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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 08:14:33 -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/13/t1197557952kz3lz1t40410qeb.htm/, Retrieved Sun, 05 May 2024 15:03:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3599, Retrieved Sun, 05 May 2024 15:03:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-13 15:14:33] [919a0fafa615dc0e3c6b6d22cd1007a0] [Current]
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Dataseries X:
0,7
1,9
-4,1
-8,7
-8,6
-10,7
-4,2
-1,5
-10
4
-22
-23,3
5,3
12
-11,9
-8,3
-17,8
-13,2
7,6
0,8
-7,5
12,8
-22,8
-14,9
9,7
6,9
2,1
-0,4
-14,7
-9,4
1,5
-2,1
-7
14,2
-31,9
-15,1
5,3
0,4
5,4
-0,8
-9,7
-7,6
11
-4,3
9,4
19,6
-22,9
-7,5
17
24
21,4
9,4
8,6
8,5
26
14,2
21,3
34,7
-8,5
5,3




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=3599&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=3599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3599&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 Mean-0.1733333333333331.75389295273178-0.0988277722784381
Geometric MeanNaN
Harmonic Mean34.5711162670328
Quadratic Mean13.4730224275525
Winsorized Mean ( 1 / 20 )-0.1751.67118251208555-0.104716270505733
Winsorized Mean ( 2 / 20 )-0.2283333333333331.65092354168497-0.138306425202642
Winsorized Mean ( 3 / 20 )-0.3533333333333341.61876786976881-0.218273008707416
Winsorized Mean ( 4 / 20 )-0.3066666666666671.60487052941845-0.191084988505454
Winsorized Mean ( 5 / 20 )-0.09833333333333321.49757523728763-0.0656616982472494
Winsorized Mean ( 6 / 20 )-0.08833333333333331.3895739534577-0.0635686449890141
Winsorized Mean ( 7 / 20 )-0.3916666666666671.32054451118710-0.296594823838676
Winsorized Mean ( 8 / 20 )-0.3651.31559920613629-0.27744011876683
Winsorized Mean ( 9 / 20 )-0.351.23631834526851-0.283098605904765
Winsorized Mean ( 10 / 20 )-0.2666666666666671.17521645239554-0.226908554694837
Winsorized Mean ( 11 / 20 )-0.2300000000000001.10711438428331-0.207747278208196
Winsorized Mean ( 12 / 20 )-0.351.04124138211042-0.336137235816167
Winsorized Mean ( 13 / 20 )-0.351.02050862470993-0.342966234214322
Winsorized Mean ( 14 / 20 )-0.281.00971495670081-0.277305984368981
Winsorized Mean ( 15 / 20 )-0.3050.951090438706472-0.320684540173503
Winsorized Mean ( 16 / 20 )-0.3050.942881222636234-0.323476587164648
Winsorized Mean ( 17 / 20 )-0.5316666666666670.898896032482515-0.591466251328692
Winsorized Mean ( 18 / 20 )-0.6816666666666670.858041034097937-0.794445299907255
Winsorized Mean ( 19 / 20 )-0.9350.755334419145429-1.23786229820937
Winsorized Mean ( 20 / 20 )-0.9350.745623104228485-1.25398474738450
Trimmed Mean ( 1 / 20 )-0.2275862068965521.61910066136235-0.140563346262273
Trimmed Mean ( 2 / 20 )-0.2839285714285711.55486621294791-0.182606432028814
Trimmed Mean ( 3 / 20 )-0.3148148148148151.48895164158115-0.211433874696230
Trimmed Mean ( 4 / 20 )-0.31.42270163409907-0.210866419781668
Trimmed Mean ( 5 / 20 )-0.2981.34474180815956-0.221603878299767
Trimmed Mean ( 6 / 20 )-0.3479166666666671.28549597729968-0.270647806613523
Trimmed Mean ( 7 / 20 )-0.4043478260869561.24514887269992-0.324738539264135
Trimmed Mean ( 8 / 20 )-0.4068181818181821.21345259751643-0.33525675634204
Trimmed Mean ( 9 / 20 )-0.4142857142857141.17272809706538-0.353266639831021
Trimmed Mean ( 10 / 20 )-0.4251.14078105272502-0.372551769671129
Trimmed Mean ( 11 / 20 )-0.451.11375564458564-0.404038356337505
Trimmed Mean ( 12 / 20 )-0.4833333333333331.09394799795156-0.441824779823525
Trimmed Mean ( 13 / 20 )-0.5029411764705881.08201539435474-0.464818873275384
Trimmed Mean ( 14 / 20 )-0.5251.06772670781462-0.491698855294675
Trimmed Mean ( 15 / 20 )-0.561.04695068992118-0.534886700387159
Trimmed Mean ( 16 / 20 )-0.5964285714285711.03087883274440-0.578563214690095
Trimmed Mean ( 17 / 20 )-0.6384615384615391.00503466336053-0.635263202093665
Trimmed Mean ( 18 / 20 )-0.6541666666666670.976981063681518-0.669579678649653
Trimmed Mean ( 19 / 20 )-0.650.943598849023666-0.688852048381099
Trimmed Mean ( 20 / 20 )-0.6050.926807622120714-0.652778403586759
Median0
Midrange1.40000000000000
Midmean - Weighted Average at Xnp-0.84516129032258
Midmean - Weighted Average at X(n+1)p-0.56
Midmean - Empirical Distribution Function-0.84516129032258
Midmean - Empirical Distribution Function - Averaging-0.56
Midmean - Empirical Distribution Function - Interpolation-0.56
Midmean - Closest Observation-0.84516129032258
Midmean - True Basic - Statistics Graphics Toolkit-0.56
Midmean - MS Excel (old versions)-0.224242424242424
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.173333333333333 & 1.75389295273178 & -0.0988277722784381 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 34.5711162670328 &  &  \tabularnewline
