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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 17 Oct 2010 19:30:29 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/17/t1287344126u13inlxzxk7a8nb.htm/, Retrieved Fri, 03 May 2024 16:58:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84351, Retrieved Fri, 03 May 2024 16:58:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten siga...] [2010-10-17 19:30:29] [384a4ac05535402cc728b569fb124a5f] [Current]
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Dataseries X:
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48
5,48
5,48
5,5
5,55
5,57
5,58
5,58
5,58
5,59
5,59
5,59
5,55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84351&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84351&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.973611111111110.053337846623717693.2473173541938
Geometric Mean4.95328357828909
Harmonic Mean4.93303028748875
Quadratic Mean4.99387597185014
Winsorized Mean ( 1 / 24 )4.975694444444440.052968169786390793.9374432703708
Winsorized Mean ( 2 / 24 )4.977083333333330.052756726610550994.3402605334873
Winsorized Mean ( 3 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 4 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 5 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 6 / 24 )4.976250.052495039448186694.7946711214806
Winsorized Mean ( 7 / 24 )4.974305555555560.052189099703777295.3131129639996
Winsorized Mean ( 8 / 24 )4.975416666666670.052029972665335595.6259711814436
Winsorized Mean ( 9 / 24 )4.969166666666670.051086301983909997.2700405723584
Winsorized Mean ( 10 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 11 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 12 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 13 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 14 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 15 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 16 / 24 )4.968611111111110.050367314942694898.6475280003338
Winsorized Mean ( 17 / 24 )4.966250.050031069181175699.26331939891
Winsorized Mean ( 18 / 24 )4.966250.050031069181175699.26331939891
Winsorized Mean ( 19 / 24 )4.963611111111110.0481688579011441103.046061862165
Winsorized Mean ( 20 / 24 )4.966388888888890.0409517567784057121.274135216287
Winsorized Mean ( 21 / 24 )4.978055555555560.0357124223251376139.392828361899
Winsorized Mean ( 22 / 24 )4.981111111111110.0353434720348125140.934402432360
Winsorized Mean ( 23 / 24 )4.981111111111110.0353434720348125140.934402432360
Winsorized Mean ( 24 / 24 )4.984444444444440.0349456815751911142.634060054592
Trimmed Mean ( 1 / 24 )4.975428571428570.053083272101379193.7287468249213
Trimmed Mean ( 2 / 24 )4.975147058823530.053165590477727593.5783279019116
Trimmed Mean ( 3 / 24 )4.974090909090910.05333317771221293.2644766815003
Trimmed Mean ( 4 / 24 )4.972968750.053522117372083492.91427533459
Trimmed Mean ( 5 / 24 )4.971774193548390.053678796845248792.6208202445665
Trimmed Mean ( 6 / 24 )4.97050.053795713709916792.3958370884805
Trimmed Mean ( 7 / 24 )4.969310344827590.053897609717600292.1990858382142
Trimmed Mean ( 8 / 24 )4.968392857142860.054015255652715491.9812893062387
Trimmed Mean ( 9 / 24 )4.967222222222220.054108889790350491.800483090083
Trimmed Mean ( 10 / 24 )4.966923076923080.0543295475146691.4221322307687
Trimmed Mean ( 11 / 24 )4.9670.054576103015955391.0105288856535
Trimmed Mean ( 12 / 24 )4.967083333333330.054768175464727990.6928757656399
Trimmed Mean ( 13 / 24 )4.967173913043480.054889139958285290.4946573551425
Trimmed Mean ( 14 / 24 )4.967272727272730.054917161945500990.4502809559275
Trimmed Mean ( 15 / 24 )4.967380952380950.054823186939710390.6073001163474
Trimmed Mean ( 16 / 24 )4.96750.054567941654512391.0333036098537
Trimmed Mean ( 17 / 24 )4.967368421052630.054164656255464191.70866695109
Trimmed Mean ( 18 / 24 )4.96750.053562565404379392.7420104413792
Trimmed Mean ( 19 / 24 )4.967647058823530.052604295561318694.4342473521568
Trimmed Mean ( 20 / 24 )4.9681250.051625663902627996.2336292540562
Trimmed Mean ( 21 / 24 )4.968333333333330.051944009054253395.6478605289037
Trimmed Mean ( 22 / 24 )4.967142857142860.053308171502162893.1778884395112
Trimmed Mean ( 23 / 24 )4.965384615384620.054843078994613990.5380351798312
Trimmed Mean ( 24 / 24 )4.963333333333330.05649056182123987.8612846698092
Median4.8
Midrange4.91
Midmean - Weighted Average at Xnp4.95435897435898
Midmean - Weighted Average at X(n+1)p4.95435897435898
Midmean - Empirical Distribution Function4.95435897435898
Midmean - Empirical Distribution Function - Averaging4.95435897435898
Midmean - Empirical Distribution Function - Interpolation4.95435897435898
Midmean - Closest Observation4.95435897435898
Midmean - True Basic - Statistics Graphics Toolkit4.95435897435898
Midmean - MS Excel (old versions)4.95435897435898
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.97361111111111 & 0.0533378466237176 & 93.2473173541938 \tabularnewline
Geometric Mean & 4.95328357828909 &  &  \tabularnewline
