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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 02 Dec 2007 10:45:10 -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/02/t1196616821ypw5dx0ly34audz.htm/, Retrieved Sat, 27 Apr 2024 19:27:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2285, Retrieved Sat, 27 Apr 2024 19:27:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 8, question 4, central tendency, intermediaire goederen.
Estimated Impact261
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 8, quest...] [2007-12-02 17:45:10] [181c187d2008ac66a37ecc12859b08c5] [Current]
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Dataseries X:
0.088099611374169 
9.09991342500542 
-7.35508782875268 
-9.63027351884776 
-8.09956276694137 
5.87134934771151 
4.37120744692289 
4.35919376476607 
0.222071828911728 
-1.24229027856226 
4.33825947016836 
4.60664694708622 
1.38965789536273 
1.30823467988426 
-4.23042787999216 
5.65497514243973 
0.365790807112413 
-5.64334390187382 
-2.30920343133455 
-8.40101680066219 
-0.115668145864661 
3.20442920089574 
0.720817841422331 
-11.1170708927648 
3.10544632144646 
-0.481935480703685 
-9.94595584047646 
2.04038292149759 
-1.79771230527272 
6.61622067546187 
3.30704370980918 
8.49625922330628 
-4.82549712290729 
5.40142546409244 
-1.11941631167184 
1.85003070016295 
4.75478842969535 
0.412885821124111 
7.83541035014212 
-0.429980727281771 
-2.00026896923221 
3.72129138881134 
2.60840936447653 
-2.70203740450562 
2.18163020292025 
-1.0420752310215 
-2.58895494096853 
2.55997197094756 
3.88161047460306 




Summary of compuational 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 compuational 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=2285&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]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=2285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2285&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3937892785290360.6987545460790110.563558807221712
Geometric MeanNaN
Harmonic Mean4.65855502719913
Quadratic Mean4.85710304068758
Winsorized Mean ( 1 / 16 )0.405370112214530.6877944313165020.589376845402215
Winsorized Mean ( 2 / 16 )0.3912816815396140.6773938968369570.5776279995534
Winsorized Mean ( 3 / 16 )0.391898031141980.6388325857373110.613459676121044
Winsorized Mean ( 4 / 16 )0.355700701017120.6199937702158560.573716572818594
Winsorized Mean ( 5 / 16 )0.40958853090660.5947874074586780.688630131993936
Winsorized Mean ( 6 / 16 )0.5881429286859760.53492901465161.09947845896719
Winsorized Mean ( 7 / 16 )0.6126014636244680.4904177336092331.24914215298868
Winsorized Mean ( 8 / 16 )0.6855692612254470.4642084214963281.47685657880912
Winsorized Mean ( 9 / 16 )0.9230500526113430.3986206629381122.31561014877608
Winsorized Mean ( 10 / 16 )0.9436763345256840.3938355832253112.39611750364825
Winsorized Mean ( 11 / 16 )1.001778158309340.3814334517390662.62635108101279
Winsorized Mean ( 12 / 16 )0.9656031705224890.3478945464772972.77556282586195
Winsorized Mean ( 13 / 16 )0.9768090586078160.3310407305375952.95072167410192
Winsorized Mean ( 14 / 16 )1.017144586524470.2837810939832713.58425775391659
Winsorized Mean ( 15 / 16 )1.023346461415380.2723160880455333.75793611299335
Winsorized Mean ( 16 / 16 )1.016279751603490.2628123545702413.86694055256777
Trimmed Mean ( 1 / 16 )0.3937892785290360.6593519738049990.59723682369001
Trimmed Mean ( 2 / 16 )0.453464513099620.6223776660368010.728600233982058
Trimmed Mean ( 3 / 16 )0.5711021372455340.5813235257413890.982417039663381
Trimmed Mean ( 4 / 16 )0.5711021372455340.5483139130142411.04156054349601
Trimmed Mean ( 5 / 16 )0.7325743960509790.51231922984211.42991781955318
Trimmed Mean ( 6 / 16 )0.8181220035757060.4738435599399161.72656562786132
Trimmed Mean ( 7 / 16 )0.8717837877166430.4455314306663501.95672791572253
Trimmed Mean ( 8 / 16 )0.8717837877166430.422582747037712.06298954187746
Trimmed Mean ( 9 / 16 )0.9744168450387220.3994187751322652.43958698415229
Trimmed Mean ( 10 / 16 )0.9840604190959690.389692760869952.52522119451014
Trimmed Mean ( 11 / 16 )0.9913893825920580.3758206017508832.63793250815242
Trimmed Mean ( 12 / 16 )0.989538291646070.3583660409176132.76125017066994
Trimmed Mean ( 13 / 16 )0.993787642860040.3436386536603112.89195534982629
Trimmed Mean ( 14 / 16 )0.9968350810591560.3255776683775853.06174279712295
