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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 computationMon, 20 Oct 2008 16:36:45 -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/2008/Oct/21/t1224542325upf2vhj4nr393ge.htm/, Retrieved Sat, 18 May 2024 23:25:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18271, Retrieved Sat, 18 May 2024 23:25:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
-   PD    [Central Tendency] [porto trimmed and...] [2008-10-20 22:36:45] [3efbb18563b4564408d69b3c9a8e9a6e] [Current]
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Dataseries X:
107,31
107,42
107,51
107,09
107,42
107,58
108,65
108,47
108,38
107,96
107,67
106,09
107,83
107,82
107,88
107,91
107,98
107,58
107,7
107,97
109,13
108,92
109,17
108,39
109,32
109,48
109,55
109,31
109,05
109,26
109,14
109,76
110,7
110,14
111,47
110,89
110,45
110,2
110,23
112,3
112,77
112,95
112,67
112,68
112,33
111,95
111,66
110,65
111,9
113,7
113,53
113,73
114,85
113,48
113,13
112,45
110,77
110,01
109,41
107,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18271&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18271&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18271&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.87850.278981280885915393.856174332116
Geometric Mean109.857719741194
Harmonic Mean109.837056662345
Quadratic Mean109.899393833633
Winsorized Mean ( 1 / 20 )109.8751666666670.270756055033124405.808714612956
Winsorized Mean ( 2 / 20 )109.8768333333330.270043048636251406.886360853294
Winsorized Mean ( 3 / 20 )109.8793333333330.266172692197308412.812195068764
Winsorized Mean ( 4 / 20 )109.8833333333330.264221344748519415.876065720271
Winsorized Mean ( 5 / 20 )109.8541666666670.257712042218309426.267106965878
Winsorized Mean ( 6 / 20 )109.8451666666670.252470448197024435.081283576386
Winsorized Mean ( 7 / 20 )109.8323333333330.246891907392628444.859997612919
Winsorized Mean ( 8 / 20 )109.8203333333330.244492321539762449.177023808796
Winsorized Mean ( 9 / 20 )109.8323333333330.242124467998933453.619306801398
Winsorized Mean ( 10 / 20 )109.8006666666670.23420714510306468.818603370748
Winsorized Mean ( 11 / 20 )109.8006666666670.226715913560106484.309482040644
Winsorized Mean ( 12 / 20 )109.7966666666670.225287596066937487.362236463493
Winsorized Mean ( 13 / 20 )109.7316666666670.209725023989467523.21685118595
Winsorized Mean ( 14 / 20 )109.7270.206593749666175531.124490345438
Winsorized Mean ( 15 / 20 )109.67950.194185016470038564.819582858614
Winsorized Mean ( 16 / 20 )109.63150.185136203487616592.166728790749
Winsorized Mean ( 17 / 20 )109.470.158266027918882691.683499228957
Winsorized Mean ( 18 / 20 )109.5540.134243896430391816.081795247999
Winsorized Mean ( 19 / 20 )109.5350.130393255691940840.035778068014
Winsorized Mean ( 20 / 20 )109.5450.123926463524067883.951634581468
Trimmed Mean ( 1 / 20 )109.8581034482760.267422264759017410.803878081254
Trimmed Mean ( 2 / 20 )109.8398214285710.263163507895291417.382418660702
Trimmed Mean ( 3 / 20 )109.8192592592590.258212537099370425.305682260488
Trimmed Mean ( 4 / 20 )109.7961538461540.253725210001902432.736478355189
Trimmed Mean ( 5 / 20 )109.770.248649741358303441.464364291543
Trimmed Mean ( 6 / 20 )109.7489583333330.244298503532686449.241222301018
Trimmed Mean ( 7 / 20 )109.7280434782610.240131127536807456.950519509145
Trimmed Mean ( 8 / 20 )109.7077272727270.236111662325893464.64340724222
Trimmed Mean ( 9 / 20 )109.6876190476190.231264214686655474.295684683587
Trimmed Mean ( 10 / 20 )109.66350.225191243510591486.97941487606
Trimmed Mean ( 11 / 20 )109.6418421052630.219062354400910500.505175364845
Trimmed Mean ( 12 / 20 )109.6177777777780.212515960599905515.809624219946
Trimmed Mean ( 13 / 20 )109.5914705882350.203558858749918538.377308957474
Trimmed Mean ( 14 / 20 )109.571250.195685699899511559.934885667514
Trimmed Mean ( 15 / 20 )109.5490.185040753510599592.026339720484
Trimmed Mean ( 16 / 20 )109.5303571428570.173654679340467630.736571907238
Trimmed Mean ( 17 / 20 )109.5157692307690.159785599694786685.391984258658
Trimmed Mean ( 18 / 20 )109.52250.149560043199175732.297862833219
Trimmed Mean ( 19 / 20 )109.5177272727270.143285401959856764.332763664305
Trimmed Mean ( 20 / 20 )109.5150.133923583867031817.74245310471
Median109.365
Midrange110.47
Midmean - Weighted Average at Xnp109.496129032258
Midmean - Weighted Average at X(n+1)p109.549
Midmean - Empirical Distribution Function109.496129032258
Midmean - Empirical Distribution Function - Averaging109.549
Midmean - Empirical Distribution Function - Interpolation109.549
Midmean - Closest Observation109.496129032258
Midmean - True Basic - Statistics Graphics Toolkit109.549
