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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, 04 Dec 2007 14:39:23 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t1196803625q687chp2crxxik6.htm/, Retrieved Wed, 01 May 2024 23:43:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2454, Retrieved Wed, 01 May 2024 23:43:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Variance reductio...] [2007-11-30 14:45:44] [6c50c82828af94f83a614a64264ea782]
- RMPD    [Central Tendency] [Residuals - duurz...] [2007-12-04 21:39:23] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
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Dataseries X:
0.0570995506747299 
-4.02433691114591 
2.12923805817709 
-10.6122939294846 
-4.33592967347822 
-6.22733887934561 
3.22296488971418 
2.91903775786582 
-4.77029181464147 
2.60234151268745 
14.5497833196297 
-3.19704622303658 
-1.53934717938419 
-14.1675778665002 
-7.69834859633814 
-9.46063257356501 
3.20599318735003 
0.934025985972693 
-1.74643708941751 
-1.60436910416306 
-2.76609879854714 
-1.06819785304358 
4.10693305127507 
0.883404304002277 
5.54361022112565 
-4.41494681931158 
-11.9754052150113 
8.31266134673431 
3.01450252845769 
3.68094694148618 
-0.890415043695038 
2.59514547831168 
-7.01589731743944 
7.19258696175249 
-3.71176628364015 
-2.03097845619725 
-0.536909685093532 
-4.50694465524361 
6.65189348266821 
-3.19831963840527 
-4.0561778497255 
0.994872465591811 
0.731299482811721 
-4.30310906068591 
-5.91630665073181 
-0.541566355927785 
-4.30524234788582 
11.4524575972973 
1.15801877147329 




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=2454&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=2454&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2454&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 Mean-0.911906428082160.805294674508622-1.13238849945033
Geometric MeanNaN
Harmonic Mean3.36027876898794
Quadratic Mean5.65327780562667
Winsorized Mean ( 1 / 16 )-0.9303789397320270.767581889108612-1.21209079178831
Winsorized Mean ( 2 / 16 )-1.002896693406980.712256143439728-1.40805622056645
Winsorized Mean ( 3 / 16 )-1.000962797227110.675093682753289-1.48270206461540
Winsorized Mean ( 4 / 16 )-0.9012411239093520.628924369103672-1.43298807962200
Winsorized Mean ( 5 / 16 )-0.9446933670362770.586339835454942-1.61117036556673
Winsorized Mean ( 6 / 16 )-1.024054844394250.527759130651935-1.94038299845091
Winsorized Mean ( 7 / 16 )-1.040476827419260.506664099987547-2.05358308876597
Winsorized Mean ( 8 / 16 )-0.9281449442652440.457060670543804-2.03068214808540
Winsorized Mean ( 9 / 16 )-0.8828923092998690.44815800248695-1.97004695754725
Winsorized Mean ( 10 / 16 )-0.9031969670468710.437648028377646-2.06375193873261
Winsorized Mean ( 11 / 16 )-0.906889290972250.430712735582939-2.10555485373526
Winsorized Mean ( 12 / 16 )-0.9769322916871820.415319362968192-2.35224354748421
Winsorized Mean ( 13 / 16 )-0.978275469509350.414882192807474-2.35795964847139
Winsorized Mean ( 14 / 16 )-1.040840100701970.379614017931163-2.74183789727890
Winsorized Mean ( 15 / 16 )-1.328404901148160.328497573081322-4.04388041192408
Winsorized Mean ( 16 / 16 )-1.279613285923900.302857736157758-4.22512993116133
Trimmed Mean ( 1 / 16 )-0.911906428082160.716654860258427-1.27244853645913
Trimmed Mean ( 2 / 16 )-0.958842987854370.649375139334277-1.47656251336839
Trimmed Mean ( 3 / 16 )-0.9823962843881640.60260226025742-1.63025655424608
Trimmed Mean ( 4 / 16 )-0.9823962843881640.561519477970634-1.74953198050868
Trimmed Mean ( 5 / 16 )-0.9981676795694510.52834942107552-1.88921883842999
Trimmed Mean ( 6 / 16 )-1.012331146132290.501266833343618-2.01954543726682
Trimmed Mean ( 7 / 16 )-1.009595616537840.486184014517037-2.0765709821635
Trimmed Mean ( 8 / 16 )-1.009595616537840.471947636412596-2.13921108750973
Trimmed Mean ( 9 / 16 )-1.017843869182300.467376123737974-2.17778319748515
Trimmed Mean ( 10 / 16 )-1.043179602646820.461733149787854-2.25926945710117
Trimmed Mean ( 11 / 16 )-1.068583858737180.454896356047449-2.34907104559378
Trimmed Mean ( 12 / 16 )-1.097394890811660.444724485855435-2.46758369668089
Trimmed Mean ( 13 / 16 )-1.118781366743180.432565347155599-2.58638694500126
Trimmed Mean ( 14 / 16 )-1.144000373938990.410378788495192-2.78766935818954
