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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 18 Dec 2010 14:29:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292682700s3x5ln2wii9f7ru.htm/, Retrieved Tue, 30 Apr 2024 07:00:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112007, Retrieved Tue, 30 Apr 2024 07:00:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
1,03
1,02
1,02
1,02
1,02
1,03
1,03
1,03
1,04
1,04
1,04
1,04
1,04
1,04
1,04
1,04
1,04
1,05
1,05
1,04
1,04
1,04
1,05
1,05
1,05
1,06
1,06
1,07
1,06
1,07
1,07
1,07
1,07
1,07
1,07
1,07
1,07
1,08
1,07
1,07
1,08
1,08
1,08
1,08
1,08
1,08
1,08
1,09
1,09
1,08
1,08
1,08
1,08




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112007&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112007&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112007&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.056981132075470.00285835045425342369.787102383688
Geometric Mean1.05677955623346
Harmonic Mean1.05657740596773
Quadratic Mean1.05718208567122
Winsorized Mean ( 1 / 17 )1.056981132075470.00285835045425342369.787102383688
Winsorized Mean ( 2 / 17 )1.056603773584910.00278581567174215379.279858428014
Winsorized Mean ( 3 / 17 )1.056603773584910.00278581567174215379.279858428014
Winsorized Mean ( 4 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 5 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 6 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 7 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 8 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 9 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 10 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 11 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 12 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 13 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 14 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 15 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 16 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 17 / 17 )1.056226415094340.00192806811826628547.815922626271
Trimmed Mean ( 1 / 17 )1.057058823529410.00280467561504921376.891651161899
Trimmed Mean ( 2 / 17 )1.057142857142860.00273550602216097386.452396221649
Trimmed Mean ( 3 / 17 )1.057446808510640.00269422387442318392.486614994841
Trimmed Mean ( 4 / 17 )1.057777777777780.00263789189034356400.993604646934
Trimmed Mean ( 5 / 17 )1.057906976744190.00263207364774261401.929094062964
Trimmed Mean ( 6 / 17 )1.058048780487800.00261840372604682404.081605125583
Trimmed Mean ( 7 / 17 )1.058205128205130.0025942892456029407.897897275215
Trimmed Mean ( 8 / 17 )1.058378378378380.0025560830556957414.062593161831
Trimmed Mean ( 9 / 17 )1.058285714285710.00257609287522805410.810388267554
Trimmed Mean ( 10 / 17 )1.058181818181820.00259130778431622408.358213789352
Trimmed Mean ( 11 / 17 )1.058064516129030.00259939425692763407.042722860987
Trimmed Mean ( 12 / 17 )1.057931034482760.00259685819765462407.388834491710
Trimmed Mean ( 13 / 17 )1.057777777777780.00257830822717921410.260405108755
Trimmed Mean ( 14 / 17 )1.05760.00253508711224421417.184874985913
Trimmed Mean ( 15 / 17 )1.057826086956520.00258885737451586408.607325134836
Trimmed Mean ( 16 / 17 )1.058095238095240.00263845622422763401.028157442702
Trimmed Mean ( 17 / 17 )1.058421052631580.00267795395131119395.234971129116
Median1.06
Midrange1.055
Midmean - Weighted Average at Xnp1.05419354838710
Midmean - Weighted Average at X(n+1)p1.06139534883721
Midmean - Empirical Distribution Function1.06139534883721
Midmean - Empirical Distribution Function - Averaging1.06139534883721
Midmean - Empirical Distribution Function - Interpolation1.06139534883721
Midmean - Closest Observation1.06139534883721
Midmean - True Basic - Statistics Graphics Toolkit1.06139534883721
Midmean - MS Excel (old versions)1.06139534883721
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.05698113207547 & 0.00285835045425342 & 369.787102383688 \tabularnewline
Geometric Mean & 1.05677955623346 &  &  \tabularnewline
Harmonic Mean & 1.05657740596773 &  &  \tabularnewline
Quadratic Mean & 1.05718208567122 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 1.05698113207547 & 0.00285835045425342 & 369.787102383688 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 1.05660377358491 & 0.00278581567174215 & 379.279858428014 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 1.05660377358491 & 0.00278581567174215 & 379.279858428014 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 1.05735849056604 & 0.00261389253962834 & 404.514904318285 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 1.05735849056604 & 0.00261389253962834 & 404.514904318285 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 1.05735849056604 & 0.00261389253962834 & 404.514904318285 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 1.05735849056604 & 0.00261389253962834 & 404.514904318285 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 1.05886792452830 & 0.00234320153257071 & 451.889395687885 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 1.05622641509434 & 