Quadratic Mean & 13.4730224275525 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -0.175 & 1.67118251208555 & -0.104716270505733 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -0.228333333333333 & 1.65092354168497 & -0.138306425202642 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -0.353333333333334 & 1.61876786976881 & -0.218273008707416 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -0.306666666666667 & 1.60487052941845 & -0.191084988505454 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -0.0983333333333332 & 1.49757523728763 & -0.0656616982472494 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -0.0883333333333333 & 1.3895739534577 & -0.0635686449890141 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -0.391666666666667 & 1.32054451118710 & -0.296594823838676 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -0.365 & 1.31559920613629 & -0.27744011876683 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -0.35 & 1.23631834526851 & -0.283098605904765 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -0.266666666666667 & 1.17521645239554 & -0.226908554694837 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -0.230000000000000 & 1.10711438428331 & -0.207747278208196 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -0.35 & 1.04124138211042 & -0.336137235816167 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -0.35 & 1.02050862470993 & -0.342966234214322 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -0.28 & 1.00971495670081 & -0.277305984368981 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -0.305 & 0.951090438706472 & -0.320684540173503 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -0.305 & 0.942881222636234 & -0.323476587164648 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -0.531666666666667 & 0.898896032482515 & -0.591466251328692 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -0.681666666666667 & 0.858041034097937 & -0.794445299907255 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -0.935 & 0.755334419145429 & -1.23786229820937 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -0.935 & 0.745623104228485 & -1.25398474738450 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -0.227586206896552 & 1.61910066136235 & -0.140563346262273 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -0.283928571428571 & 1.55486621294791 & -0.182606432028814 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -0.314814814814815 & 1.48895164158115 & -0.211433874696230 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -0.3 & 1.42270163409907 & -0.210866419781668 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -0.298 & 1.34474180815956 & -0.221603878299767 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -0.347916666666667 & 1.28549597729968 & -0.270647806613523 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -0.404347826086956 & 1.24514887269992 & -0.324738539264135 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -0.406818181818182 & 1.21345259751643 & -0.33525675634204 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -0.414285714285714 & 1.17272809706538 & -0.353266639831021 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -0.425 & 1.14078105272502 & -0.372551769671129 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -0.45 & 1.11375564458564 & -0.404038356337505 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -0.483333333333333 & 1.09394799795156 & -0.441824779823525 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -0.502941176470588 & 1.08201539435474 & -0.464818873275384 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -0.525 & 1.06772670781462 & -0.491698855294675 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -0.56 & 1.04695068992118 & -0.534886700387159 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -0.596428571428571 & 1.03087883274440 & -0.578563214690095 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -0.638461538461539 & 1.00503466336053 & -0.635263202093665 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -0.654166666666667 & 0.976981063681518 & -0.669579678649653 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -0.65 & 0.943598849023666 & -0.688852048381099 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -0.605 & 0.926807622120714 & -0.652778403586759 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 1.40000000000000 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.84516129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.56 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.84516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.56 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.56 &  &  \tabularnewline
