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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 13:42:58 -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/2009/Oct/20/t12560678191lf8whxqyhwj9i4.htm/, Retrieved Thu, 02 May 2024 17:32:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49084, Retrieved Thu, 02 May 2024 17:32:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [Workshop 3: Part ...] [2009-10-20 17:47:21] [03d5b865e91ca35b5a5d21b8d6da5aba]
-    D          [Central Tendency] [WS3-PArt2] [2009-10-20 19:42:58] [b32ceebc68d054278e6bda97f3d57f91] [Current]
-    D            [Central Tendency] [WS3-Part 2] [2009-10-20 19:44:46] [408e92805dcb18620260f240a7fb9d53]
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Dataseries X:
-2,3
-1,7
-1,6
-1,7
-1,8
-1,7
-1,6
-1,4
-1,9
-2,6
-2,8
-2,6
-1,9
-1,5
-1,4
-1,3
-1,2
-1
-0,8
-1,1
-1,7
-2,9
-3,4
-3,1
-2,4
-2
-1,9
-1,9
-2
-2,2
-2,2
-2
-1,9
-1,7
-1,5
-1,3
-1,6
-1,7
-1,5
-1,1
-0,8
-0,7
-0,7
-0,7
-0,8
-1
-1,4
-1,4
-1,8
-1,7
-1,6
-1,2
-0,7
-0,3
0
0,2
0,2
-0,1
-0,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49084&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49084&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-1.505084745762710.100420615378844-14.9878064387941
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.68824449992453
Winsorized Mean ( 1 / 19 )-1.50.0988833032232506-15.1693961579482
Winsorized Mean ( 2 / 19 )-1.50.0951482278961143-15.7648758486364
Winsorized Mean ( 3 / 19 )-1.50.0925323959571891-16.2105388548891
Winsorized Mean ( 4 / 19 )-1.50.0859845173835978-17.4450010960477
Winsorized Mean ( 5 / 19 )-1.508474576271190.0840002273657975-17.9579820623842
Winsorized Mean ( 6 / 19 )-1.518644067796610.0731472728930089-20.7614584622711
Winsorized Mean ( 7 / 19 )-1.506779661016950.0707670426375752-21.2921100678707
Winsorized Mean ( 8 / 19 )-1.493220338983050.0682444298247267-21.8804720446506
Winsorized Mean ( 9 / 19 )-1.493220338983050.0682444298247267-21.8804720446506
Winsorized Mean ( 10 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 11 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 12 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 13 / 19 )-1.498305084745760.0475889474754581-31.4843081057518
Winsorized Mean ( 14 / 19 )-1.498305084745760.0475889474754581-31.4843081057518
Winsorized Mean ( 15 / 19 )-1.523728813559320.0431340172338319-35.3254556676023
Winsorized Mean ( 16 / 19 )-1.523728813559320.0431340172338319-35.3254556676023
Winsorized Mean ( 17 / 19 )-1.552542372881360.038404468085457-40.4260871268068
Winsorized Mean ( 18 / 19 )-1.522033898305080.0338515165116043-44.9620594629293
Winsorized Mean ( 19 / 19 )-1.554237288135590.028739548085982-54.0800879500847
Trimmed Mean ( 1 / 19 )-1.501754385964910.0936750110471052-16.0315367906361
Trimmed Mean ( 2 / 19 )-1.503636363636360.0871533976560148-17.2527566804803
Trimmed Mean ( 3 / 19 )-1.505660377358490.0815940202398081-18.4530725772954
Trimmed Mean ( 4 / 19 )-1.50784313725490.075917557826322-19.8615864422881
Trimmed Mean ( 5 / 19 )-1.510204081632650.0715620715511152-21.1034148243451
Trimmed Mean ( 6 / 19 )-1.510638297872340.066721426654225-22.6409771736600
Trimmed Mean ( 7 / 19 )-1.508888888888890.0642613211518722-23.4805145901506
Trimmed Mean ( 8 / 19 )-1.509302325581400.0617943176263087-24.4246135171952
Trimmed Mean ( 9 / 19 )-1.512195121951220.0592838482045633-25.5077085538253
Trimmed Mean ( 10 / 19 )-1.515384615384620.0558987977894983-27.1094312455734
Trimmed Mean ( 11 / 19 )-1.521621621621620.0539902025278293-28.1832916043851
