Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Nov 2007 14:56:18 -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/07/t119447238125j14crxmowmfsj.htm/, Retrieved Tue, 30 Apr 2024 02:58:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=592, Retrieved Tue, 30 Apr 2024 02:58:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact259
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper stat] [2007-11-07 21:56:18] [0c12eff582f43eaf43ae2f09e879befe] [Current]
Feedback Forum

Post a new message
Dataseries X:
0.83
0.82
0.90
0.94
0.89
0.88
0.86
0.87
0.84
0.81
0.85
0.93
0.91
0.92
0.88
0.90
0.85
0.85
0.85
0.83
0.88
0.82
1.05
0.79
0.81
0.82
0.83
0.91
0.80
0.79
0.77
0.77
0.87
0.80
0.89
0.85
0.86
0.85
0.83
0.88
0.84
0.82
0.82
0.86
0.79
0.83
0.84
0.84
0.83
0.80
0.79
0.85
0.78
0.75
0.75
0.77
0.76
0.73
0.78
0.83




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=592&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=592&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=592&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.8390.00706187344103356118.807000296115
Geometric Mean0.837295793124763
Harmonic Mean0.835633925520873
Quadratic Mean0.84075164783266
Winsorized Mean ( 1 / 20 )0.83750.00624646792851135134.075770432970
Winsorized Mean ( 2 / 20 )0.8371666666666670.00615749814677157135.958898681212
Winsorized Mean ( 3 / 20 )0.8371666666666670.00591890424785635141.439467781535
Winsorized Mean ( 4 / 20 )0.8371666666666670.00562526417040278148.822640378634
Winsorized Mean ( 5 / 20 )0.8371666666666670.00562526417040278148.822640378634
Winsorized Mean ( 6 / 20 )0.8361666666666670.00541546053498928154.403611893060
Winsorized Mean ( 7 / 20 )0.8373333333333330.00518508653838546161.488786567883
Winsorized Mean ( 8 / 20 )0.8360.00492428548833447169.770822991572
Winsorized Mean ( 9 / 20 )0.83750.0046494334749965180.129472655941
Winsorized Mean ( 10 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 11 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 12 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 13 / 20 )0.8380.00397591619686831210.769029955929
Winsorized Mean ( 14 / 20 )0.8356666666666670.00357618193228561233.675658143202
Winsorized Mean ( 15 / 20 )0.8356666666666670.00357618193228561233.675658143202
Winsorized Mean ( 16 / 20 )0.8356666666666670.00271391753729672307.918960389290
Winsorized Mean ( 17 / 20 )0.8356666666666670.00271391753729672307.918960389290
Winsorized Mean ( 18 / 20 )0.8386666666666670.00226077666104176370.963961685721
Winsorized Mean ( 19 / 20 )0.83550.00178545599423358467.947685464319
Winsorized Mean ( 20 / 20 )0.83550.00178545599423358467.947685464319
Trimmed Mean ( 1 / 20 )0.8372413793103450.00602371349132294138.990903288541
Trimmed Mean ( 2 / 20 )0.8369642857142860.00574862853693458145.593732546266
Trimmed Mean ( 3 / 20 )0.8368518518518520.00546780216561438153.050865138209
Trimmed Mean ( 4 / 20 )0.8367307692307690.00523736109796231159.761901763144
Trimmed Mean ( 5 / 20 )0.83660.00506778541175451165.081970136214
Trimmed Mean ( 6 / 20 )0.8364583333333330.00485142356213063172.415028830421
Trimmed Mean ( 7 / 20 )0.8365217391304350.00464401741066558180.128898140919
Trimmed Mean ( 8 / 20 )0.8363636363636360.00444713972131996188.067766873624
Trimmed Mean ( 9 / 20 )0.8364285714285710.00426777118812845195.987210784693
Trimmed Mean ( 10 / 20 )0.836250.00410889435499537203.521903400445
Trimmed Mean ( 11 / 20 )0.8363157894736840.00398112639499339210.070142592163
Trimmed Mean ( 12 / 20 )0.8363888888888890.00380377376895124219.883973046981
Trimmed Mean ( 13 / 20 )0.8364705882352940.00355457459118160235.322277470406
Trimmed Mean ( 14 / 20 )0.836250.00332239468630879251.700980454276
Trimmed Mean ( 15 / 20 )0.8363333333333330.00312510536220848267.617643695157
Trimmed Mean ( 16 / 20 )0.8364285714285710.0028272243064376295.847969870668
Trimmed Mean ( 17 / 20 )0.8365384615384610.00271419673298113308.208484437917
Trimmed Mean ( 18 / 20 )0.8366666666666670.00253001307972407330.696577567858
Trimmed Mean ( 19 / 20 )0.8363636363636360.00242153528501247345.385690450234
Trimmed Mean ( 20 / 20 )0.83650.00243602350693005343.387490974659
Median0.835
Midrange0.89
Midmean - Weighted Average at Xnp0.835151515151516
Midmean - Weighted Average at X(n+1)p0.835151515151516
Midmean - Empirical Distribution Function0.835151515151516
Midmean - Empirical Distribution Function - Averaging0.835151515151516
Midmean - Empirical Distribution Function - Interpolation0.835151515151516
Midmean - Closest Observation0.835151515151516
Midmean - True Basic - Statistics Graphics Toolkit0.835151515151516
Midmean - MS Excel (old versions)0.835151515151516
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.839 & 0.00706187344103356 & 118.807000296115 \tabularnewline
