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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 14:34:04 -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/t1196803309bcf34g2rnue6o6y.htm/, Retrieved Thu, 02 May 2024 06:21:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2449, Retrieved Thu, 02 May 2024 06:21:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212
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 - Inter...] [2007-12-04 21:34:04] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
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Dataseries X:
0.08809961137437 
9.09991524180072 
-7.35508311811969 
-9.63028098083566 
-8.09956524475188 
5.8713475640899 
4.37121258985326 
4.35919441605924 
0.222073701257882 
-1.24229152229338 
4.33825959980376 
4.60664935851662 
1.38965891991788 
1.3082344788982 
-4.23042811468881 
5.65497326122838 
0.365794354572384 
-5.64334631266404 
-2.30920587307938 
-8.40101781221996 
-0.115672002929808 
3.20443143908481 
0.720818100674044 
-11.1170726451288 
3.10544008897169 
-0.481932932237078 
-9.94595493878044 
2.04038263122562 
-1.79770641421038 
6.616217034654 
3.30704645390408 
8.49625730306816 
-4.82549342459572 
5.40142121912659 
-1.11941348612794 
1.85002621702113 
4.75478987946154 
0.412886287254559 
7.83541108018924 
-0.429979229217207 
-2.00027152507524 
3.72129290490124 
2.60841170542933 
-2.70203443825578 
2.18162853201989 
-1.04207453296050 
-2.58895653007671 
2.55997536337719 
3.88161105962595 




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=2449&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=2449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2449&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 Mean0.3937893738594540.69875457997490.563558916313077
Geometric MeanNaN
Harmonic Mean4.65846697329586
Quadratic Mean4.85710328248101
Winsorized Mean ( 1 / 16 )0.405370185443450.6877944280988970.589376954628604
Winsorized Mean ( 2 / 16 )0.3912815215685870.677394025534680.577627653653634
Winsorized Mean ( 3 / 16 )0.3918979984918810.6388325345508170.613459674165526
Winsorized Mean ( 4 / 16 )0.3557007002799610.6199937861428610.573716556891425
Winsorized Mean ( 5 / 16 )0.4095892537259480.5947872175250390.6886315671515
Winsorized Mean ( 6 / 16 )0.5881424900549920.5349289965379881.09947767621758
Winsorized Mean ( 7 / 16 )0.6126027112554590.4904176605389931.24914488312305
Winsorized Mean ( 8 / 16 )0.6855700237390490.4642085240652111.47685789510134
Winsorized Mean ( 9 / 16 )0.9230519047579680.3986207430505682.31561432978632
Winsorized Mean ( 10 / 16 )0.9436763403467530.3938356733533082.3961169700851
Winsorized Mean ( 11 / 16 )1.001777855615330.38143355243472.62634959410613
Winsorized Mean ( 12 / 16 )0.9656029514095350.3478946687311892.77556122067406
Winsorized Mean ( 13 / 16 )0.976811327528350.3310405003244272.95073058000774
Winsorized Mean ( 14 / 16 )1.017145167791160.2837812712873473.58425756279468
Winsorized Mean ( 15 / 16 )1.023348133509380.2723160323156773.75794302233033
Winsorized Mean ( 16 / 16 )1.016277963078140.2628119529689843.8669396562723
Trimmed Mean ( 1 / 16 )0.3937893738594540.6593519874446110.597236955917319
Trimmed Mean ( 2 / 16 )0.4534646111157730.6223777017179250.728600349697768
Trimmed Mean ( 3 / 16 )0.5711024246232570.5813234897151420.982417594897302
Trimmed Mean ( 4 / 16 )0.5711024246232570.5483138839852091.04156112275038
Trimmed Mean ( 5 / 16 )0.7325749414622560.5123191766915711.42991903249268
Trimmed Mean ( 6 / 16 )0.8181225019978190.4738435685360341.72656664840984
Trimmed Mean ( 7 / 16 )0.8717845047844780.4455314456752671.95672945927119
Trimmed Mean ( 8 / 16 )0.8717845047844780.4225827970134782.06299099477226
Trimmed Mean ( 9 / 16 )0.9744174183471970.3994188057424452.43958823254688
Trimmed Mean ( 10 / 16 )0.9840607523160560.3896927757644112.52522195307765
Trimmed Mean ( 11 / 16 )0.9913897752290040.3758205894672412.63793363911857
Trimmed Mean ( 12 / 16 )0.9895388081783490.3583659864578182.76125203164286
Trimmed Mean ( 13 / 16 )0.9937882899960.3436385322751832.89195825455390
Trimmed Mean ( 14 / 16 )0.9968354371055780.3255776038795883.06174449724818
Trimmed Mean ( 15 / 16 )0.9930941709266550.3160857809551113.14185018992578
Trimmed Mean ( 16 / 16 )0.9930941709266550.3020519280812993.28782596169808
Median0.720818100674044
Midrange-1.00857870166404
Midmean - Weighted Average at Xnp0.869035797701365
Midmean - Weighted Average at X(n+1)p0.989538808178349
Midmean - Empirical Distribution Function0.989538808178349
Midmean - Empirical Distribution Function - Averaging0.989538808178349
Midmean - Empirical Distribution Function - Interpolation0.989538808178349
Midmean - Closest Observation0.86266401274536
Midmean - True Basic - Statistics Graphics Toolkit0.989538808178349
Midmean - MS Excel (old versions)0.989538808178349
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.393789373859454 & 0.6987545799749 & 0.563558916313077 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 4.65846697329586 &  &  \tabularnewline