Midmean - MS Excel (old versions)109.57125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.8785 & 0.278981280885915 & 393.856174332116 \tabularnewline
Geometric Mean & 109.857719741194 &  &  \tabularnewline
Harmonic Mean & 109.837056662345 &  &  \tabularnewline
Quadratic Mean & 109.899393833633 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.875166666667 & 0.270756055033124 & 405.808714612956 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109.876833333333 & 0.270043048636251 & 406.886360853294 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.879333333333 & 0.266172692197308 & 412.812195068764 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109.883333333333 & 0.264221344748519 & 415.876065720271 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109.854166666667 & 0.257712042218309 & 426.267106965878 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 109.845166666667 & 0.252470448197024 & 435.081283576386 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 109.832333333333 & 0.246891907392628 & 444.859997612919 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 109.820333333333 & 0.244492321539762 & 449.177023808796 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 109.832333333333 & 0.242124467998933 & 453.619306801398 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109.800666666667 & 0.23420714510306 & 468.818603370748 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 109.800666666667 & 0.226715913560106 & 484.309482040644 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 109.796666666667 & 0.225287596066937 & 487.362236463493 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109.731666666667 & 0.209725023989467 & 523.21685118595 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109.727 & 0.206593749666175 & 531.124490345438 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 109.6795 & 0.194185016470038 & 564.819582858614 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109.6315 & 0.185136203487616 & 592.166728790749 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109.47 & 0.158266027918882 & 691.683499228957 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109.554 & 0.134243896430391 & 816.081795247999 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 109.535 & 0.130393255691940 & 840.035778068014 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 109.545 & 0.123926463524067 & 883.951634581468 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109.858103448276 & 0.267422264759017 & 410.803878081254 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109.839821428571 & 0.263163507895291 & 417.382418660702 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109.819259259259 & 0.258212537099370 & 425.305682260488 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109.796153846154 & 0.253725210001902 & 432.736478355189 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 109.77 & 0.248649741358303 & 441.464364291543 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 109.748958333333 & 0.244298503532686 & 449.241222301018 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109.728043478261 & 0.240131127536807 & 456.950519509145 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109.707727272727 & 0.236111662325893 & 464.64340724222 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109.687619047619 & 0.231264214686655 & 474.295684683587 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109.6635 & 0.225191243510591 & 486.97941487606 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.641842105263 & 0.219062354400910 & 500.505175364845 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.617777777778 & 0.212515960599905 & 515.809624219946 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109.591470588235 & 0.203558858749918 & 538.377308957474 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109.57125 & 0.195685699899511 & 559.934885667514 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109.549 & 0.185040753510599 & 592.026339720484 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109.530357142857 & 0.173654679340467 & 630.736571907238 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109.515769230769 & 0.159785599694786 & 685.391984258658 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109.5225 & 0.149560043199175 & 732.297862833219 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109.517727272727 & 0.143285401959856 & 764.332763664305 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109.515 & 0.133923583867031 & 817.74245310471 \tabularnewline
Median & 109.365 &  &  \tabularnewline
