117030827448381 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -0.0666666667 & 0.385210496264294 & -0.173065550774244 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -0.09071428575 & 0.371778435474798 & -0.244000934680756 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -0.126153846192308 & 0.356021496139747 & -0.354343340388607 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -0.156666666708333 & 0.343885162261103 & -0.455578442751712 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -0.202424242454545 & 0.329924429212217 & -0.613547299112975 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -0.2536666667 & 0.309929052426706 & -0.818466886901443 \tabularnewline
Median & -0.43 &  &  \tabularnewline
Midrange & -0.39 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.174838709709678 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.0666666667000001 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.174838709709678 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.0666666667000001 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.0666666667000001 &  &  \tabularnewline
Midmean - Closest Observation & -0.174838709709678 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.0666666667000001 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.0464583333750002 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3798&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]0.101111111083333[/C][C]0.615837925675202[/C][C]0.164184612327140[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-10.9242150359964[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.73142136657482[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.11277777775[/C][C]0.6118896726871[/C][C]0.1843106409277[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.105444444416667[/C][C]0.609052746278623[/C][C]0.173128591999533[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.112444444416667[/C][C]0.601686674401679[/C][C]0.186882058720151[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.171111111083333[/C][C]0.587970018294938[/C][C]0.291020129869106[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.221111111083333[/C][C]0.558779006243697[/C][C]0.395704041513151[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.219111111083333[/C][C]0.551437030775927[/C][C]0.397345660256117[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.233111111083333[/C][C]0.541052239475361[/C][C]0.430847696535501[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.25977777775[/C][C]0.536516863129782[/C][C]0.484193127191904[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.18477777775[/C][C]0.519413162798256[/C][C]0.355743348425248[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.0247777777499999[/C][C]0.483687709339694[/C][C]0.051226808685764[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.0174444444166667[/C][C]0.472182763610015[/C][C]0.0369442634527728[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.0734444444166667[/C][C]0.458603395638866[/C][C]0.160148060644762[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.1369999999[/C][C]0.414983536088929[/C][C]0.330133578770802[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.0949999999000002[/C][C]0.389190562287203[/C][C]0.244096360769136[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.101666666650000[/C][C]0.374392150169035[/C][C]0.271551277461609[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.154999999983333[/C][C]0.358131778814883[/C][C]0.432801580737275[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.0813333333166668[/C][C]0.323427803775548[/C][C]0.251472917192705[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.145333333216667[/C][C]0.304755355541451[/C][C]0.476885247704529[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.1221111111[/C][C]0.293495182692318[/C][C]0.416058314756102[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-0.0445555555666668[/C][C]0.265434890123825[/C][C]-0.167858699908975[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.118045976982759[/C][C]0.599516509025785[/C][C]0.196901962173791[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.123690476160714[/C][C]0.584172776819963[/C][C]0.211736118266317[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.133827160462963[/C][C]0.566975672502316[/C][C]0.236036865342607[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.142051282019231[/C][C]0.549060765090167[/C][C]0.258716868971512[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.1333333333[/C][C]0.531995396633605[/C][C]0.250628735029881[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.111388888854167[/C][C]0.520373454968275[/C][C]0.214055670577888[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.0879710144565218[/C][C]0.507511357057739[/C][C]0.17333802137262[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.0596969696590909[/C][C]0.493656635321083[/C][C]0.120928121669555[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.0239682539285715[/C][C]0.476498285466602[/C][C]0.0503008188268736[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-0.00283333337499998[/C][C]0.45861061619946[/C][C]-0.00617808065255885[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-0.00719298249999998[/C][C]0.444734103758858[/C][C]-0.0161736697033249[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-0.0109259259722222[/C][C]0.428745115529532[/C][C]-0.0254834995816288[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