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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 18 Dec 2007 12:35:08 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/18/t119800549109u1hj2wrzgeerf.htm/, Retrieved Sat, 04 May 2024 08:59:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4579, Retrieved Sat, 04 May 2024 08:59:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

PCTRPM

Estimated Impact

224

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

-       [Central Tendency] [Paper - Central t...] [2007-12-18 19:35:08] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]
-    D    [Central Tendency] [] [2008-12-27 12:06:00] [1aad2bd7746abaf3ab17fe0d80878872] 

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0,09
0,65
-1,53
-3,36
10,51
-1,02
-2,68
-9,75
3,64
9,5
-0,33
-0,99
3,16
4,27
-2,97
-7,49
0,33
-2,57
4,07
5,31
-8,09
5,29
7,38
-6,12
-3,38
-8,61
2,58
10,02
7,08
-2,75
3,42
-1,6
0,65
2,86
-3,52
5,65
4,31
-4,39
-5,85
-5,47
-2,3
-0,14
8,08
-7,43
0,02
-2,47
-2,11
7,87
4,66
3,6
-3,64
7,26
-7,62
13,83
1,28
-0,32
-2,9
4,92
11,99
10,06
-2,22
3,97
0,56
3,34
-2,86
4,38
1,43
-0,49
-1,23

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=4579&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=4579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4579&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.86695652173913	0.639836746026987	1.35496519561032
Geometric Mean	NaN
Harmonic Mean	1.37761650352215
Quadratic Mean	5.34698099838605
Winsorized Mean ( 1 / 23 )	0.856811594202899	0.628539474465498	1.36317865306951
Winsorized Mean ( 2 / 23 )	0.828985507246377	0.614699697435749	1.34860243254476
Winsorized Mean ( 3 / 23 )	0.829855072463768	0.605966163383706	1.36947427531245
Winsorized Mean ( 4 / 23 )	0.835072463768116	0.603910516820888	1.38277516371815
Winsorized Mean ( 5 / 23 )	0.801739130434783	0.594760117580773	1.34800418981675
Winsorized Mean ( 6 / 23 )	0.792173913043478	0.54712173593142	1.44789333162734
Winsorized Mean ( 7 / 23 )	0.798260869565217	0.537941474223506	1.48391768959155
Winsorized Mean ( 8 / 23 )	0.785507246376812	0.519232971586226	1.51282235405262
Winsorized Mean ( 9 / 23 )	0.91072463768116	0.492629145302416	1.84870230753822
Winsorized Mean ( 10 / 23 )	0.993333333333333	0.471204206662296	2.10807399273759
Winsorized Mean ( 11 / 23 )	0.784492753623189	0.427553037657183	1.83484312945568
Winsorized Mean ( 12 / 23 )	0.749710144927536	0.414228602957188	1.80989468031743
Winsorized Mean ( 13 / 23 )	0.749710144927536	0.413067144593523	1.81498372538267
Winsorized Mean ( 14 / 23 )	0.753768115942029	0.389739300227617	1.93403158342464
Winsorized Mean ( 15 / 23 )	0.712463768115942	0.378828195375067	1.88070417359128
Winsorized Mean ( 16 / 23 )	0.656811594202899	0.367714856073823	1.78619814607391
Winsorized Mean ( 17 / 23 )	0.666666666666667	0.361362078615513	1.84487168443592
Winsorized Mean ( 18 / 23 )	0.674492753623188	0.357286146234659	1.88782229798575
Winsorized Mean ( 19 / 23 )	0.649710144927536	0.345026035997849	1.88307570194959
Winsorized Mean ( 20 / 23 )	0.649710144927536	0.336849399503779	1.92878522533999
Winsorized Mean ( 21 / 23 )	0.601014492753623	0.315426688705102	1.90540152204914
Winsorized Mean ( 22 / 23 )	0.613768115942029	0.310181869309178	1.97873627271956
Winsorized Mean ( 23 / 23 )	0.590434782608696	0.296811518234152	1.98925832164945
Trimmed Mean ( 1 / 23 )	0.831940298507463	0.608997152936124	1.36608241023209
Trimmed Mean ( 2 / 23 )	0.805538461538462	0.5855476164196	1.37570103429679
Trimmed Mean ( 3 / 23 )	0.792698412698413	0.566383104544645	1.39957990684718
Trimmed Mean ( 4 / 23 )	0.778688524590164	0.547307541611079	1.42276227785567
Trimmed Mean ( 5 / 23 )	0.762203389830509	0.524821534209594	1.45230967128364
Trimmed Mean ( 6 / 23 )	0.752631578947368	0.500338577490333	1.50424455120475
Trimmed Mean ( 7 / 23 )	0.744363636363636	0.484838809246891	1.53528063795031
Trimmed Mean ( 8 / 23 )	0.73433962264151	0.468100065393739	1.56876633209573
Trimmed Mean ( 9 / 23 )	0.725686274509804	0.45210871978111	1.60511452833988
Trimmed Mean ( 10 / 23 )	0.696734693877551	0.438533656252573	1.58878271700147
Trimmed Mean ( 11 / 23 )	0.696734693877551	0.426175699412734	1.63485317167930
Trimmed Mean ( 12 / 23 )	0.634888888888889	0.420603297131395	1.50947197327974
Trimmed Mean ( 13 / 23 )	0.61953488372093	0.415834156594330	1.48986049822098
Trimmed Mean ( 14 / 23 )	0.602682926829268	0.409214301360344	1.47278070396313
