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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, 27 Oct 2009 06:07:36 -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/27/t12566453805llhs2wq3wzxxyk.htm/, Retrieved Tue, 07 May 2024 04:57:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50924, Retrieved Tue, 07 May 2024 04:57:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmediaan, getrimd gemiddelde
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [median werklosshe...] [2009-10-27 12:07:36] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
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
8.0
8.2
8.1
8.1
8.0
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
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
8.0
8.0
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 time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50924&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]3 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=50924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50924&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.798245614035090.087770035452007888.8486095952317
Geometric Mean7.76943284644514
Harmonic Mean7.73944189380973
Quadratic Mean7.82585682770387
Winsorized Mean ( 1 / 19 )7.803508771929820.086093326419003690.6401122655116
Winsorized Mean ( 2 / 19 )7.807017543859650.08510128305708791.7379534527417
Winsorized Mean ( 3 / 19 )7.812280701754390.08369857960000893.3382709609763
Winsorized Mean ( 4 / 19 )7.819298245614030.078975210907695499.0095266064319
Winsorized Mean ( 5 / 19 )7.82807017543860.0770197703504938101.637152900033
Winsorized Mean ( 6 / 19 )7.82807017543860.0770197703504938101.637152900033
Winsorized Mean ( 7 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 8 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 9 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 10 / 19 )7.845614035087720.0688279144024698113.988838732068
Winsorized Mean ( 11 / 19 )7.864912280701750.0652012129554793120.625244902608
Winsorized Mean ( 12 / 19 )7.84385964912280.0616714526283924127.187852966376
Winsorized Mean ( 13 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 14 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 15 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 16 / 19 )7.84385964912280.044778593716875175.169852334305
Winsorized Mean ( 17 / 19 )7.873684210526320.0396196133004779198.731980315198
Winsorized Mean ( 18 / 19 )7.84210526315790.0352174918465452222.676427308584
Winsorized Mean ( 19 / 19 )7.908771929824560.0241757223230147327.136944416987
Trimmed Mean ( 1 / 19 )7.812727272727270.083849092659141293.176050270301
Trimmed Mean ( 2 / 19 )7.822641509433960.08102399389442396.5472217973743
Trimmed Mean ( 3 / 19 )7.83137254901960.0781396535661547100.222770278722
Trimmed Mean ( 4 / 19 )7.838775510204080.0751877653314182104.255997975891
Trimmed Mean ( 5 / 19 )7.844680851063830.0733630178177875106.929636817119
Trimmed Mean ( 6 / 19 )7.848888888888890.071677040984299109.503528341916
Trimmed Mean ( 7 / 19 )7.853488372093020.0694344211434585113.106557853589
Trimmed Mean ( 8 / 19 )7.858536585365850.0678929941567034115.748858670566
Trimmed Mean ( 9 / 19 )7.864102564102560.065765212316042119.578456256033
Trimmed Mean ( 10 / 19 )7.870270270270270.0628245166544546125.273869014514
Trimmed Mean ( 11 / 19 )7.874285714285710.0598798316438438131.501467157102
Trimmed Mean ( 12 / 19 )7.875757575757580.0569140605181605138.379822210094
Trimmed Mean ( 13 / 19 )7.880645161290320.0537655913548404146.574137151769
Trimmed Mean ( 14 / 19 )7.886206896551720.0517487626112826152.39411531035
Trimmed Mean ( 15 / 19 )7.89259259259260.0486061929407315162.378333193396
Trimmed Mean ( 16 / 19 )7.90.0435889894354067181.238429757744
Trimmed Mean ( 17 / 19 )7.908695652173910.0397188953939388199.116706890615
Trimmed Mean ( 18 / 19 )7.914285714285710.036046077843382219.560245879532
Trimmed Mean ( 19 / 19 )7.926315789473680.0313834102105233252.563878058602
Median8
Midrange7.4
Midmean - Weighted Average at Xnp7.88064516129032
Midmean - Weighted Average at X(n+1)p7.88064516129032
Midmean - Empirical Distribution Function7.88064516129032
Midmean - Empirical Distribution Function - Averaging7.88064516129032
Midmean - Empirical Distribution Function - Interpolation7.88064516129032
Midmean - Closest Observation7.88064516129032
Midmean - True Basic - Statistics Graphics Toolkit7.88064516129032
Midmean - MS Excel (old versions)7.88064516129032
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.79824561403509 & 0.0877700354520078 & 88.8486095952317 \tabularnewline
Geometric Mean & 7.76943284644514 &  &  \tabularnewline
Harmonic Mean & 7.73944189380973 &  &  \tabularnewline
Quadratic Mean & 7.82585682770387 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 7.80350877192982 & 0.0860933264190036 & 90.6401122655116 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 7.80701754385965 & 0.085101283057087 & 91.7379534527417 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 7.81228070175439 & 0.083698579600008 & 93.3382709609763 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 7.81929824561403 & 0.0789752109076954 & 99.0095266064319 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 7.8280701754386 & 0.0770197703504938 & 101.637152900033 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 7.8280701754386 & 0.0770197703504938 & 101.637152900033 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 7.8280701754386 & 0.0723207483290784 & 108.241000768117 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 7.8280701754386 & 0.0723207483290784 & 108.241000768117 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 7.8280701754386 & 0.0723207483290784 & 108.241000768117 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 7.84561403508772 & 0.0688279144024698 & 113.988838732068 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 7.86491228070175 & 0.0652012129554793 & 120.625244902608 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 