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Author

*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 20 Oct 2009 09:33:02 -0600

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/2009/Oct/20/t1256052942uftghgosdrkq4lw.htm/, Retrieved Fri, 03 May 2024 03:16:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48733, Retrieved Fri, 03 May 2024 03:16:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Central tendency

Estimated Impact

105

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

-       [Central Tendency] [Ws 3 part 2 ex 1] [2009-10-20 15:33:02] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]

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Boxplots

-1,4
0
4,5
5
0,5
4,6
6,1
3,5
5,2
3,6
3,4
3,1
0,1
2,9
4,4
2
-0,1
1,8
3
2
0,8
3,2
0,8
1,1
-0,5
2,2
2,1
1,7
-1,6
-0,2
2
1,6
-0,6
3,3
0
-0,3
0,2
1,3
-0,1
1,4
-2,7
-1,5
0,8
-0,6
0
1,3
-1,2
-1,8
-1,1
-0,4
0,1
0
-3,9
-1,9
0,1
-2,4
-1,4
0,1
-2,5
-3,2
-2,9
-2,8
-1,1
-1,5
-6,1
-2,7
-2,3
-2,8
-2,4
-1,8
-3,1
-3

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48733&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48733&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' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.248611111111111	0.29285968652582	0.848908615796092
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	2.48017136504718
Winsorized Mean ( 1 / 24 )	0.266666666666667	0.281678403511336	0.94670611357656
Winsorized Mean ( 2 / 24 )	0.280555555555556	0.276573877822783	1.01439643455889
Winsorized Mean ( 3 / 24 )	0.268055555555555	0.271967749780255	0.985615227438324
Winsorized Mean ( 4 / 24 )	0.268055555555556	0.269772308712512	0.99363628844951
Winsorized Mean ( 5 / 24 )	0.268055555555556	0.267075877258094	1.00366816467110
Winsorized Mean ( 6 / 24 )	0.209722222222222	0.252074023785124	0.831986648497334
Winsorized Mean ( 7 / 24 )	0.2	0.250250265970195	0.799199949796737
Winsorized Mean ( 8 / 24 )	0.2	0.246342573536886	0.811877529443983
Winsorized Mean ( 9 / 24 )	0.1875	0.244076438647759	0.768201965903772
Winsorized Mean ( 10 / 24 )	0.201388888888889	0.237047015135822	0.84957361211023
Winsorized Mean ( 11 / 24 )	0.201388888888889	0.231907894939673	0.868400314449307
Winsorized Mean ( 12 / 24 )	0.184722222222222	0.228997780041162	0.806655078442329
Winsorized Mean ( 13 / 24 )	0.184722222222222	0.223034448259491	0.82822283133279
Winsorized Mean ( 14 / 24 )	0.126388888888889	0.188738015668576	0.66965252570435
Winsorized Mean ( 15 / 24 )	0.126388888888889	0.182413323850359	0.692870927523752
Winsorized Mean ( 16 / 24 )	0.104166666666667	0.179062913511718	0.581732222623808
Winsorized Mean ( 17 / 24 )	0.151388888888889	0.172140090340648	0.879451663986612
Winsorized Mean ( 18 / 24 )	0.176388888888889	0.168597884613736	1.04621056956321
Winsorized Mean ( 19 / 24 )	0.123611111111111	0.160696998280855	0.76921854442528
Winsorized Mean ( 20 / 24 )	0.123611111111111	0.152707605879373	0.809462700952527
Winsorized Mean ( 21 / 24 )	0.0944444444444445	0.148504396915786	0.635970694510833
Winsorized Mean ( 22 / 24 )	0.0944444444444444	0.131276519623338	0.719431355397194
Winsorized Mean ( 23 / 24 )	0.0944444444444445	0.122408806222115	0.771549428176528
Winsorized Mean ( 24 / 24 )	0.0944444444444445	0.122408806222115	0.771549428176528
Trimmed Mean ( 1 / 24 )	0.255714285714286	0.274481523016347	0.931626591488478
Trimmed Mean ( 2 / 24 )	0.244117647058824	0.265918838352252	0.918015619244888
Trimmed Mean ( 3 / 24 )	0.224242424242424	0.258947669615600	0.865975834327086
Trimmed Mean ( 4 / 24 )	0.2078125	0.252686995502207	0.822410744118348
Trimmed Mean ( 5 / 24 )	0.190322580645161	0.245915439472201	0.773935060985368
Trimmed Mean ( 6 / 24 )	0.171666666666667	0.238534741653114	0.719671547536294
Trimmed Mean ( 7 / 24 )	0.163793103448276	0.23387757299968	0.700336938456686
Trimmed Mean ( 8 / 24 )	0.157142857142857	0.228573457783200	0.687493896565653
Trimmed Mean ( 9 / 24 )	0.15	0.222929952679171	0.6728570934381
Trimmed Mean ( 10 / 24 )	0.144230769230769	0.216398141901774	0.666506504922937
Trimmed Mean ( 11 / 24 )	0.136	0.209815468000443	0.648188626396758
Trimmed Mean ( 12 / 24 )	0.127083333333333	0.2026364259674	0.627149500523555
Trimmed Mean ( 13 / 24 )	0.119565217391304	0.194106887363399	0.615976171764887
Trimmed Mean ( 14 / 24 )	0.111363636363636	0.184500236599850	0.60359617101828
Trimmed Mean ( 15 / 24 )	0.109523809523810	0.180327793022128	0.607359562762297
Trimmed Mean ( 16 / 24 )	0.1075	0.176118677208121	0.610383871285645