Trimmed Mean ( 12 / 19 )-1.528571428571430.0512976859227823-29.7980581594337
Trimmed Mean ( 13 / 19 )-1.536363636363640.0474377945589493-32.386911125357
Trimmed Mean ( 14 / 19 )-1.541935483870970.045854888823304-33.6264141826321
Trimmed Mean ( 15 / 19 )-1.548275862068970.0434420200359882-35.6400522072027
Trimmed Mean ( 16 / 19 )-1.551851851851850.0414723229612886-37.4189758625383
Trimmed Mean ( 17 / 19 )-1.5560.0383318840305735-40.5928390777489
Trimmed Mean ( 18 / 19 )-1.556521739130430.0354675640698412-43.8857807112267
Trimmed Mean ( 19 / 19 )-1.561904761904760.0327153600710813-47.7422457986457
Median-1.6
Midrange-1.6
Midmean - Weighted Average at Xnp-1.57096774193548
Midmean - Weighted Average at X(n+1)p-1.53636363636364
Midmean - Empirical Distribution Function-1.53636363636364
Midmean - Empirical Distribution Function - Averaging-1.53636363636364
Midmean - Empirical Distribution Function - Interpolation-1.57096774193548
Midmean - Closest Observation-1.57096774193548
Midmean - True Basic - Statistics Graphics Toolkit-1.53636363636364
Midmean - MS Excel (old versions)-1.53636363636364
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -1.50508474576271 & 0.100420615378844 & -14.9878064387941 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.68824449992453 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & -1.5 & 0.0988833032232506 & -15.1693961579482 \tabularnewline
Winsorized Mean ( 2 / 19 ) & -1.5 & 0.0951482278961143 & -15.7648758486364 \tabularnewline
Winsorized Mean ( 3 / 19 ) & -1.5 & 0.0925323959571891 & -16.2105388548891 \tabularnewline
Winsorized Mean ( 4 / 19 ) & -1.5 & 0.0859845173835978 & -17.4450010960477 \tabularnewline
Winsorized Mean ( 5 / 19 ) & -1.50847457627119 & 0.0840002273657975 & -17.9579820623842 \tabularnewline
Winsorized Mean ( 6 / 19 ) & -1.51864406779661 & 0.0731472728930089 & -20.7614584622711 \tabularnewline
Winsorized Mean ( 7 / 19 ) & -1.50677966101695 & 0.0707670426375752 & -21.2921100678707 \tabularnewline
Winsorized Mean ( 8 / 19 ) & -1.49322033898305 & 0.0682444298247267 & -21.8804720446506 \tabularnewline
Winsorized Mean ( 9 / 19 ) & -1.49322033898305 & 0.0682444298247267 & -21.8804720446506 \tabularnewline
Winsorized Mean ( 10 / 19 ) & -1.47627118644068 & 0.0592343009926705 & -24.9225729298865 \tabularnewline
Winsorized Mean ( 11 / 19 ) & -1.47627118644068 & 0.0592343009926705 & -24.9225729298865 \tabularnewline
Winsorized Mean ( 12 / 19 ) & -1.47627118644068 & 0.0592343009926705 & -24.9225729298865 \tabularnewline
Winsorized Mean ( 13 / 19 ) & -1.49830508474576 & 0.0475889474754581 & -31.4843081057518 \tabularnewline
Winsorized Mean ( 14 / 19 ) & -1.49830508474576 & 0.0475889474754581 & -31.4843081057518 \tabularnewline
Winsorized Mean ( 15 / 19 ) & -1.52372881355932 & 0.0431340172338319 & -35.3254556676023 \tabularnewline
Winsorized Mean ( 16 / 19 ) & -1.52372881355932 & 0.0431340172338319 & -35.3254556676023 \tabularnewline
Winsorized Mean ( 17 / 19 ) & -1.55254237288136 & 0.038404468085457 & -40.4260871268068 \tabularnewline
Winsorized Mean ( 18 / 19 ) & -1.52203389830508 & 0.0338515165116043 & -44.9620594629293 \tabularnewline
Winsorized Mean ( 19 / 19 ) & -1.55423728813559 & 0.028739548085982 & -54.0800879500847 \tabularnewline
Trimmed Mean ( 1 / 19 ) & -1.50175438596491 & 0.0936750110471052 & -16.0315367906361 \tabularnewline
Trimmed Mean ( 2 / 19 ) & -1.50363636363636 & 0.0871533976560148 & -17.2527566804803 \tabularnewline
Trimmed Mean ( 3 / 19 ) & -1.50566037735849 & 0.0815940202398081 & -18.4530725772954 \tabularnewline