Midrange & 110.47 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.496129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.549 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.496129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.549 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.549 &  &  \tabularnewline
Midmean - Closest Observation & 109.496129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.549 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.57125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18271&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]109.8785[/C][C]0.278981280885915[/C][C]393.856174332116[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.857719741194[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.837056662345[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.899393833633[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.875166666667[/C][C]0.270756055033124[/C][C]405.808714612956[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109.876833333333[/C][C]0.270043048636251[/C][C]406.886360853294[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.879333333333[/C][C]0.266172692197308[/C][C]412.812195068764[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109.883333333333[/C][C]0.264221344748519[/C][C]415.876065720271[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109.854166666667[/C][C]0.257712042218309[/C][C]426.267106965878[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]109.845166666667[/C][C]0.252470448197024[/C][C]435.081283576386[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]109.832333333333[/C][C]0.246891907392628[/C][C]444.859997612919[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]109.820333333333[/C][C]0.244492321539762[/C][C]449.177023808796[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]109.832333333333[/C][C]0.242124467998933[/C][C]453.619306801398[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109.800666666667[/C][C]0.23420714510306[/C][C]468.818603370748[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]109.800666666667[/C][C]0.226715913560106[/C][C]484.309482040644[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]109.796666666667[/C][C]0.225287596066937[/C][C]487.362236463493[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109.731666666667[/C][C]0.209725023989467[/C][C]523.21685118595[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109.727[/C][C]0.206593749666175[/C][C]531.124490345438[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]109.6795[/C][C]0.194185016470038[/C][C]564.819582858614[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109.6315[/C][C]0.185136203487616[/C][C]592.166728790749[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109.47[/C][C]0.158266027918882[/C][C]691.683499228957[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109.554[/C][C]0.134243896430391[/C][C]816.081795247999[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]109.535[/C][C]0.130393255691940[/C][C]840.035778068014[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]109.545[/C][C]0.123926463524067[/C][C]883.951634581468[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109.858103448276[/C][C]0.267422264759017[/C][C]410.803878081254[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109.839821428571[/C][C]0.263163507895291[/C][C]417.382418660702[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109.819259259259[/C][C]0.258212537099370[/C][C]425.305682260488[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109.796153846154[/C][C]0.253725210001902[/C][C]432.736478355189[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]109.77[/C][C]0.248649741358303[/C][C]441.464364291543[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]109.748958333333[/C][C]0.244298503532686[/C][C]449.241222301018[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109.728043478261[/C][C]0.240131127536807[/C][C]456.950519509145[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109.707727272727[/C][C]0.236111662325893[/C][C]464.64340724222[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109.687619047619[/C][C]0.231264214686655[/C][C]474.295684683587[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109.6635[/C][C]0.225191243510591[/C][C]486.97941487606[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.641842105263[/C][C]0.219062354400910[/C][C]500.505175364845[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.617777777778[/C][C]0.212515960599905[/C][C]515.809624219946[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109.591470588235[/C][C]0.203558858749918[/C][C]538.377308957474[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109.57125[/C][C]0.195685699899511[/C][C]559.934885667514[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109.549[/C][C]0.185040753510599[/C][C]592.026339720484[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109.530357142857[/C][C]0.173654679340467[/C][C]630.736571907238[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109.515769230769[/C][C]0.159785599694786[/C][C]685.391984258658[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109.5225[/C][C]0.149560043199175[/C][C]732.297862833219[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109.517727272727[/C][C]0.143285401959856[/C][C]764.332763664305[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109.515[/C][C]0.133923583867031[/C][C]817.74245310471[/C][/ROW]
