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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 computationMon, 03 Dec 2007 03:20:53 -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/03/t1196676632y01izm3w5adxrux.htm/, Retrieved Fri, 03 May 2024 21:26:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2302, Retrieved Fri, 03 May 2024 21:26:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS 8 Q4 Central Tendency marleen
Estimated Impact247
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS 8 Q4 Central T...] [2007-12-03 10:20:53] [87b6915e48e03972eaa4a0940182012f] [Current]
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Dataseries X:
-0.0157849668492955 
-0.0271242952386908 
-0.00792488985144561 
0.0459148738449478 
-0.107916158530197 
-0.0438458505911499 
-0.0271360746689603 
0.00521599839841529 
0.00344739361931397 
0.0462884578538337 
-0.0097691824539114 
0.00508668680791504 
-0.0268378684186578 
-0.0460202870761644 
0.00457411626605104 
0.0202703340483053 
0.0138780833152714 
-0.0368570822698068 
-0.0373042026304117 
-0.0141720103403002 
0.0279211562227211 
-0.0237502468290586 
-0.087199455220258 
-0.0268651911387560 
0.0225803013509109 
-0.0294893626090131 
0.012381175068433 
-0.0285515363835311 
-0.0382291533140091 
0.00431996843958038 
0.0646841362279952 
-0.0335672308356738 
0.0472155970591788 
0.0146421330059951 
-0.0178345535627121 
-0.00226478825584639 
-0.0249815003522722 
0.00796397164537458 
0.0239811662159118 
-0.00474979291749824 
-0.0102587626954571 
-0.0409266362533724 
-0.0134088275301494 
-0.0362048270251369 
0.0235300656231686 
-0.0139176178293481 
-0.00425407973487355 
-0.0107326426657964 




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=2302&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=2302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2302&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-0.009457988730383980.00465545478010783-2.03159286839102
Geometric MeanNaN
Harmonic Mean-0.119875882978817
Quadratic Mean0.0332880869633061
Winsorized Mean ( 1 / 16 )-0.009390318644110590.00436373768325254-2.15189805751831
Winsorized Mean ( 2 / 16 )-0.007713150771662730.00383566328877336-2.01090403170644
Winsorized Mean ( 3 / 16 )-0.00760059749190470.00380043796066649-1.99992673754153
Winsorized Mean ( 4 / 16 )-0.008856806098942130.003347989887-2.64541005136618
Winsorized Mean ( 5 / 16 )-0.008986233918467760.00319897584595943-2.80909714583125
Winsorized Mean ( 6 / 16 )-0.008927002657110980.00316436570768385-2.82110333689751
Winsorized Mean ( 7 / 16 )-0.009000304894227010.00312193496127623-2.88292517488825
Winsorized Mean ( 8 / 16 )-0.00927659023721630.00301977545948842-3.07194702442805
Winsorized Mean ( 9 / 16 )-0.009837328647125130.00271531798640430-3.62290114689367
Winsorized Mean ( 10 / 16 )-0.009146949785471590.00253286993397823-3.61129865484447
Winsorized Mean ( 11 / 16 )-0.00927507274869910.00243066776783399-3.81585376308514
Winsorized Mean ( 12 / 16 )-0.0100255081758210.00216856619714064-4.62310451442069
Winsorized Mean ( 13 / 16 )-0.01076656066784120.0020402112586688-5.27717932253062
Winsorized Mean ( 14 / 16 )-0.01072870451925610.00202106339783835-5.30844531187447
Winsorized Mean ( 15 / 16 )-0.01088034446355790.00199306238048221-5.45910884180427
Winsorized Mean ( 16 / 16 )-0.01034627105025290.0018748946983191-5.51832114066388
Trimmed Mean ( 1 / 16 )-0.008929379059918020.00403433052631477-2.2133484110125
Trimmed Mean ( 2 / 16 )-0.00842653587716250.00359125704298551-2.34640288241726
Trimmed Mean ( 3 / 16 )-0.008834184508876650.0034069141665655-2.59301645916790
Trimmed Mean ( 4 / 16 )-0.009327619315665430.00317788322321399-2.93516742450713
Trimmed Mean ( 5 / 16 )-0.009476297173578050.00308342284923431-3.07330445317652
Trimmed Mean ( 6 / 16 )-0.009606980708274120.00301066841513976-3.19097933866229
Trimmed Mean ( 7 / 16 )-0.009766975543841920.00291818417460080-3.34693595724747
Trimmed Mean ( 8 / 16 )-0.009931262111616550.00279934512295956-3.54770908029979
Trimmed Mean ( 9 / 16 )-0.01006219648649660.00266322152045662-3.77820485799146
Trimmed Mean ( 10 / 16 )-0.01010502845590070.00257374040973509-3.9262034421493
Trimmed Mean ( 11 / 16 )-0.01028190451813370.00249802818738901-4.11600820600851
Trimmed Mean ( 12 / 16 )-0.01046496483984910.00241068546893947-4.34107434366085
Trimmed Mean ( 13 / 16 )-0.01054486605149060.00236780497747934-4.45343520762265
Trimmed Mean ( 14 / 16 )-0.01050393781462590.00233220438261097-4.50386676782867
Trimmed Mean ( 15 / 16 )-0.01046112510898210.00225505690847820-4.63896279940964
