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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Oct 2011 07:49:09 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/15/t1318679393hm96u9bq29r9z3u.htm/, Retrieved Thu, 16 May 2024 02:32:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129765, Retrieved Thu, 16 May 2024 02:32:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gemi...] [2011-10-15 11:49:09] [27830603f12132457d99d827849f2486] [Current]
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Dataseries X:
3,11
3,1
3,13
3,14
3,16
3,17
3,19
3,18
3,17
3,17
3,2
3,21
3,25
3,22
3,25
3,31
3,35
3,37
3,38
3,38
3,39
3,44
3,56
3,65
3,69
3,71
3,71
3,74
3,75
3,77
3,75
3,78
3,8
3,78
3,79
3,8
3,82
3,82
3,84
3,86
3,8
3,85
3,78
3,79
3,77
3,78
3,77
3,76
3,78
3,76
3,75
3,71
3,72
3,7
3,69
3,7
3,72
3,73
3,73
3,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129765&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129765&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.56450.0336913751138499105.798590528135
Geometric Mean3.55479322248357
Harmonic Mean3.54479580247468
Quadratic Mean3.57388187642886
Winsorized Mean ( 1 / 20 )3.56450.0336284324482506105.996614783792
Winsorized Mean ( 2 / 20 )3.564833333333330.0334313460157058106.631462928792
Winsorized Mean ( 3 / 20 )3.564333333333330.0331869951612717107.40150821165
Winsorized Mean ( 4 / 20 )3.565666666666670.0329031850386461108.36843492442
Winsorized Mean ( 5 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 6 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 7 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 8 / 20 )3.564833333333330.0320852428076579111.105075772794
Winsorized Mean ( 9 / 20 )3.566333333333330.0317822452182207112.211497609639
Winsorized Mean ( 10 / 20 )3.566333333333330.0312534442546382114.110089892063
Winsorized Mean ( 11 / 20 )3.568166666666670.0308911810378524115.507615662037
Winsorized Mean ( 12 / 20 )3.570166666666670.0305000617454841117.054407838872
Winsorized Mean ( 13 / 20 )3.576666666666670.0292521346622354122.270279005797
Winsorized Mean ( 14 / 20 )3.576666666666670.0292521346622354122.270279005797
Winsorized Mean ( 15 / 20 )3.589166666666670.0261798340327277137.096616509479
Winsorized Mean ( 16 / 20 )3.599833333333330.0242846719537669148.234793543297
Winsorized Mean ( 17 / 20 )3.60550.0233051787363282154.708103327255
Winsorized Mean ( 18 / 20 )3.60550.0224381447313063160.686190555207
Winsorized Mean ( 19 / 20 )3.60550.0224381447313063160.686190555207
Winsorized Mean ( 20 / 20 )3.60550.0214863312219311167.804357233396
Trimmed Mean ( 1 / 20 )3.567413793103450.0335205513839396106.424675186359
Trimmed Mean ( 2 / 20 )3.570535714285710.0333472673025717107.071313576881
Trimmed Mean ( 3 / 20 )3.57370370370370.0332170890241038107.58629996477
Trimmed Mean ( 4 / 20 )3.577307692307690.0331163169952285108.0225102575
Trimmed Mean ( 5 / 20 )3.58080.033041519953179108.372738453743
Trimmed Mean ( 6 / 20 )3.584791666666670.0330027797874628108.620900716626
Trimmed Mean ( 7 / 20 )3.589130434782610.0328807332201891109.156034044242
Trimmed Mean ( 8 / 20 )3.593863636363640.032649422175635110.074341194485
Trimmed Mean ( 9 / 20 )3.599047619047620.0323845389828954111.134749237855
Trimmed Mean ( 10 / 20 )3.60450.0320355371583752112.515672272961
Trimmed Mean ( 11 / 20 )3.610526315789470.0316136603898732114.207790912628
Trimmed Mean ( 12 / 20 )3.616944444444440.0310473766098886116.497586572015
Trimmed Mean ( 13 / 20 )3.623823529411760.0302809621332482119.673328524553
Trimmed Mean ( 14 / 20 )3.6306250.0294982828231768123.079198262599
Trimmed Mean ( 15 / 20 )3.638333333333330.0282480121702551128.79962354181
Trimmed Mean ( 16 / 20 )3.645357142857140.0274029414810538133.027950498581
Trimmed Mean ( 17 / 20 )3.651923076923080.0267122514719038136.713413347587
Trimmed Mean ( 18 / 20 )3.658750.0258641412837895141.460331501249
Trimmed Mean ( 19 / 20 )3.666818181818180.0246129023606145148.979511968723
Trimmed Mean ( 20 / 20 )3.67650.0221867077323338165.707325501118
Median3.71
Midrange3.48
Midmean - Weighted Average at Xnp3.6140625
Midmean - Weighted Average at X(n+1)p3.63833333333333
Midmean - Empirical Distribution Function3.6140625
Midmean - Empirical Distribution Function - Averaging3.63833333333333
Midmean - Empirical Distribution Function - Interpolation3.63833333333333
Midmean - Closest Observation3.6140625
Midmean - True Basic - Statistics Graphics Toolkit3.63833333333333
Midmean - MS Excel (old versions)3.63648648648649
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.5645 & 0.0336913751138499 & 105.798590528135 \tabularnewline
Geometric Mean & 3.55479322248357 &  &  \tabularnewline
Harmonic Mean & 3.54479580247468 &  &  \tabularnewline
