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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 22 Oct 2012 12:03:38 -0400

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/2012/Oct/22/t1350921828920ir8dk4qjrgwo.htm/, Retrieved Fri, 03 May 2024 15:16:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181719, Retrieved Fri, 03 May 2024 15:16:28 +0000

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Estimated Impact

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

-       [Central Tendency] [] [2012-10-22 16:03:38] [b1ddf6ea300953275cf6f348bdbfb169] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181719&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181719&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	'George Udny Yule' @ yule.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.41125	0.00315817678331647	130.217536324277
Geometric Mean	0.410381852795425
Harmonic Mean	0.409508036283584
Quadratic Mean	0.412110085077061
Winsorized Mean ( 1 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 2 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 3 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 4 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 5 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 6 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 7 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 8 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 9 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 10 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 11 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 12 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 13 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 14 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 15 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 16 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 17 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 18 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 19 / 24 )	0.408333333333333	0.00247838859254344	164.757590703031
Winsorized Mean ( 20 / 24 )	0.408333333333333	0.00247838859254344	164.757590703031
Winsorized Mean ( 21 / 24 )	0.41125	0.00202621222820814	202.964918617476
Winsorized Mean ( 22 / 24 )	0.41125	0.00202621222820814	202.964918617476
Winsorized Mean ( 23 / 24 )	0.408055555555556	0.00165061387652044	247.214422076562
Winsorized Mean ( 24 / 24 )	0.408055555555556	0.00165061387652044	247.214422076562
Trimmed Mean ( 1 / 24 )	0.411428571428571	0.00311468647107105	132.093093558496
Trimmed Mean ( 2 / 24 )	0.411470588235294	0.00309538659438077	132.930274034998
Trimmed Mean ( 3 / 24 )	0.411515151515152	0.00307059460800886	134.018066221383
Trimmed Mean ( 4 / 24 )	0.4115625	0.00303925010004687	135.415805363847
Trimmed Mean ( 5 / 24 )	0.411612903225806	0.00300003127418122	137.202870772787
Trimmed Mean ( 6 / 24 )	0.4115	0.00298607881119482	137.80614177271
Trimmed Mean ( 7 / 24 )	0.411379310344828	0.00296631905760091	138.683433021376
Trimmed Mean ( 8 / 24 )	0.41125	0.00293945948737554	139.906673919558
Trimmed Mean ( 9 / 24 )	0.411296296296296	0.00294423237592736	139.695595924812
Trimmed Mean ( 10 / 24 )	0.411346153846154	0.00294531412171164	139.661216715012
Trimmed Mean ( 11 / 24 )	0.4114	0.00294174736356139	139.848854832301
Trimmed Mean ( 12 / 24 )	0.411458333333333	0.00293229727633214	140.319447367903
Trimmed Mean ( 13 / 24 )	0.411521739130435	0.00291534986928215	141.156896284206
Trimmed Mean ( 14 / 24 )	0.411590909090909	0.00288876188425237	142.480040094212
Trimmed Mean ( 15 / 24 )	0.411666666666667	0.00284963201705023	144.463097060792
Trimmed Mean ( 16 / 24 )	0.41175	0.00279393803503044	147.372631331645
Trimmed Mean ( 17 / 24 )	0.411842105263158	0.00271593116615164	151.63937525218
Trimmed Mean ( 18 / 24 )	0.411944444444444	0.00260705527624634	158.01139630517
Trimmed Mean ( 19 / 24 )	0.412058823529412	0.00245383078462135	167.924710257882
Trimmed Mean ( 20 / 24 )	0.4125	0.00233314131314345	176.800263951538
Trimmed Mean ( 21 / 24 )	0.413	0.0021522508933779	191.892126178564
Trimmed Mean ( 22 / 24 )	0.413214285714286	0.002060819392476	200.509703675597
Trimmed Mean ( 23 / 24 )	0.413461538461538	0.00191691319913494	215.691320112003
Trimmed Mean ( 24 / 24 )	0.414166666666667	0.00179740822533514	230.424374846422
Median	0.42
Midrange	0.405
Midmean - Weighted Average at Xnp	0.409661016949153
Midmean - Weighted Average at X(n+1)p	0.409661016949153
Midmean - Empirical Distribution Function	0.409661016949153
Midmean - Empirical Distribution Function - Averaging	0.409661016949153
Midmean - Empirical Distribution Function - Interpolation	0.409661016949153
Midmean - Closest Observation	0.409661016949153
Midmean - True Basic - Statistics Graphics Toolkit	0.409661016949153