Midmean - Closest Observation & -0.84516129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.56 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.224242424242424 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3599&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]-0.173333333333333[/C][C]1.75389295273178[/C][C]-0.0988277722784381[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]34.5711162670328[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.4730224275525[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-0.175[/C][C]1.67118251208555[/C][C]-0.104716270505733[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-0.228333333333333[/C][C]1.65092354168497[/C][C]-0.138306425202642[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-0.353333333333334[/C][C]1.61876786976881[/C][C]-0.218273008707416[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-0.306666666666667[/C][C]1.60487052941845[/C][C]-0.191084988505454[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-0.0983333333333332[/C][C]1.49757523728763[/C][C]-0.0656616982472494[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-0.0883333333333333[/C][C]1.3895739534577[/C][C]-0.0635686449890141[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-0.391666666666667[/C][C]1.32054451118710[/C][C]-0.296594823838676[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-0.365[/C][C]1.31559920613629[/C][C]-0.27744011876683[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-0.35[/C][C]1.23631834526851[/C][C]-0.283098605904765[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-0.266666666666667[/C][C]1.17521645239554[/C][C]-0.226908554694837[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-0.230000000000000[/C][C]1.10711438428331[/C][C]-0.207747278208196[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-0.35[/C][C]1.04124138211042[/C][C]-0.336137235816167[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-0.35[/C][C]1.02050862470993[/C][C]-0.342966234214322[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-0.28[/C][C]1.00971495670081[/C][C]-0.277305984368981[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-0.305[/C][C]0.951090438706472[/C][C]-0.320684540173503[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-0.305[/C][C]0.942881222636234[/C][C]-0.323476587164648[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-0.531666666666667[/C][C]0.898896032482515[/C][C]-0.591466251328692[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-0.681666666666667[/C][C]0.858041034097937[/C][C]-0.794445299907255[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-0.935[/C][C]0.755334419145429[/C][C]-1.23786229820937[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-0.935[/C][C]0.745623104228485[/C][C]-1.25398474738450[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-0.227586206896552[/C][C]1.61910066136235[/C][C]-0.140563346262273[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-0.283928571428571[/C][C]1.55486621294791[/C][C]-0.182606432028814[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-0.314814814814815[/C][C]1.48895164158115[/C][C]-0.211433874696230[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-0.3[/C][C]1.42270163409907[/C][C]-0.210866419781668[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-0.298[/C][C]1.34474180815956[/C][C]-0.221603878299767[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-0.347916666666667[/C][C]1.28549597729968[/C][C]-0.270647806613523[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-0.404347826086956[/C][C]1.24514887269992[/C][C]-0.324738539264135[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-0.406818181818182[/C][C]1.21345259751643[/C][C]-0.33525675634204[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-0.414285714285714[/C][C]1.17272809706538[/C][C]-0.353266639831021[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-0.425[/C][C]1.14078105272502[/C][C]-0.372551769671129[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-0.45[/C][C]1.11375564458564[/C][C]-0.404038356337505[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-0.483333333333333[/C][C]1.09394799795156[/C][C]-0.441824779823525[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-0.502941176470588[/C][C]1.08201539435474[/C][C]-0.464818873275384[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-0.525[/C][C]1.06772670781462[/C][C]-0.491698855294675[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-0.56[/C][C]1.04695068992118[/C][C]-0.534886