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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 12 Oct 2012 10:24:52 -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/12/t1350051915krcnmz33h9ytmqp.htm/, Retrieved Mon, 20 May 2024 18:41:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175493, Retrieved Mon, 20 May 2024 18:41:33 +0000

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IsPrivate?

No (this computation is public)

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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] [Prijs van limonad...] [2012-10-12 14:24:52] [778963f9ed1fb67b9d5ff0854a52552f] [Current]

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1,26
1,27
1,24
1,25
1,27
1,25
1,26
1,27
1,26
1,26
1,28
1,27
1,28
1,27
1,26
1,27
1,27
1,28
1,27
1,26
1,3
1,31
1,28
1,29
1,31
1,29
1,29
1,32
1,3
1,29
1,31
1,29
1,33
1,35
1,32
1,33
1,34
1,34
1,33
1,33
1,35
1,32
1,35
1,32
1,36
1,37
1,34
1,32
1,34
1,32
1,33
1,35
1,33
1,33
1,35
1,33
1,36
1,39
1,37
1,37
1,39
1,37
1,39
1,39
1,39
1,37
1,38
1,37
1,41
1,41
1,42
1,42

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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175493&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175493&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175493&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.32166666666667	0.0055770320408777	236.98387546984
Geometric Mean	1.32083503424496
Harmonic Mean	1.32000744281683
Quadratic Mean	1.32250183784791
Winsorized Mean ( 1 / 24 )	1.32180555555556	0.00555005106804773	238.16097173688
Winsorized Mean ( 2 / 24 )	1.32152777777778	0.00548386351812082	240.984804492478
Winsorized Mean ( 3 / 24 )	1.32194444444444	0.00541197481482304	244.262859617108
Winsorized Mean ( 4 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 5 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 6 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 7 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 8 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 9 / 24 )	1.32083333333333	0.00475433251059318	277.816776674827
Winsorized Mean ( 10 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 11 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 12 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 13 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 14 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 15 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 16 / 24 )	1.31722222222222	0.00418761037844027	314.552239387858
Winsorized Mean ( 17 / 24 )	1.31958333333333	0.00382744751238915	344.768498865613
Winsorized Mean ( 18 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 19 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 20 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 21 / 24 )	1.32	0.00305146261654252	432.579443327946
Winsorized Mean ( 22 / 24 )	1.32	0.00305146261654252	432.579443327946
Winsorized Mean ( 23 / 24 )	1.31680555555556	0.00263022628914627	500.643446911547
Winsorized Mean ( 24 / 24 )	1.31680555555556	0.00263022628914627	500.643446911547
Trimmed Mean ( 1 / 24 )	1.32142857142857	0.00543467021475027	243.147885559288
Trimmed Mean ( 2 / 24 )	1.32102941176471	0.00529689104021767	249.397127812246
Trimmed Mean ( 3 / 24 )	1.32075757575758	0.0051743972817066	255.248583332969
Trimmed Mean ( 4 / 24 )	1.3203125	0.00505902045815509	260.9818463714
Trimmed Mean ( 5 / 24 )	1.32016129032258	0.00500392197045502	263.825315046336
Trimmed Mean ( 6 / 24 )	1.32	0.00493460053964611	267.49885616773
Trimmed Mean ( 7 / 24 )	1.3198275862069	0.00484790684782861	272.246894924982
Trimmed Mean ( 8 / 24 )	1.31964285714286	0.00473974823783611	278.420454193856
Trimmed Mean ( 9 / 24 )	1.31944444444444	0.00460468471888729	286.543927542402
Trimmed Mean ( 10 / 24 )	1.31923076923077	0.00453614737636157	290.826258446858
Trimmed Mean ( 11 / 24 )	1.3192	0.00449798140666387	293.287117204525
Trimmed Mean ( 12 / 24 )	1.31916666666667	0.00444462913327847	296.800166472746
Trimmed Mean ( 13 / 24 )	1.31913043478261	0.00437191395043431	301.72836193438
Trimmed Mean ( 14 / 24 )	1.31909090909091	0.0042741439781678	308.621074963498
Trimmed Mean ( 15 / 24 )	1.31904761904762	0.00414333103674858	318.354388618372
Trimmed Mean ( 16 / 24 )	1.319	0.00396781926800979	332.424415253569
Trimmed Mean ( 17 / 24 )	1.31921052631579	0.00381621864462457	345.685257885839
Trimmed Mean ( 18 / 24 )	1.31916666666667	0.00370274458480699	356.267259718491
Trimmed Mean ( 19 / 24 )	1.31941176470588	0.00363046076416977	363.428184578552
Trimmed Mean ( 20 / 24 )	1.3196875	0.00352080152050271	374.825871982574
Trimmed Mean ( 21 / 24 )	1.32	0.00335624311039769	393.296896732725
Trimmed Mean ( 22 / 24 )	1.32	0.00325300024316178	405.779250332
Trimmed Mean ( 23 / 24 )	1.32	0.00308843998459765	427.400243029804
Trimmed Mean ( 24 / 24 )	1.32041666666667	0.00297813083745899	443.370939267825
Median	1.32
Midrange	1.33
Midmean - Weighted Average at Xnp	1.31810810810811
Midmean - Weighted Average at X(n+1)p	1.31810810810811
Midmean - Empirical Distribution Function	1.31810810810811
Midmean - Empirical Distribution Function - Averaging	1.31810810810811
Midmean - Empirical Distribution Function - Interpolation	1.31810810810811
Midmean - Closest Observation	1.31810810810811
Midmean - True Basic - Statistics Graphics Toolkit	1.31810810810811
Midmean - MS Excel (old versions)	1.32025641025641
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.32166666666667 & 0.0055770320408777 & 236.98387546984 \tabularnewline
