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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 computationMon, 04 Mar 2013 03:22:35 -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/04/t1362385422kgdbs7jdiozo5hx.htm/, Retrieved Sat, 27 Apr 2024 20:11:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207296, Retrieved Sat, 27 Apr 2024 20:11:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten gemi...] [2013-03-04 08:22:35] [bc4d9ad98829fcb778aa9177827398a7] [Current]
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Dataseries X:
4,00
4,00
4,00
4,00
4,00
4,00
4,00
4,00
4,06
4,07
4,07
4,07
4,07
4,07
4,30
4,44
4,52
4,52
4,52
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,70
4,72
4,73
4,73
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,98
5,00
5,03
5,04
5,04
5,05
5,05
5,05
5,06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207296&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207296&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.621666666666670.0407067838759233113.535539450962
Geometric Mean4.60848557028621
Harmonic Mean4.59485983057024
Quadratic Mean4.63437728047445
Winsorized Mean ( 1 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 2 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 3 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 4 / 24 )4.620972222222220.040604373768118113.804789814307
Winsorized Mean ( 5 / 24 )4.620972222222220.040604373768118113.804789814307
Winsorized Mean ( 6 / 24 )4.620138888888890.0404843973188893114.121468883352
Winsorized Mean ( 7 / 24 )4.617222222222220.0400802316556493115.19948941142
Winsorized Mean ( 8 / 24 )4.621666666666670.0383736265065944120.438621193971
Winsorized Mean ( 9 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 10 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 11 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 12 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 13 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 14 / 24 )4.666388888888890.0293635578091732158.917693803136
Winsorized Mean ( 15 / 24 )4.695555555555560.0246317867278374190.629920900091
Winsorized Mean ( 16 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 17 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 18 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 19 / 24 )4.715972222222220.0219141336494982215.202311788868
Winsorized Mean ( 20 / 24 )4.693750.0184200228497154254.817816367287
Winsorized Mean ( 21 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 22 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 23 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 24 / 24 )4.690833333333330.0179851159989611260.817518975374
Trimmed Mean ( 1 / 24 )4.624285714285710.0404214707457477114.401718417734
Trimmed Mean ( 2 / 24 )4.627205882352940.0400837827496192115.438353492146
Trimmed Mean ( 3 / 24 )4.630303030303030.0396587833914737116.753531861961
Trimmed Mean ( 4 / 24 )4.633593750.0391288870397212118.418746367518
Trimmed Mean ( 5 / 24 )4.637258064516130.0384998776532417120.448644182267
Trimmed Mean ( 6 / 24 )4.641166666666670.037719670471647123.043669486861
Trimmed Mean ( 7 / 24 )4.645517241379310.0367840384104052126.291659157936
Trimmed Mean ( 8 / 24 )4.650714285714290.0357179218928169130.206743260995
Trimmed Mean ( 9 / 24 )4.655555555555560.0348237718379576133.689009255483
Trimmed Mean ( 10 / 24 )4.660769230769230.0337878285333931137.942254151163
Trimmed Mean ( 11 / 24 )4.66640.0324594063597055143.761101120838
Trimmed Mean ( 12 / 24 )4.67250.0307392661309522152.004279480672
Trimmed Mean ( 13 / 24 )4.679130434782610.0284729316103655164.33609643059
Trimmed Mean ( 14 / 24 )4.686363636363640.0253955825699826184.534598623576
Trimmed Mean ( 15 / 24 )4.688809523809520.0239802531542463195.527940995871
Trimmed Mean ( 16 / 24 )4.6880.0233320512468281200.925325870665
Trimmed Mean ( 17 / 24 )4.6850.0229593926892683204.055920093647
Trimmed Mean ( 18 / 24 )4.681666666666670.0224014597030059208.989357333642
Trimmed Mean ( 19 / 24 )4.677941176470590.0215809193624476216.762830994612
Trimmed Mean ( 20 / 24 )4.67343750.0204466722536945228.567144913059
Trimmed Mean ( 21 / 24 )4.6710.019973257983683233.862698004298
Trimmed Mean ( 22 / 24 )4.668571428571430.01935954904118241.150835623332
Trimmed Mean ( 23 / 24 )4.665769230769230.018365293998971254.053609543668
Trimmed Mean ( 24 / 24 )4.66250.0167380716774144278.556579865253
Median4.63
Midrange4.53
Midmean - Weighted Average at Xnp4.73
Midmean - Weighted Average at X(n+1)p4.73
Midmean - Empirical Distribution Function4.73
Midmean - Empirical Distribution Function - Averaging4.73
Midmean - Empirical Distribution Function - Interpolation4.73
Midmean - Closest Observation4.73
Midmean - True Basic - Statistics Graphics Toolkit4.73
Midmean - MS Excel (old versions)4.73
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.62166666666667 & 0.0407067838759233 & 113.535539450962 \tabularnewline
Geometric Mean & 4.60848557028621 &  &  \tabularnewline
Harmonic Mean & 4.59485983057024 &  &  \tabularnewline