Midmean - MS Excel (old versions)	0.409661016949153
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.41125 & 0.00315817678331647 & 130.217536324277 \tabularnewline
Geometric Mean & 0.410381852795425 &  &  \tabularnewline
Harmonic Mean & 0.409508036283584 &  &  \tabularnewline
Quadratic Mean & 0.412110085077061 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.411388888888889 & 0.00312935490332069 & 131.461244121703 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.411388888888889 & 0.00312935490332069 & 131.461244121703 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.411388888888889 & 0.00312935490332069 & 131.461244121703 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.411388888888889 & 0.00312935490332069 & 131.461244121703 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.412083333333333 & 0.0030123474383281 & 136.79807584282 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.412083333333333 & 0.0030123474383281 & 136.79807584282 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.412083333333333 & 0.0030123474383281 & 136.79807584282 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.410972222222222 & 0.00283312428269259 & 145.05972248829 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.408333333333333 & 0.00247838859254344 & 164.757590703031 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.408333333333333 & 0.00247838859254344 & 164.757590703031 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.41125 & 0.00202621222820814 & 202.964918617476 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.41125 & 0.00202621222820814 & 202.964918617476 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.408055555555556 & 0.00165061387652044 & 247.214422076562 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.408055555555556 & 0.00165061387652044 & 247.214422076562 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.411428571428571 & 0.00311468647107105 & 132.093093558496 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.411470588235294 & 0.00309538659438077 & 132.930274034998 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.411515151515152 & 0.00307059460800886 & 134.018066221383 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.4115625 & 0.00303925010004687 & 135.415805363847 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.411612903225806 & 0.00300003127418122 & 137.202870772787 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.4115 & 0.00298607881119482 & 137.80614177271 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.411379310344828 & 0.00296631905760091 & 138.683433021376 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.41125 & 0.00293945948737554 & 139.906673919558 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.411296296296296 & 0.00294423237592736 & 139.695595924812 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.411346153846154 & 0.00294531412171164 & 139.661216715012 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.4114 & 0.00294174736356139 & 139.848854832301 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.411458333333333 & 0.00293229727633214 & 140.319447367903 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.411521739130435 & 0.00291534986928215 & 141.156896284206 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.411590909090909 & 0.00288876188425237 & 142.480040094212 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.411666666666667 & 0.00284963201705023 & 144.463097060792 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.41175 & 0.00279393803503044 & 147.372631331645 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.411842105263158 & 0.00271593116615164 & 151.63937525218 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.411944444444444 & 0.00260705527624634 & 158.01139630517 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.412058823529412 & 0.00245383078462135 & 167.924710257882 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.4125 & 0.00233314131314345 & 176.800263951538 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.413 & 0.0021522508933779 & 191.892126178564 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.413214285714286 & 0.002060819392476 & 200.509703675597 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.413461538461538 & 0.00191691319913494 & 215.691320112003 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.414166666666667 & 0.00179740822533514 & 230.424374846422 \tabularnewline
Median & 0.42 &  &  \tabularnewline
Midrange & 0.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.409661016949153 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.409661016949153 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.409661016949153 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.409661016949153 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.409661016949153 &  &  \tabularnewline