Geometric Mean & 1.32083503424496 &  &  \tabularnewline
Harmonic Mean & 1.32000744281683 &  &  \tabularnewline
Quadratic Mean & 1.32250183784791 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.32180555555556 & 0.00555005106804773 & 238.16097173688 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.32152777777778 & 0.00548386351812082 & 240.984804492478 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.32194444444444 & 0.00541197481482304 & 244.262859617108 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.32083333333333 & 0.00517967467452921 & 255.003145241624 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.32083333333333 & 0.00517967467452921 & 255.003145241624 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.32083333333333 & 0.00517967467452921 & 255.003145241624 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.32083333333333 & 0.00517967467452921 & 255.003145241624 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.32083333333333 & 0.00517967467452921 & 255.003145241624 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.32083333333333 & 0.00475433251059318 & 277.816776674827 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.31944444444444 & 0.0045229759862137 & 291.720417810351 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.31722222222222 & 0.00418761037844027 & 314.552239387858 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.31958333333333 & 0.00382744751238915 & 344.768498865613 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.31708333333333 & 0.00347378681494429 & 379.149154365841 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.31708333333333 & 0.00347378681494429 & 379.149154365841 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.31708333333333 & 0.00347378681494429 & 379.149154365841 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.32 & 0.00305146261654252 & 432.579443327946 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.32 & 0.00305146261654252 & 432.579443327946 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.31680555555556 & 0.00263022628914627 & 500.643446911547 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.31680555555556 & 0.00263022628914627 & 500.643446911547 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.32142857142857 & 0.00543467021475027 & 243.147885559288 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.32102941176471 & 0.00529689104021767 & 249.397127812246 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.32075757575758 & 0.0051743972817066 & 255.248583332969 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.3203125 & 0.00505902045815509 & 260.9818463714 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.32016129032258 & 0.00500392197045502 & 263.825315046336 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.32 & 0.00493460053964611 & 267.49885616773 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.3198275862069 & 0.00484790684782861 & 272.246894924982 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.31964285714286 & 0.00473974823783611 & 278.420454193856 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.31944444444444 & 0.00460468471888729 & 286.543927542402 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.31923076923077 & 0.00453614737636157 & 290.826258446858 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.3192 & 0.00449798140666387 & 293.287117204525 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.31916666666667 & 0.00444462913327847 & 296.800166472746 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.31913043478261 & 0.00437191395043431 & 301.72836193438 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.31909090909091 & 0.0042741439781678 & 308.621074963498 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.31904761904762 & 0.00414333103674858 & 318.354388618372 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.319 & 0.00396781926800979 & 332.424415253569 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.31921052631579 & 0.00381621864462457 & 345.685257885839 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.31916666666667 & 0.00370274458480699 & 356.267259718491 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.31941176470588 & 0.00363046076416977 & 363.428184578552 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.3196875 & 0.00352080152050271 & 374.825871982574 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.32 & 0.00335624311039769 & 393.296896732725 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.32 & 0.00325300024316178 & 405.779250332 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.32 & 0.00308843998459765 & 427.400243029804 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.32041666666667 & 0.00297813083745899 & 443.370939267825 \tabularnewline
Median & 1.32 &  &  \tabularnewline
Midrange & 1.33 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.31810810810811 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.31810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.31810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.31810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.31810810810811 &  &  \tabularnewline