-0.0233333333823529[/C][C]0.410244457549133[/C][C]-0.0568766572051944[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-0.046458333375[/C][C]0.396975176437947[/C][C]-0.117030827448381[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-0.0666666667[/C][C]0.385210496264294[/C][C]-0.173065550774244[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-0.09071428575[/C][C]0.371778435474798[/C][C]-0.244000934680756[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-0.126153846192308[/C][C]0.356021496139747[/C][C]-0.354343340388607[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-0.156666666708333[/C][C]0.343885162261103[/C][C]-0.455578442751712[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-0.202424242454545[/C][C]0.329924429212217[/C][C]-0.613547299112975[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-0.2536666667[/C][C]0.309929052426706[/C][C]-0.818466886901443[/C][/ROW]
[ROW][C]Median[/C][C]-0.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.174838709709678[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.0666666667000001[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.174838709709678[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.0666666667000001[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.0666666667000001[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.174838709709678[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.0666666667000001[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.0464583333750002[/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=3798&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3798&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 Mean0.1011111110833330.6158379256752020.164184612327140
Geometric MeanNaN
Harmonic Mean-10.9242150359964
Quadratic Mean4.73142136657482
Winsorized Mean ( 1 / 20 )0.112777777750.61188967268710.1843106409277
Winsorized Mean ( 2 / 20 )0.1054444444166670.6090527462786230.173128591999533
Winsorized Mean ( 3 / 20 )0.1124444444166670.6016866744016790.186882058720151
Winsorized Mean ( 4 / 20 )0.1711111110833330.5879700182949380.291020129869106
Winsorized Mean ( 5 / 20 )0.2211111110833330.5587790062436970.395704041513151
Winsorized Mean ( 6 / 20 )0.2191111110833330.5514370307759270.397345660256117
Winsorized Mean ( 7 / 20 )0.2331111110833330.5410522394753610.430847696535501
Winsorized Mean ( 8 / 20 )0.259777777750.5365168631297820.484193127191904
Winsorized Mean ( 9 / 20 )0.184777777750.5194131627982560.355743348425248
Winsorized Mean ( 10 / 20 )0.02477777774999990.4836877093396940.051226808685764
Winsorized Mean ( 11 / 20 )0.01744444441666670.4721827636100150.0369442634527728
Winsorized Mean ( 12 / 20 )0.07344444441666670.4586033956388660.160148060644762
Winsorized Mean ( 13 / 20 )0.13699999990.4149835360889290.330133578770802
Winsorized Mean ( 14 / 20 )0.09499999990000020.3891905622872030.244096360769136
Winsorized Mean ( 15 / 20 )0.1016666666500000.3743921501690350.271551277461609
Winsorized Mean ( 16 / 20 )0.1549999999833330.3581317788148830.432801580737275
Winsorized Mean ( 17 / 20 )0.08133333331666680.3234278037755480.251472917192705
Winsorized Mean ( 18 / 20 )0.1453333332166670.3047553555414510.476885247704529
Winsorized Mean ( 19 / 20 )0.12211111110.2934951826923180.416058314756102
Winsorized Mean ( 20 / 20 )-0.04455555556666680.265434890123825-0.167858699908975
Trimmed Mean ( 1 / 20 )0.1180459769827590.5995165090257850.196901962173791
Trimmed Mean ( 2 / 20 )0.1236904761607140.5841727768199630.211736118266317
Trimmed Mean ( 3 / 20 )0.1338271604629630.5669756725023160.236036865342607
Trimmed Mean ( 4 / 20 )0.1420512820192310.5490607650901670.258716868971512
Trimmed Mean ( 5 / 20 )0.13333333330.5319953966336050.250628735029881
Trimmed Mean ( 6 / 20 )0.1113888888541670.5203734549682750.214055670577888
Trimmed Mean ( 7 / 20 )0.08797101445652180.5075113570577390.17333802137262
Trimmed Mean ( 8 / 20 )0.05969696965909090.4936566353210830.120928121669555
Trimmed Mean ( 9 / 20 )0.02396825392857150.4764982854666020.0503008188268736
Trimmed Mean ( 10 / 20 )-0.002833333374999980.45861061619946-0.00617808065255885
Trimmed Mean ( 11 / 20 )-0.007192982499999980.444734103758858-0.0161736697033249
Trimmed Mean ( 12 / 20 )-0.01092592597222220.428745115529532-0.0254834995816288
Trimmed Mean ( 13 / 20 )-0.02333333338235290.410244457549133-0.0568766572051944
Trimmed Mean ( 14 / 20 )-0.0464583333750.396975176437947-0.117030827448381
Trimmed Mean ( 15 / 20 )-0.06666666670.385210496264294-0.173065550774244
Trimmed Mean ( 16 / 20 )-0.090714285750.371778435474798-0.244000934680756
Trimmed Mean ( 17 / 20 )-0.1261538461923080.356021496139747-0.354343340388607
Trimmed Mean ( 18 / 20 )-0.1566666667083330.343885162261103-0.455578442751712
Trimmed Mean ( 19 / 20 )-0.2024242424545450.329924429212217-0.613547299112975
Trimmed Mean ( 20 / 20 )-0.25366666670.309929052426706-0.818466886901443
Median-0.43
Midrange-0.39
Midmean - Weighted Average at Xnp-0.174838709709678
Midmean - Weighted Average at X(n+1)p-0.0666666667000001
Midmean - Empirical Distribution Function-0.174838709709678
Midmean - Empirical Distribution Function - Averaging-0.0666666667000001
Midmean - Empirical Distribution Function - Interpolation-0.0666666667000001
Midmean - Closest Observation-0.174838709709678
Midmean - True Basic - Statistics Graphics Toolkit-0.0666666667000001
Midmean - MS Excel (old versions)-0.0464583333750002
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')