Quadratic Mean & 4.63437728047445 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.62152777777778 & 0.040685951193257 & 113.590260083282 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.62152777777778 & 0.040685951193257 & 113.590260083282 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.62152777777778 & 0.040685951193257 & 113.590260083282 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.62097222222222 & 0.040604373768118 & 113.804789814307 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.62097222222222 & 0.040604373768118 & 113.804789814307 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.62013888888889 & 0.0404843973188893 & 114.121468883352 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.61722222222222 & 0.0400802316556493 & 115.19948941142 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.62166666666667 & 0.0383736265065944 & 120.438621193971 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.62166666666667 & 0.037953826654851 & 121.770769221658 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.62166666666667 & 0.037953826654851 & 121.770769221658 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.62166666666667 & 0.037953826654851 & 121.770769221658 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.62166666666667 & 0.037953826654851 & 121.770769221658 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.62166666666667 & 0.037953826654851 & 121.770769221658 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.66638888888889 & 0.0293635578091732 & 158.917693803136 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.69555555555556 & 0.0246317867278374 & 190.629920900091 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.71333333333333 & 0.0222334674208146 & 211.992724487085 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.71333333333333 & 0.0222334674208146 & 211.992724487085 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.71333333333333 & 0.0222334674208146 & 211.992724487085 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.71597222222222 & 0.0219141336494982 & 215.202311788868 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.69375 & 0.0184200228497154 & 254.817816367287 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.69083333333333 & 0.0179851159989611 & 260.817518975374 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.69083333333333 & 0.0179851159989611 & 260.817518975374 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.69083333333333 & 0.0179851159989611 & 260.817518975374 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.69083333333333 & 0.0179851159989611 & 260.817518975374 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.62428571428571 & 0.0404214707457477 & 114.401718417734 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.62720588235294 & 0.0400837827496192 & 115.438353492146 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.63030303030303 & 0.0396587833914737 & 116.753531861961 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.63359375 & 0.0391288870397212 & 118.418746367518 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.63725806451613 & 0.0384998776532417 & 120.448644182267 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.64116666666667 & 0.037719670471647 & 123.043669486861 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.64551724137931 & 0.0367840384104052 & 126.291659157936 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.65071428571429 & 0.0357179218928169 & 130.206743260995 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.65555555555556 & 0.0348237718379576 & 133.689009255483 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.66076923076923 & 0.0337878285333931 & 137.942254151163 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.6664 & 0.0324594063597055 & 143.761101120838 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.6725 & 0.0307392661309522 & 152.004279480672 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.67913043478261 & 0.0284729316103655 & 164.33609643059 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.68636363636364 & 0.0253955825699826 & 184.534598623576 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.68880952380952 & 0.0239802531542463 & 195.527940995871 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.688 & 0.0233320512468281 & 200.925325870665 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.685 & 0.0229593926892683 & 204.055920093647 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.68166666666667 & 0.0224014597030059 & 208.989357333642 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.67794117647059 & 0.0215809193624476 & 216.762830994612 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.6734375 & 0.0204466722536945 & 228.567144913059 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.671 & 0.019973257983683 & 233.862698004298 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.66857142857143 & 0.01935954904118 & 241.150835623332 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.66576923076923 & 0.018365293998971 & 254.053609543668 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.6625 & 0.0167380716774144 & 278.556579865253 \tabularnewline
Median & 4.63 &  &  \tabularnewline
Midrange & 4.53 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.73 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.73 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.73 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.73 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.73 &  &  \tabularnewline
