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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 24 Feb 2014 17:15:44 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/24/t1393280177a5f4ysyo3gkn26n.htm/, Retrieved Thu, 16 May 2024 22:32:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234037, Retrieved Thu, 16 May 2024 22:32:58 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [indicator consume...] [2014-02-24 22:15:44] [7e257b479a74cf54c1843b0823401607] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234037&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234037&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	-1.93150684931507	1.38544411321366	-1.39414273798079
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	11.9135010324134
Winsorized Mean ( 1 / 24 )	-1.93150684931507	1.37980222248784	-1.39984326582145
Winsorized Mean ( 2 / 24 )	-1.9041095890411	1.37383746116351	-1.38597879506684
Winsorized Mean ( 3 / 24 )	-1.9041095890411	1.35795816366426	-1.40218575210234
Winsorized Mean ( 4 / 24 )	-1.95890410958904	1.34871808410141	-1.45241925105065
Winsorized Mean ( 5 / 24 )	-1.95890410958904	1.34871808410141	-1.45241925105065
Winsorized Mean ( 6 / 24 )	-1.79452054794521	1.31594814567737	-1.36367117035717
Winsorized Mean ( 7 / 24 )	-1.79452054794521	1.28211543112651	-1.3996559938199
Winsorized Mean ( 8 / 24 )	-1.68493150684932	1.26206155072229	-1.33506286273044
Winsorized Mean ( 9 / 24 )	-1.68493150684932	1.26206155072229	-1.33506286273044
Winsorized Mean ( 10 / 24 )	-1.68493150684932	1.21599510964066	-1.38564003546629
Winsorized Mean ( 11 / 24 )	-1.68493150684932	1.21599510964066	-1.38564003546629
Winsorized Mean ( 12 / 24 )	-1.68493150684932	1.16223501297778	-1.4497339075445
Winsorized Mean ( 13 / 24 )	-1.68493150684932	1.1055203793261	-1.52410714298765
Winsorized Mean ( 14 / 24 )	-1.68493150684932	1.04609819224907	-1.61068197931475
Winsorized Mean ( 15 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 16 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 17 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 18 / 24 )	-1.84931506849315	0.949980219468168	-1.94668797370166
Winsorized Mean ( 19 / 24 )	-1.06849315068493	0.827451564135688	-1.29130597728826
Winsorized Mean ( 20 / 24 )	-1.06849315068493	0.827451564135688	-1.29130597728826
Winsorized Mean ( 21 / 24 )	-1.06849315068493	0.746205206167886	-1.43190256762231
Winsorized Mean ( 22 / 24 )	-1.36986301369863	0.707512107698505	-1.93616900515627
Winsorized Mean ( 23 / 24 )	-1.05479452054795	0.660902711312322	-1.59599060874405
Winsorized Mean ( 24 / 24 )	-0.397260273972603	0.567626009728785	-0.699862703899731
Trimmed Mean ( 1 / 24 )	-1.87323943661972	1.36039548893097	-1.37698151152482
Trimmed Mean ( 2 / 24 )	-1.81159420289855	1.3371017763838	-1.35486634966414
Trimmed Mean ( 3 / 24 )	-1.76119402985075	1.31289563867262	-1.34145775031393
Trimmed Mean ( 4 / 24 )	-1.70769230769231	1.29081873930908	-1.32295283271636
Trimmed Mean ( 5 / 24 )	-1.63492063492063	1.26723683248497	-1.29014608241354
Trimmed Mean ( 6 / 24 )	-1.55737704918033	1.23839411926297	-1.25757787844406
Trimmed Mean ( 7 / 24 )	-1.50847457627119	1.21248446370494	-1.2441186847556
Trimmed Mean ( 8 / 24 )	-1.45614035087719	1.18920325032164	-1.22446718042803
Trimmed Mean ( 9 / 24 )	-1.41818181818182	1.16506120678247	-1.21725949669064
Trimmed Mean ( 10 / 24 )	-1.37735849056604	1.13469701303441	-1.21385574716787
Trimmed Mean ( 11 / 24 )	-1.33333333333333	1.10707764634315	-1.2043720128733
Trimmed Mean ( 12 / 24 )	-1.28571428571429	1.07182532336642	-1.19955580231682
Trimmed Mean ( 13 / 24 )	-1.23404255319149	1.03911153875312	-1.18759392728164
Trimmed Mean ( 14 / 24 )	-1.17777777777778	1.00969486784394	-1.1664690148349
Trimmed Mean ( 15 / 24 )	-1.11627906976744	0.984491764101227	-1.13386328913226
Trimmed Mean ( 16 / 24 )	-1	0.962086147960546	-1.03940795958847
Trimmed Mean ( 17 / 24 )	-0.871794871794872	0.930934468181241	-0.936472868491044
Trimmed Mean ( 18 / 24 )	-0.72972972972973	0.887558862108131	-0.822176151783866
Trimmed Mean ( 19 / 24 )	-0.6	0.839367508976879	-0.714823952062847
Trimmed Mean ( 20 / 24 )	-0.545454545454545	0.809614233207131	-0.673721536853215
Trimmed Mean ( 21 / 24 )	-0.483870967741935	0.766041307937456	-0.631651273538687