7.8438596491228 & 0.0616714526283924 & 127.187852966376 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 7.8438596491228 & 0.0539201084416445 & 145.471881934583 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 7.8438596491228 & 0.0539201084416445 & 145.471881934583 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 7.8438596491228 & 0.0539201084416445 & 145.471881934583 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 7.8438596491228 & 0.044778593716875 & 175.169852334305 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 7.87368421052632 & 0.0396196133004779 & 198.731980315198 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 7.8421052631579 & 0.0352174918465452 & 222.676427308584 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 7.90877192982456 & 0.0241757223230147 & 327.136944416987 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 7.81272727272727 & 0.0838490926591412 & 93.176050270301 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 7.82264150943396 & 0.081023993894423 & 96.5472217973743 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 7.8313725490196 & 0.0781396535661547 & 100.222770278722 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 7.83877551020408 & 0.0751877653314182 & 104.255997975891 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 7.84468085106383 & 0.0733630178177875 & 106.929636817119 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 7.84888888888889 & 0.071677040984299 & 109.503528341916 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 7.85348837209302 & 0.0694344211434585 & 113.106557853589 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 7.85853658536585 & 0.0678929941567034 & 115.748858670566 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 7.86410256410256 & 0.065765212316042 & 119.578456256033 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 7.87027027027027 & 0.0628245166544546 & 125.273869014514 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 7.87428571428571 & 0.0598798316438438 & 131.501467157102 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 7.87575757575758 & 0.0569140605181605 & 138.379822210094 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 7.88064516129032 & 0.0537655913548404 & 146.574137151769 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 7.88620689655172 & 0.0517487626112826 & 152.39411531035 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 7.8925925925926 & 0.0486061929407315 & 162.378333193396 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 7.9 & 0.0435889894354067 & 181.238429757744 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 7.90869565217391 & 0.0397188953939388 & 199.116706890615 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 7.91428571428571 & 0.036046077843382 & 219.560245879532 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 7.92631578947368 & 0.0313834102105233 & 252.563878058602 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.88064516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.88064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.88064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.88064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.88064516129032 &  &  \tabularnewline
Midmean - Closest Observation & 7.88064516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.88064516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.88064516129032 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50924&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]7.79824561403509[/C][C]0.0877700354520078[/C][C]88.8486095952317[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.76943284644514[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.73944189380973[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.82585682770387[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]7.80350877192982[/C][C]0.0860933264190036[/C][C]90.6401122655116[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]7.80701754385965[/C][C]0.085101283057087[/C][C]91.7379534527417[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]7.81228070175439[/C][C]0.083698579600008[/C][C]93.3382709609763[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]7.81929824561403[/C][C]0.0789752109076954[/C][C]99.0095266064319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]7.8280701754386[/C][C]0.0770197703504938[/C][C]101.637152900033[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]7.8280701754386[/C][C]0.0770197703504938[/C][C]101.637152900033[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]7.8280701754386[/C][C]0.0723207483290784[/C][C]108.241000768117[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]7.8280701754386[/C][C]0.0723207483290784[/C][C]108.241000768117[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]7.8280701754386[/C][C]0.0723207483290784[/C][C]108.241000768117[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]7.84561403508772[/C][C]0.0688279144024698[/C][C]113.988838732068[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]7.86491228070175[/C][C]0.0652012129554793[/C][C]120.625244902608[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]7.8438596491228[/C][C]0.0616714526283924[/C][C]127.187852966376[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]7.8438596491228[/C][C]0.0539201084416445[/C][C]145.471881934583[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]7.8438596491228[/C][C]0.0539201084416445[/C][C]145.471881934583[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]7.8438596491228[/C][C]0.0539201084416445[/C][C]145.471881934583[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]7.8438596491228[/C][C]0.044778593716875[/C][C]175.169852334305[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]7.87368421052632[/C][C]0.0396196133004779[/C][C]198.731980315198[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]7.8421052631579[/C][C]0.0352174918465452[/C][C]222.676427308584[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