Trimmed Mean ( 15 / 16 )-1.163003582166870.388168537501809-2.99613046861493
Trimmed Mean ( 16 / 16 )-1.163003582166870.373473561601594-3.11401850556562
Median-1.06819785304358
Midrange0.191102726564750
Midmean - Weighted Average at Xnp-1.25155057429079
Midmean - Weighted Average at X(n+1)p-1.09739489081166
Midmean - Empirical Distribution Function-1.09739489081166
Midmean - Empirical Distribution Function - Averaging-1.09739489081166
Midmean - Empirical Distribution Function - Interpolation-1.09739489081166
Midmean - Closest Observation-1.22195392091422
Midmean - True Basic - Statistics Graphics Toolkit-1.09739489081166
Midmean - MS Excel (old versions)-1.09739489081166
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.91190642808216 & 0.805294674508622 & -1.13238849945033 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.36027876898794 &  &  \tabularnewline
Quadratic Mean & 5.65327780562667 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.930378939732027 & 0.767581889108612 & -1.21209079178831 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -1.00289669340698 & 0.712256143439728 & -1.40805622056645 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -1.00096279722711 & 0.675093682753289 & -1.48270206461540 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.901241123909352 & 0.628924369103672 & -1.43298807962200 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.944693367036277 & 0.586339835454942 & -1.61117036556673 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -1.02405484439425 & 0.527759130651935 & -1.94038299845091 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -1.04047682741926 & 0.506664099987547 & -2.05358308876597 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.928144944265244 & 0.457060670543804 & -2.03068214808540 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.882892309299869 & 0.44815800248695 & -1.97004695754725 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.903196967046871 & 0.437648028377646 & -2.06375193873261 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.90688929097225 & 0.430712735582939 & -2.10555485373526 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.976932291687182 & 0.415319362968192 & -2.35224354748421 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.97827546950935 & 0.414882192807474 & -2.35795964847139 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -1.04084010070197 & 0.379614017931163 & -2.74183789727890 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -1.32840490114816 & 0.328497573081322 & -4.04388041192408 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -1.27961328592390 & 0.302857736157758 & -4.22512993116133 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.91190642808216 & 0.716654860258427 & -1.27244853645913 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.95884298785437 & 0.649375139334277 & -1.47656251336839 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.982396284388164 & 0.60260226025742 & -1.63025655424608 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.982396284388164 & 0.561519477970634 & -1.74953198050868 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.998167679569451 & 0.52834942107552 & -1.88921883842999 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -1.01233114613229 & 0.501266833343618 & -2.01954543726682 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -1.00959561653784 & 0.486184014517037 & -2.0765709821635 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -1.00959561653784 & 0.471947636412596 & -2.13921108750973 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -1.01784386918230 & 0.467376123737974 & -2.17778319748515 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -1.04317960264682 & 0.461733149787854 & -2.25926945710117 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -1.06858385873718 & 0.454896356047449 & -2.34907104559378 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -1.09739489081166 & 0.444724485855435 & -2.46758369668089 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -1.11878136674318 & 0.432565347155599 & -2.58638694500126 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -1.14400037393899 & 0.410378788495192 & -2.78766935818954 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -1.16300358216687 & 0.388168537501809 & -2.99613046861493 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -1.16300358216687 & 0.373473561601594 & -3.11401850556562 \tabularnewline