Midmean - Closest Observation & 1.31810810810811 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.31810810810811 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.32025641025641 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175493&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.32166666666667[/C][C]0.0055770320408777[/C][C]236.98387546984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.32083503424496[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.32000744281683[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.32250183784791[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.32180555555556[/C][C]0.00555005106804773[/C][C]238.16097173688[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.32152777777778[/C][C]0.00548386351812082[/C][C]240.984804492478[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.32194444444444[/C][C]0.00541197481482304[/C][C]244.262859617108[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.32083333333333[/C][C]0.00517967467452921[/C][C]255.003145241624[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.32083333333333[/C][C]0.00517967467452921[/C][C]255.003145241624[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.32083333333333[/C][C]0.00517967467452921[/C][C]255.003145241624[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.32083333333333[/C][C]0.00517967467452921[/C][C]255.003145241624[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.32083333333333[/C][C]0.00517967467452921[/C][C]255.003145241624[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.32083333333333[/C][C]0.00475433251059318[/C][C]277.816776674827[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.31944444444444[/C][C]0.0045229759862137[/C][C]291.720417810351[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.31722222222222[/C][C]0.00418761037844027[/C][C]314.552239387858[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.31958333333333[/C][C]0.00382744751238915[/C][C]344.768498865613[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.31708333333333[/C][C]0.00347378681494429[/C][C]379.149154365841[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.31708333333333[/C][C]0.00347378681494429[/C][C]379.149154365841[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.31708333333333[/C][C]0.00347378681494429[/C][C]379.149154365841[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.32[/C][C]0.00305146261654252[/C][C]432.579443327946[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.32[/C][C]0.00305146261654252[/C][C]432.579443327946[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.31680555555556[/C][C]0.00263022628914627[/C][C]500.643446911547[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.31680555555556[/C][C]0.00263022628914627[/C][C]500.643446911547[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.32142857142857[/C][C]0.00543467021475027[/C][C]243.147885559288[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.32102941176471[/C][C]0.00529689104021767[/C][C]249.397127812246[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.32075757575758[/C][C]0.0051743972817066[/C][C]255.248583332969[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.3203125[/C][C]0.00505902045815509[/C][C]260.9818463714[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.32016129032258[/C][C]0.00500392197045502[/C][C]263.825315046336[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.32[/C][C]0.00493460053964611[/C][C]267.49885616773[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.3198275862069[/C][C]0.00484790684782861[/C][C]272.246894924982[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.31964285714286[/C][C]0.00473974823783611[/C][C]278.420454193856[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.31944444444444[/C][C]0.00460468471888729[/C][C]286.543927542402[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.31923076923077[/C][C]0.00453614737636157[/C][C]290.826258446858[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.3192[/C][C]0.00449798140666387[/C][C]293.287117204525[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.31916666666667[/C][C]0.00444462913327847[/C][C]296.800166472746[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.31913043478261[/C][C]0.00437191395043431[/C][C]301.72836193438[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.31909090909091[/C][C]0.0042741439781678[/C][C]308.621074963498[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.31904761904762[/C][C]0.00414333103674858[/C][C]318.354388618372[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.319[/C][C]0.00396781926800979[/C][C]332.424415253569[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.31921052631579[/C][C]0.00381621864462457[/C][C]345.685257885839[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.31916666666667[/C][C]0.00370274458480699[/C][C]356.267259718491[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.31941176470588[/C][C]0.00363046076416977[/C][C]363.428184578552[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.3196875[/C][C]0.00352080152050271[/C][C]374.825871982574[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.32[/C][C]0.00335624311039769[/C][C]393.296896732725[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.32[/C][C]0.00325300024316178[/C][C]405.779250332[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.32[/C][C]0.00308843998459765[/C][C]427.400243029804[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.32041666666667[/C][C]0.00297813083745899[/C][C]443.370939267825[/C][/ROW]
[ROW][C]Median[/C][C]1.32[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.31810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.32025641025641[/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=175493&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175493&T=1

