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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 computationTue, 15 Apr 2008 05:12:22 -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/Apr/15/t1208258045xchpf5teeaxp995.htm/, Retrieved Thu, 16 May 2024 07:34:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10106, Retrieved Thu, 16 May 2024 07:34:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact272
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten vruc...] [2008-04-15 11:12:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1,08
1,08
1,09
1,1
1,1
1,11
1,1
1,1
1,11
1,11
1,11
1,11
1,11
1,12
1,11
1,11
1,12
1,12
1,11
1,12
1,11
1,11
1,1
1,1
1,1
1,11
1,1
1,1
1,09
1,1
1,1
1,11
1,13
1,13
1,13
1,13
1,14
1,14
1,14
1,15
1,15
1,15
1,15
1,15
1,15
1,14
1,14
1,14
1,13
1,12
1,13
1,13
1,13
1,12
1,13
1,12
1,12
1,11
1,11
1,11
1,11
1,14
1,15
1,15
1,16
1,15
1,16
1,13
1,13
1,12
1,12
1,11
1,11




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10106&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10106&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.120684931506850.00224395659822933499.423621825469
Geometric Mean1.12052348230917
Harmonic Mean1.12036233990535
Quadratic Mean1.12084667117049
Winsorized Mean ( 1 / 24 )1.120684931506850.00224395659822933499.423621825469
Winsorized Mean ( 2 / 24 )1.120684931506850.00212193701824764528.142410387064
Winsorized Mean ( 3 / 24 )1.120684931506850.00212193701824764528.142410387064
Winsorized Mean ( 4 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 5 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 6 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 7 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 8 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 9 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 10 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 11 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 12 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 13 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 14 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 15 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 16 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 17 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 18 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 19 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 20 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 21 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 22 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 23 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 24 / 24 )1.119315068493150.001091839927051891025.16407466014
Trimmed Mean ( 1 / 24 )1.120704225352110.00216357204884471517.987938488362
Trimmed Mean ( 2 / 24 )1.120724637681160.00206788911999769541.965537147567
Trimmed Mean ( 3 / 24 )1.120746268656720.00203223049370602551.485804453656
Trimmed Mean ( 4 / 24 )1.120769230769230.00198924623707472563.414025815816
Trimmed Mean ( 5 / 24 )1.120634920634920.00197102690222877568.55384336345
Trimmed Mean ( 6 / 24 )1.120491803278690.00194776359788213575.27094381322
Trimmed Mean ( 7 / 24 )1.120338983050850.00191835243842719584.01102978209
Trimmed Mean ( 8 / 24 )1.120175438596490.00188136934995852595.404320061444
Trimmed Mean ( 9 / 24 )1.120.00183493960854392610.374311386058
Trimmed Mean ( 10 / 24 )1.119811320754720.00177653153611741630.335740170451
Trimmed Mean ( 11 / 24 )1.119607843137250.00170261124283077657.582785178719
Trimmed Mean ( 12 / 24 )1.119591836734690.00167411220439791668.76750183979
Trimmed Mean ( 13 / 24 )1.119574468085110.00163669323244843684.046616610169
Trimmed Mean ( 14 / 24 )1.119555555555560.00158769114988710705.14693971505
Trimmed Mean ( 15 / 24 )1.119534883720930.00152329596795578734.942458505497
Trimmed Mean ( 16 / 24 )1.119268292682930.00149756892029352747.390171841674
Trimmed Mean ( 17 / 24 )1.118974358974360.00145998686491751766.427689085809
Trimmed Mean ( 18 / 24 )1.118648648648650.00140580959768712795.73268705028
Trimmed Mean ( 19 / 24 )1.118571428571430.00142857142857141783.000000000008
Trimmed Mean ( 20 / 24 )1.118484848484850.00145130636823241770.674526734892
Trimmed Mean ( 21 / 24 )1.118387096774190.00147354989360221758.974705661445
Trimmed Mean ( 22 / 24 )1.118275862068970.00149456861638206748.22651152411
Trimmed Mean ( 23 / 24 )1.118148148148150.00151319335896175738.932761980493
Trimmed Mean ( 24 / 24 )1.1180.00152752523165193731.902803851525
Median1.12
Midrange1.12
Midmean - Weighted Average at Xnp1.118
Midmean - Weighted Average at X(n+1)p1.118
Midmean - Empirical Distribution Function1.118
Midmean - Empirical Distribution Function - Averaging1.118
Midmean - Empirical Distribution Function - Interpolation1.118
Midmean - Closest Observation1.118
Midmean - True Basic - Statistics Graphics Toolkit1.118
Midmean - MS Excel (old versions)1.118
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.12068493150685 & 0.00224395659822933 & 499.423621825469 \tabularnewline
Geometric Mean & 1.12052348230917 &  &  \tabularnewline
Harmonic Mean & 1.12036233990535 &  &  \tabularnewline
Quadratic Mean & 1.12084667117049 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.12068493150685 & 0.00224395659822933 & 499.423621825469 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.12068493150685 & 0.00212193701824764 & 528.142410387064 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.12068493150685 & 0.00212193701824764 & 528.142410387064 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.12123287671233 & 0.00202669781015270 & 553.231404847599 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.11972602739726 & 0.00175532027479683 & 637.904115547723 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.11972602739726 & 0.00175532027479683 & 637.904115547723 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.11972602739726 & 0.00175532027479683 & 637.904115547723 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.11972602739726 & 0.00175532027479683 & 637.904115547723 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.12178082191781 & 