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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Nov 2007 13:03:20 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/06/z32121e4u2lw7sk1194379245.htm/, Retrieved Fri, 03 May 2024 20:41:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=568, Retrieved Fri, 03 May 2024 20:41:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact261

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-06 20:03:20] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112.6
113.8
107.8
103.2
103.3
101.2
107.7
110.4
101.9
115.9
89.9
88.6
117.2
123.9
100
103.6
94.1
98.7
119.5
112.7
104.4
124.7
89.1
97
121.6
118.8
114
111.5
97.2
102.5
113.4
109.8
104.9
126.1
80
96.8
117.2
112.3
117.3
111.1
102.2
104.3
122.9
107.6
121.3
131.5
89
104.4
128.9
135.9
133.3
121.3
120.5
120.4
137.9
126.1
133.2
146.6
103.4
117.2

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=568&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=568&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.7266666666671.7538929527317863.7021013697825
Geometric Mean110.909390027782
Harmonic Mean110.085026840872
Quadratic Mean112.535951292613
Winsorized Mean ( 1 / 20 )111.7251.6711825120855566.8538589843027
Winsorized Mean ( 2 / 20 )111.6716666666671.6509235416849767.6419372835959
Winsorized Mean ( 3 / 20 )111.5466666666671.6187678697688168.9083770130658
Winsorized Mean ( 4 / 20 )111.5933333333331.6048705294184569.5341657085391
Winsorized Mean ( 5 / 20 )111.8016666666671.4975752372876374.655125086843
Winsorized Mean ( 6 / 20 )111.8116666666671.389573953457780.4647110637357
Winsorized Mean ( 7 / 20 )111.5083333333331.3205445111871084.4411773996876
Winsorized Mean ( 8 / 20 )111.5351.3155992061362984.7788593059134
Winsorized Mean ( 9 / 20 )111.551.2363183452685190.2275699676472
Winsorized Mean ( 10 / 20 )111.6333333333331.1752164523955494.9895937091262
Winsorized Mean ( 11 / 20 )111.671.10711438428331100.865819815258
Winsorized Mean ( 12 / 20 )111.551.04124138211042107.131739015124
Winsorized Mean ( 13 / 20 )111.551.02050862470993109.308238361736
Winsorized Mean ( 14 / 20 )111.621.00971495670081110.546049911663
Winsorized Mean ( 15 / 20 )111.5950.951090438706472117.333741838236
Winsorized Mean ( 16 / 20 )111.5950.942881222636235118.355310638160
Winsorized Mean ( 17 / 20 )111.3683333333330.898896032482514123.894565454654
Winsorized Mean ( 18 / 20 )111.2183333333330.858041034097937129.618898063841
Winsorized Mean ( 19 / 20 )110.9650.755334419145429146.908438417971
Winsorized Mean ( 20 / 20 )110.9650.745623104228485148.821836891466
Trimmed Mean ( 1 / 20 )111.6724137931031.6191006613623568.9718783136926
Trimmed Mean ( 2 / 20 )111.6160714285711.5548662129479171.7850002135912
Trimmed Mean ( 3 / 20 )111.5851851851851.4889516415811574.9421150217413
Trimmed Mean ( 4 / 20 )111.61.4227016340990778.4423081587804
Trimmed Mean ( 5 / 20 )111.6021.3447418081595682.9913960604383
Trimmed Mean ( 6 / 20 )111.5520833333331.2854959772996886.7774658989288
Trimmed Mean ( 7 / 20 )111.4956521739131.2451488726999289.5440333428975
Trimmed Mean ( 8 / 20 )111.4931818181821.2134525975164391.8809536082205
Trimmed Mean ( 9 / 20 )111.4857142857141.1727280970653895.0652709393547
Trimmed Mean ( 10 / 20 )111.4751.1407810527250297.718137703739
Trimmed Mean ( 11 / 20 )111.451.11375564458564100.066832919589
Trimmed Mean ( 12 / 20 )111.4166666666671.09394799795156101.848229417940
Trimmed Mean ( 13 / 20 )111.3970588235291.08201539435474102.95330307196
Trimmed Mean ( 14 / 20 )111.3751.06772670781462104.310400016085
Trimmed Mean ( 15 / 20 )111.341.04695068992118106.346937894833
Trimmed Mean ( 16 / 20 )111.3035714285711.03087883274440107.969596322256
Trimmed Mean ( 17 / 20 )111.2615384615381.00503466336053110.70418018172
Trimmed Mean ( 18 / 20 )111.2458333333330.976981063681518113.866928918899
Trimmed Mean ( 19 / 20 )111.250.943598849023666117.899677511380
Trimmed Mean ( 20 / 20 )111.2950.926807622120714120.084251945766
Median111.9
Midrange113.3
Midmean - Weighted Average at Xnp111.054838709677
Midmean - Weighted Average at X(n+1)p111.34
Midmean - Empirical Distribution Function111.054838709677
Midmean - Empirical Distribution Function - Averaging111.34
Midmean - Empirical Distribution Function - Interpolation111.34
Midmean - Closest Observation111.054838709677
Midmean - True Basic - Statistics Graphics Toolkit111.34
Midmean - MS Excel (old versions)111.675757575758
