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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 13:50:42 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362509483krpwe37h127mf0f.htm/, Retrieved Sat, 04 May 2024 19:56:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207463, Retrieved Sat, 04 May 2024 19:56:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5: oefenin...] [2013-03-05 18:50:42] [6c59e828142382ec266fd8d68378aa9e] [Current]
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Dataseries X:
105,28
107
106,29
108,07
105,41
104,4
102,77
102,44
103,43
102,95
103,52
105,2
105,88
104,88
106,59
107,8
106,31
106,53
106,25
105,87
107,83
108,01
107,9
108,55
108,83
109,39
108,65
108,33
109,76
110,07
109,23
108,4
108,9
109,14
109,27
109,38
109,66
109,87
109,98
111,24
110,03
111,43
110,28
109,53
111,97
111,89
112,93
113,11
112,95
114,08
115,27
114,73
114,97
113,78
113,7
113,91
114,22
115,32
113,5
115,35
113,23
113,65
114,82
113,54
113,97
113,79
113,27
114,35
113,68
115,3
113,69
115,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207463&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207463&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207463&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.011250.436821368928874251.844936683747
Geometric Mean109.949303703001
Harmonic Mean109.88700292721
Quadratic Mean110.072807009977
Winsorized Mean ( 1 / 24 )110.0154166666670.435653500520367252.52962855861
Winsorized Mean ( 2 / 24 )110.0201388888890.434447218298502253.241669539925
Winsorized Mean ( 3 / 24 )110.0397222222220.429917421749295255.955485066133
Winsorized Mean ( 4 / 24 )110.0430555555560.42855334217887256.777966066184
Winsorized Mean ( 5 / 24 )110.0833333333330.412533727933021266.846868218267
Winsorized Mean ( 6 / 24 )110.1108333333330.402921633961545273.28101559283
Winsorized Mean ( 7 / 24 )110.1331944444440.395910670793794278.176878192319
Winsorized Mean ( 8 / 24 )110.0998611111110.387637879607242284.02761160149
Winsorized Mean ( 9 / 24 )110.0998611111110.382322994580855287.976037726465
Winsorized Mean ( 10 / 24 )110.1443055555560.368643880854659298.782405665323
Winsorized Mean ( 11 / 24 )110.1290277777780.365888213328428300.990914071681
Winsorized Mean ( 12 / 24 )110.1806944444440.354546886564596310.7648060657
Winsorized Mean ( 13 / 24 )110.166250.350236307299378314.548342658921
Winsorized Mean ( 14 / 24 )110.1681944444440.349347498547434315.354181445458
Winsorized Mean ( 15 / 24 )110.1973611111110.339875816929237324.22830817073
Winsorized Mean ( 16 / 24 )110.2084722222220.337533320659816326.511385621973
Winsorized Mean ( 17 / 24 )110.3029166666670.322898795507296341.602131074454
Winsorized Mean ( 18 / 24 )110.4954166666670.294409500078219375.311994474737
Winsorized Mean ( 19 / 24 )110.4743055555560.289030191738951382.224102232665
Winsorized Mean ( 20 / 24 )110.4826388888890.284877179768816387.825514765865
Winsorized Mean ( 21 / 24 )110.4476388888890.27086689882691407.756131765171
Winsorized Mean ( 22 / 24 )110.453750.266758598993421414.058817285676
Winsorized Mean ( 23 / 24 )110.4984722222220.250850716859165440.494942991371
Winsorized Mean ( 24 / 24 )110.4684722222220.240224664971134459.854828959783
Trimmed Mean ( 1 / 24 )110.0431428571430.429149649964296256.421373910705
Trimmed Mean ( 2 / 24 )110.07250.421319438359537261.256638024065
Trimmed Mean ( 3 / 24 )110.1010606060610.412655459370913266.811108652017
Trimmed Mean ( 4 / 24 )110.12406250.404266293486245272.404759621017
Trimmed Mean ( 5 / 24 )110.1475806451610.394577918495638279.152926410855
Trimmed Mean ( 6 / 24 )110.1630.387852795478455284.033017898203
Trimmed Mean ( 7 / 24 )110.1737931034480.382194829022174288.26604845838
Trimmed Mean ( 8 / 24 )110.181250.37685308916299292.371890183303
Trimmed Mean ( 9 / 24 )110.1948148148150.371976771358804296.241118530819
Trimmed Mean ( 10 / 24 )110.2094230769230.366847214577477300.423224431072
Trimmed Mean ( 11 / 24 )110.21880.36313910754499303.516745263645
Trimmed Mean ( 12 / 24 )110.2310416666670.35864305923117307.355848187808
Trimmed Mean ( 13 / 24 )110.2376086956520.354945894329969310.575810163258
Trimmed Mean ( 14 / 24 )110.2465909090910.350615276646571314.437499596523
Trimmed Mean ( 15 / 24 )110.256190476190.344695989938649319.865022206421
Trimmed Mean ( 16 / 24 )110.263250.338599753793813325.644802645497
Trimmed Mean ( 17 / 24 )110.2697368421050.330541924706866333.602876367031
Trimmed Mean ( 18 / 24 )110.2658333333330.322804027973925341.587538499489