Trimmed Mean ( 4 / 19 ) & -1.5078431372549 & 0.075917557826322 & -19.8615864422881 \tabularnewline
Trimmed Mean ( 5 / 19 ) & -1.51020408163265 & 0.0715620715511152 & -21.1034148243451 \tabularnewline
Trimmed Mean ( 6 / 19 ) & -1.51063829787234 & 0.066721426654225 & -22.6409771736600 \tabularnewline
Trimmed Mean ( 7 / 19 ) & -1.50888888888889 & 0.0642613211518722 & -23.4805145901506 \tabularnewline
Trimmed Mean ( 8 / 19 ) & -1.50930232558140 & 0.0617943176263087 & -24.4246135171952 \tabularnewline
Trimmed Mean ( 9 / 19 ) & -1.51219512195122 & 0.0592838482045633 & -25.5077085538253 \tabularnewline
Trimmed Mean ( 10 / 19 ) & -1.51538461538462 & 0.0558987977894983 & -27.1094312455734 \tabularnewline
Trimmed Mean ( 11 / 19 ) & -1.52162162162162 & 0.0539902025278293 & -28.1832916043851 \tabularnewline
Trimmed Mean ( 12 / 19 ) & -1.52857142857143 & 0.0512976859227823 & -29.7980581594337 \tabularnewline
Trimmed Mean ( 13 / 19 ) & -1.53636363636364 & 0.0474377945589493 & -32.386911125357 \tabularnewline
Trimmed Mean ( 14 / 19 ) & -1.54193548387097 & 0.045854888823304 & -33.6264141826321 \tabularnewline
Trimmed Mean ( 15 / 19 ) & -1.54827586206897 & 0.0434420200359882 & -35.6400522072027 \tabularnewline
Trimmed Mean ( 16 / 19 ) & -1.55185185185185 & 0.0414723229612886 & -37.4189758625383 \tabularnewline
Trimmed Mean ( 17 / 19 ) & -1.556 & 0.0383318840305735 & -40.5928390777489 \tabularnewline
Trimmed Mean ( 18 / 19 ) & -1.55652173913043 & 0.0354675640698412 & -43.8857807112267 \tabularnewline
Trimmed Mean ( 19 / 19 ) & -1.56190476190476 & 0.0327153600710813 & -47.7422457986457 \tabularnewline
Median & -1.6 &  &  \tabularnewline
Midrange & -1.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -1.57096774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -1.53636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -1.53636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -1.53636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -1.57096774193548 &  &  \tabularnewline
Midmean - Closest Observation & -1.57096774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -1.53636363636364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -1.53636363636364 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49084&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]-1.50508474576271[/C][C]0.100420615378844[/C][C]-14.9878064387941[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.68824449992453[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]-1.5[/C][C]0.0988833032232506[/C][C]-15.1693961579482[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]-1.5[/C][C]0.0951482278961143[/C][C]-15.7648758486364[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]-1.5[/C][C]0.0925323959571891[/C][C]-16.2105388548891[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]-1.5[/C][C]0.0859845173835978[/C][C]-17.4450010960477[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]-1.50847457627119[/C][C]0.0840002273657975[/C][C]-17.9579820623842[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]-1.51864406779661[/C][C]0.0731472728930089[/C][C]-20.7614584622711[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]-1.50677966101695[/C][C]0.0707670426375752[/C][C]-21.2921100678707[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]-1.49322033898305[/C][C]0.0682444298247267[/C][C]-21.8804720446506[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]-1.49322033898305[/C][C]0.0682444298247267[/C][C]-21.8804720446506[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]-1.47627118644068[/C][C]0.0592343009