Trimmed Mean ( 22 / 24 )	-0.413793103448276	0.728581254076307	-0.567943659177563
Trimmed Mean ( 23 / 24 )	-0.296296296296296	0.683160943055355	-0.433713752679049
Trimmed Mean ( 24 / 24 )	-0.2	0.632455532033676	-0.316227766016838
Median	0
Midrange	-4
Midmean - Weighted Average at Xnp	-0.15
Midmean - Weighted Average at X(n+1)p	-0.15
Midmean - Empirical Distribution Function	-0.15
Midmean - Empirical Distribution Function - Averaging	-0.15
Midmean - Empirical Distribution Function - Interpolation	-0.15
Midmean - Closest Observation	-1.40909090909091
Midmean - True Basic - Statistics Graphics Toolkit	-0.15
Midmean - MS Excel (old versions)	-0.15
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -1.93150684931507 & 1.38544411321366 & -1.39414273798079 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 11.9135010324134 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -1.93150684931507 & 1.37980222248784 & -1.39984326582145 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -1.9041095890411 & 1.37383746116351 & -1.38597879506684 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -1.9041095890411 & 1.35795816366426 & -1.40218575210234 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -1.95890410958904 & 1.34871808410141 & -1.45241925105065 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -1.95890410958904 & 1.34871808410141 & -1.45241925105065 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -1.79452054794521 & 1.31594814567737 & -1.36367117035717 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -1.79452054794521 & 1.28211543112651 & -1.3996559938199 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -1.68493150684932 & 1.26206155072229 & -1.33506286273044 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -1.68493150684932 & 1.26206155072229 & -1.33506286273044 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -1.68493150684932 & 1.21599510964066 & -1.38564003546629 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -1.68493150684932 & 1.21599510964066 & -1.38564003546629 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -1.68493150684932 & 1.16223501297778 & -1.4497339075445 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -1.68493150684932 & 1.1055203793261 & -1.52410714298765 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -1.68493150684932 & 1.04609819224907 & -1.61068197931475 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -2.0958904109589 & 0.990665025695411 & -2.11563985463973 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -2.0958904109589 & 0.990665025695411 & -2.11563985463973 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -2.0958904109589 & 0.990665025695411 & -2.11563985463973 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -1.84931506849315 & 0.949980219468168 & -1.94668797370166 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -1.06849315068493 & 0.827451564135688 & -1.29130597728826 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -1.06849315068493 & 0.827451564135688 & -1.29130597728826 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -1.06849315068493 & 0.746205206167886 & -1.43190256762231 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -1.36986301369863 & 0.707512107698505 & -1.93616900515627 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -1.05479452054795 & 0.660902711312322 & -1.59599060874405 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -0.397260273972603 & 0.567626009728785 & -0.699862703899731 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -1.87323943661972 & 1.36039548893097 & -1.37698151152482 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -1.81159420289855 & 1.3371017763838 & -1.35486634966414 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -1.76119402985075 & 1.31289563867262 & -1.34145775031393 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -1.70769230769231 & 1.29081873930908 & -1.32295283271636 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -1.63492063492063 & 1.26723683248497 & -1.29014608241354 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -1.55737704918033 & 1.23839411926297 & -1.25757787844406 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -1.50847457627119 & 1.21248446370494 & -1.2441186847556 