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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 05 Mar 2013 05:17:22 -0500

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/2013/Mar/05/t13624787953axf8w3rvnlv4my.htm/, Retrieved Sat, 04 May 2024 18:57:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207359, Retrieved Sat, 04 May 2024 18:57:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

122

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

-       [Central Tendency] [robustness of cen...] [2013-03-05 10:17:22] [86531c41dade6c5b3fb1cb68f8179a3e] [Current]

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Dataseries X:

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2,27
2,35
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07
3,07

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207359&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207359&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.71763888888889	0.0240991797336004	112.768937321954
Geometric Mean	2.71019954515687
Harmonic Mean	2.70291332408267
Quadratic Mean	2.72521482333656
Winsorized Mean ( 1 / 24 )	2.71875	0.0238326336119748	114.076775746427
Winsorized Mean ( 2 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 3 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 4 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 5 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 6 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 7 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 8 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 9 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 10 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 11 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 12 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 13 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 14 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 15 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 16 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 17 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 18 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 19 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 20 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 21 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 22 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 23 / 24 )	2.61833333333333	0.00678013761222356	386.177019270652
Winsorized Mean ( 24 / 24 )	2.61833333333333	0.00678013761222356	386.177019270652
Trimmed Mean ( 1 / 24 )	2.719	0.0233978551865164	116.207232599973
Trimmed Mean ( 2 / 24 )	2.71926470588235	0.0228791497878804	118.853398447647
Trimmed Mean ( 3 / 24 )	2.71666666666667	0.0227956701950739	119.174678498978
Trimmed Mean ( 4 / 24 )	2.71390625	0.0226730746232624	119.697319181209
Trimmed Mean ( 5 / 24 )	2.71096774193548	0.0225029637596996	120.471586360128
Trimmed Mean ( 6 / 24 )	2.70783333333333	0.022274724936531	121.565287160625
Trimmed Mean ( 7 / 24 )	2.70448275862069	0.0219747592292083	123.072236214809
Trimmed Mean ( 8 / 24 )	2.70089285714286	0.0215853437315096	125.126238003807
Trimmed Mean ( 9 / 24 )	2.69703703703704	0.0210828945764037	127.925367518349
Trimmed Mean ( 10 / 24 )	2.69288461538462	0.0204351908240835	131.776827462309
Trimmed Mean ( 11 / 24 )	2.6912	0.020481230830361	131.398353072151
Trimmed Mean ( 12 / 24 )	2.689375	0.0204956452951311	131.216898090975
Trimmed Mean ( 13 / 24 )	2.68739130434783	0.0204689815586694	131.290914335189
Trimmed Mean ( 14 / 24 )	2.68522727272727	0.0203886358834657	131.702154478362
Trimmed Mean ( 15 / 24 )	2.68285714285714	0.0202375145096704	132.56850991139
Trimmed Mean ( 16 / 24 )	2.68025	0.0199919454935078	134.066491971499
Trimmed Mean ( 17 / 24 )	2.67736842105263	0.0196182783037301	136.473159346688
Trimmed Mean ( 18 / 24 )	2.67416666666667	0.0190670288010898	140.250832710434
Trimmed Mean ( 19 / 24 )	2.67058823529412	0.018262012511636	146.237345615249
Trimmed Mean ( 20 / 24 )	2.6665625	0.0170779131022329	156.141004116677
Trimmed Mean ( 21 / 24 )	2.662	0.0152857833431523	174.1487459452
Trimmed Mean ( 22 / 24 )	2.65678571428571	0.0123769453222596	214.65601124597
Trimmed Mean ( 23 / 24 )	2.65076923076923	0.00639526452025432	414.489380755718
Trimmed Mean ( 24 / 24 )	2.655	0.00500000000000001	530.999999999999
Median	2.66
Midrange	2.67
Midmean - Weighted Average at Xnp	2.6725
Midmean - Weighted Average at X(n+1)p	2.6725
Midmean - Empirical Distribution Function	2.6725
Midmean - Empirical Distribution Function - Averaging	2.6725
Midmean - Empirical Distribution Function - Interpolation	2.6725
Midmean - Closest Observation	2.6725
Midmean - True Basic - Statistics Graphics Toolkit	2.6725
Midmean - MS Excel (old versions)	2.6725
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.71763888888889 & 0.0240991797336004 & 112.768937321954 \tabularnewline
Geometric Mean & 2.71019954515687 &  &  \tabularnewline
Harmonic Mean & 2.70291332408267 &  &  \tabularnewline