Trimmed Mean ( 15 / 16 )0.9930938563681770.3160859467399763.14184754687982
Trimmed Mean ( 16 / 16 )0.9930938563681770.3020521337415393.28782268168961
Median0.720817841422331
Midrange-1.00857873387969
Midmean - Weighted Average at Xnp0.869035284022862
Midmean - Weighted Average at X(n+1)p0.98953829164607
Midmean - Empirical Distribution Function0.98953829164607
Midmean - Empirical Distribution Function - Averaging0.98953829164607
Midmean - Empirical Distribution Function - Interpolation0.98953829164607
Midmean - Closest Observation0.86266360999297
Midmean - True Basic - Statistics Graphics Toolkit0.98953829164607
Midmean - MS Excel (old versions)0.98953829164607
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.393789278529036 & 0.698754546079011 & 0.563558807221712 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 4.65855502719913 &  &  \tabularnewline
Quadratic Mean & 4.85710304068758 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.40537011221453 & 0.687794431316502 & 0.589376845402215 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.391281681539614 & 0.677393896836957 & 0.5776279995534 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.39189803114198 & 0.638832585737311 & 0.613459676121044 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.35570070101712 & 0.619993770215856 & 0.573716572818594 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.4095885309066 & 0.594787407458678 & 0.688630131993936 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.588142928685976 & 0.5349290146516 & 1.09947845896719 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.612601463624468 & 0.490417733609233 & 1.24914215298868 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.685569261225447 & 0.464208421496328 & 1.47685657880912 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.923050052611343 & 0.398620662938112 & 2.31561014877608 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.943676334525684 & 0.393835583225311 & 2.39611750364825 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 1.00177815830934 & 0.381433451739066 & 2.62635108101279 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.965603170522489 & 0.347894546477297 & 2.77556282586195 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.976809058607816 & 0.331040730537595 & 2.95072167410192 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 1.01714458652447 & 0.283781093983271 & 3.58425775391659 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 1.02334646141538 & 0.272316088045533 & 3.75793611299335 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 1.01627975160349 & 0.262812354570241 & 3.86694055256777 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.393789278529036 & 0.659351973804999 & 0.59723682369001 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.45346451309962 & 0.622377666036801 & 0.728600233982058 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.571102137245534 & 0.581323525741389 & 0.982417039663381 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.571102137245534 & 0.548313913014241 & 1.04156054349601 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.732574396050979 & 0.5123192298421 & 1.42991781955318 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.818122003575706 & 0.473843559939916 & 1.72656562786132 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.871783787716643 & 0.445531430666350 & 1.95672791572253 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.871783787716643 & 0.42258274703771 & 2.06298954187746 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.974416845038722 & 0.399418775132265 & 2.43958698415229 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.984060419095969 & 0.38969276086995 & 2.52522119451014 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.991389382592058 & 0.375820601750883 & 2.63793250815242 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.98953829164607 & 0.358366040917613 & 2.76125017066994 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.99378764286004 & 0.343638653660311 & 2.89195534982629 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.996835081059156 & 0.325577668377585 & 3.06174279712295 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.993093856368177 & 0.316085946739976 & 3.14184754687982 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.993093856368177 & 0.302052133741539 & 3.28782268168961 \tabularnewline