Quadratic Mean & 3.57388187642886 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.5645 & 0.0336284324482506 & 105.996614783792 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.56483333333333 & 0.0334313460157058 & 106.631462928792 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.56433333333333 & 0.0331869951612717 & 107.40150821165 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.56566666666667 & 0.0329031850386461 & 108.36843492442 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.56483333333333 & 0.032519000674935 & 109.623089865767 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.56483333333333 & 0.032519000674935 & 109.623089865767 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.56483333333333 & 0.032519000674935 & 109.623089865767 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.56483333333333 & 0.0320852428076579 & 111.105075772794 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.56633333333333 & 0.0317822452182207 & 112.211497609639 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.56633333333333 & 0.0312534442546382 & 114.110089892063 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.56816666666667 & 0.0308911810378524 & 115.507615662037 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.57016666666667 & 0.0305000617454841 & 117.054407838872 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.57666666666667 & 0.0292521346622354 & 122.270279005797 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.57666666666667 & 0.0292521346622354 & 122.270279005797 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.58916666666667 & 0.0261798340327277 & 137.096616509479 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.59983333333333 & 0.0242846719537669 & 148.234793543297 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.6055 & 0.0233051787363282 & 154.708103327255 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.6055 & 0.0224381447313063 & 160.686190555207 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.6055 & 0.0224381447313063 & 160.686190555207 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.6055 & 0.0214863312219311 & 167.804357233396 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.56741379310345 & 0.0335205513839396 & 106.424675186359 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.57053571428571 & 0.0333472673025717 & 107.071313576881 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.5737037037037 & 0.0332170890241038 & 107.58629996477 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.57730769230769 & 0.0331163169952285 & 108.0225102575 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.5808 & 0.033041519953179 & 108.372738453743 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.58479166666667 & 0.0330027797874628 & 108.620900716626 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.58913043478261 & 0.0328807332201891 & 109.156034044242 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.59386363636364 & 0.032649422175635 & 110.074341194485 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.59904761904762 & 0.0323845389828954 & 111.134749237855 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.6045 & 0.0320355371583752 & 112.515672272961 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.61052631578947 & 0.0316136603898732 & 114.207790912628 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.61694444444444 & 0.0310473766098886 & 116.497586572015 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.62382352941176 & 0.0302809621332482 & 119.673328524553 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.630625 & 0.0294982828231768 & 123.079198262599 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.63833333333333 & 0.0282480121702551 & 128.79962354181 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.64535714285714 & 0.0274029414810538 & 133.027950498581 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.65192307692308 & 0.0267122514719038 & 136.713413347587 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.65875 & 0.0258641412837895 & 141.460331501249 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.66681818181818 & 0.0246129023606145 & 148.979511968723 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.6765 & 0.0221867077323338 & 165.707325501118 \tabularnewline
Median & 3.71 &  &  \tabularnewline
Midrange & 3.48 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.6140625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.63833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.6140625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.63833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.63833333333333 &  &  \tabularnewline
