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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 12:52:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t125606480125qwmr1b86q4vgx.htm/, Retrieved Fri, 03 May 2024 03:38:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48992, Retrieved Fri, 03 May 2024 03:38:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [question 2] [2009-10-20 18:52:07] [8d715e37b704efc17e617746691e8069] [Current]
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Post a new message
Dataseries X:
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3




Summary of computational 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 computational 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=48992&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]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=48992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48992&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.86885245901640.090189266188138887.2482146888923
Geometric Mean7.8368075487419
Harmonic Mean7.80368521992802
Quadratic Mean7.89980286120493
Winsorized Mean ( 1 / 20 )7.873770491803280.088703522867439388.7650257540507
Winsorized Mean ( 2 / 20 )7.857377049180330.083484857315905394.1173920852275
Winsorized Mean ( 3 / 20 )7.862295081967210.082188771600459695.6614258719892
Winsorized Mean ( 4 / 20 )7.875409836065570.079019114299117899.6646179335055
Winsorized Mean ( 5 / 20 )7.883606557377050.0772187414561402102.094470962789
Winsorized Mean ( 6 / 20 )7.883606557377050.0772187414561402102.094470962789
Winsorized Mean ( 7 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 8 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 9 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 10 / 20 )7.883606557377050.0670282677448775117.616146479924
Winsorized Mean ( 11 / 20 )7.90163934426230.0636113456594408124.217453071433
Winsorized Mean ( 12 / 20 )7.90163934426230.0636113456594408124.217453071433
Winsorized Mean ( 13 / 20 )7.922950819672130.0597990004221771132.493031049626
Winsorized Mean ( 14 / 20 )7.922950819672130.0597990004221771132.493031049626
Winsorized Mean ( 15 / 20 )7.89836065573770.055980666221419141.090865630243
Winsorized Mean ( 16 / 20 )7.89836065573770.0475343880859238166.160983106809
Winsorized Mean ( 17 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 18 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 19 / 20 )7.957377049180330.0282899716145710281.279075058591
Winsorized Mean ( 20 / 20 )7.957377049180330.0282899716145710281.279075058591
Trimmed Mean ( 1 / 20 )7.874576271186440.084772643311374792.8905359511166
Trimmed Mean ( 2 / 20 )7.875438596491230.079915396278632398.5472007050155
Trimmed Mean ( 3 / 20 )7.885454545454550.077434372422366101.834034405849
Trimmed Mean ( 4 / 20 )7.894339622641510.0749656473982424105.306095480029
Trimmed Mean ( 5 / 20 )7.90.0731369920617681108.016473979789
Trimmed Mean ( 6 / 20 )7.904081632653060.0714261418440054110.660906897583
Trimmed Mean ( 7 / 20 )7.908510638297870.0692118833963875114.265213576180
Trimmed Mean ( 8 / 20 )7.913333333333330.0676144745725142117.036084113122
Trimmed Mean ( 9 / 20 )7.91860465116280.0654870003883324120.918725918215
Trimmed Mean ( 10 / 20 )7.924390243902440.062643054605466126.500699779270
Trimmed Mean ( 11 / 20 )7.930769230769230.0604921165890038131.104178163455
Trimmed Mean ( 12 / 20 )7.935135135135130.0585377648459215135.555827183039
Trimmed Mean ( 13 / 20 )7.940.0557907254121759142.317561590034
Trimmed Mean ( 14 / 20 )7.942424242424240.0531276163402628149.497093781809
Trimmed Mean ( 15 / 20 )7.945161290322580.0492609268872802161.287287762629
Trimmed Mean ( 16 / 20 )7.951724137931030.0448370584914623177.347141080746
Trimmed Mean ( 17 / 20 )7.959259259259260.0414341406702771192.094227863856
Trimmed Mean ( 18 / 20 )7.9640.0382448253580359208.237321662305
Trimmed Mean ( 19 / 20 )7.96956521739130.032929906760223242.016027419124
Trimmed Mean ( 20 / 20 )7.971428571428570.0317301547599193251.225644241038
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.890625
Midmean - Weighted Average at X(n+1)p7.9060606060606
Midmean - Empirical Distribution Function7.9060606060606
Midmean - Empirical Distribution Function - Averaging7.9060606060606
Midmean - Empirical Distribution Function - Interpolation7.9060606060606
Midmean - Closest Observation7.9060606060606
Midmean - True Basic - Statistics Graphics Toolkit7.9060606060606
Midmean - MS Excel (old versions)7.9060606060606
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.8688524590164 & 0.0901892661881388 & 87.2482146888923 \tabularnewline