Quadratic Mean & 2.72521482333656 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.71875 & 0.0238326336119748 & 114.076775746427 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.72402777777778 & 0.0229543840039516 & 118.671351725615 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.70458333333333 & 0.0192463006831014 & 140.52484048054 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.61833333333333 & 0.00678013761222356 & 386.177019270652 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.61833333333333 & 0.00678013761222356 & 386.177019270652 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.719 & 0.0233978551865164 & 116.207232599973 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.71926470588235 & 0.0228791497878804 & 118.853398447647 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.71666666666667 & 0.0227956701950739 & 119.174678498978 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.71390625 & 0.0226730746232624 & 119.697319181209 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.71096774193548 & 0.0225029637596996 & 120.471586360128 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.70783333333333 & 0.022274724936531 & 121.565287160625 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.70448275862069 & 0.0219747592292083 & 123.072236214809 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.70089285714286 & 0.0215853437315096 & 125.126238003807 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.69703703703704 & 0.0210828945764037 & 127.925367518349 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.69288461538462 & 0.0204351908240835 & 131.776827462309 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.6912 & 0.020481230830361 & 131.398353072151 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.689375 & 0.0204956452951311 & 131.216898090975 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.68739130434783 & 0.0204689815586694 & 131.290914335189 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.68522727272727 & 0.0203886358834657 & 131.702154478362 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.68285714285714 & 0.0202375145096704 & 132.56850991139 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.68025 & 0.0199919454935078 & 134.066491971499 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.67736842105263 & 0.0196182783037301 & 136.473159346688 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.67416666666667 & 0.0190670288010898 & 140.250832710434 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.67058823529412 & 0.018262012511636 & 146.237345615249 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.6665625 & 0.0170779131022329 & 156.141004116677 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.662 & 0.0152857833431523 & 174.1487459452 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.65678571428571 & 0.0123769453222596 & 214.65601124597 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.65076923076923 & 0.00639526452025432 & 414.489380755718 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.655 & 0.00500000000000001 & 530.999999999999 \tabularnewline
Median & 2.66 &  &  \tabularnewline
Midrange & 2.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.6725 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.6725 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.6725 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.6725 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.6725 &  &  \tabularnewline
Midmean - Closest Observation & 2.6725 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.6725 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.6725 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207359&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]2.71763888888889[/C][C]0.0240991797336004[/C][C]112.768937321954[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.71019954515687[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.70291332408267[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.72521482333656[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.71875[/C][C]0.0238326336119748[/C][C]114.076775746427[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.72402777777778[/C][C]0.0229543840039516[/C][C]118.671351725615[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.70458333333333[/C][C]0.0192463006831014[/C][C]140.52484048054[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.61833333333333[/C][C]0.00678013761222356[/C][C]386.177019270652[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.61833333333333[/C][C]0.00678013761222356[/C][C]386.177019270652[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.719[/C][C]0.0233978551865164[/C][C]116.207232599973[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.71926470588235[/C][C]0.0228791497878804[/C][C]118.853398447647[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.71666666666667[/C][C]0.0227956701950739[/C][C]119.174678498978[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.71390625[/C][C]0.0226730746232624[/C][C]119.697319181209[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.71096774193548[/C][C]0.0225029637596996[/C][C]120.471586360128[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.70783333333333[/C][C]0.022274724936531[/C][C]121.565287160625[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.70448275862069[/C][C]0.0219747592292083[/C][C]123.072236214809[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.70089285714286[/C][C]0.0215853437315096[/C][C]125.126238003807[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.69703703703704[/C][C]0.0210828945764037[/C][C]127.925367518349[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.69288461538462[/C][C]0.0204351908240835[/C][C]131.776827462309[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.6912[/C][C]0.020481230830361[/C][C]131.398353072151[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.689375[/C][C]0.0204956452951311[/C][C]131.216898090975[