Midmean - Closest Observation & 4.73 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.73 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.73 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207296&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]4.62166666666667[/C][C]0.0407067838759233[/C][C]113.535539450962[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.60848557028621[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.59485983057024[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.63437728047445[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.62152777777778[/C][C]0.040685951193257[/C][C]113.590260083282[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.62152777777778[/C][C]0.040685951193257[/C][C]113.590260083282[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.62152777777778[/C][C]0.040685951193257[/C][C]113.590260083282[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.62097222222222[/C][C]0.040604373768118[/C][C]113.804789814307[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.62097222222222[/C][C]0.040604373768118[/C][C]113.804789814307[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.62013888888889[/C][C]0.0404843973188893[/C][C]114.121468883352[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.61722222222222[/C][C]0.0400802316556493[/C][C]115.19948941142[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.62166666666667[/C][C]0.0383736265065944[/C][C]120.438621193971[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.62166666666667[/C][C]0.037953826654851[/C][C]121.770769221658[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.62166666666667[/C][C]0.037953826654851[/C][C]121.770769221658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.62166666666667[/C][C]0.037953826654851[/C][C]121.770769221658[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.62166666666667[/C][C]0.037953826654851[/C][C]121.770769221658[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.62166666666667[/C][C]0.037953826654851[/C][C]121.770769221658[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.66638888888889[/C][C]0.0293635578091732[/C][C]158.917693803136[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.69555555555556[/C][C]0.0246317867278374[/C][C]190.629920900091[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.71333333333333[/C][C]0.0222334674208146[/C][C]211.992724487085[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.71333333333333[/C][C]0.0222334674208146[/C][C]211.992724487085[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.71333333333333[/C][C]0.0222334674208146[/C][C]211.992724487085[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.71597222222222[/C][C]0.0219141336494982[/C][C]215.202311788868[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.69375[/C][C]0.0184200228497154[/C][C]254.817816367287[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.69083333333333[/C][C]0.0179851159989611[/C][C]260.817518975374[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.69083333333333[/C][C]0.0179851159989611[/C][C]260.817518975374[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.69083333333333[/C][C]0.0179851159989611[/C][C]260.817518975374[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.69083333333333[/C][C]0.0179851159989611[/C][C]260.817518975374[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.62428571428571[/C][C]0.0404214707457477[/C][C]114.401718417734[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.62720588235294[/C][C]0.0400837827496192[/C][C]115.438353492146[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.63030303030303[/C][C]0.0396587833914737[/C][C]116.753531861961[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.63359375[/C][C]0.0391288870397212[/C][C]118.418746367518[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.63725806451613[/C][C]0.0384998776532417[/C][C]120.448644182267[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.64116666666667[/C][C]0.037719670471647[/C][C]123.043669486861[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.64551724137931[/C][C]0.0367840384104052[/C][C]126.291659157936[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.65071428571429[/C][C]0.0357179218928169[/C][C]130.206743260995[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.65555555555556[/C][C]0.0348237718379576[/C][C]133.689009255483[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.66076923076923[/C][C]0.0337878285333931[/C][C]137.942254151163[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.6664[/C][C]0.0324594063597055[/C][C]143.761101120838[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.6725[/C][C]0.0307392661309522[/C][C]152.004279480672[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.67913043478261[/C][C]0.0284729316103655[/C][C]164.33609643059[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.68636363636364[/C][C]0.0253955825699826[/C][C]184.534598623576[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.68880952380952[/C][C]0.0239802531542463[/C][C]195.527940995871[