Midmean - Closest Observation & 0.409661016949153 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.409661016949153 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.409661016949153 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181719&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]0.41125[/C][C]0.00315817678331647[/C][C]130.217536324277[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.410381852795425[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.409508036283584[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.412110085077061[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.411388888888889[/C][C]0.00312935490332069[/C][C]131.461244121703[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.411388888888889[/C][C]0.00312935490332069[/C][C]131.461244121703[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.411388888888889[/C][C]0.00312935490332069[/C][C]131.461244121703[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.411388888888889[/C][C]0.00312935490332069[/C][C]131.461244121703[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.412083333333333[/C][C]0.0030123474383281[/C][C]136.79807584282[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.412083333333333[/C][C]0.0030123474383281[/C][C]136.79807584282[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.412083333333333[/C][C]0.0030123474383281[/C][C]136.79807584282[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.410972222222222[/C][C]0.00283312428269259[/C][C]145.05972248829[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.408333333333333[/C][C]0.00247838859254344[/C][C]164.757590703031[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.408333333333333[/C][C]0.00247838859254344[/C][C]164.757590703031[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.41125[/C][C]0.00202621222820814[/C][C]202.964918617476[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.41125[/C][C]0.00202621222820814[/C][C]202.964918617476[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.408055555555556[/C][C]0.00165061387652044[/C][C]247.214422076562[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.408055555555556[/C][C]0.00165061387652044[/C][C]247.214422076562[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.411428571428571[/C][C]0.00311468647107105[/C][C]132.093093558496[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.411470588235294[/C][C]0.00309538659438077[/C][C]132.930274034998[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.411515151515152[/C][C]0.00307059460800886[/C][C]134.018066221383[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.4115625[/C][C]0.00303925010004687[/C][C]135.415805363847[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.411612903225806[/C][C]0.00300003127418122[/C][C]137.202870772787[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.4115[/C][C]0.00298607881119482[/C][C]137.80614177271[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.411379310344828[/C][C]0.00296631905760091[/C][C]138.683433021376[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.41125[/C][C]0.00293945948737554[/C][C]139.906673919558[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.411296296296296[/C][C]0.00294423237592736[/C][C]139.695595924812[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.411346153846154[/C][C]0.00294531412171164[/C][C]139.661216715012[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.4114[/C][C]0.00294174736356139[/C][C]139.848854832301[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.411458333333333[/C][C]0.00293229727633214[/C][C]140.319447367903[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.411521739130435[/C][C]0.00291534986928215[/C][C]141.156896284206[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.411590909090909[/C][C]0.00288876188425237[/C][C]142.480040094212[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.411666666666667[/C][C]0.00284963201705023[/C][C]144.463097060792[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.41175[/C][C]0.00279393803503044[/C][C]147.372631331645[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.411842105263158[/C][C]0.00271593116615164[/C][C]151.63937525218[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.411944444444444[/C][C]0.00260705527624634[/C][C]158.01139630517[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.412058823529412[/C][C]0.00245383078462135[/C][C]167.924710257882[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.4125[/C][C]0.00233314131314345[/C][C]176.800263951538[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.413[/C][C]0.0021522508933779[/C][C]191.892126178564[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.413214285714286[/C][C]0.002060819392476[/C][C]200.509703675597[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.413461538461538[/C][C]0.00191691319913494[/C][C]215.691320112003[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.414166666666667[/C][C]0.00179740822533514[/C][C]230.424374846422[/C][/ROW]