Trimmed Mean ( 17 / 24 )	0.107894736842105	0.171113896458263	0.630543392882311
Trimmed Mean ( 18 / 24 )	0.102777777777778	0.165878427040165	0.619597012171401
Trimmed Mean ( 19 / 24 )	0.0941176470588235	0.159373840296817	0.590546396344215
Trimmed Mean ( 20 / 24 )	0.090625	0.152423921729244	0.594558905005611
Trimmed Mean ( 21 / 24 )	0.0866666666666667	0.144773571390569	0.598635965350735
Trimmed Mean ( 22 / 24 )	0.0857142857142857	0.134785179436079	0.635932571169185
Trimmed Mean ( 23 / 24 )	0.0846153846153846	0.126210118781500	0.670432651773939
Trimmed Mean ( 24 / 24 )	0.0833333333333333	0.116355693212645	0.716194721826272
Median	0
Midrange	0
Midmean - Weighted Average at Xnp	0.156410256410256
Midmean - Weighted Average at X(n+1)p	0.202631578947368
Midmean - Empirical Distribution Function	0.156410256410256
Midmean - Empirical Distribution Function - Averaging	0.202631578947368
Midmean - Empirical Distribution Function - Interpolation	0.202631578947368
Midmean - Closest Observation	0.156410256410256
Midmean - True Basic - Statistics Graphics Toolkit	0.202631578947368
Midmean - MS Excel (old versions)	0.156410256410256
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.248611111111111 & 0.29285968652582 & 0.848908615796092 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.48017136504718 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.266666666666667 & 0.281678403511336 & 0.94670611357656 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.280555555555556 & 0.276573877822783 & 1.01439643455889 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.268055555555555 & 0.271967749780255 & 0.985615227438324 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.268055555555556 & 0.269772308712512 & 0.99363628844951 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.268055555555556 & 0.267075877258094 & 1.00366816467110 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.209722222222222 & 0.252074023785124 & 0.831986648497334 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.2 & 0.250250265970195 & 0.799199949796737 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.2 & 0.246342573536886 & 0.811877529443983 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.1875 & 0.244076438647759 & 0.768201965903772 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.201388888888889 & 0.237047015135822 & 0.84957361211023 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.201388888888889 & 0.231907894939673 & 0.868400314449307 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.184722222222222 & 0.228997780041162 & 0.806655078442329 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.184722222222222 & 0.223034448259491 & 0.82822283133279 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.126388888888889 & 0.188738015668576 & 0.66965252570435 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.126388888888889 & 0.182413323850359 & 0.692870927523752 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.104166666666667 & 0.179062913511718 & 0.581732222623808 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.151388888888889 & 0.172140090340648 & 0.879451663986612 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.176388888888889 & 0.168597884613736 & 1.04621056956321 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.123611111111111 & 0.160696998280855 & 0.76921854442528 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.123611111111111 & 0.152707605879373 & 0.809462700952527 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.0944444444444445 & 0.148504396915786 & 0.635970694510833 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.0944444444444444 & 0.131276519623338 & 0.719431355397194 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.0944444444444445 & 0.122408806222115 & 0.771549428176528 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.0944444444444445 & 0.122408806222115 & 0.771549428176528 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.255714285714286 & 0.274481523016347 & 0.931626591488478 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.244117647058824 & 0.265918838352252 & 0.918015619244888 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.224242424242424 & 0.258947669615600 & 0.865975834327086 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.2078125 & 0.252686995502207 & 0.822410744118348 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.190322580645161 & 0.245915439472201 & 0.773935060985368 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.171666666666667 & 