Trimmed Mean ( 15 / 23 )	0.583589743589744	0.405104822605429	1.44058947468556
Trimmed Mean ( 16 / 23 )	0.567567567567568	0.401245135134720	1.41451576073814
Trimmed Mean ( 17 / 23 )	0.556571428571429	0.397641987295135	1.39967972788129
Trimmed Mean ( 18 / 23 )	0.543030303030303	0.393043313609097	1.38160422586498
Trimmed Mean ( 19 / 23 )	0.526774193548387	0.386391741462307	1.36331638858222
Trimmed Mean ( 20 / 23 )	0.511379310344828	0.379097230771738	1.34893971476341
Trimmed Mean ( 21 / 23 )	0.493703703703704	0.369486495189848	1.33618876503194
Trimmed Mean ( 22 / 23 )	0.493703703703704	0.360851529949184	1.36816297764687
Trimmed Mean ( 23 / 23 )	0.461304347826087	0.347480658515865	1.32756841717861
Median	0.09
Midrange	2.04
Midmean - Weighted Average at Xnp	0.446176470588235
Midmean - Weighted Average at X(n+1)p	0.556571428571428
Midmean - Empirical Distribution Function	0.556571428571428
Midmean - Empirical Distribution Function - Averaging	0.556571428571428
Midmean - Empirical Distribution Function - Interpolation	0.556571428571428
Midmean - Closest Observation	0.461666666666667
Midmean - True Basic - Statistics Graphics Toolkit	0.556571428571428
Midmean - MS Excel (old versions)	0.556571428571428
Number of observations	69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.86695652173913 & 0.639836746026987 & 1.35496519561032 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1.37761650352215 &  &  \tabularnewline
Quadratic Mean & 5.34698099838605 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 0.856811594202899 & 0.628539474465498 & 1.36317865306951 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 0.828985507246377 & 0.614699697435749 & 1.34860243254476 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 0.829855072463768 & 0.605966163383706 & 1.36947427531245 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 0.835072463768116 & 0.603910516820888 & 1.38277516371815 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 0.801739130434783 & 0.594760117580773 & 1.34800418981675 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 0.792173913043478 & 0.54712173593142 & 1.44789333162734 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 0.798260869565217 & 0.537941474223506 & 1.48391768959155 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 0.785507246376812 & 0.519232971586226 & 1.51282235405262 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 0.91072463768116 & 0.492629145302416 & 1.84870230753822 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 0.993333333333333 & 0.471204206662296 & 2.10807399273759 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 0.784492753623189 & 0.427553037657183 & 1.83484312945568 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 0.749710144927536 & 0.414228602957188 & 1.80989468031743 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 0.749710144927536 & 0.413067144593523 & 1.81498372538267 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 0.753768115942029 & 0.389739300227617 & 1.93403158342464 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 0.712463768115942 & 0.378828195375067 & 1.88070417359128 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 0.656811594202899 & 0.367714856073823 & 1.78619814607391 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 0.666666666666667 & 0.361362078615513 & 1.84487168443592 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 0.674492753623188 & 0.357286146234659 & 1.88782229798575 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 0.649710144927536 & 0.345026035997849 & 1.88307570194959 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 0.649710144927536 & 0.336849399503779 & 1.92878522533999 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 0.601014492753623 & 0.315426688705102 & 1.90540152204914 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 0.613768115942029 & 0.310181869309178 & 1.97873627271956 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 0.590434782608696 & 0.296811518234152 & 1.98925832164945 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 0.831940298507463 & 0.608997152936124 & 1.36608241023209 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 0.805538461538462 & 0.5855476164196 & 1.37570103429679 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 0.792698412698413 & 0.566383104544645 & 1.39957990684718 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 