Trimmed Mean ( 16 / 16 )-0.01037728123806690.00210329850745786-4.93381286644346
Median-0.0104957026806267
Midrange-0.0216160111511009
Midmean - Weighted Average at Xnp-0.0111884277015964
Midmean - Weighted Average at X(n+1)p-0.0104649648398491
Midmean - Empirical Distribution Function-0.0111884277015964
Midmean - Empirical Distribution Function - Averaging-0.0104649648398491
Midmean - Empirical Distribution Function - Interpolation-0.0104649648398491
Midmean - Closest Observation-0.0111884277015964
Midmean - True Basic - Statistics Graphics Toolkit-0.0104649648398491
Midmean - MS Excel (old versions)-0.0102819045181338
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.00945798873038398 & 0.00465545478010783 & -2.03159286839102 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.119875882978817 &  &  \tabularnewline
Quadratic Mean & 0.0332880869633061 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.00939031864411059 & 0.00436373768325254 & -2.15189805751831 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.00771315077166273 & 0.00383566328877336 & -2.01090403170644 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.0076005974919047 & 0.00380043796066649 & -1.99992673754153 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.00885680609894213 & 0.003347989887 & -2.64541005136618 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.00898623391846776 & 0.00319897584595943 & -2.80909714583125 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -0.00892700265711098 & 0.00316436570768385 & -2.82110333689751 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -0.00900030489422701 & 0.00312193496127623 & -2.88292517488825 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.0092765902372163 & 0.00301977545948842 & -3.07194702442805 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.00983732864712513 & 0.00271531798640430 & -3.62290114689367 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.00914694978547159 & 0.00253286993397823 & -3.61129865484447 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.0092750727486991 & 0.00243066776783399 & -3.81585376308514 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.010025508175821 & 0.00216856619714064 & -4.62310451442069 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.0107665606678412 & 0.0020402112586688 & -5.27717932253062 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.0107287045192561 & 0.00202106339783835 & -5.30844531187447 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.0108803444635579 & 0.00199306238048221 & -5.45910884180427 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.0103462710502529 & 0.0018748946983191 & -5.51832114066388 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.00892937905991802 & 0.00403433052631477 & -2.2133484110125 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.0084265358771625 & 0.00359125704298551 & -2.34640288241726 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.00883418450887665 & 0.0034069141665655 & -2.59301645916790 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.00932761931566543 & 0.00317788322321399 & -2.93516742450713 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.00947629717357805 & 0.00308342284923431 & -3.07330445317652 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -0.00960698070827412 & 0.00301066841513976 & -3.19097933866229 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -0.00976697554384192 & 0.00291818417460080 & -3.34693595724747 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -0.00993126211161655 & 0.00279934512295956 & -3.54770908029979 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -0.0100621964864966 & 0.00266322152045662 & -3.77820485799146 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -0.0101050284559007 & 0.00257374040973509 & -3.9262034421493 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -0.0102819045181337 & 0.00249802818738901 & -4.11600820600851 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -0.0104649648398491 & 0.00241068546893947 & -4.34107434366085 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -0.0105448660514906 & 0.00236780497747934 & -4.45343520762265 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -0.0105039378146259 & 0.00233220438261097 & -4.50386676782867 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -0.0104611251089821 & 0.00225505690847820 & -4.63896279940964 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.0103772812380669 & 0.00210329850745786 & -4.93381286644346 \tabularnewline
