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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 07:44:01 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331124282p3ik2cqj1zqrwaw.htm/, Retrieved Mon, 29 Apr 2024 05:47:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163599, Retrieved Mon, 29 Apr 2024 05:47:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gem Consumptiepri...] [2012-03-07 12:44:01] [b3616d670e39c9c081ac68ec1f5d1a32] [Current]
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Dataseries X:
0,9
0,9
0,9
0,9
0,9
0,91
0,91
0,91
0,91
0,91
0,92
0,92
0,92
0,92
0,92
0,93
0,93
0,93
0,93
0,93
0,92
0,93
0,93
0,93
0,94
0,95
0,95
0,96
0,97
0,97
0,97
0,98
0,98
0,98
0,98
0,98
0,98
1
1,01
1,01
1,02
1,02
1,02
1,02
1,03
1,03
1,03
1,03
1,03
1,04
1,05
1,05
1,05
1,05
1,06
1,06
1,06
1,06
1,06
1,06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163599&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163599&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9741666666666670.00718713408959688135.543132286448
Geometric Mean0.972612219759778
Harmonic Mean0.971069917020514
Quadratic Mean0.975729641516201
Winsorized Mean ( 1 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 2 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 3 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 4 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 5 / 20 )0.9750.00704906132309282138.316288554036
Winsorized Mean ( 6 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 7 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 8 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 9 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 10 / 20 )0.9740.00629410988218664154.747854459386
Winsorized Mean ( 11 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 12 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 13 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 14 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 15 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 16 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 17 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 18 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 19 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 20 / 20 )0.9688333333333330.00465833598637524207.9784146457
Trimmed Mean ( 1 / 20 )0.9739655172413790.0071706350463176135.826954091263
Trimmed Mean ( 2 / 20 )0.973750.00714216717446826136.338169663817
Trimmed Mean ( 3 / 20 )0.9735185185185190.00709896798341761137.135217512257
Trimmed Mean ( 4 / 20 )0.9732692307692310.007037505395416138.297475608784
Trimmed Mean ( 5 / 20 )0.9730.00695319629922169139.9356437138
Trimmed Mean ( 6 / 20 )0.97250.00688365831321178141.276622945314
Trimmed Mean ( 7 / 20 )0.9721739130434780.00684481568673249142.03069264931
Trimmed Mean ( 8 / 20 )0.9718181818181820.00678320840032142143.268218292119
Trimmed Mean ( 9 / 20 )0.9714285714285710.0066919216347093145.164367494983
Trimmed Mean ( 10 / 20 )0.9710.00656134757891106147.987892475154
Trimmed Mean ( 11 / 20 )0.9705263157894740.00652108265388598148.829016177418
Trimmed Mean ( 12 / 20 )0.9702777777777780.00652815770593126148.629647365323
Trimmed Mean ( 13 / 20 )0.970.00651338947278929148.923997874275
Trimmed Mean ( 14 / 20 )0.96968750.00646772968032384149.927029719561
Trimmed Mean ( 15 / 20 )0.9693333333333330.00637764294249182151.989275987063
Trimmed Mean ( 16 / 20 )0.9689285714285710.00622206531224247155.724590277463
Trimmed Mean ( 17 / 20 )0.9684615384615380.00621888705581776155.729076564519
Trimmed Mean ( 18 / 20 )0.9679166666666670.00616732761831985156.942638135763
Trimmed Mean ( 19 / 20 )0.9672727272727270.00603674958344759160.230719181218
Trimmed Mean ( 20 / 20 )0.96650.00577084322945506167.479857201261
Median0.97
Midrange0.98
Midmean - Weighted Average at Xnp0.969230769230769
Midmean - Weighted Average at X(n+1)p0.969230769230769
Midmean - Empirical Distribution Function0.969230769230769
Midmean - Empirical Distribution Function - Averaging0.969230769230769
Midmean - Empirical Distribution Function - Interpolation0.969230769230769
Midmean - Closest Observation0.969230769230769
Midmean - True Basic - Statistics Graphics Toolkit0.969230769230769
Midmean - MS Excel (old versions)0.969230769230769
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.974166666666667 & 0.00718713408959688 & 135.543132286448 \tabularnewline
Geometric Mean & 0.972612219759778 &  &  \tabularnewline
Harmonic Mean & 0.971069917020514 &  &  \tabularnewline
Quadratic Mean & 0.975729641516201 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.974166666666667 & 0.00718713408959688 & 135.543132286448 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.974166666666667 & 0.00718713408959688 & 135.543132286448 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.974166666666667 & 0.00718713408959688 & 135.543132286448 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.974166666666667 & 0.00718713408959688 & 135.543132286448 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.975 & 0.00704906132309282 & 138.316288554036 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.974 & 0.00685276965740139 & 142.132312728186 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.974 & 0.00685276965740139 & 142.132312728186 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.974 & 0.00685276965740139 & 142.132312728186 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.974 & 0.00685276965740139 & 142.132312728186 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.974 & 0.00629410988218664 & 154.747854459386 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.972166666666667 & 0.00598062628594431 & 162.552652546014 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.972166666666667 & 0.00598062628594431 & 162.552652546014 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.972166666666667 & 0.00598062628594431 & 162.552652546014 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.972166666666667 & 0.00598062628594431 & 162.552652546014 