Harmonic Mean & 4.93303028748875 &  &  \tabularnewline
Quadratic Mean & 4.99387597185014 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.97569444444444 & 0.0529681697863907 & 93.9374432703708 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.97708333333333 & 0.0527567266105509 & 94.3402605334873 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.97708333333333 & 0.052628647617797 & 94.5698504259166 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.97708333333333 & 0.052628647617797 & 94.5698504259166 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.97708333333333 & 0.052628647617797 & 94.5698504259166 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.97625 & 0.0524950394481866 & 94.7946711214806 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.97430555555556 & 0.0521890997037772 & 95.3131129639996 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.97541666666667 & 0.0520299726653355 & 95.6259711814436 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.96916666666667 & 0.0510863019839099 & 97.2700405723584 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.96638888888889 & 0.0506847885631222 & 97.985786854054 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.96861111111111 & 0.0503673149426948 & 98.6475280003338 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.96625 & 0.0500310691811756 & 99.26331939891 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.96625 & 0.0500310691811756 & 99.26331939891 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.96361111111111 & 0.0481688579011441 & 103.046061862165 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.96638888888889 & 0.0409517567784057 & 121.274135216287 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.97805555555556 & 0.0357124223251376 & 139.392828361899 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.98111111111111 & 0.0353434720348125 & 140.934402432360 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.98111111111111 & 0.0353434720348125 & 140.934402432360 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.98444444444444 & 0.0349456815751911 & 142.634060054592 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.97542857142857 & 0.0530832721013791 & 93.7287468249213 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.97514705882353 & 0.0531655904777275 & 93.5783279019116 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.97409090909091 & 0.053333177712212 & 93.2644766815003 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.97296875 & 0.0535221173720834 & 92.91427533459 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.97177419354839 & 0.0536787968452487 & 92.6208202445665 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.9705 & 0.0537957137099167 & 92.3958370884805 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.96931034482759 & 0.0538976097176002 & 92.1990858382142 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.96839285714286 & 0.0540152556527154 & 91.9812893062387 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.96722222222222 & 0.0541088897903504 & 91.800483090083 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.96692307692308 & 0.05432954751466 & 91.4221322307687 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.967 & 0.0545761030159553 & 91.0105288856535 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.96708333333333 & 0.0547681754647279 & 90.6928757656399 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.96717391304348 & 0.0548891399582852 & 90.4946573551425 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.96727272727273 & 0.0549171619455009 & 90.4502809559275 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.96738095238095 & 0.0548231869397103 & 90.6073001163474 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.9675 & 0.0545679416545123 & 91.0333036098537 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.96736842105263 & 0.0541646562554641 & 91.70866695109 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.9675 & 0.0535625654043793 & 92.7420104413792 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.96764705882353 & 0.0526042955613186 & 94.4342473521568 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.968125 & 0.0516256639026279 & 96.2336292540562 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.96833333333333 & 0.0519440090542533 & 95.6478605289037 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.96714285714286 & 0.0533081715021628 & 93.1778884395112 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.96538461538462 & 0.0548430789946139 & 90.5380351798312 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.96333333333333 & 0.056490561821239 & 87.8612846698092 \tabularnewline
Median & 4.8 &  &  \tabularnewline
Midrange & 4.91 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.95435897435898 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.95435897435898 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.95435897435898 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.95435897435898 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.95435897435898 &  &  \tabularnewline