0.238534741653114 & 0.719671547536294 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.163793103448276 & 0.23387757299968 & 0.700336938456686 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.157142857142857 & 0.228573457783200 & 0.687493896565653 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.15 & 0.222929952679171 & 0.6728570934381 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.144230769230769 & 0.216398141901774 & 0.666506504922937 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.136 & 0.209815468000443 & 0.648188626396758 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.127083333333333 & 0.2026364259674 & 0.627149500523555 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.119565217391304 & 0.194106887363399 & 0.615976171764887 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.111363636363636 & 0.184500236599850 & 0.60359617101828 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.109523809523810 & 0.180327793022128 & 0.607359562762297 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.1075 & 0.176118677208121 & 0.610383871285645 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.107894736842105 & 0.171113896458263 & 0.630543392882311 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.102777777777778 & 0.165878427040165 & 0.619597012171401 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.0941176470588235 & 0.159373840296817 & 0.590546396344215 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.090625 & 0.152423921729244 & 0.594558905005611 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.0866666666666667 & 0.144773571390569 & 0.598635965350735 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.0857142857142857 & 0.134785179436079 & 0.635932571169185 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.0846153846153846 & 0.126210118781500 & 0.670432651773939 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.0833333333333333 & 0.116355693212645 & 0.716194721826272 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 0 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.156410256410256 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.202631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.156410256410256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.202631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.202631578947368 &  &  \tabularnewline
Midmean - Closest Observation & 0.156410256410256 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.202631578947368 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.156410256410256 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48733&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.248611111111111[/C][C]0.29285968652582[/C][C]0.848908615796092[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.48017136504718[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.266666666666667[/C][C]0.281678403511336[/C][C]0.94670611357656[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.280555555555556[/C][C]0.276573877822783[/C][C]1.01439643455889[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.268055555555555[/C][C]0.271967749780255[/C][C]0.985615227438324[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.268055555555556[/C][C]0.269772308712512[/C][C]0.99363628844951[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.268055555555556[/C][C]0.267075877258094[/C][C]1.00366816467110[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.209722222222222[/C][C]0.252074023785124[/C][C]0.831986648497334[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.2[/C][C]0.250250265970195[/C][C]0.799199949796737[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.2[/C][C]0.246342573536886[/C][C]0.811877529443983[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.1875[/C][C]0.244076438647759[/C][C]0.768201965903772[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.201388888888889[/C][C]0.237047015135822[/C][C]0.84957361211023[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.201388888888889[/C][C]0.231907894939673[/C][C]0.868400314449307[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.184722222222222[/C][C]0.228997780041162[/C][C]0.806655078442329[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.184722222222222[/C][C]0.223034448259491[/C][C]0.82822283133279[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.126388888888889[/C][C]0.188738015668576[/C][C]0.66965252570435[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.126388888888889[/C][C]0