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.972166666666667 & 0.00598062628594431 & 162.552652546014 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.972166666666667 & 0.00516994610702367 & 188.041934391912 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.972166666666667 & 0.00516994610702367 & 188.041934391912 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.972166666666667 & 0.00516994610702367 & 188.041934391912 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.972166666666667 & 0.00516994610702367 & 188.041934391912 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.968833333333333 & 0.00465833598637524 & 207.9784146457 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.973965517241379 & 0.0071706350463176 & 135.826954091263 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.97375 & 0.00714216717446826 & 136.338169663817 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.973518518518519 & 0.00709896798341761 & 137.135217512257 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.973269230769231 & 0.007037505395416 & 138.297475608784 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.973 & 0.00695319629922169 & 139.9356437138 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.9725 & 0.00688365831321178 & 141.276622945314 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.972173913043478 & 0.00684481568673249 & 142.03069264931 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.971818181818182 & 0.00678320840032142 & 143.268218292119 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.971428571428571 & 0.0066919216347093 & 145.164367494983 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.971 & 0.00656134757891106 & 147.987892475154 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.970526315789474 & 0.00652108265388598 & 148.829016177418 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.970277777777778 & 0.00652815770593126 & 148.629647365323 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.97 & 0.00651338947278929 & 148.923997874275 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.9696875 & 0.00646772968032384 & 149.927029719561 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.969333333333333 & 0.00637764294249182 & 151.989275987063 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.968928571428571 & 0.00622206531224247 & 155.724590277463 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.968461538461538 & 0.00621888705581776 & 155.729076564519 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.967916666666667 & 0.00616732761831985 & 156.942638135763 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.967272727272727 & 0.00603674958344759 & 160.230719181218 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.9665 & 0.00577084322945506 & 167.479857201261 \tabularnewline
Median & 0.97 &  &  \tabularnewline
Midrange & 0.98 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.969230769230769 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.969230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.969230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.969230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.969230769230769 &  &  \tabularnewline
Midmean - Closest Observation & 0.969230769230769 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.969230769230769 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.969230769230769 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163599&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.974166666666667[/C][C]0.00718713408959688[/C][C]135.543132286448[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.972612219759778[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.971069917020514[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.975729641516201[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.974166666666667[/C][C]0.00718713408959688[/C][C]135.543132286448[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.974166666666667[/C][C]0.00718713408959688[/C][C]135.543132286448[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.974166666666667[/C][C]0.00718713408959688[/C][C]135.543132286448[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.974166666666667[/C][C]0.00718713408959688[/C][C]135.543132286448[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.975[/C][C]0.00704906132309282[/C][C]138.316288554036[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.974[/C][C]0.00685276965740139[/C][C]142.132312728186[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.974[/C][C]0.00685276965740139[/C][C]142.132312728186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.974[/C][C]0.00685276965740139[/C][C]142.132312728186[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.974[/C][C]0.00685276965740139[/C][C]142.132312728186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.974[/C][C]0.00629410988218664[/C][C]154.747854459386[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.972166666666667[/C][C]0.00598062628594431[/C][C]162.552652546014[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.972166666666667[/C][C]0.00598062628594431[/C][C]162.552652546014[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.972166666666667[/C][C]0.00598062628594431[/C][C]162.552652546014[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.972166666666667[/C][C]0.00598062628594431[/C][C]162.552652546014[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.972166666666667[/C][C]0.00598062628594431[/C][C]162.552652546014[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.972166666666667[/C][C]0.00516994610702367[/C][C]188.041934391912[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.972166666666667[/C][C]0.00516994610702367[/C][C]188.041934391912[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.972166666666667[/C][C]0.00516994610702367[/C][C]188.041934391912[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.972166666666667[/C][C]0.00516994610702367[/C][C]188.041934391912[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.968833333333333[/C][C]0.00465833598637524[/C][C]