Midmean - Closest Observation & 4.95435897435898 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.95435897435898 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.95435897435898 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84351&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]4.97361111111111[/C][C]0.0533378466237176[/C][C]93.2473173541938[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.95328357828909[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.93303028748875[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.99387597185014[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.97569444444444[/C][C]0.0529681697863907[/C][C]93.9374432703708[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.97708333333333[/C][C]0.0527567266105509[/C][C]94.3402605334873[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.97708333333333[/C][C]0.052628647617797[/C][C]94.5698504259166[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.97708333333333[/C][C]0.052628647617797[/C][C]94.5698504259166[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.97708333333333[/C][C]0.052628647617797[/C][C]94.5698504259166[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.97625[/C][C]0.0524950394481866[/C][C]94.7946711214806[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.97430555555556[/C][C]0.0521890997037772[/C][C]95.3131129639996[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.97541666666667[/C][C]0.0520299726653355[/C][C]95.6259711814436[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.96916666666667[/C][C]0.0510863019839099[/C][C]97.2700405723584[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.96638888888889[/C][C]0.0506847885631222[/C][C]97.985786854054[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.96861111111111[/C][C]0.0503673149426948[/C][C]98.6475280003338[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.96625[/C][C]0.0500310691811756[/C][C]99.26331939891[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.96625[/C][C]0.0500310691811756[/C][C]99.26331939891[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.96361111111111[/C][C]0.0481688579011441[/C][C]103.046061862165[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.96638888888889[/C][C]0.0409517567784057[/C][C]121.274135216287[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.97805555555556[/C][C]0.0357124223251376[/C][C]139.392828361899[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.98111111111111[/C][C]0.0353434720348125[/C][C]140.934402432360[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.98111111111111[/C][C]0.0353434720348125[/C][C]140.934402432360[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.98444444444444[/C][C]0.0349456815751911[/C][C]142.634060054592[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.97542857142857[/C][C]0.0530832721013791[/C][C]93.7287468249213[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.97514705882353[/C][C]0.0531655904777275[/C][C]93.5783279019116[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.97409090909091[/C][C]0.053333177712212[/C][C]93.2644766815003[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.97296875[/C][C]0.0535221173720834[/C][C]92.91427533459[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.97177419354839[/C][C]0.0536787968452487[/C][C]92.6208202445665[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.9705[/C][C]0.0537957137099167[/C][C]92.3958370884805[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.96931034482759[/C][C]0.0538976097176002[/C][C]92.1990858382142[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.96839285714286[/C][C]0.0540152556527154[/C][C]91.9812893062387[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.96722222222222[/C][C]0.0541088897903504[/C][C]91.800483090083[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.96692307692308[/C][C]0.05432954751466[/C][C]91.4221322307687[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.967[/C][C]0.0545761030159553[/C][C]91.0105288856535[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.96708333333333[/C][C]0.0547681754647279[/C][C]90.6928757656399[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.96717391304348[/C][C]0.0548891399582852[/C][C]90.4946573551425[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.96727272727273[/C][C]0.0549171619455009[/C][C]90.4502809559275[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.96738095238095[/C][C]0.0548231869397103[/C][C]90.6073001163474[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.9675[/C][C]0.0545679416545123[/C][C]91.0333036098537[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.96736842105263[/C][C]0.0541646562554641[/C][C]91.70866695109[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.9675[/C][C]0.0535625654043793[/C][C]92.7420104413792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.96764705882353[/C][C]0.0526042955613186[/C][C]94.4342473521568[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.968125[/C][C]0.0516256639026279[/C][C]96.2336292540562[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.96833333333333[/C][C]0.0519440090542533[/C][C]95.6478605289037[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.96714285714286[/C][C]0.0533081715021628[/C][C]93.1778884395112[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.96538461538462[/C][C]0.0548430789946139[/C][C]90.5380351798312[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.96333333333333[/C][C]0.056490561821239[/C][C]87.8612846698092[/C][/ROW]