Quadratic Mean & 4.85710328248101 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.40537018544345 & 0.687794428098897 & 0.589376954628604 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.391281521568587 & 0.67739402553468 & 0.577627653653634 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.391897998491881 & 0.638832534550817 & 0.613459674165526 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.355700700279961 & 0.619993786142861 & 0.573716556891425 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.409589253725948 & 0.594787217525039 & 0.6886315671515 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.588142490054992 & 0.534928996537988 & 1.09947767621758 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.612602711255459 & 0.490417660538993 & 1.24914488312305 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.685570023739049 & 0.464208524065211 & 1.47685789510134 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.923051904757968 & 0.398620743050568 & 2.31561432978632 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.943676340346753 & 0.393835673353308 & 2.3961169700851 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 1.00177785561533 & 0.3814335524347 & 2.62634959410613 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.965602951409535 & 0.347894668731189 & 2.77556122067406 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.97681132752835 & 0.331040500324427 & 2.95073058000774 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 1.01714516779116 & 0.283781271287347 & 3.58425756279468 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 1.02334813350938 & 0.272316032315677 & 3.75794302233033 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 1.01627796307814 & 0.262811952968984 & 3.8669396562723 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.393789373859454 & 0.659351987444611 & 0.597236955917319 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.453464611115773 & 0.622377701717925 & 0.728600349697768 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.571102424623257 & 0.581323489715142 & 0.982417594897302 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.571102424623257 & 0.548313883985209 & 1.04156112275038 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.732574941462256 & 0.512319176691571 & 1.42991903249268 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.818122501997819 & 0.473843568536034 & 1.72656664840984 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.871784504784478 & 0.445531445675267 & 1.95672945927119 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.871784504784478 & 0.422582797013478 & 2.06299099477226 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.974417418347197 & 0.399418805742445 & 2.43958823254688 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.984060752316056 & 0.389692775764411 & 2.52522195307765 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.991389775229004 & 0.375820589467241 & 2.63793363911857 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.989538808178349 & 0.358365986457818 & 2.76125203164286 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.993788289996 & 0.343638532275183 & 2.89195825455390 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.996835437105578 & 0.325577603879588 & 3.06174449724818 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.993094170926655 & 0.316085780955111 & 3.14185018992578 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.993094170926655 & 0.302051928081299 & 3.28782596169808 \tabularnewline
Median & 0.720818100674044 &  &  \tabularnewline
Midrange & -1.00857870166404 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.869035797701365 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.989538808178349 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.989538808178349 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.989538808178349 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.989538808178349 &  &  \tabularnewline
Midmean - Closest Observation & 0.86266401274536 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.989538808178349 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.989538808178349 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2449&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]0.393789373859454[/C][C]0.6987545799749[/C][C]0.563558916313077[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.65846697329586[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.85710328248101[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.40537018544345[/C][C]0.687794428098897[/C][C]0.589376954628604[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.391281521568587[/C][C]0.67739402553468[/C][C]0.577627653653634[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.391897998491881[/C][C]0.638832534550817[/C][C]0.613459674165526[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.355700700279961[/C][C]0.619993786142861[/C][C]0.573716556891425[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.409589253725948[/C][C]0.594787217525039[/C][C]0.6886315671515[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.588142490054992[/C][C]0.534928996537988[/C][C]1.09947767621758[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.612602711255459[/C][C]0.490417660538993[/C][C]1.24914488312305[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.685570023739049[/C][C]0.464208524065211[/C][C]1.47685789510134[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.923051904757968[/C][C]0.398620743050568[/C][C]2.31561432978632[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.943676340346753[/C][C]0.393835673353308[/C][C]2.3961169700851[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]1.00177785561533[/C][C]0.3814335524347[/C][C]2.62634959410613[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.965602951409535[/C][C]0.347894668731189[/C][C]2.77556122067406[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.97681132752835[/C][C]0.331040500324427[/C][C]2.95073058000774[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]1.01714516779116[/C][C]0.283781271287347[/C][C]3.58425756279468[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]1.02334813350938[/C][C]0.272316032315677[/C][C]3.75794302233033[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]1.01627796307814[/C][C]0.262811952968984[/C][C]3.8669396562723[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.393789373859454[/C][C]0.659351987444611[/C][C]0.597236