0.00192806811826628 & 547.815922626271 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 1.05622641509434 & 0.00192806811826628 & 547.815922626271 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 1.05622641509434 & 0.00192806811826628 & 547.815922626271 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 1.05622641509434 & 0.00192806811826628 & 547.815922626271 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 1.05705882352941 & 0.00280467561504921 & 376.891651161899 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 1.05714285714286 & 0.00273550602216097 & 386.452396221649 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 1.05744680851064 & 0.00269422387442318 & 392.486614994841 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 1.05777777777778 & 0.00263789189034356 & 400.993604646934 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 1.05790697674419 & 0.00263207364774261 & 401.929094062964 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 1.05804878048780 & 0.00261840372604682 & 404.081605125583 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 1.05820512820513 & 0.0025942892456029 & 407.897897275215 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 1.05837837837838 & 0.0025560830556957 & 414.062593161831 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 1.05828571428571 & 0.00257609287522805 & 410.810388267554 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 1.05818181818182 & 0.00259130778431622 & 408.358213789352 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 1.05806451612903 & 0.00259939425692763 & 407.042722860987 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 1.05793103448276 & 0.00259685819765462 & 407.388834491710 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 1.05777777777778 & 0.00257830822717921 & 410.260405108755 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 1.0576 & 0.00253508711224421 & 417.184874985913 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 1.05782608695652 & 0.00258885737451586 & 408.607325134836 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 1.05809523809524 & 0.00263845622422763 & 401.028157442702 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 1.05842105263158 & 0.00267795395131119 & 395.234971129116 \tabularnewline
Median & 1.06 &  &  \tabularnewline
Midrange & 1.055 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.05419354838710 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.06139534883721 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.06139534883721 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.06139534883721 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.06139534883721 &  &  \tabularnewline
Midmean - Closest Observation & 1.06139534883721 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.06139534883721 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.06139534883721 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112007&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.05698113207547[/C][C]0.00285835045425342[/C][C]369.787102383688[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.05677955623346[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.05657740596773[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.05718208567122[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]1.05698113207547[/C][C]0.00285835045425342[/C][C]369.787102383688[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]1.05660377358491[/C][C]0.00278581567174215[/C][C]379.279858428014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]1.05660377358491[/C][C]0.00278581567174215[/C][C]379.279858428014[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]1.05735849056604[/C][C]0.00261389253962834[/C][C]404.514904318285[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]1.05735849056604[/C][C]0.00261389253962834[/C][C]404.514904318285[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]1.05735849056604[/C][C]0.00261389253962834[/C][C]404.514904318285[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]1.05735849056604[/C][C]0.00261389253962834[/C][C]404.514904318285[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]1.05886792452830[/C][C]0.00234320153257071[/C][C]451.889395687885[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]1.05622641509434[/C][C]0.00192806811826628[/C][C]547.815922626271[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]1.05622641509434[/C][C]0.00192806811826628[/C][C]547.815922626271[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]1.05622641509434[/C][C]0.00192806811826628[/C][C]547.815922626271[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]1.05622641509434[/C][C]0.00192806811826628[/C][C]547.815922626271[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]1.05705882352941[/C][C]0.00280467561504921[/C][C]376.891651161899[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]1.05714285714286[/C][C]0.00273550602216097[/C][C]386.452396221649[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]1.05744680851064[/C][C]0.00269422387442318[/C][C]392.486614994841[