Geometric Mean & 0.837295793124763 &  &  \tabularnewline
Harmonic Mean & 0.835633925520873 &  &  \tabularnewline
Quadratic Mean & 0.84075164783266 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.8375 & 0.00624646792851135 & 134.075770432970 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.837166666666667 & 0.00615749814677157 & 135.958898681212 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.837166666666667 & 0.00591890424785635 & 141.439467781535 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.837166666666667 & 0.00562526417040278 & 148.822640378634 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.837166666666667 & 0.00562526417040278 & 148.822640378634 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.836166666666667 & 0.00541546053498928 & 154.403611893060 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.837333333333333 & 0.00518508653838546 & 161.488786567883 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.836 & 0.00492428548833447 & 169.770822991572 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.8375 & 0.0046494334749965 & 180.129472655941 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.835833333333333 & 0.00434586410739276 & 192.328455901669 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.835833333333333 & 0.00434586410739276 & 192.328455901669 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.835833333333333 & 0.00434586410739276 & 192.328455901669 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.838 & 0.00397591619686831 & 210.769029955929 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.835666666666667 & 0.00357618193228561 & 233.675658143202 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.835666666666667 & 0.00357618193228561 & 233.675658143202 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.835666666666667 & 0.00271391753729672 & 307.918960389290 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.835666666666667 & 0.00271391753729672 & 307.918960389290 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.838666666666667 & 0.00226077666104176 & 370.963961685721 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.8355 & 0.00178545599423358 & 467.947685464319 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.8355 & 0.00178545599423358 & 467.947685464319 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.837241379310345 & 0.00602371349132294 & 138.990903288541 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.836964285714286 & 0.00574862853693458 & 145.593732546266 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.836851851851852 & 0.00546780216561438 & 153.050865138209 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.836730769230769 & 0.00523736109796231 & 159.761901763144 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.8366 & 0.00506778541175451 & 165.081970136214 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.836458333333333 & 0.00485142356213063 & 172.415028830421 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.836521739130435 & 0.00464401741066558 & 180.128898140919 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.836363636363636 & 0.00444713972131996 & 188.067766873624 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.836428571428571 & 0.00426777118812845 & 195.987210784693 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.83625 & 0.00410889435499537 & 203.521903400445 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.836315789473684 & 0.00398112639499339 & 210.070142592163 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.836388888888889 & 0.00380377376895124 & 219.883973046981 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.836470588235294 & 0.00355457459118160 & 235.322277470406 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.83625 & 0.00332239468630879 & 251.700980454276 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.836333333333333 & 0.00312510536220848 & 267.617643695157 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.836428571428571 & 0.0028272243064376 & 295.847969870668 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.836538461538461 & 0.00271419673298113 & 308.208484437917 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.836666666666667 & 0.00253001307972407 & 330.696577567858 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.836363636363636 & 0.00242153528501247 & 345.385690450234 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.8365 & 0.00243602350693005 & 343.387490974659 \tabularnewline
Median & 0.835 &  &  \tabularnewline