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.726666666667 & 1.75389295273178 & 63.7021013697825 \tabularnewline
Geometric Mean & 110.909390027782 &  &  \tabularnewline
Harmonic Mean & 110.085026840872 &  &  \tabularnewline
Quadratic Mean & 112.535951292613 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.725 & 1.67118251208555 & 66.8538589843027 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.671666666667 & 1.65092354168497 & 67.6419372835959 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.546666666667 & 1.61876786976881 & 68.9083770130658 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.593333333333 & 1.60487052941845 & 69.5341657085391 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.801666666667 & 1.49757523728763 & 74.655125086843 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.811666666667 & 1.3895739534577 & 80.4647110637357 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.508333333333 & 1.32054451118710 & 84.4411773996876 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.535 & 1.31559920613629 & 84.7788593059134 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.55 & 1.23631834526851 & 90.2275699676472 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.633333333333 & 1.17521645239554 & 94.9895937091262 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.67 & 1.10711438428331 & 100.865819815258 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.55 & 1.04124138211042 & 107.131739015124 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.55 & 1.02050862470993 & 109.308238361736 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.62 & 1.00971495670081 & 110.546049911663 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.595 & 0.951090438706472 & 117.333741838236 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.595 & 0.942881222636235 & 118.355310638160 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.368333333333 & 0.898896032482514 & 123.894565454654 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.218333333333 & 0.858041034097937 & 129.618898063841 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.965 & 0.755334419145429 & 146.908438417971 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.965 & 0.745623104228485 & 148.821836891466 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.672413793103 & 1.61910066136235 & 68.9718783136926 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.616071428571 & 1.55486621294791 & 71.7850002135912 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.585185185185 & 1.48895164158115 & 74.9421150217413 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.6 & 1.42270163409907 & 78.4423081587804 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.602 & 1.34474180815956 & 82.9913960604383 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.552083333333 & 1.28549597729968 & 86.7774658989288 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.495652173913 & 1.24514887269992 & 89.5440333428975 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.493181818182 & 1.21345259751643 & 91.8809536082205 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.485714285714 & 1.17272809706538 & 95.0652709393547 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.475 & 1.14078105272502 & 97.718137703739 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.45 & 1.11375564458564 & 100.066832919589 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.416666666667 & 1.09394799795156 & 101.848229417940 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.397058823529 & 1.08201539435474 & 102.95330307196 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.375 & 1.06772670781462 & 104.310400016085 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.34 & 1.04695068992118 & 106.346937894833 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.303571428571 & 1.03087883274440 & 107.969596322256 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.261538461538 & 1.00503466336053 & 110.70418018172 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.245833333333 & 0.976981063681518 & 113.866928918899 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.25 & 0.943598849023666 & 117.899677511380 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.295 & 0.926807622120714 & 120.084251945766 \tabularnewline
Median & 111.9 &  &  \tabularnewline
Midrange & 113.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.054838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.34 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.054838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.34 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.34 &  &  \tabularnewline