0.778688524590164 & 0.547307541611079 & 1.42276227785567 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 0.762203389830509 & 0.524821534209594 & 1.45230967128364 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 0.752631578947368 & 0.500338577490333 & 1.50424455120475 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 0.744363636363636 & 0.484838809246891 & 1.53528063795031 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 0.73433962264151 & 0.468100065393739 & 1.56876633209573 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 0.725686274509804 & 0.45210871978111 & 1.60511452833988 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 0.696734693877551 & 0.438533656252573 & 1.58878271700147 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 0.696734693877551 & 0.426175699412734 & 1.63485317167930 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 0.634888888888889 & 0.420603297131395 & 1.50947197327974 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 0.61953488372093 & 0.415834156594330 & 1.48986049822098 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 0.602682926829268 & 0.409214301360344 & 1.47278070396313 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 0.583589743589744 & 0.405104822605429 & 1.44058947468556 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 0.567567567567568 & 0.401245135134720 & 1.41451576073814 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 0.556571428571429 & 0.397641987295135 & 1.39967972788129 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 0.543030303030303 & 0.393043313609097 & 1.38160422586498 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 0.526774193548387 & 0.386391741462307 & 1.36331638858222 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 0.511379310344828 & 0.379097230771738 & 1.34893971476341 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 0.493703703703704 & 0.369486495189848 & 1.33618876503194 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 0.493703703703704 & 0.360851529949184 & 1.36816297764687 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 0.461304347826087 & 0.347480658515865 & 1.32756841717861 \tabularnewline
Median & 0.09 &  &  \tabularnewline
Midrange & 2.04 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.446176470588235 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.556571428571428 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.556571428571428 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.556571428571428 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.556571428571428 &  &  \tabularnewline
Midmean - Closest Observation & 0.461666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.556571428571428 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.556571428571428 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4579&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]0.86695652173913[/C][C]0.639836746026987[/C][C]1.35496519561032[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.37761650352215[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.34698099838605[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]0.856811594202899[/C][C]0.628539474465498[/C][C]1.36317865306951[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]0.828985507246377[/C][C]0.614699697435749[/C][C]1.34860243254476[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]0.829855072463768[/C][C]0.605966163383706[/C][C]1.36947427531245[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]0.835072463768116[/C][C]0.603910516820888[/C][C]1.38277516371815[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]0.801739130434783[/C][C]0.594760117580773[/C][C]1.34800418981675[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]0.792173913043478[/C][C]0.54712173593142[/C][C]1.44789333162734[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]0.798260869565217[/C][C]0.537941474223506[/C][C]1.48391768959155[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]0.785507246376812[/C][C]0.519232971586226[/C][C]1.51282235405262[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]0.91072463768116[/C][C]0.492629145302416[/C][C]1.84870230753822[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]0.993333333333333[/C][C]0.471204206662296[/C][C]2.10807399273759[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]0.784492753623189[/C][C]0.427553037657183[/C][C]1.83484312945568[