Median & 0.720817841422331 &  &  \tabularnewline
Midrange & -1.00857873387969 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.869035284022862 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.98953829164607 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.98953829164607 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.98953829164607 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.98953829164607 &  &  \tabularnewline
Midmean - Closest Observation & 0.86266360999297 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.98953829164607 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.98953829164607 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2285&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]0.393789278529036[/C][C]0.698754546079011[/C][C]0.563558807221712[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.65855502719913[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.85710304068758[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.40537011221453[/C][C]0.687794431316502[/C][C]0.589376845402215[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.391281681539614[/C][C]0.677393896836957[/C][C]0.5776279995534[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.39189803114198[/C][C]0.638832585737311[/C][C]0.613459676121044[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.35570070101712[/C][C]0.619993770215856[/C][C]0.573716572818594[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.4095885309066[/C][C]0.594787407458678[/C][C]0.688630131993936[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.588142928685976[/C][C]0.5349290146516[/C][C]1.09947845896719[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.612601463624468[/C][C]0.490417733609233[/C][C]1.24914215298868[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.685569261225447[/C][C]0.464208421496328[/C][C]1.47685657880912[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.923050052611343[/C][C]0.398620662938112[/C][C]2.31561014877608[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.943676334525684[/C][C]0.393835583225311[/C][C]2.39611750364825[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]1.00177815830934[/C][C]0.381433451739066[/C][C]2.62635108101279[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.965603170522489[/C][C]0.347894546477297[/C][C]2.77556282586195[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.976809058607816[/C][C]0.331040730537595[/C][C]2.95072167410192[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]1.01714458652447[/C][C]0.283781093983271[/C][C]3.58425775391659[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]1.02334646141538[/C][C]0.272316088045533[/C][C]3.75793611299335[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]1.01627975160349[/C][C]0.262812354570241[/C][C]3.86694055256777[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.393789278529036[/C][C]0.659351973804999[/C][C]0.59723682369001[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.45346451309962[/C][C]0.622377666036801[/C][C]0.728600233982058[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.571102137245534[/C][C]0.581323525741389[/C][C]0.982417039663381[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.571102137245534[/C][C]0.548313913014241[/C][C]1.04156054349601[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.732574396050979[/C][C]0.5123192298421[/C][C]1.42991781955318[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.818122003575706[/C][C]0.473843559939916[/C][C]1.72656562786132[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.871783787716643[/C][C]0.445531430666350[/C][C]1.95672791572253[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.871783787716643[/C][C]0.42258274703771[/C][C]2.06298954187746[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.974416845038722[/C][C]0.399418775132265[/C][C]2.43958698415229[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.984060419095969[/C][C]0.38969276086995[/C][C]2.52522119451014[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.991389382592058[/C][C]0.375820601750883[/C][C]2.63793250815242[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.98953829164607[/C][C]0.358366040917613[/C][C]2.76125017066994[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.99378764286004[/C][C]0.343638653660311[/C][C]2.89195534982629[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.996835081059156[/C][C]0.325577668377585[/C][C]3.06174279712295[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.993093856368177[/C][C]0.316085946739976[/C][C]3.14184754687982[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.993093856368177[/C][C]0.302052133741539[/C][C]3.28782268168961[/C][/ROW]