Midmean - Closest Observation & 111.054838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.34 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.675757575758 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=568&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]111.726666666667[/C][C]1.75389295273178[/C][C]63.7021013697825[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.909390027782[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.085026840872[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.535951292613[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.725[/C][C]1.67118251208555[/C][C]66.8538589843027[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.671666666667[/C][C]1.65092354168497[/C][C]67.6419372835959[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.546666666667[/C][C]1.61876786976881[/C][C]68.9083770130658[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.593333333333[/C][C]1.60487052941845[/C][C]69.5341657085391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.801666666667[/C][C]1.49757523728763[/C][C]74.655125086843[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.811666666667[/C][C]1.3895739534577[/C][C]80.4647110637357[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.508333333333[/C][C]1.32054451118710[/C][C]84.4411773996876[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.535[/C][C]1.31559920613629[/C][C]84.7788593059134[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.55[/C][C]1.23631834526851[/C][C]90.2275699676472[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.633333333333[/C][C]1.17521645239554[/C][C]94.9895937091262[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.67[/C][C]1.10711438428331[/C][C]100.865819815258[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.55[/C][C]1.04124138211042[/C][C]107.131739015124[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.55[/C][C]1.02050862470993[/C][C]109.308238361736[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.62[/C][C]1.00971495670081[/C][C]110.546049911663[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.595[/C][C]0.951090438706472[/C][C]117.333741838236[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.595[/C][C]0.942881222636235[/C][C]118.355310638160[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.368333333333[/C][C]0.898896032482514[/C][C]123.894565454654[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.218333333333[/C][C]0.858041034097937[/C][C]129.618898063841[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.965[/C][C]0.755334419145429[/C][C]146.908438417971[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.965[/C][C]0.745623104228485[/C][C]148.821836891466[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.672413793103[/C][C]1.61910066136235[/C][C]68.9718783136926[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.616071428571[/C][C]1.55486621294791[/C][C]71.7850002135912[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.585185185185[/C][C]1.48895164158115[/C][C]74.9421150217413[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.6[/C][C]1.42270163409907[/C][C]78.4423081587804[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.602[/C][C]1.34474180815956[/C][C]82.9913960604383[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.552083333333[/C][C]1.28549597729968[/C][C]86.7774658989288[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.495652173913[/C][C]1.24514887269992[/C][C]89.5440333428975[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.493181818182[/C][C]1.21345259751643[/C][C]91.8809536082205[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.485714285714[/C][C]1.17272809706538[/C][C]95.0652709393547[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.475[/C][C]1.14078105272502[/C][C]97.718137703739[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.45[/C][C]1.11375564458564[/C][C]100.066832919589[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.416666666667[/C][C]1.09394799795156[/C][C]101.848229417940[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.397058823529[/C][C]1.08201539435474[/C][C]102.95330307196[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.375[/C][C]1.06772670781462[/C][C]104.310400016085[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.34[/C][C]1.04695068992118[/C][C]106.346937894833[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.303571428571[/C][C]1.03087883274440[/C][C]107.969596322256[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.261538461538[/C][C]1.00503466336053[/C][C]110.70418018172[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.245833333333[/C][C]0.976981063681518[/C][C]113.866928918899[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.25[/C][C]0.943598849023666[/C][C]117.899677511380[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.295[/C][C]0.926807622120714[/C][C]120.084251945766[/C][/ROW]