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.68739130434783[/C][C]0.0204689815586694[/C][C]131.290914335189[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.68522727272727[/C][C]0.0203886358834657[/C][C]131.702154478362[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.68285714285714[/C][C]0.0202375145096704[/C][C]132.56850991139[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.68025[/C][C]0.0199919454935078[/C][C]134.066491971499[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.67736842105263[/C][C]0.0196182783037301[/C][C]136.473159346688[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.67416666666667[/C][C]0.0190670288010898[/C][C]140.250832710434[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.67058823529412[/C][C]0.018262012511636[/C][C]146.237345615249[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.6665625[/C][C]0.0170779131022329[/C][C]156.141004116677[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.662[/C][C]0.0152857833431523[/C][C]174.1487459452[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.65678571428571[/C][C]0.0123769453222596[/C][C]214.65601124597[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.65076923076923[/C][C]0.00639526452025432[/C][C]414.489380755718[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.655[/C][C]0.00500000000000001[/C][C]530.999999999999[/C][/ROW]
[ROW][C]Median[/C][C]2.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.6725[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207359&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	2.71763888888889	0.0240991797336004	112.768937321954
Geometric Mean	2.71019954515687
Harmonic Mean	2.70291332408267
Quadratic Mean	2.72521482333656
Winsorized Mean ( 1 / 24 )	2.71875	0.0238326336119748	114.076775746427
Winsorized Mean ( 2 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 3 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 4 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 5 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 6 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 7 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 8 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 9 / 24 )	2.72402777777778	0.0229543840039516	118.671351725615
Winsorized Mean ( 10 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 11 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 12 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 13 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 14 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 15 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 16 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 17 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 18 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 19 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 20 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 21 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 22 / 24 )	2.70458333333333	0.0192463006831014	140.52484048054
Winsorized Mean ( 23 / 24 )	2.61833333333333	0.00678013761222356	386.177019270652
Winsorized Mean ( 24 / 24 )	2.61833333333333	0.00678013761222356	386.177019270652
Trimmed Mean ( 1 / 24 )	2.719	0.0233978551865164	116.207232599973
Trimmed Mean ( 2 / 24 )	2.71926470588235	0.0228791497878804	118.853398447647
Trimmed Mean ( 3 / 24 )	2.71666666666667	0.0227956701950739	119.174678498978
Trimmed Mean ( 4 / 24 )	2.71390625	0.0226730746232624	119.697319181209
Trimmed Mean ( 5 / 24 )	2.71096774193548	0.0225029637596996	120.471586360128
Trimmed Mean ( 6 / 24 )	2.70783333333333	0.022274724936531	121.565287160625
Trimmed Mean ( 7 / 24 )	2.70448275862069	0.0219747592292083	123.072236214809
Trimmed Mean ( 8 / 24 )	2.70089285714286	0.0215853437315096	125.126238003807
Trimmed Mean ( 9 / 24 )	2.69703703703704	0.0210828945764037	127.925367518349
Trimmed Mean ( 10 / 24 )	2.69288461538462	0.0204351908240835	131.776827462309
Trimmed Mean ( 11 / 24 )	2.6912	0.020481230830361	131.398353072151
Trimmed Mean ( 12 / 24 )	2.689375	0.0204956452951311	131.216898090975
Trimmed Mean ( 13 / 24 )	2.68739130434783	0.0204689815586694	131.290914335189
Trimmed Mean ( 14 / 24 )	2.68522727272727	0.0203886358834657	131.702154478362
Trimmed Mean ( 15 / 24 )	2.68285714285714	0.0202375145096704	132.56850991139
Trimmed Mean ( 16 / 24 )	2.68025	0.0199919454935078	134.066491971499
Trimmed Mean ( 17 / 24 )	2.67736842105263	0.0196182783037301	136.473159346688
Trimmed Mean ( 18 / 24 )	2.67416666666667	0.0190670288010898	140.250832710434
Trimmed Mean ( 19 / 24 )	2.67058823529412	0.018262012511636	146.237345615249
Trimmed Mean ( 20 / 24 )	2.6665625	0.0170779131022329	156.141004116677
Trimmed Mean ( 21 / 24 )	2.662	0.0152857833431523	174.1487459452
Trimmed Mean ( 22 / 24 )	2.65678571428571	0.0123769453222596	214.65601124597
Trimmed Mean ( 23 / 24 )	2.65076923076923	0.00639526452025432	414.489380755718
Trimmed Mean ( 24 / 24 )	2.655	0.00500000000000001	530.999999999999
Median	2.66
Midrange	2.67
Midmean - Weighted Average at Xnp	2.6725
Midmean - Weighted Average at X(n+1)p	2.6725
Midmean - Empirical Distribution Function	2.6725
Midmean - Empirical Distribution Function - Averaging	2.6725
Midmean - Empirical Distribution Function - Interpolation	2.6725
Midmean - Closest Observation	2.6725
Midmean - True Basic - Statistics Graphics Toolkit	2.6725
Midmean - MS Excel (old versions)	2.6725
Number of observations	72

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