0.00147715307028509 & 759.420837612521 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.12178082191781 & 0.00147715307028509 & 759.420837612521 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.12178082191781 & 0.00147715307028509 & 759.420837612521 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.11931506849315 & 0.00109183992705189 & 1025.16407466014 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.12070422535211 & 0.00216357204884471 & 517.987938488362 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.12072463768116 & 0.00206788911999769 & 541.965537147567 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.12074626865672 & 0.00203223049370602 & 551.485804453656 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.12076923076923 & 0.00198924623707472 & 563.414025815816 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.12063492063492 & 0.00197102690222877 & 568.55384336345 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.12049180327869 & 0.00194776359788213 & 575.27094381322 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.12033898305085 & 0.00191835243842719 & 584.01102978209 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.12017543859649 & 0.00188136934995852 & 595.404320061444 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.12 & 0.00183493960854392 & 610.374311386058 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.11981132075472 & 0.00177653153611741 & 630.335740170451 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.11960784313725 & 0.00170261124283077 & 657.582785178719 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.11959183673469 & 0.00167411220439791 & 668.76750183979 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.11957446808511 & 0.00163669323244843 & 684.046616610169 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.11955555555556 & 0.00158769114988710 & 705.14693971505 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.11953488372093 & 0.00152329596795578 & 734.942458505497 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.11926829268293 & 0.00149756892029352 & 747.390171841674 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.11897435897436 & 0.00145998686491751 & 766.427689085809 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.11864864864865 & 0.00140580959768712 & 795.73268705028 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.11857142857143 & 0.00142857142857141 & 783.000000000008 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.11848484848485 & 0.00145130636823241 & 770.674526734892 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.11838709677419 & 0.00147354989360221 & 758.974705661445 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.11827586206897 & 0.00149456861638206 & 748.22651152411 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.11814814814815 & 0.00151319335896175 & 738.932761980493 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.118 & 0.00152752523165193 & 731.902803851525 \tabularnewline
Median & 1.12 &  &  \tabularnewline
Midrange & 1.12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.118 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.118 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.118 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.118 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.118 &  &  \tabularnewline
Midmean - Closest Observation & 1.118 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.118 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.118 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10106&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]1.12068493150685[/C][C]0.00224395659822933[/C][C]499.423621825469[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.12052348230917[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.12036233990535[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.12084667117049[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.12068493150685[/C][C]0.00224395659822933[/C][C]499.423621825469[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.12068493150685[/C][C]0.00212193701824764[/C][C]528.142410387064[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.12068493150685[/C][C]0.00212193701824764[/C][C]528.142410387064[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.12123287671233[/C][C]0.00202669781015270[/C][C]553.231404847599[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.11972602739726[/C][C]0.00175532027479683[/C][C]637.904115547723[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.11972602739726[/C][C]0.00175532027479683[/C][C]637.904115547723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.11972602739726[/C][C]0.00175532027479683[/C][C]637.904115547723[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.11972602739726[/C][C]0.00175532027479683[/C][C]637.904115547723[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.12178082191781[/C][C]0.00147715307028509[/C][C]759.420837612521[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.12178082191781[/C][C]0.00147715307028509[/C][C]759.420837612521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.12178082191781[/C][C]0.00147715307028509[/C][C]759.420837612521[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.11931506849315[/C][C]0.00109183992705189[/C][C]1025.16407466014[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.12070422535211[/C][C]0.00216357204884471[/C][C]517.987938488362[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.12072463768116[/C][C]0.00206788911999769[/C][C]541.965537147567[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.12074626865672[/C][C]0.00203223049370602[/C][C]551.485804453656[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.12076923076923[/C][C]0.00198924623707472[/C][C]563.414025815816[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.12063492063492[/C][C]0.00197102690222877[/C][C]568.55384336345[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.12049180327869[/C][C]0.00194776359788213[/C][C]575.27094381322[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.12033898305085[/C][C]0.00191835243842719[