Midmean - Closest Observation & 3.6140625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.63833333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.63648648648649 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129765&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]3.5645[/C][C]0.0336913751138499[/C][C]105.798590528135[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.55479322248357[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.54479580247468[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.57388187642886[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.5645[/C][C]0.0336284324482506[/C][C]105.996614783792[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.56483333333333[/C][C]0.0334313460157058[/C][C]106.631462928792[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.56433333333333[/C][C]0.0331869951612717[/C][C]107.40150821165[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.56566666666667[/C][C]0.0329031850386461[/C][C]108.36843492442[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.56483333333333[/C][C]0.032519000674935[/C][C]109.623089865767[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.56483333333333[/C][C]0.032519000674935[/C][C]109.623089865767[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.56483333333333[/C][C]0.032519000674935[/C][C]109.623089865767[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.56483333333333[/C][C]0.0320852428076579[/C][C]111.105075772794[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.56633333333333[/C][C]0.0317822452182207[/C][C]112.211497609639[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.56633333333333[/C][C]0.0312534442546382[/C][C]114.110089892063[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.56816666666667[/C][C]0.0308911810378524[/C][C]115.507615662037[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.57016666666667[/C][C]0.0305000617454841[/C][C]117.054407838872[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.57666666666667[/C][C]0.0292521346622354[/C][C]122.270279005797[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.57666666666667[/C][C]0.0292521346622354[/C][C]122.270279005797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.58916666666667[/C][C]0.0261798340327277[/C][C]137.096616509479[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.59983333333333[/C][C]0.0242846719537669[/C][C]148.234793543297[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.6055[/C][C]0.0233051787363282[/C][C]154.708103327255[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.6055[/C][C]0.0224381447313063[/C][C]160.686190555207[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.6055[/C][C]0.0224381447313063[/C][C]160.686190555207[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.6055[/C][C]0.0214863312219311[/C][C]167.804357233396[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.56741379310345[/C][C]0.0335205513839396[/C][C]106.424675186359[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.57053571428571[/C][C]0.0333472673025717[/C][C]107.071313576881[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.5737037037037[/C][C]0.0332170890241038[/C][C]107.58629996477[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.57730769230769[/C][C]0.0331163169952285[/C][C]108.0225102575[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.5808[/C][C]0.033041519953179[/C][C]108.372738453743[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.58479166666667[/C][C]0.0330027797874628[/C][C]108.620900716626[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.58913043478261[/C][C]0.0328807332201891[/C][C]109.156034044242[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.59386363636364[/C][C]0.032649422175635[/C][C]110.074341194485[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.59904761904762[/C][C]0.0323845389828954[/C][C]111.134749237855[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.6045[/C][C]0.0320355371583752[/C][C]112.515672272961[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.61052631578947[/C][C]0.0316136603898732[/C][C]114.207790912628[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.61694444444444[/C][C]0.0310473766098886[/C][C]116.497586572015[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.62382352941176[/C][C]0.0302809621332482[/C][C]119.673328524553[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.630625[/C][C]0.0294982828231768[/C][C]123.079198262599[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.63833333333333[/C][C]0.0282480121702551[/C][C]128.79962354181[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.64535714285714[/C][C]0.0274029414810538[/C][C]133.027950498581[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.65192307692308[/C][C]0.0267122514719038[/C][C]136.713413347587[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.65875[/C][C]0.0258641412837895[/C][C]141.460331501249[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.66681818181818[/C][C]0.0246129023606145[/C][C]148.979511968723[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.6765[/C][C]0.0221867077323338[/C][C]165.707325501118[/C][/ROW]