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -1.45614035087719 & 1.18920325032164 & -1.22446718042803 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -1.41818181818182 & 1.16506120678247 & -1.21725949669064 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -1.37735849056604 & 1.13469701303441 & -1.21385574716787 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -1.33333333333333 & 1.10707764634315 & -1.2043720128733 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -1.28571428571429 & 1.07182532336642 & -1.19955580231682 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -1.23404255319149 & 1.03911153875312 & -1.18759392728164 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -1.17777777777778 & 1.00969486784394 & -1.1664690148349 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -1.11627906976744 & 0.984491764101227 & -1.13386328913226 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -1 & 0.962086147960546 & -1.03940795958847 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -0.871794871794872 & 0.930934468181241 & -0.936472868491044 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -0.72972972972973 & 0.887558862108131 & -0.822176151783866 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -0.6 & 0.839367508976879 & -0.714823952062847 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -0.545454545454545 & 0.809614233207131 & -0.673721536853215 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -0.483870967741935 & 0.766041307937456 & -0.631651273538687 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -0.413793103448276 & 0.728581254076307 & -0.567943659177563 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -0.296296296296296 & 0.683160943055355 & -0.433713752679049 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -0.2 & 0.632455532033676 & -0.316227766016838 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & -4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.15 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.15 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.15 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.15 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.15 &  &  \tabularnewline
Midmean - Closest Observation & -1.40909090909091 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.15 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.15 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234037&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]-1.93150684931507[/C][C]1.38544411321366[/C][C]-1.39414273798079[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.9135010324134[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-1.93150684931507[/C][C]1.37980222248784[/C][C]-1.39984326582145[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-1.9041095890411[/C][C]1.37383746116351[/C][C]-1.38597879506684[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-1.9041095890411[/C][C]1.35795816366426[/C][C]-1.40218575210234[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-1.95890410958904[/C][C]1.34871808410141[/C][C]-1.45241925105065[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-1.95890410958904[/C][C]1.34871808410141[/C][C]-1.45241925105065[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-1.79452054794521[/C][C]1.31594814567737[/C][C]-1.36367117035717[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-1.79452054794521[/C][C]1.28211543112651[/C][C]-1.3996559938199[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-1.68493150684932[/C][C]1.26206155072229[/C][C]-1.33506286273044[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-1.68493150684932[/C][C]1.26206155072229[/C][C]-1.33506286273044[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-1.68493150684932[/C][C]1.21599510964066[/C][C]-1.38564003546629[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-1.68493150684932[/C][C]1.21599510964066[/C][C]-1.38564003546629[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-1.68493150684932[/C][C]1.16223501297778[/C][C]-1.4497339075445[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-1.68493150684932[/C][C]1.1055203793261[/C][C]-1.52410714298765[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-1.68493150684932[/C][C]1.04609819224907[/C][C]-1.61068197931475[