207.9784146457[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.973965517241379[/C][C]0.0071706350463176[/C][C]135.826954091263[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.97375[/C][C]0.00714216717446826[/C][C]136.338169663817[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.973518518518519[/C][C]0.00709896798341761[/C][C]137.135217512257[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.973269230769231[/C][C]0.007037505395416[/C][C]138.297475608784[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.973[/C][C]0.00695319629922169[/C][C]139.9356437138[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.9725[/C][C]0.00688365831321178[/C][C]141.276622945314[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.972173913043478[/C][C]0.00684481568673249[/C][C]142.03069264931[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.971818181818182[/C][C]0.00678320840032142[/C][C]143.268218292119[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.971428571428571[/C][C]0.0066919216347093[/C][C]145.164367494983[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.971[/C][C]0.00656134757891106[/C][C]147.987892475154[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.970526315789474[/C][C]0.00652108265388598[/C][C]148.829016177418[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.970277777777778[/C][C]0.00652815770593126[/C][C]148.629647365323[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.97[/C][C]0.00651338947278929[/C][C]148.923997874275[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.9696875[/C][C]0.00646772968032384[/C][C]149.927029719561[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.969333333333333[/C][C]0.00637764294249182[/C][C]151.989275987063[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.968928571428571[/C][C]0.00622206531224247[/C][C]155.724590277463[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.968461538461538[/C][C]0.00621888705581776[/C][C]155.729076564519[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.967916666666667[/C][C]0.00616732761831985[/C][C]156.942638135763[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.967272727272727[/C][C]0.00603674958344759[/C][C]160.230719181218[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.9665[/C][C]0.00577084322945506[/C][C]167.479857201261[/C][/ROW]
[ROW][C]Median[/C][C]0.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.969230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.969230769230769[/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=163599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163599&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9741666666666670.00718713408959688135.543132286448
Geometric Mean0.972612219759778
Harmonic Mean0.971069917020514
Quadratic Mean0.975729641516201
Winsorized Mean ( 1 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 2 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 3 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 4 / 20 )0.9741666666666670.00718713408959688135.543132286448
Winsorized Mean ( 5 / 20 )0.9750.00704906132309282138.316288554036
Winsorized Mean ( 6 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 7 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 8 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 9 / 20 )0.9740.00685276965740139142.132312728186
Winsorized Mean ( 10 / 20 )0.9740.00629410988218664154.747854459386
Winsorized Mean ( 11 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 12 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 13 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 14 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 15 / 20 )0.9721666666666670.00598062628594431162.552652546014
Winsorized Mean ( 16 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 17 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 18 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 19 / 20 )0.9721666666666670.00516994610702367188.041934391912
Winsorized Mean ( 20 / 20 )0.9688333333333330.00465833598637524207.9784146457
Trimmed Mean ( 1 / 20 )0.9739655172413790.0071706350463176135.826954091263
Trimmed Mean ( 2 / 20 )0.973750.00714216717446826136.338169663817
Trimmed Mean ( 3 / 20 )0.9735185185185190.00709896798341761137.135217512257
Trimmed Mean ( 4 / 20 )0.9732692307692310.007037505395416138.297475608784
Trimmed Mean ( 5 / 20 )0.9730.00695319629922169139.9356437138
Trimmed Mean ( 6 / 20 )0.97250.00688365831321178141.276622945314
Trimmed Mean ( 7 / 20 )0.9721739130434780.00684481568673249142.03069264931
Trimmed Mean ( 8 / 20 )0.9718181818181820.00678320840032142143.268218292119
Trimmed Mean ( 9 / 20 )0.9714285714285710.0066919216347093145.164367494983
Trimmed Mean ( 10 / 20 )0.9710.00656134757891106147.987892475154
Trimmed Mean ( 11 / 20 )0.9705263157894740.00652108265388598148.829016177418
Trimmed Mean ( 12 / 20 )0.9702777777777780.00652815770593126148.629647365323
Trimmed Mean ( 13 / 20 )0.970.00651338947278929148.923997874275
Trimmed Mean ( 14 / 20 )0.96968750.00646772968032384149.927029719561
Trimmed Mean ( 15 / 20 )0.9693333333333330.00637764294249182151.989275987063
Trimmed Mean ( 16 / 20 )0.9689285714285710.00622206531224247155.724590277463
Trimmed Mean ( 17 / 20 )0.9684615384615380.00621888705581776155.729076564519
Trimmed Mean ( 18 / 20 )0.9679166666666670.00616732761831985156.942638135763
Trimmed Mean ( 19 / 20 )0.9672727272727270.00603674958344759160.230719181218
Trimmed Mean ( 20 / 20 )0.96650.00577084322945506167.479857201261
Median0.97
Midrange0.98
Midmean - Weighted Average at Xnp0.969230769230769
Midmean - Weighted Average at X(n+1)p0.969230769230769
Midmean - Empirical Distribution Function0.969230769230769
Midmean - Empirical Distribution Function - Averaging0.969230769230769
Midmean - Empirical Distribution Function - Interpolation0.969230769230769
Midmean - Closest Observation0.969230769230769
Midmean - True Basic - Statistics Graphics Toolkit0.969230769230769
Midmean - MS Excel (old versions)0.969230769230769
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')