]7.90877192982456[/C][C]0.0241757223230147[/C][C]327.136944416987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]7.81272727272727[/C][C]0.0838490926591412[/C][C]93.176050270301[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]7.82264150943396[/C][C]0.081023993894423[/C][C]96.5472217973743[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]7.8313725490196[/C][C]0.0781396535661547[/C][C]100.222770278722[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]7.83877551020408[/C][C]0.0751877653314182[/C][C]104.255997975891[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]7.84468085106383[/C][C]0.0733630178177875[/C][C]106.929636817119[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]7.84888888888889[/C][C]0.071677040984299[/C][C]109.503528341916[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]7.85348837209302[/C][C]0.0694344211434585[/C][C]113.106557853589[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]7.85853658536585[/C][C]0.0678929941567034[/C][C]115.748858670566[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]7.86410256410256[/C][C]0.065765212316042[/C][C]119.578456256033[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]7.87027027027027[/C][C]0.0628245166544546[/C][C]125.273869014514[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]7.87428571428571[/C][C]0.0598798316438438[/C][C]131.501467157102[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]7.87575757575758[/C][C]0.0569140605181605[/C][C]138.379822210094[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]7.88064516129032[/C][C]0.0537655913548404[/C][C]146.574137151769[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]7.88620689655172[/C][C]0.0517487626112826[/C][C]152.39411531035[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]7.8925925925926[/C][C]0.0486061929407315[/C][C]162.378333193396[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]7.9[/C][C]0.0435889894354067[/C][C]181.238429757744[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]7.90869565217391[/C][C]0.0397188953939388[/C][C]199.116706890615[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]7.91428571428571[/C][C]0.036046077843382[/C][C]219.560245879532[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]7.92631578947368[/C][C]0.0313834102105233[/C][C]252.563878058602[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.88064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50924&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 Mean7.798245614035090.087770035452007888.8486095952317
Geometric Mean7.76943284644514
Harmonic Mean7.73944189380973
Quadratic Mean7.82585682770387
Winsorized Mean ( 1 / 19 )7.803508771929820.086093326419003690.6401122655116
Winsorized Mean ( 2 / 19 )7.807017543859650.08510128305708791.7379534527417
Winsorized Mean ( 3 / 19 )7.812280701754390.08369857960000893.3382709609763
Winsorized Mean ( 4 / 19 )7.819298245614030.078975210907695499.0095266064319
Winsorized Mean ( 5 / 19 )7.82807017543860.0770197703504938101.637152900033
Winsorized Mean ( 6 / 19 )7.82807017543860.0770197703504938101.637152900033
Winsorized Mean ( 7 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 8 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 9 / 19 )7.82807017543860.0723207483290784108.241000768117
Winsorized Mean ( 10 / 19 )7.845614035087720.0688279144024698113.988838732068
Winsorized Mean ( 11 / 19 )7.864912280701750.0652012129554793120.625244902608
Winsorized Mean ( 12 / 19 )7.84385964912280.0616714526283924127.187852966376
Winsorized Mean ( 13 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 14 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 15 / 19 )7.84385964912280.0539201084416445145.471881934583
Winsorized Mean ( 16 / 19 )7.84385964912280.044778593716875175.169852334305
Winsorized Mean ( 17 / 19 )7.873684210526320.0396196133004779198.731980315198
Winsorized Mean ( 18 / 19 )7.84210526315790.0352174918465452222.676427308584
Winsorized Mean ( 19 / 19 )7.908771929824560.0241757223230147327.136944416987
Trimmed Mean ( 1 / 19 )7.812727272727270.083849092659141293.176050270301
Trimmed Mean ( 2 / 19 )7.822641509433960.08102399389442396.5472217973743
Trimmed Mean ( 3 / 19 )7.83137254901960.0781396535661547100.222770278722
Trimmed Mean ( 4 / 19 )7.838775510204080.0751877653314182104.255997975891
Trimmed Mean ( 5 / 19 )7.844680851063830.0733630178177875106.929636817119
Trimmed Mean ( 6 / 19 )7.848888888888890.071677040984299109.503528341916
Trimmed Mean ( 7 / 19 )7.853488372093020.0694344211434585113.106557853589
Trimmed Mean ( 8 / 19 )7.858536585365850.0678929941567034115.748858670566
Trimmed Mean ( 9 / 19 )7.864102564102560.065765212316042119.578456256033
Trimmed Mean ( 10 / 19 )7.870270270270270.0628245166544546125.273869014514
Trimmed Mean ( 11 / 19 )7.874285714285710.0598798316438438131.501467157102
Trimmed Mean ( 12 / 19 )7.875757575757580.0569140605181605138.379822210094
Trimmed Mean ( 13 / 19 )7.880645161290320.0537655913548404146.574137151769
Trimmed Mean ( 14 / 19 )7.886206896551720.0517487626112826152.39411531035
Trimmed Mean ( 15 / 19 )7.89259259259260.0486061929407315162.378333193396
Trimmed Mean ( 16 / 19 )7.90.0435889894354067181.238429757744
Trimmed Mean ( 17 / 19 )7.908695652173910.0397188953939388199.116706890615
Trimmed Mean ( 18 / 19 )7.914285714285710.036046077843382219.560245879532
Trimmed Mean ( 19 / 19 )7.926315789473680.0313834102105233252.563878058602
Median8
Midrange7.4
Midmean - Weighted Average at Xnp7.88064516129032
Midmean - Weighted Average at X(n+1)p7.88064516129032
Midmean - Empirical Distribution Function7.88064516129032
Midmean - Empirical Distribution Function - Averaging7.88064516129032
Midmean - Empirical Distribution Function - Interpolation7.88064516129032
Midmean - Closest Observation7.88064516129032
Midmean - True Basic - Statistics Graphics Toolkit7.88064516129032
Midmean - MS Excel (old versions)7.88064516129032
Number of observations57



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')