Geometric Mean & 7.8368075487419 &  &  \tabularnewline
Harmonic Mean & 7.80368521992802 &  &  \tabularnewline
Quadratic Mean & 7.89980286120493 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.87377049180328 & 0.0887035228674393 & 88.7650257540507 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.85737704918033 & 0.0834848573159053 & 94.1173920852275 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.86229508196721 & 0.0821887716004596 & 95.6614258719892 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.87540983606557 & 0.0790191142991178 & 99.6646179335055 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.88360655737705 & 0.0772187414561402 & 102.094470962789 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.88360655737705 & 0.0772187414561402 & 102.094470962789 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.88360655737705 & 0.0728866298303503 & 108.162588608182 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.88360655737705 & 0.0728866298303503 & 108.162588608182 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.88360655737705 & 0.0728866298303503 & 108.162588608182 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.88360655737705 & 0.0670282677448775 & 117.616146479924 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.9016393442623 & 0.0636113456594408 & 124.217453071433 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.9016393442623 & 0.0636113456594408 & 124.217453071433 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.92295081967213 & 0.0597990004221771 & 132.493031049626 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.92295081967213 & 0.0597990004221771 & 132.493031049626 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.8983606557377 & 0.055980666221419 & 141.090865630243 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.8983606557377 & 0.0475343880859238 & 166.160983106809 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.92622950819672 & 0.0427792426648031 & 185.282137187484 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.92622950819672 & 0.0427792426648031 & 185.282137187484 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.95737704918033 & 0.0282899716145710 & 281.279075058591 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.95737704918033 & 0.0282899716145710 & 281.279075058591 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.87457627118644 & 0.0847726433113747 & 92.8905359511166 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.87543859649123 & 0.0799153962786323 & 98.5472007050155 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.88545454545455 & 0.077434372422366 & 101.834034405849 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.89433962264151 & 0.0749656473982424 & 105.306095480029 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.9 & 0.0731369920617681 & 108.016473979789 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.90408163265306 & 0.0714261418440054 & 110.660906897583 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.90851063829787 & 0.0692118833963875 & 114.265213576180 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.91333333333333 & 0.0676144745725142 & 117.036084113122 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.9186046511628 & 0.0654870003883324 & 120.918725918215 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.92439024390244 & 0.062643054605466 & 126.500699779270 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.93076923076923 & 0.0604921165890038 & 131.104178163455 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.93513513513513 & 0.0585377648459215 & 135.555827183039 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.94 & 0.0557907254121759 & 142.317561590034 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.94242424242424 & 0.0531276163402628 & 149.497093781809 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.94516129032258 & 0.0492609268872802 & 161.287287762629 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.95172413793103 & 0.0448370584914623 & 177.347141080746 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.95925925925926 & 0.0414341406702771 & 192.094227863856 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.964 & 0.0382448253580359 & 208.237321662305 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.9695652173913 & 0.032929906760223 & 242.016027419124 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.97142857142857 & 0.0317301547599193 & 251.225644241038 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.890625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.9060606060606 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.9060606060606 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.9060606060606 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.9060606060606 &  &  \tabularnewline