[ROW][C]Median[/C][C]0.720817841422331[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.00857873387969[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.869035284022862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.98953829164607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.98953829164607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.98953829164607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.98953829164607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.86266360999297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.98953829164607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.98953829164607[/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=2285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2285&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 Mean0.3937892785290360.6987545460790110.563558807221712
Geometric MeanNaN
Harmonic Mean4.65855502719913
Quadratic Mean4.85710304068758
Winsorized Mean ( 1 / 16 )0.405370112214530.6877944313165020.589376845402215
Winsorized Mean ( 2 / 16 )0.3912816815396140.6773938968369570.5776279995534
Winsorized Mean ( 3 / 16 )0.391898031141980.6388325857373110.613459676121044
Winsorized Mean ( 4 / 16 )0.355700701017120.6199937702158560.573716572818594
Winsorized Mean ( 5 / 16 )0.40958853090660.5947874074586780.688630131993936
Winsorized Mean ( 6 / 16 )0.5881429286859760.53492901465161.09947845896719
Winsorized Mean ( 7 / 16 )0.6126014636244680.4904177336092331.24914215298868
Winsorized Mean ( 8 / 16 )0.6855692612254470.4642084214963281.47685657880912
Winsorized Mean ( 9 / 16 )0.9230500526113430.3986206629381122.31561014877608
Winsorized Mean ( 10 / 16 )0.9436763345256840.3938355832253112.39611750364825
Winsorized Mean ( 11 / 16 )1.001778158309340.3814334517390662.62635108101279
Winsorized Mean ( 12 / 16 )0.9656031705224890.3478945464772972.77556282586195
Winsorized Mean ( 13 / 16 )0.9768090586078160.3310407305375952.95072167410192
Winsorized Mean ( 14 / 16 )1.017144586524470.2837810939832713.58425775391659
Winsorized Mean ( 15 / 16 )1.023346461415380.2723160880455333.75793611299335
Winsorized Mean ( 16 / 16 )1.016279751603490.2628123545702413.86694055256777
Trimmed Mean ( 1 / 16 )0.3937892785290360.6593519738049990.59723682369001
Trimmed Mean ( 2 / 16 )0.453464513099620.6223776660368010.728600233982058
Trimmed Mean ( 3 / 16 )0.5711021372455340.5813235257413890.982417039663381
Trimmed Mean ( 4 / 16 )0.5711021372455340.5483139130142411.04156054349601
Trimmed Mean ( 5 / 16 )0.7325743960509790.51231922984211.42991781955318
Trimmed Mean ( 6 / 16 )0.8181220035757060.4738435599399161.72656562786132
Trimmed Mean ( 7 / 16 )0.8717837877166430.4455314306663501.95672791572253
Trimmed Mean ( 8 / 16 )0.8717837877166430.422582747037712.06298954187746
Trimmed Mean ( 9 / 16 )0.9744168450387220.3994187751322652.43958698415229
Trimmed Mean ( 10 / 16 )0.9840604190959690.389692760869952.52522119451014
Trimmed Mean ( 11 / 16 )0.9913893825920580.3758206017508832.63793250815242
Trimmed Mean ( 12 / 16 )0.989538291646070.3583660409176132.76125017066994
Trimmed Mean ( 13 / 16 )0.993787642860040.3436386536603112.89195534982629
Trimmed Mean ( 14 / 16 )0.9968350810591560.3255776683775853.06174279712295
Trimmed Mean ( 15 / 16 )0.9930938563681770.3160859467399763.14184754687982
Trimmed Mean ( 16 / 16 )0.9930938563681770.3020521337415393.28782268168961
Median0.720817841422331
Midrange-1.00857873387969
Midmean - Weighted Average at Xnp0.869035284022862
Midmean - Weighted Average at X(n+1)p0.98953829164607
Midmean - Empirical Distribution Function0.98953829164607
Midmean - Empirical Distribution Function - Averaging0.98953829164607
Midmean - Empirical Distribution Function - Interpolation0.98953829164607
Midmean - Closest Observation0.86266360999297
Midmean - True Basic - Statistics Graphics Toolkit0.98953829164607
Midmean - MS Excel (old versions)0.98953829164607
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')