Midrange & 0.89 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.835151515151516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.835151515151516 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.835151515151516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.835151515151516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.835151515151516 &  &  \tabularnewline
Midmean - Closest Observation & 0.835151515151516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.835151515151516 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.835151515151516 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=592&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]0.839[/C][C]0.00706187344103356[/C][C]118.807000296115[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.837295793124763[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.835633925520873[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.84075164783266[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.8375[/C][C]0.00624646792851135[/C][C]134.075770432970[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.837166666666667[/C][C]0.00615749814677157[/C][C]135.958898681212[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.837166666666667[/C][C]0.00591890424785635[/C][C]141.439467781535[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.837166666666667[/C][C]0.00562526417040278[/C][C]148.822640378634[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.837166666666667[/C][C]0.00562526417040278[/C][C]148.822640378634[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.836166666666667[/C][C]0.00541546053498928[/C][C]154.403611893060[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.837333333333333[/C][C]0.00518508653838546[/C][C]161.488786567883[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.836[/C][C]0.00492428548833447[/C][C]169.770822991572[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.8375[/C][C]0.0046494334749965[/C][C]180.129472655941[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.835833333333333[/C][C]0.00434586410739276[/C][C]192.328455901669[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.835833333333333[/C][C]0.00434586410739276[/C][C]192.328455901669[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.835833333333333[/C][C]0.00434586410739276[/C][C]192.328455901669[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.838[/C][C]0.00397591619686831[/C][C]210.769029955929[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.835666666666667[/C][C]0.00357618193228561[/C][C]233.675658143202[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.835666666666667[/C][C]0.00357618193228561[/C][C]233.675658143202[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.835666666666667[/C][C]0.00271391753729672[/C][C]307.918960389290[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.835666666666667[/C][C]0.00271391753729672[/C][C]307.918960389290[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.838666666666667[/C][C]0.00226077666104176[/C][C]370.963961685721[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.8355[/C][C]0.00178545599423358[/C][C]467.947685464319[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.8355[/C][C]0.00178545599423358[/C][C]467.947685464319[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.837241379310345[/C][C]0.00602371349132294[/C][C]138.990903288541[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.836964285714286[/C][C]0.00574862853693458[/C][C]145.593732546266[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.836851851851852[/C][C]0.00546780216561438[/C][C]153.050865138209[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.836730769230769[/C][C]0.00523736109796231[/C][C]159.761901763144[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.8366[/C][C]0.00506778541175451[/C][C]165.081970136214[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.836458333333333[/C][C]0.00485142356213063[/C][C]172.415028830421[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.836521739130435[/C][C]0.00464401741066558[/C][C]180.128898140919[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.836363636363636[/C][C]0.00444713972131996[/C][C]188.067766873624[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.836428571428571[/C][C]0.00426777118812845[/C][C]195.987210784693[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.83625[/C][C]0.00410889435499537[/C][C]203.521903400445[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.836315789473684[/C][C]0.00398112639499339[/C][C]210.070142592163[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.836388888888889[/C][C]0.00380377376895124[/C][C]219.883973046981[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.836470588235294[/C][C]0.00355457459118160[/C][C]235.322277470406[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.83625[/C][C]0.00332239468630879[/C][C]251.700