Trimmed Mean ( 19 / 24 )110.2388235294120.318386855550201346.241754669517
Trimmed Mean ( 20 / 24 )110.21093750.312721327872357352.425394998913
Trimmed Mean ( 21 / 24 )110.1783333333330.304793158932088361.48558491066
Trimmed Mean ( 22 / 24 )110.1453571428570.296655734658068371.290166596015
Trimmed Mean ( 23 / 24 )110.1065384615380.28465954958792386.800789297008
Trimmed Mean ( 24 / 24 )110.0554166666670.270635978819153406.654788276355
Median109.71
Midrange108.895
Midmean - Weighted Average at Xnp110.177567567568
Midmean - Weighted Average at X(n+1)p110.265833333333
Midmean - Empirical Distribution Function110.177567567568
Midmean - Empirical Distribution Function - Averaging110.265833333333
Midmean - Empirical Distribution Function - Interpolation110.265833333333
Midmean - Closest Observation110.177567567568
Midmean - True Basic - Statistics Graphics Toolkit110.265833333333
Midmean - MS Excel (old versions)110.269736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.01125 & 0.436821368928874 & 251.844936683747 \tabularnewline
Geometric Mean & 109.949303703001 &  &  \tabularnewline
Harmonic Mean & 109.88700292721 &  &  \tabularnewline
Quadratic Mean & 110.072807009977 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 110.015416666667 & 0.435653500520367 & 252.52962855861 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 110.020138888889 & 0.434447218298502 & 253.241669539925 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 110.039722222222 & 0.429917421749295 & 255.955485066133 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 110.043055555556 & 0.42855334217887 & 256.777966066184 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 110.083333333333 & 0.412533727933021 & 266.846868218267 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 110.110833333333 & 0.402921633961545 & 273.28101559283 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 110.133194444444 & 0.395910670793794 & 278.176878192319 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 110.099861111111 & 0.387637879607242 & 284.02761160149 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 110.099861111111 & 0.382322994580855 & 287.976037726465 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 110.144305555556 & 0.368643880854659 & 298.782405665323 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 110.129027777778 & 0.365888213328428 & 300.990914071681 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 110.180694444444 & 0.354546886564596 & 310.7648060657 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 110.16625 & 0.350236307299378 & 314.548342658921 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 110.168194444444 & 0.349347498547434 & 315.354181445458 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 110.197361111111 & 0.339875816929237 & 324.22830817073 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 110.208472222222 & 0.337533320659816 & 326.511385621973 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 110.302916666667 & 0.322898795507296 & 341.602131074454 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 110.495416666667 & 0.294409500078219 & 375.311994474737 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 110.474305555556 & 0.289030191738951 & 382.224102232665 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 110.482638888889 & 0.284877179768816 & 387.825514765865 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 110.447638888889 & 0.27086689882691 & 407.756131765171 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 110.45375 & 0.266758598993421 & 414.058817285676 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 110.498472222222 & 0.250850716859165 & 440.494942991371 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 110.468472222222 & 0.240224664971134 & 459.854828959783 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 110.043142857143 & 0.429149649964296 & 256.421373910705 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 110.0725 & 0.421319438359537 & 261.256638024065 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 110.101060606061 & 0.412655459370913 & 266.811108652017 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 110.1240625 & 0.404266293486245 & 272.404759621017 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 110.147580645161 & 0.394577918495638 & 279.152926410855 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 110.163 & 0.387852795478455 & 284.033017898203 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 