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]1.05777777777778[/C][C]0.00263789189034356[/C][C]400.993604646934[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]1.05790697674419[/C][C]0.00263207364774261[/C][C]401.929094062964[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]1.05804878048780[/C][C]0.00261840372604682[/C][C]404.081605125583[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]1.05820512820513[/C][C]0.0025942892456029[/C][C]407.897897275215[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]1.05837837837838[/C][C]0.0025560830556957[/C][C]414.062593161831[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]1.05828571428571[/C][C]0.00257609287522805[/C][C]410.810388267554[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]1.05818181818182[/C][C]0.00259130778431622[/C][C]408.358213789352[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]1.05806451612903[/C][C]0.00259939425692763[/C][C]407.042722860987[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]1.05793103448276[/C][C]0.00259685819765462[/C][C]407.388834491710[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]1.05777777777778[/C][C]0.00257830822717921[/C][C]410.260405108755[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]1.0576[/C][C]0.00253508711224421[/C][C]417.184874985913[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]1.05782608695652[/C][C]0.00258885737451586[/C][C]408.607325134836[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]1.05809523809524[/C][C]0.00263845622422763[/C][C]401.028157442702[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]1.05842105263158[/C][C]0.00267795395131119[/C][C]395.234971129116[/C][/ROW]
[ROW][C]Median[/C][C]1.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.05419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.06139534883721[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112007&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112007&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 Mean1.056981132075470.00285835045425342369.787102383688
Geometric Mean1.05677955623346
Harmonic Mean1.05657740596773
Quadratic Mean1.05718208567122
Winsorized Mean ( 1 / 17 )1.056981132075470.00285835045425342369.787102383688
Winsorized Mean ( 2 / 17 )1.056603773584910.00278581567174215379.279858428014
Winsorized Mean ( 3 / 17 )1.056603773584910.00278581567174215379.279858428014
Winsorized Mean ( 4 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 5 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 6 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 7 / 17 )1.057358490566040.00261389253962834404.514904318285
Winsorized Mean ( 8 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 9 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 10 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 11 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 12 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 13 / 17 )1.058867924528300.00234320153257071451.889395687885
Winsorized Mean ( 14 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 15 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 16 / 17 )1.056226415094340.00192806811826628547.815922626271
Winsorized Mean ( 17 / 17 )1.056226415094340.00192806811826628547.815922626271
Trimmed Mean ( 1 / 17 )1.057058823529410.00280467561504921376.891651161899
Trimmed Mean ( 2 / 17 )1.057142857142860.00273550602216097386.452396221649
Trimmed Mean ( 3 / 17 )1.057446808510640.00269422387442318392.486614994841
Trimmed Mean ( 4 / 17 )1.057777777777780.00263789189034356400.993604646934
Trimmed Mean ( 5 / 17 )1.057906976744190.00263207364774261401.929094062964
Trimmed Mean ( 6 / 17 )1.058048780487800.00261840372604682404.081605125583
Trimmed Mean ( 7 / 17 )1.058205128205130.0025942892456029407.897897275215
Trimmed Mean ( 8 / 17 )1.058378378378380.0025560830556957414.062593161831
Trimmed Mean ( 9 / 17 )1.058285714285710.00257609287522805410.810388267554
Trimmed Mean ( 10 / 17 )1.058181818181820.00259130778431622408.358213789352
Trimmed Mean ( 11 / 17 )1.058064516129030.00259939425692763407.042722860987
Trimmed Mean ( 12 / 17 )1.057931034482760.00259685819765462407.388834491710
Trimmed Mean ( 13 / 17 )1.057777777777780.00257830822717921410.260405108755
Trimmed Mean ( 14 / 17 )1.05760.00253508711224421417.184874985913
Trimmed Mean ( 15 / 17 )1.057826086956520.00258885737451586408.607325134836
Trimmed Mean ( 16 / 17 )1.058095238095240.00263845622422763401.028157442702
Trimmed Mean ( 17 / 17 )1.058421052631580.00267795395131119395.234971129116
Median1.06
Midrange1.055
Midmean - Weighted Average at Xnp1.05419354838710
Midmean - Weighted Average at X(n+1)p1.06139534883721
Midmean - Empirical Distribution Function1.06139534883721
Midmean - Empirical Distribution Function - Averaging1.06139534883721
Midmean - Empirical Distribution Function - Interpolation1.06139534883721
Midmean - Closest Observation1.06139534883721
Midmean - True Basic - Statistics Graphics Toolkit1.06139534883721
Midmean - MS Excel (old versions)1.06139534883721
Number of observations53



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')