Median & -0.0104957026806267 &  &  \tabularnewline
Midrange & -0.0216160111511009 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.0111884277015964 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.0104649648398491 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.0111884277015964 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.0104649648398491 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.0104649648398491 &  &  \tabularnewline
Midmean - Closest Observation & -0.0111884277015964 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.0104649648398491 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.0102819045181338 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2302&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]-0.00945798873038398[/C][C]0.00465545478010783[/C][C]-2.03159286839102[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.119875882978817[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.0332880869633061[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.00939031864411059[/C][C]0.00436373768325254[/C][C]-2.15189805751831[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.00771315077166273[/C][C]0.00383566328877336[/C][C]-2.01090403170644[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.0076005974919047[/C][C]0.00380043796066649[/C][C]-1.99992673754153[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.00885680609894213[/C][C]0.003347989887[/C][C]-2.64541005136618[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.00898623391846776[/C][C]0.00319897584595943[/C][C]-2.80909714583125[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-0.00892700265711098[/C][C]0.00316436570768385[/C][C]-2.82110333689751[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-0.00900030489422701[/C][C]0.00312193496127623[/C][C]-2.88292517488825[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.0092765902372163[/C][C]0.00301977545948842[/C][C]-3.07194702442805[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.00983732864712513[/C][C]0.00271531798640430[/C][C]-3.62290114689367[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.00914694978547159[/C][C]0.00253286993397823[/C][C]-3.61129865484447[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.0092750727486991[/C][C]0.00243066776783399[/C][C]-3.81585376308514[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.010025508175821[/C][C]0.00216856619714064[/C][C]-4.62310451442069[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.0107665606678412[/C][C]0.0020402112586688[/C][C]-5.27717932253062[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.0107287045192561[/C][C]0.00202106339783835[/C][C]-5.30844531187447[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.0108803444635579[/C][C]0.00199306238048221[/C][C]-5.45910884180427[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.0103462710502529[/C][C]0.0018748946983191[/C][C]-5.51832114066388[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.00892937905991802[/C][C]0.00403433052631477[/C][C]-2.2133484110125[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.0084265358771625[/C][C]0.00359125704298551[/C][C]-2.34640288241726[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.00883418450887665[/C][C]0.0034069141665655[/C][C]-2.59301645916790[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.00932761931566543[/C][C]0.00317788322321399[/C][C]-2.93516742450713[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.00947629717357805[/C][C]0.00308342284923431[/C][C]-3.07330445317652[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-0.00960698070827412[/C][C]0.00301066841513976[/C][C]-3.19097933866229[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-0.00976697554384192[/C][C]0.00291818417460080[/C][C]-3.34693595724747[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-0.00993126211161655[/C][C]0.00279934512295956[/C][C]-3.54770908029979[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-0.0100621964864966[/C][C]0.00266322152045662[/C][C]-3.77820485799146[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-0.0101050284559007[/C][C]0.00257374040973509[/C][C]-3.9262034421493[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-0.0102819045181337[/C][C]0.00249802818738901[/C][C]-4.11600820600851[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-0.0104649648398491[/C][C]0.00241068546893947[/C][C]-4.34107434366085[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-0.0105448660514906[/C][C]0.00236780497747934[/C][C]-4.45343520762265[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-0.0105039378146259[/C][C]0.00233220438261097[/C][C]-4.50386676782867[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-0.0104611251089821[/C][C]0.00225505690847820[/C][C]-4.63896279940964[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.0103772812380669[/C][C]0.00210329850745786[/C][C]-4.93381286644346[/C][/ROW]