[ROW][C]Median[/C][C]111.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.054838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.054838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.054838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.675757575758[/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=568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=568&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.7266666666671.7538929527317863.7021013697825
Geometric Mean110.909390027782
Harmonic Mean110.085026840872
Quadratic Mean112.535951292613
Winsorized Mean ( 1 / 20 )111.7251.6711825120855566.8538589843027
Winsorized Mean ( 2 / 20 )111.6716666666671.6509235416849767.6419372835959
Winsorized Mean ( 3 / 20 )111.5466666666671.6187678697688168.9083770130658
Winsorized Mean ( 4 / 20 )111.5933333333331.6048705294184569.5341657085391
Winsorized Mean ( 5 / 20 )111.8016666666671.4975752372876374.655125086843
Winsorized Mean ( 6 / 20 )111.8116666666671.389573953457780.4647110637357
Winsorized Mean ( 7 / 20 )111.5083333333331.3205445111871084.4411773996876
Winsorized Mean ( 8 / 20 )111.5351.3155992061362984.7788593059134
Winsorized Mean ( 9 / 20 )111.551.2363183452685190.2275699676472
Winsorized Mean ( 10 / 20 )111.6333333333331.1752164523955494.9895937091262
Winsorized Mean ( 11 / 20 )111.671.10711438428331100.865819815258
Winsorized Mean ( 12 / 20 )111.551.04124138211042107.131739015124
Winsorized Mean ( 13 / 20 )111.551.02050862470993109.308238361736
Winsorized Mean ( 14 / 20 )111.621.00971495670081110.546049911663
Winsorized Mean ( 15 / 20 )111.5950.951090438706472117.333741838236
Winsorized Mean ( 16 / 20 )111.5950.942881222636235118.355310638160
Winsorized Mean ( 17 / 20 )111.3683333333330.898896032482514123.894565454654
Winsorized Mean ( 18 / 20 )111.2183333333330.858041034097937129.618898063841
Winsorized Mean ( 19 / 20 )110.9650.755334419145429146.908438417971
Winsorized Mean ( 20 / 20 )110.9650.745623104228485148.821836891466
Trimmed Mean ( 1 / 20 )111.6724137931031.6191006613623568.9718783136926
Trimmed Mean ( 2 / 20 )111.6160714285711.5548662129479171.7850002135912
Trimmed Mean ( 3 / 20 )111.5851851851851.4889516415811574.9421150217413
Trimmed Mean ( 4 / 20 )111.61.4227016340990778.4423081587804
Trimmed Mean ( 5 / 20 )111.6021.3447418081595682.9913960604383
Trimmed Mean ( 6 / 20 )111.5520833333331.2854959772996886.7774658989288
Trimmed Mean ( 7 / 20 )111.4956521739131.2451488726999289.5440333428975
Trimmed Mean ( 8 / 20 )111.4931818181821.2134525975164391.8809536082205
Trimmed Mean ( 9 / 20 )111.4857142857141.1727280970653895.0652709393547
Trimmed Mean ( 10 / 20 )111.4751.1407810527250297.718137703739
Trimmed Mean ( 11 / 20 )111.451.11375564458564100.066832919589
Trimmed Mean ( 12 / 20 )111.4166666666671.09394799795156101.848229417940
Trimmed Mean ( 13 / 20 )111.3970588235291.08201539435474102.95330307196
Trimmed Mean ( 14 / 20 )111.3751.06772670781462104.310400016085
Trimmed Mean ( 15 / 20 )111.341.04695068992118106.346937894833
Trimmed Mean ( 16 / 20 )111.3035714285711.03087883274440107.969596322256
Trimmed Mean ( 17 / 20 )111.2615384615381.00503466336053110.70418018172
Trimmed Mean ( 18 / 20 )111.2458333333330.976981063681518113.866928918899
Trimmed Mean ( 19 / 20 )111.250.943598849023666117.899677511380
Trimmed Mean ( 20 / 20 )111.2950.926807622120714120.084251945766
Median111.9
Midrange113.3
Midmean - Weighted Average at Xnp111.054838709677
Midmean - Weighted Average at X(n+1)p111.34
Midmean - Empirical Distribution Function111.054838709677
Midmean - Empirical Distribution Function - Averaging111.34
Midmean - Empirical Distribution Function - Interpolation111.34
Midmean - Closest Observation111.054838709677
Midmean - True Basic - Statistics Graphics Toolkit111.34
Midmean - MS Excel (old versions)111.675757575758
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')