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-2.0958904109589[/C][C]0.990665025695411[/C][C]-2.11563985463973[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-2.0958904109589[/C][C]0.990665025695411[/C][C]-2.11563985463973[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-2.0958904109589[/C][C]0.990665025695411[/C][C]-2.11563985463973[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-1.84931506849315[/C][C]0.949980219468168[/C][C]-1.94668797370166[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-1.06849315068493[/C][C]0.827451564135688[/C][C]-1.29130597728826[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-1.06849315068493[/C][C]0.827451564135688[/C][C]-1.29130597728826[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-1.06849315068493[/C][C]0.746205206167886[/C][C]-1.43190256762231[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-1.36986301369863[/C][C]0.707512107698505[/C][C]-1.93616900515627[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-1.05479452054795[/C][C]0.660902711312322[/C][C]-1.59599060874405[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-0.397260273972603[/C][C]0.567626009728785[/C][C]-0.699862703899731[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-1.87323943661972[/C][C]1.36039548893097[/C][C]-1.37698151152482[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-1.81159420289855[/C][C]1.3371017763838[/C][C]-1.35486634966414[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-1.76119402985075[/C][C]1.31289563867262[/C][C]-1.34145775031393[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-1.70769230769231[/C][C]1.29081873930908[/C][C]-1.32295283271636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-1.63492063492063[/C][C]1.26723683248497[/C][C]-1.29014608241354[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-1.55737704918033[/C][C]1.23839411926297[/C][C]-1.25757787844406[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-1.50847457627119[/C][C]1.21248446370494[/C][C]-1.2441186847556[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-1.45614035087719[/C][C]1.18920325032164[/C][C]-1.22446718042803[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-1.41818181818182[/C][C]1.16506120678247[/C][C]-1.21725949669064[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-1.37735849056604[/C][C]1.13469701303441[/C][C]-1.21385574716787[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-1.33333333333333[/C][C]1.10707764634315[/C][C]-1.2043720128733[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-1.28571428571429[/C][C]1.07182532336642[/C][C]-1.19955580231682[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-1.23404255319149[/C][C]1.03911153875312[/C][C]-1.18759392728164[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-1.17777777777778[/C][C]1.00969486784394[/C][C]-1.1664690148349[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-1.11627906976744[/C][C]0.984491764101227[/C][C]-1.13386328913226[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-1[/C][C]0.962086147960546[/C][C]-1.03940795958847[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-0.871794871794872[/C][C]0.930934468181241[/C][C]-0.936472868491044[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-0.72972972972973[/C][C]0.887558862108131[/C][C]-0.822176151783866[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-0.6[/C][C]0.839367508976879[/C][C]-0.714823952062847[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-0.545454545454545[/C][C]0.809614233207131[/C][C]-0.673721536853215[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-0.483870967741935[/C][C]0.766041307937456[/C][C]-0.631651273538687[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-0.413793103448276[/C][C]0.728581254076307[/C][C]-0.567943659177563[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-0.296296296296296[/C][C]0.683160943055355[/C][C]-0.433713752679049[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-0.2[/C][C]0.632455532033676[/C][C]-0.316227766016838[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-1.40909090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234037&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	-1.93150684931507	1.38544411321366	-1.39414273798079
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	11.9135010324134