[ROW][C]Median[/C][C]-0.0104957026806267[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.0216160111511009[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.0111884277015964[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.0104649648398491[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.0111884277015964[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.0104649648398491[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.0104649648398491[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.0111884277015964[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.0104649648398491[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.0102819045181338[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2302&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-0.009457988730383980.00465545478010783-2.03159286839102
Geometric MeanNaN
Harmonic Mean-0.119875882978817
Quadratic Mean0.0332880869633061
Winsorized Mean ( 1 / 16 )-0.009390318644110590.00436373768325254-2.15189805751831
Winsorized Mean ( 2 / 16 )-0.007713150771662730.00383566328877336-2.01090403170644
Winsorized Mean ( 3 / 16 )-0.00760059749190470.00380043796066649-1.99992673754153
Winsorized Mean ( 4 / 16 )-0.008856806098942130.003347989887-2.64541005136618
Winsorized Mean ( 5 / 16 )-0.008986233918467760.00319897584595943-2.80909714583125
Winsorized Mean ( 6 / 16 )-0.008927002657110980.00316436570768385-2.82110333689751
Winsorized Mean ( 7 / 16 )-0.009000304894227010.00312193496127623-2.88292517488825
Winsorized Mean ( 8 / 16 )-0.00927659023721630.00301977545948842-3.07194702442805
Winsorized Mean ( 9 / 16 )-0.009837328647125130.00271531798640430-3.62290114689367
Winsorized Mean ( 10 / 16 )-0.009146949785471590.00253286993397823-3.61129865484447
Winsorized Mean ( 11 / 16 )-0.00927507274869910.00243066776783399-3.81585376308514
Winsorized Mean ( 12 / 16 )-0.0100255081758210.00216856619714064-4.62310451442069
Winsorized Mean ( 13 / 16 )-0.01076656066784120.0020402112586688-5.27717932253062
Winsorized Mean ( 14 / 16 )-0.01072870451925610.00202106339783835-5.30844531187447
Winsorized Mean ( 15 / 16 )-0.01088034446355790.00199306238048221-5.45910884180427
Winsorized Mean ( 16 / 16 )-0.01034627105025290.0018748946983191-5.51832114066388
Trimmed Mean ( 1 / 16 )-0.008929379059918020.00403433052631477-2.2133484110125
Trimmed Mean ( 2 / 16 )-0.00842653587716250.00359125704298551-2.34640288241726
Trimmed Mean ( 3 / 16 )-0.008834184508876650.0034069141665655-2.59301645916790
Trimmed Mean ( 4 / 16 )-0.009327619315665430.00317788322321399-2.93516742450713
Trimmed Mean ( 5 / 16 )-0.009476297173578050.00308342284923431-3.07330445317652
Trimmed Mean ( 6 / 16 )-0.009606980708274120.00301066841513976-3.19097933866229
Trimmed Mean ( 7 / 16 )-0.009766975543841920.00291818417460080-3.34693595724747
Trimmed Mean ( 8 / 16 )-0.009931262111616550.00279934512295956-3.54770908029979
Trimmed Mean ( 9 / 16 )-0.01006219648649660.00266322152045662-3.77820485799146
Trimmed Mean ( 10 / 16 )-0.01010502845590070.00257374040973509-3.9262034421493
Trimmed Mean ( 11 / 16 )-0.01028190451813370.00249802818738901-4.11600820600851
Trimmed Mean ( 12 / 16 )-0.01046496483984910.00241068546893947-4.34107434366085
Trimmed Mean ( 13 / 16 )-0.01054486605149060.00236780497747934-4.45343520762265
Trimmed Mean ( 14 / 16 )-0.01050393781462590.00233220438261097-4.50386676782867
Trimmed Mean ( 15 / 16 )-0.01046112510898210.00225505690847820-4.63896279940964
Trimmed Mean ( 16 / 16 )-0.01037728123806690.00210329850745786-4.93381286644346
Median-0.0104957026806267
Midrange-0.0216160111511009
Midmean - Weighted Average at Xnp-0.0111884277015964
Midmean - Weighted Average at X(n+1)p-0.0104649648398491
Midmean - Empirical Distribution Function-0.0111884277015964
Midmean - Empirical Distribution Function - Averaging-0.0104649648398491
Midmean - Empirical Distribution Function - Interpolation-0.0104649648398491
Midmean - Closest Observation-0.0111884277015964
Midmean - True Basic - Statistics Graphics Toolkit-0.0104649648398491
Midmean - MS Excel (old versions)-0.0102819045181338
Number of observations48



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')