.182413323850359[/C][C]0.692870927523752[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.104166666666667[/C][C]0.179062913511718[/C][C]0.581732222623808[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.151388888888889[/C][C]0.172140090340648[/C][C]0.879451663986612[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.176388888888889[/C][C]0.168597884613736[/C][C]1.04621056956321[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.123611111111111[/C][C]0.160696998280855[/C][C]0.76921854442528[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.123611111111111[/C][C]0.152707605879373[/C][C]0.809462700952527[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.0944444444444445[/C][C]0.148504396915786[/C][C]0.635970694510833[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.0944444444444444[/C][C]0.131276519623338[/C][C]0.719431355397194[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.0944444444444445[/C][C]0.122408806222115[/C][C]0.771549428176528[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.0944444444444445[/C][C]0.122408806222115[/C][C]0.771549428176528[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.255714285714286[/C][C]0.274481523016347[/C][C]0.931626591488478[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.244117647058824[/C][C]0.265918838352252[/C][C]0.918015619244888[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.224242424242424[/C][C]0.258947669615600[/C][C]0.865975834327086[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.2078125[/C][C]0.252686995502207[/C][C]0.822410744118348[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.190322580645161[/C][C]0.245915439472201[/C][C]0.773935060985368[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.171666666666667[/C][C]0.238534741653114[/C][C]0.719671547536294[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.163793103448276[/C][C]0.23387757299968[/C][C]0.700336938456686[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.157142857142857[/C][C]0.228573457783200[/C][C]0.687493896565653[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.15[/C][C]0.222929952679171[/C][C]0.6728570934381[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.144230769230769[/C][C]0.216398141901774[/C][C]0.666506504922937[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.136[/C][C]0.209815468000443[/C][C]0.648188626396758[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.127083333333333[/C][C]0.2026364259674[/C][C]0.627149500523555[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.119565217391304[/C][C]0.194106887363399[/C][C]0.615976171764887[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.111363636363636[/C][C]0.184500236599850[/C][C]0.60359617101828[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.109523809523810[/C][C]0.180327793022128[/C][C]0.607359562762297[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.1075[/C][C]0.176118677208121[/C][C]0.610383871285645[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.107894736842105[/C][C]0.171113896458263[/C][C]0.630543392882311[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.102777777777778[/C][C]0.165878427040165[/C][C]0.619597012171401[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.0941176470588235[/C][C]0.159373840296817[/C][C]0.590546396344215[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.090625[/C][C]0.152423921729244[/C][C]0.594558905005611[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.0866666666666667[/C][C]0.144773571390569[/C][C]0.598635965350735[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.0857142857142857[/C][C]0.134785179436079[/C][C]0.635932571169185[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.0846153846153846[/C][C]0.126210118781500[/C][C]0.670432651773939[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.0833333333333333[/C][C]0.116355693212645[/C][C]0.716194721826272[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.156410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.202631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.156410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.202631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.202631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.156410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.202631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.156410256410256[/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=48733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48733&T=1