955917319[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.453464611115773[/C][C]0.622377701717925[/C][C]0.728600349697768[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.571102424623257[/C][C]0.581323489715142[/C][C]0.982417594897302[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.571102424623257[/C][C]0.548313883985209[/C][C]1.04156112275038[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.732574941462256[/C][C]0.512319176691571[/C][C]1.42991903249268[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.818122501997819[/C][C]0.473843568536034[/C][C]1.72656664840984[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.871784504784478[/C][C]0.445531445675267[/C][C]1.95672945927119[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.871784504784478[/C][C]0.422582797013478[/C][C]2.06299099477226[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.974417418347197[/C][C]0.399418805742445[/C][C]2.43958823254688[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.984060752316056[/C][C]0.389692775764411[/C][C]2.52522195307765[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.991389775229004[/C][C]0.375820589467241[/C][C]2.63793363911857[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.989538808178349[/C][C]0.358365986457818[/C][C]2.76125203164286[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.993788289996[/C][C]0.343638532275183[/C][C]2.89195825455390[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.996835437105578[/C][C]0.325577603879588[/C][C]3.06174449724818[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.993094170926655[/C][C]0.316085780955111[/C][C]3.14185018992578[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.993094170926655[/C][C]0.302051928081299[/C][C]3.28782596169808[/C][/ROW]
[ROW][C]Median[/C][C]0.720818100674044[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.00857870166404[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.869035797701365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.989538808178349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.989538808178349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.989538808178349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.989538808178349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.86266401274536[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.989538808178349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.989538808178349[/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=2449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2449&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 Mean0.3937893738594540.69875457997490.563558916313077
Geometric MeanNaN
Harmonic Mean4.65846697329586
Quadratic Mean4.85710328248101
Winsorized Mean ( 1 / 16 )0.405370185443450.6877944280988970.589376954628604
Winsorized Mean ( 2 / 16 )0.3912815215685870.677394025534680.577627653653634
Winsorized Mean ( 3 / 16 )0.3918979984918810.6388325345508170.613459674165526
Winsorized Mean ( 4 / 16 )0.3557007002799610.6199937861428610.573716556891425
Winsorized Mean ( 5 / 16 )0.4095892537259480.5947872175250390.6886315671515
Winsorized Mean ( 6 / 16 )0.5881424900549920.5349289965379881.09947767621758
Winsorized Mean ( 7 / 16 )0.6126027112554590.4904176605389931.24914488312305
Winsorized Mean ( 8 / 16 )0.6855700237390490.4642085240652111.47685789510134
Winsorized Mean ( 9 / 16 )0.9230519047579680.3986207430505682.31561432978632
Winsorized Mean ( 10 / 16 )0.9436763403467530.3938356733533082.3961169700851
Winsorized Mean ( 11 / 16 )1.001777855615330.38143355243472.62634959410613
Winsorized Mean ( 12 / 16 )0.9656029514095350.3478946687311892.77556122067406
Winsorized Mean ( 13 / 16 )0.976811327528350.3310405003244272.95073058000774
Winsorized Mean ( 14 / 16 )1.017145167791160.2837812712873473.58425756279468
Winsorized Mean ( 15 / 16 )1.023348133509380.2723160323156773.75794302233033
Winsorized Mean ( 16 / 16 )1.016277963078140.2628119529689843.8669396562723
Trimmed Mean ( 1 / 16 )0.3937893738594540.6593519874446110.597236955917319
Trimmed Mean ( 2 / 16 )0.4534646111157730.6223777017179250.728600349697768
Trimmed Mean ( 3 / 16 )0.5711024246232570.5813234897151420.982417594897302
Trimmed Mean ( 4 / 16 )0.5711024246232570.5483138839852091.04156112275038
Trimmed Mean ( 5 / 16 )0.7325749414622560.5123191766915711.42991903249268
Trimmed Mean ( 6 / 16 )0.8181225019978190.4738435685360341.72656664840984
Trimmed Mean ( 7 / 16 )0.8717845047844780.4455314456752671.95672945927119
Trimmed Mean ( 8 / 16 )0.8717845047844780.4225827970134782.06299099477226
Trimmed Mean ( 9 / 16 )0.9744174183471970.3994188057424452.43958823254688
Trimmed Mean ( 10 / 16 )0.9840607523160560.3896927757644112.52522195307765
Trimmed Mean ( 11 / 16 )0.9913897752290040.3758205894672412.63793363911857
Trimmed Mean ( 12 / 16 )0.9895388081783490.3583659864578182.76125203164286
Trimmed Mean ( 13 / 16 )0.9937882899960.3436385322751832.89195825455390
Trimmed Mean ( 14 / 16 )0.9968354371055780.3255776038795883.06174449724818
Trimmed Mean ( 15 / 16 )0.9930941709266550.3160857809551113.14185018992578
Trimmed Mean ( 16 / 16 )0.9930941709266550.3020519280812993.28782596169808
Median0.720818100674044
Midrange-1.00857870166404
Midmean - Weighted Average at Xnp0.869035797701365
Midmean - Weighted Average at X(n+1)p0.989538808178349
Midmean - Empirical Distribution Function0.989538808178349
Midmean - Empirical Distribution Function - Averaging0.989538808178349
Midmean - Empirical Distribution Function - Interpolation0.989538808178349
Midmean - Closest Observation0.86266401274536
Midmean - True Basic - Statistics Graphics Toolkit0.989538808178349
Midmean - MS Excel (old versions)0.989538808178349
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')