[ROW][C]Median[/C][C]109.365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.496129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.496129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.496129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.57125[/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=18271&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18271&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 Mean109.87850.278981280885915393.856174332116
Geometric Mean109.857719741194
Harmonic Mean109.837056662345
Quadratic Mean109.899393833633
Winsorized Mean ( 1 / 20 )109.8751666666670.270756055033124405.808714612956
Winsorized Mean ( 2 / 20 )109.8768333333330.270043048636251406.886360853294
Winsorized Mean ( 3 / 20 )109.8793333333330.266172692197308412.812195068764
Winsorized Mean ( 4 / 20 )109.8833333333330.264221344748519415.876065720271
Winsorized Mean ( 5 / 20 )109.8541666666670.257712042218309426.267106965878
Winsorized Mean ( 6 / 20 )109.8451666666670.252470448197024435.081283576386
Winsorized Mean ( 7 / 20 )109.8323333333330.246891907392628444.859997612919
Winsorized Mean ( 8 / 20 )109.8203333333330.244492321539762449.177023808796
Winsorized Mean ( 9 / 20 )109.8323333333330.242124467998933453.619306801398
Winsorized Mean ( 10 / 20 )109.8006666666670.23420714510306468.818603370748
Winsorized Mean ( 11 / 20 )109.8006666666670.226715913560106484.309482040644
Winsorized Mean ( 12 / 20 )109.7966666666670.225287596066937487.362236463493
Winsorized Mean ( 13 / 20 )109.7316666666670.209725023989467523.21685118595
Winsorized Mean ( 14 / 20 )109.7270.206593749666175531.124490345438
Winsorized Mean ( 15 / 20 )109.67950.194185016470038564.819582858614
Winsorized Mean ( 16 / 20 )109.63150.185136203487616592.166728790749
Winsorized Mean ( 17 / 20 )109.470.158266027918882691.683499228957
Winsorized Mean ( 18 / 20 )109.5540.134243896430391816.081795247999
Winsorized Mean ( 19 / 20 )109.5350.130393255691940840.035778068014
Winsorized Mean ( 20 / 20 )109.5450.123926463524067883.951634581468
Trimmed Mean ( 1 / 20 )109.8581034482760.267422264759017410.803878081254
Trimmed Mean ( 2 / 20 )109.8398214285710.263163507895291417.382418660702
Trimmed Mean ( 3 / 20 )109.8192592592590.258212537099370425.305682260488
Trimmed Mean ( 4 / 20 )109.7961538461540.253725210001902432.736478355189
Trimmed Mean ( 5 / 20 )109.770.248649741358303441.464364291543
Trimmed Mean ( 6 / 20 )109.7489583333330.244298503532686449.241222301018
Trimmed Mean ( 7 / 20 )109.7280434782610.240131127536807456.950519509145
Trimmed Mean ( 8 / 20 )109.7077272727270.236111662325893464.64340724222
Trimmed Mean ( 9 / 20 )109.6876190476190.231264214686655474.295684683587
Trimmed Mean ( 10 / 20 )109.66350.225191243510591486.97941487606
Trimmed Mean ( 11 / 20 )109.6418421052630.219062354400910500.505175364845
Trimmed Mean ( 12 / 20 )109.6177777777780.212515960599905515.809624219946
Trimmed Mean ( 13 / 20 )109.5914705882350.203558858749918538.377308957474
Trimmed Mean ( 14 / 20 )109.571250.195685699899511559.934885667514
Trimmed Mean ( 15 / 20 )109.5490.185040753510599592.026339720484
Trimmed Mean ( 16 / 20 )109.5303571428570.173654679340467630.736571907238
Trimmed Mean ( 17 / 20 )109.5157692307690.159785599694786685.391984258658
Trimmed Mean ( 18 / 20 )109.52250.149560043199175732.297862833219
Trimmed Mean ( 19 / 20 )109.5177272727270.143285401959856764.332763664305
Trimmed Mean ( 20 / 20 )109.5150.133923583867031817.74245310471
Median109.365
Midrange110.47
Midmean - Weighted Average at Xnp109.496129032258
Midmean - Weighted Average at X(n+1)p109.549
Midmean - Empirical Distribution Function109.496129032258
Midmean - Empirical Distribution Function - Averaging109.549
Midmean - Empirical Distribution Function - Interpolation109.549
Midmean - Closest Observation109.496129032258
Midmean - True Basic - Statistics Graphics Toolkit109.549
Midmean - MS Excel (old versions)109.57125
Number of observations60



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
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')