As an alternative you can also use a QR Code:

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.248611111111111	0.29285968652582	0.848908615796092
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	2.48017136504718
Winsorized Mean ( 1 / 24 )	0.266666666666667	0.281678403511336	0.94670611357656
Winsorized Mean ( 2 / 24 )	0.280555555555556	0.276573877822783	1.01439643455889
Winsorized Mean ( 3 / 24 )	0.268055555555555	0.271967749780255	0.985615227438324
Winsorized Mean ( 4 / 24 )	0.268055555555556	0.269772308712512	0.99363628844951
Winsorized Mean ( 5 / 24 )	0.268055555555556	0.267075877258094	1.00366816467110
Winsorized Mean ( 6 / 24 )	0.209722222222222	0.252074023785124	0.831986648497334
Winsorized Mean ( 7 / 24 )	0.2	0.250250265970195	0.799199949796737
Winsorized Mean ( 8 / 24 )	0.2	0.246342573536886	0.811877529443983
Winsorized Mean ( 9 / 24 )	0.1875	0.244076438647759	0.768201965903772
Winsorized Mean ( 10 / 24 )	0.201388888888889	0.237047015135822	0.84957361211023
Winsorized Mean ( 11 / 24 )	0.201388888888889	0.231907894939673	0.868400314449307
Winsorized Mean ( 12 / 24 )	0.184722222222222	0.228997780041162	0.806655078442329
Winsorized Mean ( 13 / 24 )	0.184722222222222	0.223034448259491	0.82822283133279
Winsorized Mean ( 14 / 24 )	0.126388888888889	0.188738015668576	0.66965252570435
Winsorized Mean ( 15 / 24 )	0.126388888888889	0.182413323850359	0.692870927523752
Winsorized Mean ( 16 / 24 )	0.104166666666667	0.179062913511718	0.581732222623808
Winsorized Mean ( 17 / 24 )	0.151388888888889	0.172140090340648	0.879451663986612
Winsorized Mean ( 18 / 24 )	0.176388888888889	0.168597884613736	1.04621056956321
Winsorized Mean ( 19 / 24 )	0.123611111111111	0.160696998280855	0.76921854442528
Winsorized Mean ( 20 / 24 )	0.123611111111111	0.152707605879373	0.809462700952527
Winsorized Mean ( 21 / 24 )	0.0944444444444445	0.148504396915786	0.635970694510833
Winsorized Mean ( 22 / 24 )	0.0944444444444444	0.131276519623338	0.719431355397194
Winsorized Mean ( 23 / 24 )	0.0944444444444445	0.122408806222115	0.771549428176528
Winsorized Mean ( 24 / 24 )	0.0944444444444445	0.122408806222115	0.771549428176528
Trimmed Mean ( 1 / 24 )	0.255714285714286	0.274481523016347	0.931626591488478
Trimmed Mean ( 2 / 24 )	0.244117647058824	0.265918838352252	0.918015619244888
Trimmed Mean ( 3 / 24 )	0.224242424242424	0.258947669615600	0.865975834327086
Trimmed Mean ( 4 / 24 )	0.2078125	0.252686995502207	0.822410744118348
Trimmed Mean ( 5 / 24 )	0.190322580645161	0.245915439472201	0.773935060985368
Trimmed Mean ( 6 / 24 )	0.171666666666667	0.238534741653114	0.719671547536294
Trimmed Mean ( 7 / 24 )	0.163793103448276	0.23387757299968	0.700336938456686
Trimmed Mean ( 8 / 24 )	0.157142857142857	0.228573457783200	0.687493896565653
Trimmed Mean ( 9 / 24 )	0.15	0.222929952679171	0.6728570934381
Trimmed Mean ( 10 / 24 )	0.144230769230769	0.216398141901774	0.666506504922937
Trimmed Mean ( 11 / 24 )	0.136	0.209815468000443	0.648188626396758
Trimmed Mean ( 12 / 24 )	0.127083333333333	0.2026364259674	0.627149500523555
Trimmed Mean ( 13 / 24 )	0.119565217391304	0.194106887363399	0.615976171764887
Trimmed Mean ( 14 / 24 )	0.111363636363636	0.184500236599850	0.60359617101828
Trimmed Mean ( 15 / 24 )	0.109523809523810	0.180327793022128	0.607359562762297
Trimmed Mean ( 16 / 24 )	0.1075	0.176118677208121	0.610383871285645
Trimmed Mean ( 17 / 24 )	0.107894736842105	0.171113896458263	0.630543392882311
Trimmed Mean ( 18 / 24 )	0.102777777777778	0.165878427040165	0.619597012171401
Trimmed Mean ( 19 / 24 )	0.0941176470588235	0.159373840296817	0.590546396344215
Trimmed Mean ( 20 / 24 )	0.090625	0.152423921729244	0.594558905005611
Trimmed Mean ( 21 / 24 )	0.0866666666666667	0.144773571390569	0.598635965350735
Trimmed Mean ( 22 / 24 )	0.0857142857142857	0.134785179436079	0.635932571169185
Trimmed Mean ( 23 / 24 )	0.0846153846153846	0.126210118781500	0.670432651773939
Trimmed Mean ( 24 / 24 )	0.0833333333333333	0.116355693212645	0.716194721826272
Median	0
Midrange	0
Midmean - Weighted Average at Xnp	0.156410256410256
Midmean - Weighted Average at X(n+1)p	0.202631578947368
Midmean - Empirical Distribution Function	0.156410256410256
Midmean - Empirical Distribution Function - Averaging	0.202631578947368
Midmean - Empirical Distribution Function - Interpolation	0.202631578947368
Midmean - Closest Observation	0.156410256410256
Midmean - True Basic - Statistics Graphics Toolkit	0.202631578947368
Midmean - MS Excel (old versions)	0.156410256410256
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