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]0.749710144927536[/C][C]0.414228602957188[/C][C]1.80989468031743[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]0.749710144927536[/C][C]0.413067144593523[/C][C]1.81498372538267[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]0.753768115942029[/C][C]0.389739300227617[/C][C]1.93403158342464[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]0.712463768115942[/C][C]0.378828195375067[/C][C]1.88070417359128[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]0.656811594202899[/C][C]0.367714856073823[/C][C]1.78619814607391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]0.666666666666667[/C][C]0.361362078615513[/C][C]1.84487168443592[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]0.674492753623188[/C][C]0.357286146234659[/C][C]1.88782229798575[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]0.649710144927536[/C][C]0.345026035997849[/C][C]1.88307570194959[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]0.649710144927536[/C][C]0.336849399503779[/C][C]1.92878522533999[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]0.601014492753623[/C][C]0.315426688705102[/C][C]1.90540152204914[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]0.613768115942029[/C][C]0.310181869309178[/C][C]1.97873627271956[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]0.590434782608696[/C][C]0.296811518234152[/C][C]1.98925832164945[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]0.831940298507463[/C][C]0.608997152936124[/C][C]1.36608241023209[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]0.805538461538462[/C][C]0.5855476164196[/C][C]1.37570103429679[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]0.792698412698413[/C][C]0.566383104544645[/C][C]1.39957990684718[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]0.778688524590164[/C][C]0.547307541611079[/C][C]1.42276227785567[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]0.762203389830509[/C][C]0.524821534209594[/C][C]1.45230967128364[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]0.752631578947368[/C][C]0.500338577490333[/C][C]1.50424455120475[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]0.744363636363636[/C][C]0.484838809246891[/C][C]1.53528063795031[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]0.73433962264151[/C][C]0.468100065393739[/C][C]1.56876633209573[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]0.725686274509804[/C][C]0.45210871978111[/C][C]1.60511452833988[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]0.696734693877551[/C][C]0.438533656252573[/C][C]1.58878271700147[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]0.696734693877551[/C][C]0.426175699412734[/C][C]1.63485317167930[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]0.634888888888889[/C][C]0.420603297131395[/C][C]1.50947197327974[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]0.61953488372093[/C][C]0.415834156594330[/C][C]1.48986049822098[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]0.602682926829268[/C][C]0.409214301360344[/C][C]1.47278070396313[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]0.583589743589744[/C][C]0.405104822605429[/C][C]1.44058947468556[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]0.567567567567568[/C][C]0.401245135134720[/C][C]1.41451576073814[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]0.556571428571429[/C][C]0.397641987295135[/C][C]1.39967972788129[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]0.543030303030303[/C][C]0.393043313609097[/C][C]1.38160422586498[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]0.526774193548387[/C][C]0.386391741462307[/C][C]1.36331638858222[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]0.511379310344828[/C][C]0.379097230771738[/C][C]1.34893971476341[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]0.493703703703704[/C][C]0.369486495189848[/C][C]1.33618876503194[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]0.493703703703704[/C][C]0.360851529949184[/C][C]1.36816297764687[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]0.461304347826087[/C][C]0.347480658515865[/C][C]1.32756841717861[/C][/ROW]
[ROW][C]Median[/C][C]0.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.446176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.461666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.556571428571428[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4579&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	0.86695652173913	0.639836746026987	1.35496519561032