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.688[/C][C]0.0233320512468281[/C][C]200.925325870665[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.685[/C][C]0.0229593926892683[/C][C]204.055920093647[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.68166666666667[/C][C]0.0224014597030059[/C][C]208.989357333642[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.67794117647059[/C][C]0.0215809193624476[/C][C]216.762830994612[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.6734375[/C][C]0.0204466722536945[/C][C]228.567144913059[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.671[/C][C]0.019973257983683[/C][C]233.862698004298[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.66857142857143[/C][C]0.01935954904118[/C][C]241.150835623332[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.66576923076923[/C][C]0.018365293998971[/C][C]254.053609543668[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.6625[/C][C]0.0167380716774144[/C][C]278.556579865253[/C][/ROW]
[ROW][C]Median[/C][C]4.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.73[/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=207296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207296&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 Mean4.621666666666670.0407067838759233113.535539450962
Geometric Mean4.60848557028621
Harmonic Mean4.59485983057024
Quadratic Mean4.63437728047445
Winsorized Mean ( 1 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 2 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 3 / 24 )4.621527777777780.040685951193257113.590260083282
Winsorized Mean ( 4 / 24 )4.620972222222220.040604373768118113.804789814307
Winsorized Mean ( 5 / 24 )4.620972222222220.040604373768118113.804789814307
Winsorized Mean ( 6 / 24 )4.620138888888890.0404843973188893114.121468883352
Winsorized Mean ( 7 / 24 )4.617222222222220.0400802316556493115.19948941142
Winsorized Mean ( 8 / 24 )4.621666666666670.0383736265065944120.438621193971
Winsorized Mean ( 9 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 10 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 11 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 12 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 13 / 24 )4.621666666666670.037953826654851121.770769221658
Winsorized Mean ( 14 / 24 )4.666388888888890.0293635578091732158.917693803136
Winsorized Mean ( 15 / 24 )4.695555555555560.0246317867278374190.629920900091
Winsorized Mean ( 16 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 17 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 18 / 24 )4.713333333333330.0222334674208146211.992724487085
Winsorized Mean ( 19 / 24 )4.715972222222220.0219141336494982215.202311788868
Winsorized Mean ( 20 / 24 )4.693750.0184200228497154254.817816367287
Winsorized Mean ( 21 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 22 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 23 / 24 )4.690833333333330.0179851159989611260.817518975374
Winsorized Mean ( 24 / 24 )4.690833333333330.0179851159989611260.817518975374
Trimmed Mean ( 1 / 24 )4.624285714285710.0404214707457477114.401718417734
Trimmed Mean ( 2 / 24 )4.627205882352940.0400837827496192115.438353492146
Trimmed Mean ( 3 / 24 )4.630303030303030.0396587833914737116.753531861961
Trimmed Mean ( 4 / 24 )4.633593750.0391288870397212118.418746367518
Trimmed Mean ( 5 / 24 )4.637258064516130.0384998776532417120.448644182267
Trimmed Mean ( 6 / 24 )4.641166666666670.037719670471647123.043669486861
Trimmed Mean ( 7 / 24 )4.645517241379310.0367840384104052126.291659157936
Trimmed Mean ( 8 / 24 )4.650714285714290.0357179218928169130.206743260995
Trimmed Mean ( 9 / 24 )4.655555555555560.0348237718379576133.689009255483
Trimmed Mean ( 10 / 24 )4.660769230769230.0337878285333931137.942254151163
Trimmed Mean ( 11 / 24 )4.66640.0324594063597055143.761101120838
Trimmed Mean ( 12 / 24 )4.67250.0307392661309522152.004279480672
Trimmed Mean ( 13 / 24 )4.679130434782610.0284729316103655164.33609643059
Trimmed Mean ( 14 / 24 )4.686363636363640.0253955825699826184.534598623576
Trimmed Mean ( 15 / 24 )4.688809523809520.0239802531542463195.527940995871
Trimmed Mean ( 16 / 24 )4.6880.0233320512468281200.925325870665
Trimmed Mean ( 17 / 24 )4.6850.0229593926892683204.055920093647
Trimmed Mean ( 18 / 24 )4.681666666666670.0224014597030059208.989357333642
Trimmed Mean ( 19 / 24 )4.677941176470590.0215809193624476216.762830994612
Trimmed Mean ( 20 / 24 )4.67343750.0204466722536945228.567144913059
Trimmed Mean ( 21 / 24 )4.6710.019973257983683233.862698004298
Trimmed Mean ( 22 / 24 )4.668571428571430.01935954904118241.150835623332
Trimmed Mean ( 23 / 24 )4.665769230769230.018365293998971254.053609543668
Trimmed Mean ( 24 / 24 )4.66250.0167380716774144278.556579865253
Median4.63
Midrange4.53
Midmean - Weighted Average at Xnp4.73
Midmean - Weighted Average at X(n+1)p4.73
Midmean - Empirical Distribution Function4.73
Midmean - Empirical Distribution Function - Averaging4.73
Midmean - Empirical Distribution Function - Interpolation4.73
Midmean - Closest Observation4.73
Midmean - True Basic - Statistics Graphics Toolkit4.73
Midmean - MS Excel (old versions)4.73
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')