110.173793103448 & 0.382194829022174 & 288.26604845838 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 110.18125 & 0.37685308916299 & 292.371890183303 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 110.194814814815 & 0.371976771358804 & 296.241118530819 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 110.209423076923 & 0.366847214577477 & 300.423224431072 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 110.2188 & 0.36313910754499 & 303.516745263645 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 110.231041666667 & 0.35864305923117 & 307.355848187808 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 110.237608695652 & 0.354945894329969 & 310.575810163258 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 110.246590909091 & 0.350615276646571 & 314.437499596523 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 110.25619047619 & 0.344695989938649 & 319.865022206421 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 110.26325 & 0.338599753793813 & 325.644802645497 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 110.269736842105 & 0.330541924706866 & 333.602876367031 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 110.265833333333 & 0.322804027973925 & 341.587538499489 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 110.238823529412 & 0.318386855550201 & 346.241754669517 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 110.2109375 & 0.312721327872357 & 352.425394998913 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 110.178333333333 & 0.304793158932088 & 361.48558491066 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 110.145357142857 & 0.296655734658068 & 371.290166596015 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 110.106538461538 & 0.28465954958792 & 386.800789297008 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 110.055416666667 & 0.270635978819153 & 406.654788276355 \tabularnewline
Median & 109.71 &  &  \tabularnewline
Midrange & 108.895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.177567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.265833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.177567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.265833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.265833333333 &  &  \tabularnewline
Midmean - Closest Observation & 110.177567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.265833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.269736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207463&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]110.01125[/C][C]0.436821368928874[/C][C]251.844936683747[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.949303703001[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.88700292721[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.072807009977[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]110.015416666667[/C][C]0.435653500520367[/C][C]252.52962855861[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]110.020138888889[/C][C]0.434447218298502[/C][C]253.241669539925[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]110.039722222222[/C][C]0.429917421749295[/C][C]255.955485066133[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]110.043055555556[/C][C]0.42855334217887[/C][C]256.777966066184[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]110.083333333333[/C][C]0.412533727933021[/C][C]266.846868218267[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]110.110833333333[/C][C]0.402921633961545[/C][C]273.28101559283[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]110.133194444444[/C][C]0.395910670793794[/C][C]278.176878192319[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]110.099861111111[/C][C]0.387637879607242[/C][C]284.02761160149[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]110.099861111111[/C][C]0.382322994580855[/C][C]287.976037726465[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]110.144305555556[/C][C]0.368643880854659[/C][C]298.782405665323[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]110.129027777778[/C][C]0.365888213328428[/C][C]300.990914071681[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]110.180694444444[/C][C]0.354546886564596[/C][C]310.7648060657[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]110.16625[/C][C]0.350236307299378[/C][C]314.548342658921[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]110.168194444444[/C][C]0.349347498547434[/C][C]315.354181