Median & -1.06819785304358 &  &  \tabularnewline
Midrange & 0.191102726564750 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -1.25155057429079 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -1.09739489081166 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -1.09739489081166 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -1.09739489081166 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -1.09739489081166 &  &  \tabularnewline
Midmean - Closest Observation & -1.22195392091422 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -1.09739489081166 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -1.09739489081166 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2454&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]-0.91190642808216[/C][C]0.805294674508622[/C][C]-1.13238849945033[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.36027876898794[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.65327780562667[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.930378939732027[/C][C]0.767581889108612[/C][C]-1.21209079178831[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-1.00289669340698[/C][C]0.712256143439728[/C][C]-1.40805622056645[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-1.00096279722711[/C][C]0.675093682753289[/C][C]-1.48270206461540[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.901241123909352[/C][C]0.628924369103672[/C][C]-1.43298807962200[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.944693367036277[/C][C]0.586339835454942[/C][C]-1.61117036556673[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-1.02405484439425[/C][C]0.527759130651935[/C][C]-1.94038299845091[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-1.04047682741926[/C][C]0.506664099987547[/C][C]-2.05358308876597[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.928144944265244[/C][C]0.457060670543804[/C][C]-2.03068214808540[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.882892309299869[/C][C]0.44815800248695[/C][C]-1.97004695754725[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.903196967046871[/C][C]0.437648028377646[/C][C]-2.06375193873261[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.90688929097225[/C][C]0.430712735582939[/C][C]-2.10555485373526[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.976932291687182[/C][C]0.415319362968192[/C][C]-2.35224354748421[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.97827546950935[/C][C]0.414882192807474[/C][C]-2.35795964847139[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-1.04084010070197[/C][C]0.379614017931163[/C][C]-2.74183789727890[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-1.32840490114816[/C][C]0.328497573081322[/C][C]-4.04388041192408[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-1.27961328592390[/C][C]0.302857736157758[/C][C]-4.22512993116133[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.91190642808216[/C][C]0.716654860258427[/C][C]-1.27244853645913[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.95884298785437[/C][C]0.649375139334277[/C][C]-1.47656251336839[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.982396284388164[/C][C]0.60260226025742[/C][C]-1.63025655424608[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.982396284388164[/C][C]0.561519477970634[/C][C]-1.74953198050868[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.998167679569451[/C][C]0.52834942107552[/C][C]-1.88921883842999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-1.01233114613229[/C][C]0.501266833343618[/C][C]-2.01954543726682[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-1.00959561653784[/C][C]0.486184014517037[/C][C]-2.0765709821635[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-1.00959561653784[/C][C]0.471947636412596[/C][C]-2.13921108750973[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-1.01784386918230[/C][C]0.467376123737974[/C][C]-2.17778319748515[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-1.04317960264682[/C][C]0.461733149787854[/C][C]-2.25926945710117[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-1.06858385873718[/C][C]0.454896356047449[/C][C]-2.34907104559378[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-1.09739489081166[/C][C]0.444724485855435[/C][C]-2.46758369668089[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-1.11878136674318[/C][C]0.432565347155599[/C][C]-2.58638694500126[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-1.14400037393899[/C][C]0.410378788495192[/C][C]-2.78766935818954[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-1.16300358216687[/C][C]0.388168537501809[/C][C]-2.99613046861493[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-1.16300358216687[/C][C]0.373473561601594[/C][C]-3.11401850556562[/C][/ROW]