Winsorized Mean ( 1 / 24 )	-1.93150684931507	1.37980222248784	-1.39984326582145
Winsorized Mean ( 2 / 24 )	-1.9041095890411	1.37383746116351	-1.38597879506684
Winsorized Mean ( 3 / 24 )	-1.9041095890411	1.35795816366426	-1.40218575210234
Winsorized Mean ( 4 / 24 )	-1.95890410958904	1.34871808410141	-1.45241925105065
Winsorized Mean ( 5 / 24 )	-1.95890410958904	1.34871808410141	-1.45241925105065
Winsorized Mean ( 6 / 24 )	-1.79452054794521	1.31594814567737	-1.36367117035717
Winsorized Mean ( 7 / 24 )	-1.79452054794521	1.28211543112651	-1.3996559938199
Winsorized Mean ( 8 / 24 )	-1.68493150684932	1.26206155072229	-1.33506286273044
Winsorized Mean ( 9 / 24 )	-1.68493150684932	1.26206155072229	-1.33506286273044
Winsorized Mean ( 10 / 24 )	-1.68493150684932	1.21599510964066	-1.38564003546629
Winsorized Mean ( 11 / 24 )	-1.68493150684932	1.21599510964066	-1.38564003546629
Winsorized Mean ( 12 / 24 )	-1.68493150684932	1.16223501297778	-1.4497339075445
Winsorized Mean ( 13 / 24 )	-1.68493150684932	1.1055203793261	-1.52410714298765
Winsorized Mean ( 14 / 24 )	-1.68493150684932	1.04609819224907	-1.61068197931475
Winsorized Mean ( 15 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 16 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 17 / 24 )	-2.0958904109589	0.990665025695411	-2.11563985463973
Winsorized Mean ( 18 / 24 )	-1.84931506849315	0.949980219468168	-1.94668797370166
Winsorized Mean ( 19 / 24 )	-1.06849315068493	0.827451564135688	-1.29130597728826
Winsorized Mean ( 20 / 24 )	-1.06849315068493	0.827451564135688	-1.29130597728826
Winsorized Mean ( 21 / 24 )	-1.06849315068493	0.746205206167886	-1.43190256762231
Winsorized Mean ( 22 / 24 )	-1.36986301369863	0.707512107698505	-1.93616900515627
Winsorized Mean ( 23 / 24 )	-1.05479452054795	0.660902711312322	-1.59599060874405
Winsorized Mean ( 24 / 24 )	-0.397260273972603	0.567626009728785	-0.699862703899731
Trimmed Mean ( 1 / 24 )	-1.87323943661972	1.36039548893097	-1.37698151152482
Trimmed Mean ( 2 / 24 )	-1.81159420289855	1.3371017763838	-1.35486634966414
Trimmed Mean ( 3 / 24 )	-1.76119402985075	1.31289563867262	-1.34145775031393
Trimmed Mean ( 4 / 24 )	-1.70769230769231	1.29081873930908	-1.32295283271636
Trimmed Mean ( 5 / 24 )	-1.63492063492063	1.26723683248497	-1.29014608241354
Trimmed Mean ( 6 / 24 )	-1.55737704918033	1.23839411926297	-1.25757787844406
Trimmed Mean ( 7 / 24 )	-1.50847457627119	1.21248446370494	-1.2441186847556
Trimmed Mean ( 8 / 24 )	-1.45614035087719	1.18920325032164	-1.22446718042803
Trimmed Mean ( 9 / 24 )	-1.41818181818182	1.16506120678247	-1.21725949669064
Trimmed Mean ( 10 / 24 )	-1.37735849056604	1.13469701303441	-1.21385574716787
Trimmed Mean ( 11 / 24 )	-1.33333333333333	1.10707764634315	-1.2043720128733
Trimmed Mean ( 12 / 24 )	-1.28571428571429	1.07182532336642	-1.19955580231682
Trimmed Mean ( 13 / 24 )	-1.23404255319149	1.03911153875312	-1.18759392728164
Trimmed Mean ( 14 / 24 )	-1.17777777777778	1.00969486784394	-1.1664690148349
Trimmed Mean ( 15 / 24 )	-1.11627906976744	0.984491764101227	-1.13386328913226
Trimmed Mean ( 16 / 24 )	-1	0.962086147960546	-1.03940795958847
Trimmed Mean ( 17 / 24 )	-0.871794871794872	0.930934468181241	-0.936472868491044
Trimmed Mean ( 18 / 24 )	-0.72972972972973	0.887558862108131	-0.822176151783866
Trimmed Mean ( 19 / 24 )	-0.6	0.839367508976879	-0.714823952062847
Trimmed Mean ( 20 / 24 )	-0.545454545454545	0.809614233207131	-0.673721536853215
Trimmed Mean ( 21 / 24 )	-0.483870967741935	0.766041307937456	-0.631651273538687
Trimmed Mean ( 22 / 24 )	-0.413793103448276	0.728581254076307	-0.567943659177563
Trimmed Mean ( 23 / 24 )	-0.296296296296296	0.683160943055355	-0.433713752679049
Trimmed Mean ( 24 / 24 )	-0.2	0.632455532033676	-0.316227766016838
Median	0
Midrange	-4
Midmean - Weighted Average at Xnp	-0.15
Midmean - Weighted Average at X(n+1)p	-0.15
Midmean - Empirical Distribution Function	-0.15
Midmean - Empirical Distribution Function - Averaging	-0.15
Midmean - Empirical Distribution Function - Interpolation	-0.15
Midmean - Closest Observation	-1.40909090909091
Midmean - True Basic - Statistics Graphics Toolkit	-0.15
Midmean - MS Excel (old versions)	-0.15
Number of observations	73

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code