As an alternative you can also use a QR Code:

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.32166666666667	0.0055770320408777	236.98387546984
Geometric Mean	1.32083503424496
Harmonic Mean	1.32000744281683
Quadratic Mean	1.32250183784791
Winsorized Mean ( 1 / 24 )	1.32180555555556	0.00555005106804773	238.16097173688
Winsorized Mean ( 2 / 24 )	1.32152777777778	0.00548386351812082	240.984804492478
Winsorized Mean ( 3 / 24 )	1.32194444444444	0.00541197481482304	244.262859617108
Winsorized Mean ( 4 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 5 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 6 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 7 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 8 / 24 )	1.32083333333333	0.00517967467452921	255.003145241624
Winsorized Mean ( 9 / 24 )	1.32083333333333	0.00475433251059318	277.816776674827
Winsorized Mean ( 10 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 11 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 12 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 13 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 14 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 15 / 24 )	1.31944444444444	0.0045229759862137	291.720417810351
Winsorized Mean ( 16 / 24 )	1.31722222222222	0.00418761037844027	314.552239387858
Winsorized Mean ( 17 / 24 )	1.31958333333333	0.00382744751238915	344.768498865613
Winsorized Mean ( 18 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 19 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 20 / 24 )	1.31708333333333	0.00347378681494429	379.149154365841
Winsorized Mean ( 21 / 24 )	1.32	0.00305146261654252	432.579443327946
Winsorized Mean ( 22 / 24 )	1.32	0.00305146261654252	432.579443327946
Winsorized Mean ( 23 / 24 )	1.31680555555556	0.00263022628914627	500.643446911547
Winsorized Mean ( 24 / 24 )	1.31680555555556	0.00263022628914627	500.643446911547
Trimmed Mean ( 1 / 24 )	1.32142857142857	0.00543467021475027	243.147885559288
Trimmed Mean ( 2 / 24 )	1.32102941176471	0.00529689104021767	249.397127812246
Trimmed Mean ( 3 / 24 )	1.32075757575758	0.0051743972817066	255.248583332969
Trimmed Mean ( 4 / 24 )	1.3203125	0.00505902045815509	260.9818463714
Trimmed Mean ( 5 / 24 )	1.32016129032258	0.00500392197045502	263.825315046336
Trimmed Mean ( 6 / 24 )	1.32	0.00493460053964611	267.49885616773
Trimmed Mean ( 7 / 24 )	1.3198275862069	0.00484790684782861	272.246894924982
Trimmed Mean ( 8 / 24 )	1.31964285714286	0.00473974823783611	278.420454193856
Trimmed Mean ( 9 / 24 )	1.31944444444444	0.00460468471888729	286.543927542402
Trimmed Mean ( 10 / 24 )	1.31923076923077	0.00453614737636157	290.826258446858
Trimmed Mean ( 11 / 24 )	1.3192	0.00449798140666387	293.287117204525
Trimmed Mean ( 12 / 24 )	1.31916666666667	0.00444462913327847	296.800166472746
Trimmed Mean ( 13 / 24 )	1.31913043478261	0.00437191395043431	301.72836193438
Trimmed Mean ( 14 / 24 )	1.31909090909091	0.0042741439781678	308.621074963498
Trimmed Mean ( 15 / 24 )	1.31904761904762	0.00414333103674858	318.354388618372
Trimmed Mean ( 16 / 24 )	1.319	0.00396781926800979	332.424415253569
Trimmed Mean ( 17 / 24 )	1.31921052631579	0.00381621864462457	345.685257885839
Trimmed Mean ( 18 / 24 )	1.31916666666667	0.00370274458480699	356.267259718491
Trimmed Mean ( 19 / 24 )	1.31941176470588	0.00363046076416977	363.428184578552
Trimmed Mean ( 20 / 24 )	1.3196875	0.00352080152050271	374.825871982574
Trimmed Mean ( 21 / 24 )	1.32	0.00335624311039769	393.296896732725
Trimmed Mean ( 22 / 24 )	1.32	0.00325300024316178	405.779250332
Trimmed Mean ( 23 / 24 )	1.32	0.00308843998459765	427.400243029804
Trimmed Mean ( 24 / 24 )	1.32041666666667	0.00297813083745899	443.370939267825
Median	1.32
Midrange	1.33
Midmean - Weighted Average at Xnp	1.31810810810811
Midmean - Weighted Average at X(n+1)p	1.31810810810811
Midmean - Empirical Distribution Function	1.31810810810811
Midmean - Empirical Distribution Function - Averaging	1.31810810810811
Midmean - Empirical Distribution Function - Interpolation	1.31810810810811
Midmean - Closest Observation	1.31810810810811
Midmean - True Basic - Statistics Graphics Toolkit	1.31810810810811
Midmean - MS Excel (old versions)	1.32025641025641
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