[ROW][C]Median[/C][C]-1.06819785304358[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.191102726564750[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-1.25155057429079[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-1.22195392091422[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-1.09739489081166[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2454&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2454&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-0.911906428082160.805294674508622-1.13238849945033
Geometric MeanNaN
Harmonic Mean3.36027876898794
Quadratic Mean5.65327780562667
Winsorized Mean ( 1 / 16 )-0.9303789397320270.767581889108612-1.21209079178831
Winsorized Mean ( 2 / 16 )-1.002896693406980.712256143439728-1.40805622056645
Winsorized Mean ( 3 / 16 )-1.000962797227110.675093682753289-1.48270206461540
Winsorized Mean ( 4 / 16 )-0.9012411239093520.628924369103672-1.43298807962200
Winsorized Mean ( 5 / 16 )-0.9446933670362770.586339835454942-1.61117036556673
Winsorized Mean ( 6 / 16 )-1.024054844394250.527759130651935-1.94038299845091
Winsorized Mean ( 7 / 16 )-1.040476827419260.506664099987547-2.05358308876597
Winsorized Mean ( 8 / 16 )-0.9281449442652440.457060670543804-2.03068214808540
Winsorized Mean ( 9 / 16 )-0.8828923092998690.44815800248695-1.97004695754725
Winsorized Mean ( 10 / 16 )-0.9031969670468710.437648028377646-2.06375193873261
Winsorized Mean ( 11 / 16 )-0.906889290972250.430712735582939-2.10555485373526
Winsorized Mean ( 12 / 16 )-0.9769322916871820.415319362968192-2.35224354748421
Winsorized Mean ( 13 / 16 )-0.978275469509350.414882192807474-2.35795964847139
Winsorized Mean ( 14 / 16 )-1.040840100701970.379614017931163-2.74183789727890
Winsorized Mean ( 15 / 16 )-1.328404901148160.328497573081322-4.04388041192408
Winsorized Mean ( 16 / 16 )-1.279613285923900.302857736157758-4.22512993116133
Trimmed Mean ( 1 / 16 )-0.911906428082160.716654860258427-1.27244853645913
Trimmed Mean ( 2 / 16 )-0.958842987854370.649375139334277-1.47656251336839
Trimmed Mean ( 3 / 16 )-0.9823962843881640.60260226025742-1.63025655424608
Trimmed Mean ( 4 / 16 )-0.9823962843881640.561519477970634-1.74953198050868
Trimmed Mean ( 5 / 16 )-0.9981676795694510.52834942107552-1.88921883842999
Trimmed Mean ( 6 / 16 )-1.012331146132290.501266833343618-2.01954543726682
Trimmed Mean ( 7 / 16 )-1.009595616537840.486184014517037-2.0765709821635
Trimmed Mean ( 8 / 16 )-1.009595616537840.471947636412596-2.13921108750973
Trimmed Mean ( 9 / 16 )-1.017843869182300.467376123737974-2.17778319748515
Trimmed Mean ( 10 / 16 )-1.043179602646820.461733149787854-2.25926945710117
Trimmed Mean ( 11 / 16 )-1.068583858737180.454896356047449-2.34907104559378
Trimmed Mean ( 12 / 16 )-1.097394890811660.444724485855435-2.46758369668089
Trimmed Mean ( 13 / 16 )-1.118781366743180.432565347155599-2.58638694500126
Trimmed Mean ( 14 / 16 )-1.144000373938990.410378788495192-2.78766935818954
Trimmed Mean ( 15 / 16 )-1.163003582166870.388168537501809-2.99613046861493
Trimmed Mean ( 16 / 16 )-1.163003582166870.373473561601594-3.11401850556562
Median-1.06819785304358
Midrange0.191102726564750
Midmean - Weighted Average at Xnp-1.25155057429079
Midmean - Weighted Average at X(n+1)p-1.09739489081166
Midmean - Empirical Distribution Function-1.09739489081166
Midmean - Empirical Distribution Function - Averaging-1.09739489081166
Midmean - Empirical Distribution Function - Interpolation-1.09739489081166
Midmean - Closest Observation-1.22195392091422
Midmean - True Basic - Statistics Graphics Toolkit-1.09739489081166
Midmean - MS Excel (old versions)-1.09739489081166
Number of observations49



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')