980454276[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.836333333333333[/C][C]0.00312510536220848[/C][C]267.617643695157[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.836428571428571[/C][C]0.0028272243064376[/C][C]295.847969870668[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.836538461538461[/C][C]0.00271419673298113[/C][C]308.208484437917[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.836666666666667[/C][C]0.00253001307972407[/C][C]330.696577567858[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.836363636363636[/C][C]0.00242153528501247[/C][C]345.385690450234[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.8365[/C][C]0.00243602350693005[/C][C]343.387490974659[/C][/ROW]
[ROW][C]Median[/C][C]0.835[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.835151515151516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.835151515151516[/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=592&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=592&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 Mean0.8390.00706187344103356118.807000296115
Geometric Mean0.837295793124763
Harmonic Mean0.835633925520873
Quadratic Mean0.84075164783266
Winsorized Mean ( 1 / 20 )0.83750.00624646792851135134.075770432970
Winsorized Mean ( 2 / 20 )0.8371666666666670.00615749814677157135.958898681212
Winsorized Mean ( 3 / 20 )0.8371666666666670.00591890424785635141.439467781535
Winsorized Mean ( 4 / 20 )0.8371666666666670.00562526417040278148.822640378634
Winsorized Mean ( 5 / 20 )0.8371666666666670.00562526417040278148.822640378634
Winsorized Mean ( 6 / 20 )0.8361666666666670.00541546053498928154.403611893060
Winsorized Mean ( 7 / 20 )0.8373333333333330.00518508653838546161.488786567883
Winsorized Mean ( 8 / 20 )0.8360.00492428548833447169.770822991572
Winsorized Mean ( 9 / 20 )0.83750.0046494334749965180.129472655941
Winsorized Mean ( 10 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 11 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 12 / 20 )0.8358333333333330.00434586410739276192.328455901669
Winsorized Mean ( 13 / 20 )0.8380.00397591619686831210.769029955929
Winsorized Mean ( 14 / 20 )0.8356666666666670.00357618193228561233.675658143202
Winsorized Mean ( 15 / 20 )0.8356666666666670.00357618193228561233.675658143202
Winsorized Mean ( 16 / 20 )0.8356666666666670.00271391753729672307.918960389290
Winsorized Mean ( 17 / 20 )0.8356666666666670.00271391753729672307.918960389290
Winsorized Mean ( 18 / 20 )0.8386666666666670.00226077666104176370.963961685721
Winsorized Mean ( 19 / 20 )0.83550.00178545599423358467.947685464319
Winsorized Mean ( 20 / 20 )0.83550.00178545599423358467.947685464319
Trimmed Mean ( 1 / 20 )0.8372413793103450.00602371349132294138.990903288541
Trimmed Mean ( 2 / 20 )0.8369642857142860.00574862853693458145.593732546266
Trimmed Mean ( 3 / 20 )0.8368518518518520.00546780216561438153.050865138209
Trimmed Mean ( 4 / 20 )0.8367307692307690.00523736109796231159.761901763144
Trimmed Mean ( 5 / 20 )0.83660.00506778541175451165.081970136214
Trimmed Mean ( 6 / 20 )0.8364583333333330.00485142356213063172.415028830421
Trimmed Mean ( 7 / 20 )0.8365217391304350.00464401741066558180.128898140919
Trimmed Mean ( 8 / 20 )0.8363636363636360.00444713972131996188.067766873624
Trimmed Mean ( 9 / 20 )0.8364285714285710.00426777118812845195.987210784693
Trimmed Mean ( 10 / 20 )0.836250.00410889435499537203.521903400445
Trimmed Mean ( 11 / 20 )0.8363157894736840.00398112639499339210.070142592163
Trimmed Mean ( 12 / 20 )0.8363888888888890.00380377376895124219.883973046981
Trimmed Mean ( 13 / 20 )0.8364705882352940.00355457459118160235.322277470406
Trimmed Mean ( 14 / 20 )0.836250.00332239468630879251.700980454276
Trimmed Mean ( 15 / 20 )0.8363333333333330.00312510536220848267.617643695157
Trimmed Mean ( 16 / 20 )0.8364285714285710.0028272243064376295.847969870668
Trimmed Mean ( 17 / 20 )0.8365384615384610.00271419673298113308.208484437917
Trimmed Mean ( 18 / 20 )0.8366666666666670.00253001307972407330.696577567858
Trimmed Mean ( 19 / 20 )0.8363636363636360.00242153528501247345.385690450234
Trimmed Mean ( 20 / 20 )0.83650.00243602350693005343.387490974659
Median0.835
Midrange0.89
Midmean - Weighted Average at Xnp0.835151515151516
Midmean - Weighted Average at X(n+1)p0.835151515151516
Midmean - Empirical Distribution Function0.835151515151516
Midmean - Empirical Distribution Function - Averaging0.835151515151516
Midmean - Empirical Distribution Function - Interpolation0.835151515151516
Midmean - Closest Observation0.835151515151516
Midmean - True Basic - Statistics Graphics Toolkit0.835151515151516
Midmean - MS Excel (old versions)0.835151515151516
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')