[ROW][C]Median[/C][C]3.71[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.6140625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.63833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.6140625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.63833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.63833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.6140625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.63833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.63648648648649[/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=129765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129765&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 Mean3.56450.0336913751138499105.798590528135
Geometric Mean3.55479322248357
Harmonic Mean3.54479580247468
Quadratic Mean3.57388187642886
Winsorized Mean ( 1 / 20 )3.56450.0336284324482506105.996614783792
Winsorized Mean ( 2 / 20 )3.564833333333330.0334313460157058106.631462928792
Winsorized Mean ( 3 / 20 )3.564333333333330.0331869951612717107.40150821165
Winsorized Mean ( 4 / 20 )3.565666666666670.0329031850386461108.36843492442
Winsorized Mean ( 5 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 6 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 7 / 20 )3.564833333333330.032519000674935109.623089865767
Winsorized Mean ( 8 / 20 )3.564833333333330.0320852428076579111.105075772794
Winsorized Mean ( 9 / 20 )3.566333333333330.0317822452182207112.211497609639
Winsorized Mean ( 10 / 20 )3.566333333333330.0312534442546382114.110089892063
Winsorized Mean ( 11 / 20 )3.568166666666670.0308911810378524115.507615662037
Winsorized Mean ( 12 / 20 )3.570166666666670.0305000617454841117.054407838872
Winsorized Mean ( 13 / 20 )3.576666666666670.0292521346622354122.270279005797
Winsorized Mean ( 14 / 20 )3.576666666666670.0292521346622354122.270279005797
Winsorized Mean ( 15 / 20 )3.589166666666670.0261798340327277137.096616509479
Winsorized Mean ( 16 / 20 )3.599833333333330.0242846719537669148.234793543297
Winsorized Mean ( 17 / 20 )3.60550.0233051787363282154.708103327255
Winsorized Mean ( 18 / 20 )3.60550.0224381447313063160.686190555207
Winsorized Mean ( 19 / 20 )3.60550.0224381447313063160.686190555207
Winsorized Mean ( 20 / 20 )3.60550.0214863312219311167.804357233396
Trimmed Mean ( 1 / 20 )3.567413793103450.0335205513839396106.424675186359
Trimmed Mean ( 2 / 20 )3.570535714285710.0333472673025717107.071313576881
Trimmed Mean ( 3 / 20 )3.57370370370370.0332170890241038107.58629996477
Trimmed Mean ( 4 / 20 )3.577307692307690.0331163169952285108.0225102575
Trimmed Mean ( 5 / 20 )3.58080.033041519953179108.372738453743
Trimmed Mean ( 6 / 20 )3.584791666666670.0330027797874628108.620900716626
Trimmed Mean ( 7 / 20 )3.589130434782610.0328807332201891109.156034044242
Trimmed Mean ( 8 / 20 )3.593863636363640.032649422175635110.074341194485
Trimmed Mean ( 9 / 20 )3.599047619047620.0323845389828954111.134749237855
Trimmed Mean ( 10 / 20 )3.60450.0320355371583752112.515672272961
Trimmed Mean ( 11 / 20 )3.610526315789470.0316136603898732114.207790912628
Trimmed Mean ( 12 / 20 )3.616944444444440.0310473766098886116.497586572015
Trimmed Mean ( 13 / 20 )3.623823529411760.0302809621332482119.673328524553
Trimmed Mean ( 14 / 20 )3.6306250.0294982828231768123.079198262599
Trimmed Mean ( 15 / 20 )3.638333333333330.0282480121702551128.79962354181
Trimmed Mean ( 16 / 20 )3.645357142857140.0274029414810538133.027950498581
Trimmed Mean ( 17 / 20 )3.651923076923080.0267122514719038136.713413347587
Trimmed Mean ( 18 / 20 )3.658750.0258641412837895141.460331501249
Trimmed Mean ( 19 / 20 )3.666818181818180.0246129023606145148.979511968723
Trimmed Mean ( 20 / 20 )3.67650.0221867077323338165.707325501118
Median3.71
Midrange3.48
Midmean - Weighted Average at Xnp3.6140625
Midmean - Weighted Average at X(n+1)p3.63833333333333
Midmean - Empirical Distribution Function3.6140625
Midmean - Empirical Distribution Function - Averaging3.63833333333333
Midmean - Empirical Distribution Function - Interpolation3.63833333333333
Midmean - Closest Observation3.6140625
Midmean - True Basic - Statistics Graphics Toolkit3.63833333333333
Midmean - MS Excel (old versions)3.63648648648649
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')