926705[/C][C]-24.9225729298865[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]-1.47627118644068[/C][C]0.0592343009926705[/C][C]-24.9225729298865[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]-1.47627118644068[/C][C]0.0592343009926705[/C][C]-24.9225729298865[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]-1.49830508474576[/C][C]0.0475889474754581[/C][C]-31.4843081057518[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]-1.49830508474576[/C][C]0.0475889474754581[/C][C]-31.4843081057518[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]-1.52372881355932[/C][C]0.0431340172338319[/C][C]-35.3254556676023[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]-1.52372881355932[/C][C]0.0431340172338319[/C][C]-35.3254556676023[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]-1.55254237288136[/C][C]0.038404468085457[/C][C]-40.4260871268068[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]-1.52203389830508[/C][C]0.0338515165116043[/C][C]-44.9620594629293[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]-1.55423728813559[/C][C]0.028739548085982[/C][C]-54.0800879500847[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]-1.50175438596491[/C][C]0.0936750110471052[/C][C]-16.0315367906361[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]-1.50363636363636[/C][C]0.0871533976560148[/C][C]-17.2527566804803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]-1.50566037735849[/C][C]0.0815940202398081[/C][C]-18.4530725772954[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]-1.5078431372549[/C][C]0.075917557826322[/C][C]-19.8615864422881[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]-1.51020408163265[/C][C]0.0715620715511152[/C][C]-21.1034148243451[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]-1.51063829787234[/C][C]0.066721426654225[/C][C]-22.6409771736600[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]-1.50888888888889[/C][C]0.0642613211518722[/C][C]-23.4805145901506[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]-1.50930232558140[/C][C]0.0617943176263087[/C][C]-24.4246135171952[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]-1.51219512195122[/C][C]0.0592838482045633[/C][C]-25.5077085538253[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]-1.51538461538462[/C][C]0.0558987977894983[/C][C]-27.1094312455734[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]-1.52162162162162[/C][C]0.0539902025278293[/C][C]-28.1832916043851[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]-1.52857142857143[/C][C]0.0512976859227823[/C][C]-29.7980581594337[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]-1.53636363636364[/C][C]0.0474377945589493[/C][C]-32.386911125357[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]-1.54193548387097[/C][C]0.045854888823304[/C][C]-33.6264141826321[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]-1.54827586206897[/C][C]0.0434420200359882[/C][C]-35.6400522072027[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]-1.55185185185185[/C][C]0.0414723229612886[/C][C]-37.4189758625383[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]-1.556[/C][C]0.0383318840305735[/C][C]-40.5928390777489[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]-1.55652173913043[/C][C]0.0354675640698412[/C][C]-43.8857807112267[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]-1.56190476190476[/C][C]0.0327153600710813[/C][C]-47.7422457986457[/C][/ROW]
[ROW][C]Median[/C][C]-1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49084&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 Mean-1.505084745762710.100420615378844-14.9878064387941