Midmean - Closest Observation & 7.9060606060606 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.9060606060606 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.9060606060606 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48992&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]7.8688524590164[/C][C]0.0901892661881388[/C][C]87.2482146888923[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.8368075487419[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.80368521992802[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.89980286120493[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.87377049180328[/C][C]0.0887035228674393[/C][C]88.7650257540507[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.85737704918033[/C][C]0.0834848573159053[/C][C]94.1173920852275[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.86229508196721[/C][C]0.0821887716004596[/C][C]95.6614258719892[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.87540983606557[/C][C]0.0790191142991178[/C][C]99.6646179335055[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.88360655737705[/C][C]0.0772187414561402[/C][C]102.094470962789[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.88360655737705[/C][C]0.0772187414561402[/C][C]102.094470962789[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.88360655737705[/C][C]0.0728866298303503[/C][C]108.162588608182[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.88360655737705[/C][C]0.0728866298303503[/C][C]108.162588608182[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.88360655737705[/C][C]0.0728866298303503[/C][C]108.162588608182[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.88360655737705[/C][C]0.0670282677448775[/C][C]117.616146479924[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.9016393442623[/C][C]0.0636113456594408[/C][C]124.217453071433[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.9016393442623[/C][C]0.0636113456594408[/C][C]124.217453071433[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.92295081967213[/C][C]0.0597990004221771[/C][C]132.493031049626[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.92295081967213[/C][C]0.0597990004221771[/C][C]132.493031049626[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.8983606557377[/C][C]0.055980666221419[/C][C]141.090865630243[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.8983606557377[/C][C]0.0475343880859238[/C][C]166.160983106809[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.92622950819672[/C][C]0.0427792426648031[/C][C]185.282137187484[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.92622950819672[/C][C]0.0427792426648031[/C][C]185.282137187484[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.95737704918033[/C][C]0.0282899716145710[/C][C]281.279075058591[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.95737704918033[/C][C]0.0282899716145710[/C][C]281.279075058591[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.87457627118644[/C][C]0.0847726433113747[/C][C]92.8905359511166[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.87543859649123[/C][C]0.0799153962786323[/C][C]98.5472007050155[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.88545454545455[/C][C]0.077434372422366[/C][C]101.834034405849[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.89433962264151[/C][C]0.0749656473982424[/C][C]105.306095480029[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.9[/C][C]0.0731369920617681[/C][C]108.016473979789[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.90408163265306[/C][C]0.0714261418440054[/C][C]110.660906897583[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.90851063829787[/C][C]0.0692118833963875[/C][C]114.265213576180[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.91333333333333[/C][C]0.0676144745725142[/C][C]117.036084113122[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.9186046511628[/C][C]0.0654870003883324[/C][C]120.918725918215[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.92439024390244[/C][C]0.062643054605466[/C][C]126.500699779270[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.93076923076923[/C][C]0.0604921165890038[/C][C]131.104178163455[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.93513513513513[/C][C]0.0585377648459215[/C][C]135.555827183039[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.94[/C][C]0.0557907254121759[/C][C]142.317561590034[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.94242424242424[/C][C]