[ROW][C]Median[/C][C]4.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.95435897435898[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84351&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 Mean4.973611111111110.053337846623717693.2473173541938
Geometric Mean4.95328357828909
Harmonic Mean4.93303028748875
Quadratic Mean4.99387597185014
Winsorized Mean ( 1 / 24 )4.975694444444440.052968169786390793.9374432703708
Winsorized Mean ( 2 / 24 )4.977083333333330.052756726610550994.3402605334873
Winsorized Mean ( 3 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 4 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 5 / 24 )4.977083333333330.05262864761779794.5698504259166
Winsorized Mean ( 6 / 24 )4.976250.052495039448186694.7946711214806
Winsorized Mean ( 7 / 24 )4.974305555555560.052189099703777295.3131129639996
Winsorized Mean ( 8 / 24 )4.975416666666670.052029972665335595.6259711814436
Winsorized Mean ( 9 / 24 )4.969166666666670.051086301983909997.2700405723584
Winsorized Mean ( 10 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 11 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 12 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 13 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 14 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 15 / 24 )4.966388888888890.050684788563122297.985786854054
Winsorized Mean ( 16 / 24 )4.968611111111110.050367314942694898.6475280003338
Winsorized Mean ( 17 / 24 )4.966250.050031069181175699.26331939891
Winsorized Mean ( 18 / 24 )4.966250.050031069181175699.26331939891
Winsorized Mean ( 19 / 24 )4.963611111111110.0481688579011441103.046061862165
Winsorized Mean ( 20 / 24 )4.966388888888890.0409517567784057121.274135216287
Winsorized Mean ( 21 / 24 )4.978055555555560.0357124223251376139.392828361899
Winsorized Mean ( 22 / 24 )4.981111111111110.0353434720348125140.934402432360
Winsorized Mean ( 23 / 24 )4.981111111111110.0353434720348125140.934402432360
Winsorized Mean ( 24 / 24 )4.984444444444440.0349456815751911142.634060054592
Trimmed Mean ( 1 / 24 )4.975428571428570.053083272101379193.7287468249213
Trimmed Mean ( 2 / 24 )4.975147058823530.053165590477727593.5783279019116
Trimmed Mean ( 3 / 24 )4.974090909090910.05333317771221293.2644766815003
Trimmed Mean ( 4 / 24 )4.972968750.053522117372083492.91427533459
Trimmed Mean ( 5 / 24 )4.971774193548390.053678796845248792.6208202445665
Trimmed Mean ( 6 / 24 )4.97050.053795713709916792.3958370884805
Trimmed Mean ( 7 / 24 )4.969310344827590.053897609717600292.1990858382142
Trimmed Mean ( 8 / 24 )4.968392857142860.054015255652715491.9812893062387
Trimmed Mean ( 9 / 24 )4.967222222222220.054108889790350491.800483090083
Trimmed Mean ( 10 / 24 )4.966923076923080.0543295475146691.4221322307687
Trimmed Mean ( 11 / 24 )4.9670.054576103015955391.0105288856535
Trimmed Mean ( 12 / 24 )4.967083333333330.054768175464727990.6928757656399
Trimmed Mean ( 13 / 24 )4.967173913043480.054889139958285290.4946573551425
Trimmed Mean ( 14 / 24 )4.967272727272730.054917161945500990.4502809559275
Trimmed Mean ( 15 / 24 )4.967380952380950.054823186939710390.6073001163474
Trimmed Mean ( 16 / 24 )4.96750.054567941654512391.0333036098537
Trimmed Mean ( 17 / 24 )4.967368421052630.054164656255464191.70866695109
Trimmed Mean ( 18 / 24 )4.96750.053562565404379392.7420104413792
Trimmed Mean ( 19 / 24 )4.967647058823530.052604295561318694.4342473521568
Trimmed Mean ( 20 / 24 )4.9681250.051625663902627996.2336292540562
Trimmed Mean ( 21 / 24 )4.968333333333330.051944009054253395.6478605289037
Trimmed Mean ( 22 / 24 )4.967142857142860.053308171502162893.1778884395112
Trimmed Mean ( 23 / 24 )4.965384615384620.054843078994613990.5380351798312
Trimmed Mean ( 24 / 24 )4.963333333333330.05649056182123987.8612846698092
Median4.8
Midrange4.91
Midmean - Weighted Average at Xnp4.95435897435898
Midmean - Weighted Average at X(n+1)p4.95435897435898
Midmean - Empirical Distribution Function4.95435897435898
Midmean - Empirical Distribution Function - Averaging4.95435897435898
Midmean - Empirical Distribution Function - Interpolation4.95435897435898
Midmean - Closest Observation4.95435897435898
Midmean - True Basic - Statistics Graphics Toolkit4.95435897435898
Midmean - MS Excel (old versions)4.95435897435898
Number of observations72



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')