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.68824449992453
Winsorized Mean ( 1 / 19 )-1.50.0988833032232506-15.1693961579482
Winsorized Mean ( 2 / 19 )-1.50.0951482278961143-15.7648758486364
Winsorized Mean ( 3 / 19 )-1.50.0925323959571891-16.2105388548891
Winsorized Mean ( 4 / 19 )-1.50.0859845173835978-17.4450010960477
Winsorized Mean ( 5 / 19 )-1.508474576271190.0840002273657975-17.9579820623842
Winsorized Mean ( 6 / 19 )-1.518644067796610.0731472728930089-20.7614584622711
Winsorized Mean ( 7 / 19 )-1.506779661016950.0707670426375752-21.2921100678707
Winsorized Mean ( 8 / 19 )-1.493220338983050.0682444298247267-21.8804720446506
Winsorized Mean ( 9 / 19 )-1.493220338983050.0682444298247267-21.8804720446506
Winsorized Mean ( 10 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 11 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 12 / 19 )-1.476271186440680.0592343009926705-24.9225729298865
Winsorized Mean ( 13 / 19 )-1.498305084745760.0475889474754581-31.4843081057518
Winsorized Mean ( 14 / 19 )-1.498305084745760.0475889474754581-31.4843081057518
Winsorized Mean ( 15 / 19 )-1.523728813559320.0431340172338319-35.3254556676023
Winsorized Mean ( 16 / 19 )-1.523728813559320.0431340172338319-35.3254556676023
Winsorized Mean ( 17 / 19 )-1.552542372881360.038404468085457-40.4260871268068
Winsorized Mean ( 18 / 19 )-1.522033898305080.0338515165116043-44.9620594629293
Winsorized Mean ( 19 / 19 )-1.554237288135590.028739548085982-54.0800879500847
Trimmed Mean ( 1 / 19 )-1.501754385964910.0936750110471052-16.0315367906361
Trimmed Mean ( 2 / 19 )-1.503636363636360.0871533976560148-17.2527566804803
Trimmed Mean ( 3 / 19 )-1.505660377358490.0815940202398081-18.4530725772954
Trimmed Mean ( 4 / 19 )-1.50784313725490.075917557826322-19.8615864422881
Trimmed Mean ( 5 / 19 )-1.510204081632650.0715620715511152-21.1034148243451
Trimmed Mean ( 6 / 19 )-1.510638297872340.066721426654225-22.6409771736600
Trimmed Mean ( 7 / 19 )-1.508888888888890.0642613211518722-23.4805145901506
Trimmed Mean ( 8 / 19 )-1.509302325581400.0617943176263087-24.4246135171952
Trimmed Mean ( 9 / 19 )-1.512195121951220.0592838482045633-25.5077085538253
Trimmed Mean ( 10 / 19 )-1.515384615384620.0558987977894983-27.1094312455734
Trimmed Mean ( 11 / 19 )-1.521621621621620.0539902025278293-28.1832916043851
Trimmed Mean ( 12 / 19 )-1.528571428571430.0512976859227823-29.7980581594337
Trimmed Mean ( 13 / 19 )-1.536363636363640.0474377945589493-32.386911125357
Trimmed Mean ( 14 / 19 )-1.541935483870970.045854888823304-33.6264141826321
Trimmed Mean ( 15 / 19 )-1.548275862068970.0434420200359882-35.6400522072027
Trimmed Mean ( 16 / 19 )-1.551851851851850.0414723229612886-37.4189758625383
Trimmed Mean ( 17 / 19 )-1.5560.0383318840305735-40.5928390777489
Trimmed Mean ( 18 / 19 )-1.556521739130430.0354675640698412-43.8857807112267
Trimmed Mean ( 19 / 19 )-1.561904761904760.0327153600710813-47.7422457986457
Median-1.6
Midrange-1.6
Midmean - Weighted Average at Xnp-1.57096774193548
Midmean - Weighted Average at X(n+1)p-1.53636363636364
Midmean - Empirical Distribution Function-1.53636363636364
Midmean - Empirical Distribution Function - Averaging-1.53636363636364
Midmean - Empirical Distribution Function - Interpolation-1.57096774193548
Midmean - Closest Observation-1.57096774193548
Midmean - True Basic - Statistics Graphics Toolkit-1.53636363636364
Midmean - MS Excel (old versions)-1.53636363636364
Number of observations59



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')