445458[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]110.197361111111[/C][C]0.339875816929237[/C][C]324.22830817073[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]110.208472222222[/C][C]0.337533320659816[/C][C]326.511385621973[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]110.302916666667[/C][C]0.322898795507296[/C][C]341.602131074454[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]110.495416666667[/C][C]0.294409500078219[/C][C]375.311994474737[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]110.474305555556[/C][C]0.289030191738951[/C][C]382.224102232665[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]110.482638888889[/C][C]0.284877179768816[/C][C]387.825514765865[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]110.447638888889[/C][C]0.27086689882691[/C][C]407.756131765171[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]110.45375[/C][C]0.266758598993421[/C][C]414.058817285676[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]110.498472222222[/C][C]0.250850716859165[/C][C]440.494942991371[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]110.468472222222[/C][C]0.240224664971134[/C][C]459.854828959783[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]110.043142857143[/C][C]0.429149649964296[/C][C]256.421373910705[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]110.0725[/C][C]0.421319438359537[/C][C]261.256638024065[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]110.101060606061[/C][C]0.412655459370913[/C][C]266.811108652017[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]110.1240625[/C][C]0.404266293486245[/C][C]272.404759621017[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]110.147580645161[/C][C]0.394577918495638[/C][C]279.152926410855[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]110.163[/C][C]0.387852795478455[/C][C]284.033017898203[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]110.173793103448[/C][C]0.382194829022174[/C][C]288.26604845838[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]110.18125[/C][C]0.37685308916299[/C][C]292.371890183303[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]110.194814814815[/C][C]0.371976771358804[/C][C]296.241118530819[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]110.209423076923[/C][C]0.366847214577477[/C][C]300.423224431072[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]110.2188[/C][C]0.36313910754499[/C][C]303.516745263645[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]110.231041666667[/C][C]0.35864305923117[/C][C]307.355848187808[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]110.237608695652[/C][C]0.354945894329969[/C][C]310.575810163258[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]110.246590909091[/C][C]0.350615276646571[/C][C]314.437499596523[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]110.25619047619[/C][C]0.344695989938649[/C][C]319.865022206421[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]110.26325[/C][C]0.338599753793813[/C][C]325.644802645497[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]110.269736842105[/C][C]0.330541924706866[/C][C]333.602876367031[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]110.265833333333[/C][C]0.322804027973925[/C][C]341.587538499489[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]110.238823529412[/C][C]0.318386855550201[/C][C]346.241754669517[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]110.2109375[/C][C]0.312721327872357[/C][C]352.425394998913[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]110.178333333333[/C][C]0.304793158932088[/C][C]361.48558491066[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]110.145357142857[/C][C]0.296655734658068[/C][C]371.290166596015[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]110.106538461538[/C][C]0.28465954958792[/C][C]386.800789297008[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]110.055416666667[/C][C]0.270635978819153[/C][C]406.654788276355[/C][/ROW]
[ROW][C]Median[/C][C]109.71[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.177567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.265833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.177567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.265833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.265833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.177567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.265833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.269736842105[/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=207463&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207463&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