Geometric Mean	NaN
Harmonic Mean	1.37761650352215
Quadratic Mean	5.34698099838605
Winsorized Mean ( 1 / 23 )	0.856811594202899	0.628539474465498	1.36317865306951
Winsorized Mean ( 2 / 23 )	0.828985507246377	0.614699697435749	1.34860243254476
Winsorized Mean ( 3 / 23 )	0.829855072463768	0.605966163383706	1.36947427531245
Winsorized Mean ( 4 / 23 )	0.835072463768116	0.603910516820888	1.38277516371815
Winsorized Mean ( 5 / 23 )	0.801739130434783	0.594760117580773	1.34800418981675
Winsorized Mean ( 6 / 23 )	0.792173913043478	0.54712173593142	1.44789333162734
Winsorized Mean ( 7 / 23 )	0.798260869565217	0.537941474223506	1.48391768959155
Winsorized Mean ( 8 / 23 )	0.785507246376812	0.519232971586226	1.51282235405262
Winsorized Mean ( 9 / 23 )	0.91072463768116	0.492629145302416	1.84870230753822
Winsorized Mean ( 10 / 23 )	0.993333333333333	0.471204206662296	2.10807399273759
Winsorized Mean ( 11 / 23 )	0.784492753623189	0.427553037657183	1.83484312945568
Winsorized Mean ( 12 / 23 )	0.749710144927536	0.414228602957188	1.80989468031743
Winsorized Mean ( 13 / 23 )	0.749710144927536	0.413067144593523	1.81498372538267
Winsorized Mean ( 14 / 23 )	0.753768115942029	0.389739300227617	1.93403158342464
Winsorized Mean ( 15 / 23 )	0.712463768115942	0.378828195375067	1.88070417359128
Winsorized Mean ( 16 / 23 )	0.656811594202899	0.367714856073823	1.78619814607391
Winsorized Mean ( 17 / 23 )	0.666666666666667	0.361362078615513	1.84487168443592
Winsorized Mean ( 18 / 23 )	0.674492753623188	0.357286146234659	1.88782229798575
Winsorized Mean ( 19 / 23 )	0.649710144927536	0.345026035997849	1.88307570194959
Winsorized Mean ( 20 / 23 )	0.649710144927536	0.336849399503779	1.92878522533999
Winsorized Mean ( 21 / 23 )	0.601014492753623	0.315426688705102	1.90540152204914
Winsorized Mean ( 22 / 23 )	0.613768115942029	0.310181869309178	1.97873627271956
Winsorized Mean ( 23 / 23 )	0.590434782608696	0.296811518234152	1.98925832164945
Trimmed Mean ( 1 / 23 )	0.831940298507463	0.608997152936124	1.36608241023209
Trimmed Mean ( 2 / 23 )	0.805538461538462	0.5855476164196	1.37570103429679
Trimmed Mean ( 3 / 23 )	0.792698412698413	0.566383104544645	1.39957990684718
Trimmed Mean ( 4 / 23 )	0.778688524590164	0.547307541611079	1.42276227785567
Trimmed Mean ( 5 / 23 )	0.762203389830509	0.524821534209594	1.45230967128364
Trimmed Mean ( 6 / 23 )	0.752631578947368	0.500338577490333	1.50424455120475
Trimmed Mean ( 7 / 23 )	0.744363636363636	0.484838809246891	1.53528063795031
Trimmed Mean ( 8 / 23 )	0.73433962264151	0.468100065393739	1.56876633209573
Trimmed Mean ( 9 / 23 )	0.725686274509804	0.45210871978111	1.60511452833988
Trimmed Mean ( 10 / 23 )	0.696734693877551	0.438533656252573	1.58878271700147
Trimmed Mean ( 11 / 23 )	0.696734693877551	0.426175699412734	1.63485317167930
Trimmed Mean ( 12 / 23 )	0.634888888888889	0.420603297131395	1.50947197327974
Trimmed Mean ( 13 / 23 )	0.61953488372093	0.415834156594330	1.48986049822098
Trimmed Mean ( 14 / 23 )	0.602682926829268	0.409214301360344	1.47278070396313
Trimmed Mean ( 15 / 23 )	0.583589743589744	0.405104822605429	1.44058947468556
Trimmed Mean ( 16 / 23 )	0.567567567567568	0.401245135134720	1.41451576073814
Trimmed Mean ( 17 / 23 )	0.556571428571429	0.397641987295135	1.39967972788129
Trimmed Mean ( 18 / 23 )	0.543030303030303	0.393043313609097	1.38160422586498
Trimmed Mean ( 19 / 23 )	0.526774193548387	0.386391741462307	1.36331638858222
Trimmed Mean ( 20 / 23 )	0.511379310344828	0.379097230771738	1.34893971476341
Trimmed Mean ( 21 / 23 )	0.493703703703704	0.369486495189848	1.33618876503194
Trimmed Mean ( 22 / 23 )	0.493703703703704	0.360851529949184	1.36816297764687
Trimmed Mean ( 23 / 23 )	0.461304347826087	0.347480658515865	1.32756841717861
Median	0.09
Midrange	2.04
Midmean - Weighted Average at Xnp	0.446176470588235
Midmean - Weighted Average at X(n+1)p	0.556571428571428
Midmean - Empirical Distribution Function	0.556571428571428
Midmean - Empirical Distribution Function - Averaging	0.556571428571428
Midmean - Empirical Distribution Function - Interpolation	0.556571428571428
Midmean - Closest Observation	0.461666666666667
Midmean - True Basic - Statistics Graphics Toolkit	0.556571428571428
Midmean - MS Excel (old versions)	0.556571428571428
Number of observations	69

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