0.0531276163402628[/C][C]149.497093781809[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.94516129032258[/C][C]0.0492609268872802[/C][C]161.287287762629[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.95172413793103[/C][C]0.0448370584914623[/C][C]177.347141080746[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.95925925925926[/C][C]0.0414341406702771[/C][C]192.094227863856[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.964[/C][C]0.0382448253580359[/C][C]208.237321662305[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.9695652173913[/C][C]0.032929906760223[/C][C]242.016027419124[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.97142857142857[/C][C]0.0317301547599193[/C][C]251.225644241038[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.9060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48992&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 Mean7.86885245901640.090189266188138887.2482146888923
Geometric Mean7.8368075487419
Harmonic Mean7.80368521992802
Quadratic Mean7.89980286120493
Winsorized Mean ( 1 / 20 )7.873770491803280.088703522867439388.7650257540507
Winsorized Mean ( 2 / 20 )7.857377049180330.083484857315905394.1173920852275
Winsorized Mean ( 3 / 20 )7.862295081967210.082188771600459695.6614258719892
Winsorized Mean ( 4 / 20 )7.875409836065570.079019114299117899.6646179335055
Winsorized Mean ( 5 / 20 )7.883606557377050.0772187414561402102.094470962789
Winsorized Mean ( 6 / 20 )7.883606557377050.0772187414561402102.094470962789
Winsorized Mean ( 7 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 8 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 9 / 20 )7.883606557377050.0728866298303503108.162588608182
Winsorized Mean ( 10 / 20 )7.883606557377050.0670282677448775117.616146479924
Winsorized Mean ( 11 / 20 )7.90163934426230.0636113456594408124.217453071433
Winsorized Mean ( 12 / 20 )7.90163934426230.0636113456594408124.217453071433
Winsorized Mean ( 13 / 20 )7.922950819672130.0597990004221771132.493031049626
Winsorized Mean ( 14 / 20 )7.922950819672130.0597990004221771132.493031049626
Winsorized Mean ( 15 / 20 )7.89836065573770.055980666221419141.090865630243
Winsorized Mean ( 16 / 20 )7.89836065573770.0475343880859238166.160983106809
Winsorized Mean ( 17 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 18 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 19 / 20 )7.957377049180330.0282899716145710281.279075058591
Winsorized Mean ( 20 / 20 )7.957377049180330.0282899716145710281.279075058591
Trimmed Mean ( 1 / 20 )7.874576271186440.084772643311374792.8905359511166
Trimmed Mean ( 2 / 20 )7.875438596491230.079915396278632398.5472007050155
Trimmed Mean ( 3 / 20 )7.885454545454550.077434372422366101.834034405849
Trimmed Mean ( 4 / 20 )7.894339622641510.0749656473982424105.306095480029
Trimmed Mean ( 5 / 20 )7.90.0731369920617681108.016473979789
Trimmed Mean ( 6 / 20 )7.904081632653060.0714261418440054110.660906897583
Trimmed Mean ( 7 / 20 )7.908510638297870.0692118833963875114.265213576180
Trimmed Mean ( 8 / 20 )7.913333333333330.0676144745725142117.036084113122
Trimmed Mean ( 9 / 20 )7.91860465116280.0654870003883324120.918725918215
Trimmed Mean ( 10 / 20 )7.924390243902440.062643054605466126.500699779270
Trimmed Mean ( 11 / 20 )7.930769230769230.0604921165890038131.104178163455
Trimmed Mean ( 12 / 20 )7.935135135135130.0585377648459215135.555827183039
Trimmed Mean ( 13 / 20 )7.940.0557907254121759142.317561590034
Trimmed Mean ( 14 / 20 )7.942424242424240.0531276163402628149.497093781809
Trimmed Mean ( 15 / 20 )7.945161290322580.0492609268872802161.287287762629
Trimmed Mean ( 16 / 20 )7.951724137931030.0448370584914623177.347141080746
Trimmed Mean ( 17 / 20 )7.959259259259260.0414341406702771192.094227863856
Trimmed Mean ( 18 / 20 )7.9640.0382448253580359208.237321662305
Trimmed Mean ( 19 / 20 )7.96956521739130.032929906760223242.016027419124
Trimmed Mean ( 20 / 20 )7.971428571428570.0317301547599193251.225644241038
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.890625
Midmean - Weighted Average at X(n+1)p7.9060606060606
Midmean - Empirical Distribution Function7.9060606060606
Midmean - Empirical Distribution Function - Averaging7.9060606060606
Midmean - Empirical Distribution Function - Interpolation7.9060606060606
Midmean - Closest Observation7.9060606060606
Midmean - True Basic - Statistics Graphics Toolkit7.9060606060606
Midmean - MS Excel (old versions)7.9060606060606
Number of observations61



Parameters (Session):
par1 = werkloosheid laatste 5 jaar ; par2 = belgostat ; par3 = werkloosheid laatste 5 jaar ;
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')