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.011250.436821368928874251.844936683747
Geometric Mean109.949303703001
Harmonic Mean109.88700292721
Quadratic Mean110.072807009977
Winsorized Mean ( 1 / 24 )110.0154166666670.435653500520367252.52962855861
Winsorized Mean ( 2 / 24 )110.0201388888890.434447218298502253.241669539925
Winsorized Mean ( 3 / 24 )110.0397222222220.429917421749295255.955485066133
Winsorized Mean ( 4 / 24 )110.0430555555560.42855334217887256.777966066184
Winsorized Mean ( 5 / 24 )110.0833333333330.412533727933021266.846868218267
Winsorized Mean ( 6 / 24 )110.1108333333330.402921633961545273.28101559283
Winsorized Mean ( 7 / 24 )110.1331944444440.395910670793794278.176878192319
Winsorized Mean ( 8 / 24 )110.0998611111110.387637879607242284.02761160149
Winsorized Mean ( 9 / 24 )110.0998611111110.382322994580855287.976037726465
Winsorized Mean ( 10 / 24 )110.1443055555560.368643880854659298.782405665323
Winsorized Mean ( 11 / 24 )110.1290277777780.365888213328428300.990914071681
Winsorized Mean ( 12 / 24 )110.1806944444440.354546886564596310.7648060657
Winsorized Mean ( 13 / 24 )110.166250.350236307299378314.548342658921
Winsorized Mean ( 14 / 24 )110.1681944444440.349347498547434315.354181445458
Winsorized Mean ( 15 / 24 )110.1973611111110.339875816929237324.22830817073
Winsorized Mean ( 16 / 24 )110.2084722222220.337533320659816326.511385621973
Winsorized Mean ( 17 / 24 )110.3029166666670.322898795507296341.602131074454
Winsorized Mean ( 18 / 24 )110.4954166666670.294409500078219375.311994474737
Winsorized Mean ( 19 / 24 )110.4743055555560.289030191738951382.224102232665
Winsorized Mean ( 20 / 24 )110.4826388888890.284877179768816387.825514765865
Winsorized Mean ( 21 / 24 )110.4476388888890.27086689882691407.756131765171
Winsorized Mean ( 22 / 24 )110.453750.266758598993421414.058817285676
Winsorized Mean ( 23 / 24 )110.4984722222220.250850716859165440.494942991371
Winsorized Mean ( 24 / 24 )110.4684722222220.240224664971134459.854828959783
Trimmed Mean ( 1 / 24 )110.0431428571430.429149649964296256.421373910705
Trimmed Mean ( 2 / 24 )110.07250.421319438359537261.256638024065
Trimmed Mean ( 3 / 24 )110.1010606060610.412655459370913266.811108652017
Trimmed Mean ( 4 / 24 )110.12406250.404266293486245272.404759621017
Trimmed Mean ( 5 / 24 )110.1475806451610.394577918495638279.152926410855
Trimmed Mean ( 6 / 24 )110.1630.387852795478455284.033017898203
Trimmed Mean ( 7 / 24 )110.1737931034480.382194829022174288.26604845838
Trimmed Mean ( 8 / 24 )110.181250.37685308916299292.371890183303
Trimmed Mean ( 9 / 24 )110.1948148148150.371976771358804296.241118530819
Trimmed Mean ( 10 / 24 )110.2094230769230.366847214577477300.423224431072
Trimmed Mean ( 11 / 24 )110.21880.36313910754499303.516745263645
Trimmed Mean ( 12 / 24 )110.2310416666670.35864305923117307.355848187808
Trimmed Mean ( 13 / 24 )110.2376086956520.354945894329969310.575810163258
Trimmed Mean ( 14 / 24 )110.2465909090910.350615276646571314.437499596523
Trimmed Mean ( 15 / 24 )110.256190476190.344695989938649319.865022206421
Trimmed Mean ( 16 / 24 )110.263250.338599753793813325.644802645497
Trimmed Mean ( 17 / 24 )110.2697368421050.330541924706866333.602876367031
Trimmed Mean ( 18 / 24 )110.2658333333330.322804027973925341.587538499489
Trimmed Mean ( 19 / 24 )110.2388235294120.318386855550201346.241754669517
Trimmed Mean ( 20 / 24 )110.21093750.312721327872357352.425394998913
Trimmed Mean ( 21 / 24 )110.1783333333330.304793158932088361.48558491066
Trimmed Mean ( 22 / 24 )110.1453571428570.296655734658068371.290166596015
Trimmed Mean ( 23 / 24 )110.1065384615380.28465954958792386.800789297008
Trimmed Mean ( 24 / 24 )110.0554166666670.270635978819153406.654788276355
Median109.71
Midrange108.895
Midmean - Weighted Average at Xnp110.177567567568
Midmean - Weighted Average at X(n+1)p110.265833333333
Midmean - Empirical Distribution Function110.177567567568
Midmean - Empirical Distribution Function - Averaging110.265833333333
Midmean - Empirical Distribution Function - Interpolation110.265833333333
Midmean - Closest Observation110.177567567568
Midmean - True Basic - Statistics Graphics Toolkit110.265833333333
Midmean - MS Excel (old versions)110.269736842105
Number of observations72



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')