[ROW][C]Median[/C][C]0.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.409661016949153[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.409661016949153[/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=181719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181719&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	0.41125	0.00315817678331647	130.217536324277
Geometric Mean	0.410381852795425
Harmonic Mean	0.409508036283584
Quadratic Mean	0.412110085077061
Winsorized Mean ( 1 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 2 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 3 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 4 / 24 )	0.411388888888889	0.00312935490332069	131.461244121703
Winsorized Mean ( 5 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 6 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 7 / 24 )	0.412083333333333	0.0030123474383281	136.79807584282
Winsorized Mean ( 8 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 9 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 10 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 11 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 12 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 13 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 14 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 15 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 16 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 17 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 18 / 24 )	0.410972222222222	0.00283312428269259	145.05972248829
Winsorized Mean ( 19 / 24 )	0.408333333333333	0.00247838859254344	164.757590703031
Winsorized Mean ( 20 / 24 )	0.408333333333333	0.00247838859254344	164.757590703031
Winsorized Mean ( 21 / 24 )	0.41125	0.00202621222820814	202.964918617476
Winsorized Mean ( 22 / 24 )	0.41125	0.00202621222820814	202.964918617476
Winsorized Mean ( 23 / 24 )	0.408055555555556	0.00165061387652044	247.214422076562
Winsorized Mean ( 24 / 24 )	0.408055555555556	0.00165061387652044	247.214422076562
Trimmed Mean ( 1 / 24 )	0.411428571428571	0.00311468647107105	132.093093558496
Trimmed Mean ( 2 / 24 )	0.411470588235294	0.00309538659438077	132.930274034998
Trimmed Mean ( 3 / 24 )	0.411515151515152	0.00307059460800886	134.018066221383
Trimmed Mean ( 4 / 24 )	0.4115625	0.00303925010004687	135.415805363847
Trimmed Mean ( 5 / 24 )	0.411612903225806	0.00300003127418122	137.202870772787
Trimmed Mean ( 6 / 24 )	0.4115	0.00298607881119482	137.80614177271
Trimmed Mean ( 7 / 24 )	0.411379310344828	0.00296631905760091	138.683433021376
Trimmed Mean ( 8 / 24 )	0.41125	0.00293945948737554	139.906673919558
Trimmed Mean ( 9 / 24 )	0.411296296296296	0.00294423237592736	139.695595924812
Trimmed Mean ( 10 / 24 )	0.411346153846154	0.00294531412171164	139.661216715012
Trimmed Mean ( 11 / 24 )	0.4114	0.00294174736356139	139.848854832301
Trimmed Mean ( 12 / 24 )	0.411458333333333	0.00293229727633214	140.319447367903
Trimmed Mean ( 13 / 24 )	0.411521739130435	0.00291534986928215	141.156896284206
Trimmed Mean ( 14 / 24 )	0.411590909090909	0.00288876188425237	142.480040094212
Trimmed Mean ( 15 / 24 )	0.411666666666667	0.00284963201705023	144.463097060792
Trimmed Mean ( 16 / 24 )	0.41175	0.00279393803503044	147.372631331645
Trimmed Mean ( 17 / 24 )	0.411842105263158	0.00271593116615164	151.63937525218
Trimmed Mean ( 18 / 24 )	0.411944444444444	0.00260705527624634	158.01139630517
Trimmed Mean ( 19 / 24 )	0.412058823529412	0.00245383078462135	167.924710257882
Trimmed Mean ( 20 / 24 )	0.4125	0.00233314131314345	176.800263951538
Trimmed Mean ( 21 / 24 )	0.413	0.0021522508933779	191.892126178564
Trimmed Mean ( 22 / 24 )	0.413214285714286	0.002060819392476	200.509703675597
Trimmed Mean ( 23 / 24 )	0.413461538461538	0.00191691319913494	215.691320112003
Trimmed Mean ( 24 / 24 )	0.414166666666667	0.00179740822533514	230.424374846422
Median	0.42
Midrange	0.405
Midmean - Weighted Average at Xnp	0.409661016949153
Midmean - Weighted Average at X(n+1)p	0.409661016949153
Midmean - Empirical Distribution Function	0.409661016949153
Midmean - Empirical Distribution Function - Averaging	0.409661016949153
Midmean - Empirical Distribution Function - Interpolation	0.409661016949153
Midmean - Closest Observation	0.409661016949153
Midmean - True Basic - Statistics Graphics Toolkit	0.409661016949153
Midmean - MS Excel (old versions)	0.409661016949153
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