700387159[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-0.596428571428571[/C][C]1.03087883274440[/C][C]-0.578563214690095[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-0.638461538461539[/C][C]1.00503466336053[/C][C]-0.635263202093665[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-0.654166666666667[/C][C]0.976981063681518[/C][C]-0.669579678649653[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-0.65[/C][C]0.943598849023666[/C][C]-0.688852048381099[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-0.605[/C][C]0.926807622120714[/C][C]-0.652778403586759[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.40000000000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.84516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.84516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.84516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.224242424242424[/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=3599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3599&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 Mean-0.1733333333333331.75389295273178-0.0988277722784381
Geometric MeanNaN
Harmonic Mean34.5711162670328
Quadratic Mean13.4730224275525
Winsorized Mean ( 1 / 20 )-0.1751.67118251208555-0.104716270505733
Winsorized Mean ( 2 / 20 )-0.2283333333333331.65092354168497-0.138306425202642
Winsorized Mean ( 3 / 20 )-0.3533333333333341.61876786976881-0.218273008707416
Winsorized Mean ( 4 / 20 )-0.3066666666666671.60487052941845-0.191084988505454
Winsorized Mean ( 5 / 20 )-0.09833333333333321.49757523728763-0.0656616982472494
Winsorized Mean ( 6 / 20 )-0.08833333333333331.3895739534577-0.0635686449890141
Winsorized Mean ( 7 / 20 )-0.3916666666666671.32054451118710-0.296594823838676
Winsorized Mean ( 8 / 20 )-0.3651.31559920613629-0.27744011876683
Winsorized Mean ( 9 / 20 )-0.351.23631834526851-0.283098605904765
Winsorized Mean ( 10 / 20 )-0.2666666666666671.17521645239554-0.226908554694837
Winsorized Mean ( 11 / 20 )-0.2300000000000001.10711438428331-0.207747278208196
Winsorized Mean ( 12 / 20 )-0.351.04124138211042-0.336137235816167
Winsorized Mean ( 13 / 20 )-0.351.02050862470993-0.342966234214322
Winsorized Mean ( 14 / 20 )-0.281.00971495670081-0.277305984368981
Winsorized Mean ( 15 / 20 )-0.3050.951090438706472-0.320684540173503
Winsorized Mean ( 16 / 20 )-0.3050.942881222636234-0.323476587164648
Winsorized Mean ( 17 / 20 )-0.5316666666666670.898896032482515-0.591466251328692
Winsorized Mean ( 18 / 20 )-0.6816666666666670.858041034097937-0.794445299907255
Winsorized Mean ( 19 / 20 )-0.9350.755334419145429-1.23786229820937
Winsorized Mean ( 20 / 20 )-0.9350.745623104228485-1.25398474738450
Trimmed Mean ( 1 / 20 )-0.2275862068965521.61910066136235-0.140563346262273
Trimmed Mean ( 2 / 20 )-0.2839285714285711.55486621294791-0.182606432028814
Trimmed Mean ( 3 / 20 )-0.3148148148148151.48895164158115-0.211433874696230
Trimmed Mean ( 4 / 20 )-0.31.42270163409907-0.210866419781668
Trimmed Mean ( 5 / 20 )-0.2981.34474180815956-0.221603878299767
Trimmed Mean ( 6 / 20 )-0.3479166666666671.28549597729968-0.270647806613523
Trimmed Mean ( 7 / 20 )-0.4043478260869561.24514887269992-0.324738539264135
Trimmed Mean ( 8 / 20 )-0.4068181818181821.21345259751643-0.33525675634204
Trimmed Mean ( 9 / 20 )-0.4142857142857141.17272809706538-0.353266639831021
Trimmed Mean ( 10 / 20 )-0.4251.14078105272502-0.372551769671129
Trimmed Mean ( 11 / 20 )-0.451.11375564458564-0.404038356337505
Trimmed Mean ( 12 / 20 )-0.4833333333333331.09394799795156-0.441824779823525
Trimmed Mean ( 13 / 20 )-0.5029411764705881.08201539435474-0.464818873275384
Trimmed Mean ( 14 / 20 )-0.5251.06772670781462-0.491698855294675
Trimmed Mean ( 15 / 20 )-0.561.04695068992118-0.534886700387159
Trimmed Mean ( 16 / 20 )-0.5964285714285711.03087883274440-0.578563214690095
Trimmed Mean ( 17 / 20 )-0.6384615384615391.00503466336053-0.635263202093665
Trimmed Mean ( 18 / 20 )-0.6541666666666670.976981063681518-0.669579678649653
Trimmed Mean ( 19 / 20 )-0.650.943598849023666-0.688852048381099
Trimmed Mean ( 20 / 20 )-0.6050.926807622120714-0.652778403586759
Median0
Midrange1.40000000000000
Midmean - Weighted Average at Xnp-0.84516129032258
Midmean - Weighted Average at X(n+1)p-0.56
Midmean - Empirical Distribution Function-0.84516129032258
Midmean - Empirical Distribution Function - Averaging-0.56
Midmean - Empirical Distribution Function - Interpolation-0.56
Midmean - Closest Observation-0.84516129032258
Midmean - True Basic - Statistics Graphics Toolkit-0.56
Midmean - MS Excel (old versions)-0.224242424242424
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')