/C][C]584.01102978209[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.12017543859649[/C][C]0.00188136934995852[/C][C]595.404320061444[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.12[/C][C]0.00183493960854392[/C][C]610.374311386058[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.11981132075472[/C][C]0.00177653153611741[/C][C]630.335740170451[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.11960784313725[/C][C]0.00170261124283077[/C][C]657.582785178719[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.11959183673469[/C][C]0.00167411220439791[/C][C]668.76750183979[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.11957446808511[/C][C]0.00163669323244843[/C][C]684.046616610169[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.11955555555556[/C][C]0.00158769114988710[/C][C]705.14693971505[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.11953488372093[/C][C]0.00152329596795578[/C][C]734.942458505497[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.11926829268293[/C][C]0.00149756892029352[/C][C]747.390171841674[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.11897435897436[/C][C]0.00145998686491751[/C][C]766.427689085809[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.11864864864865[/C][C]0.00140580959768712[/C][C]795.73268705028[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.11857142857143[/C][C]0.00142857142857141[/C][C]783.000000000008[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.11848484848485[/C][C]0.00145130636823241[/C][C]770.674526734892[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.11838709677419[/C][C]0.00147354989360221[/C][C]758.974705661445[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.11827586206897[/C][C]0.00149456861638206[/C][C]748.22651152411[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.11814814814815[/C][C]0.00151319335896175[/C][C]738.932761980493[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.118[/C][C]0.00152752523165193[/C][C]731.902803851525[/C][/ROW]
[ROW][C]Median[/C][C]1.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10106&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 Mean1.120684931506850.00224395659822933499.423621825469
Geometric Mean1.12052348230917
Harmonic Mean1.12036233990535
Quadratic Mean1.12084667117049
Winsorized Mean ( 1 / 24 )1.120684931506850.00224395659822933499.423621825469
Winsorized Mean ( 2 / 24 )1.120684931506850.00212193701824764528.142410387064
Winsorized Mean ( 3 / 24 )1.120684931506850.00212193701824764528.142410387064
Winsorized Mean ( 4 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 5 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 6 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 7 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 8 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 9 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 10 / 24 )1.121232876712330.00202669781015270553.231404847599
Winsorized Mean ( 11 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 12 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 13 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 14 / 24 )1.119726027397260.00175532027479683637.904115547723
Winsorized Mean ( 15 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 16 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 17 / 24 )1.121780821917810.00147715307028509759.420837612521
Winsorized Mean ( 18 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 19 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 20 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 21 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 22 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 23 / 24 )1.119315068493150.001091839927051891025.16407466014
Winsorized Mean ( 24 / 24 )1.119315068493150.001091839927051891025.16407466014
Trimmed Mean ( 1 / 24 )1.120704225352110.00216357204884471517.987938488362
Trimmed Mean ( 2 / 24 )1.120724637681160.00206788911999769541.965537147567
Trimmed Mean ( 3 / 24 )1.120746268656720.00203223049370602551.485804453656
Trimmed Mean ( 4 / 24 )1.120769230769230.00198924623707472563.414025815816
Trimmed Mean ( 5 / 24 )1.120634920634920.00197102690222877568.55384336345
Trimmed Mean ( 6 / 24 )1.120491803278690.00194776359788213575.27094381322
Trimmed Mean ( 7 / 24 )1.120338983050850.00191835243842719584.01102978209
Trimmed Mean ( 8 / 24 )1.120175438596490.00188136934995852595.404320061444
Trimmed Mean ( 9 / 24 )1.120.00183493960854392610.374311386058
Trimmed Mean ( 10 / 24 )1.119811320754720.00177653153611741630.335740170451
Trimmed Mean ( 11 / 24 )1.119607843137250.00170261124283077657.582785178719
Trimmed Mean ( 12 / 24 )1.119591836734690.00167411220439791668.76750183979
Trimmed Mean ( 13 / 24 )1.119574468085110.00163669323244843684.046616610169
Trimmed Mean ( 14 / 24 )1.119555555555560.00158769114988710705.14693971505
Trimmed Mean ( 15 / 24 )1.119534883720930.00152329596795578734.942458505497
Trimmed Mean ( 16 / 24 )1.119268292682930.00149756892029352747.390171841674
Trimmed Mean ( 17 / 24 )1.118974358974360.00145998686491751766.427689085809
Trimmed Mean ( 18 / 24 )1.118648648648650.00140580959768712795.73268705028
Trimmed Mean ( 19 / 24 )1.118571428571430.00142857142857141783.000000000008
Trimmed Mean ( 20 / 24 )1.118484848484850.00145130636823241770.674526734892
Trimmed Mean ( 21 / 24 )1.118387096774190.00147354989360221758.974705661445
Trimmed Mean ( 22 / 24 )1.118275862068970.00149456861638206748.22651152411
Trimmed Mean ( 23 / 24 )1.118148148148150.00151319335896175738.932761980493
Trimmed Mean ( 24 / 24 )1.1180.00152752523165193731.902803851525
Median1.12
Midrange1.12
Midmean - Weighted Average at Xnp1.118
Midmean - Weighted Average at X(n+1)p1.118
Midmean - Empirical Distribution Function1.118
Midmean - Empirical Distribution Function - Averaging1.118
Midmean - Empirical Distribution Function - Interpolation1.118
Midmean - Closest Observation1.118
Midmean - True Basic - Statistics Graphics Toolkit1.118
Midmean - MS Excel (old versions)1.118
Number of observations73



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')