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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 17:46:33 -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/2012/Mar/01/t1330642050vlsm28nti38r6up.htm/, Retrieved Sun, 28 Apr 2024 03:39:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163401, Retrieved Sun, 28 Apr 2024 03:39:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Robuustheid gemid...] [2012-03-01 21:24:28] [74be16979710d4c4e7c6647856088456]
- R  D    [Central Tendency] [Central tendency ...] [2012-03-01 22:46:33] [1c41dd1c3cda3fb9bab7d6fdffb4cffd] [Current]
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Dataseries X:
2,35
2,35
2,35
2,35
2,35
2,35
2,35
2,36
2,36
2,36
2,36
2,36
2,36
2,37
2,37
2,39
2,4
2,41
2,41
2,42
2,44
2,44
2,44
2,44
2,44
2,45
2,45
2,46
2,47
2,48
2,48
2,48
2,49
2,5
2,5
2,5
2,5
2,5
2,5
2,5
2,51
2,52
2,54
2,56
2,57
2,57
2,58
2,59
2,6
2,6
2,62
2,62
2,63
2,63
2,63
2,63
2,63
2,63
2,63
2,64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163401&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163401&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.47950.0127102098734934195.079390873859
Geometric Mean2.47758628125938
Harmonic Mean2.47568200249026
Quadratic Mean2.48142129971246
Winsorized Mean ( 1 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 2 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 3 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 4 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 5 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 6 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 7 / 20 )2.48050.0124791917201676198.770886418169
Winsorized Mean ( 8 / 20 )2.479166666666670.0122134770117126202.986149176781
Winsorized Mean ( 9 / 20 )2.479166666666670.0122134770117126202.986149176781
Winsorized Mean ( 10 / 20 )2.475833333333330.0115843545052455213.722165720348
Winsorized Mean ( 11 / 20 )2.475833333333330.0115843545052455213.722165720348
Winsorized Mean ( 12 / 20 )2.473833333333330.0112272158903191220.34254596159
Winsorized Mean ( 13 / 20 )2.473833333333330.0104829473220769235.986431804679
Winsorized Mean ( 14 / 20 )2.47150.0100895006119664244.957614360888
Winsorized Mean ( 15 / 20 )2.47650.00926638112798299267.256436552277
Winsorized Mean ( 16 / 20 )2.47650.00839634370250656294.949812411882
Winsorized Mean ( 17 / 20 )2.473666666666670.00702685191492427352.03056740286
Winsorized Mean ( 18 / 20 )2.467666666666670.00610809718522106403.99924752955
Winsorized Mean ( 19 / 20 )2.467666666666670.00515503520330068478.690555805839
Winsorized Mean ( 20 / 20 )2.4710.00369531693250233668.684187347019
Trimmed Mean ( 1 / 20 )2.478965517241380.0126536285984434195.909457746083
Trimmed Mean ( 2 / 20 )2.478571428571430.0126116534736535196.530251465385
Trimmed Mean ( 3 / 20 )2.478148148148150.0125450246389459197.540317334632
Trimmed Mean ( 4 / 20 )2.477692307692310.0124478259097923199.046188920684
Trimmed Mean ( 5 / 20 )2.47720.0123123962753323201.19560356931
Trimmed Mean ( 6 / 20 )2.476666666666670.0121286445620494204.1997895145
Trimmed Mean ( 7 / 20 )2.476086956521740.0118829974783101208.372252964062
Trimmed Mean ( 8 / 20 )2.475227272727270.0116116176985617213.16816803518
Trimmed Mean ( 9 / 20 )2.474523809523810.0113245972048799218.5087703126
Trimmed Mean ( 10 / 20 )2.473750.010935050091921226.222100420707
Trimmed Mean ( 11 / 20 )2.473421052631580.0105891616117632233.580442278257
Trimmed Mean ( 12 / 20 )2.473055555555560.0101090831735736244.636977764752
Trimmed Mean ( 13 / 20 )2.472941176470590.00954891163049706258.976234377599
Trimmed Mean ( 14 / 20 )2.47281250.00899411069632467274.936854069462
Trimmed Mean ( 15 / 20 )2.4730.00832044981100608297.219508100244
Trimmed Mean ( 16 / 20 )2.47250.00762245707445125324.370472126011
Trimmed Mean ( 17 / 20 )2.471923076923080.00690639014623928357.918250284356
Trimmed Mean ( 18 / 20 )2.471666666666670.00638915143337887386.853667883645
Trimmed Mean ( 19 / 20 )2.472272727272730.00595552848697986415.122307395167
Trimmed Mean ( 20 / 20 )2.4730.00567079313119797436.094201072994
Median2.48
Midrange2.495
Midmean - Weighted Average at Xnp2.46969696969697
Midmean - Weighted Average at X(n+1)p2.47612903225806
Midmean - Empirical Distribution Function2.46969696969697
Midmean - Empirical Distribution Function - Averaging2.47612903225806
Midmean - Empirical Distribution Function - Interpolation2.47612903225806
Midmean - Closest Observation2.46969696969697
Midmean - True Basic - Statistics Graphics Toolkit2.47612903225806
Midmean - MS Excel (old versions)2.46969696969697
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.4795 & 0.0127102098734934 & 195.079390873859 \tabularnewline
Geometric Mean & 2.47758628125938 &  &  \tabularnewline
Harmonic Mean & 2.47568200249026 &  &  \tabularnewline
Quadratic Mean & 2.48142129971246 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.47933333333333 & 0.0126755841342721 & 195.599138238509 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.4805 & 0.0124791917201676 & 198.770886418169 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.47916666666667 & 0.0122134770117126 & 202.986149176781 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.47916666666667 & 0.0122134770117126 & 202.986149176781 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.47583333333333 & 0.0115843545052455 & 213.722165720348 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.47583333333333 & 0.0115843545052455 & 213.722165720348 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.47383333333333 & 0.0112272158903191 & 220.34254596159 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.47383333333333 & 0.0104829473220769 & 235.986431804679 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.4715 & 0.0100895006119664 & 244.957614360888 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.4765 & 0.00926638112798299 & 267.256436552277 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.4765 & 0.00839634370250656 & 294.949812411882 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.47366666666667 & 0.00702685191492427 & 352.03056740286 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.46766666666667 & 0.00610809718522106 & 403.99924752955 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.46766666666667 & 0.00515503520330068 & 478.690555805839 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.471 & 0.00369531693250233 & 668.684187347019 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.47896551724138 & 0.0126536285984434 & 195.909457746083 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.47857142857143 & 0.0126116534736535 & 196.530251465385 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.47814814814815 & 0.0125450246389459 & 197.540317334632 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.47769230769231 & 0.0124478259097923 & 199.046188920684 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.4772 & 0.0123123962753323 & 201.19560356931 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.47666666666667 & 0.0121286445620494 & 204.1997895145 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.47608695652174 & 0.0118829974783101 & 208.372252964062 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.47522727272727 & 0.0116116176985617 & 213.16816803518 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.47452380952381 & 0.0113245972048799 & 218.5087703126 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.47375 & 0.010935050091921 & 226.222100420707 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.47342105263158 & 0.0105891616117632 & 233.580442278257 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.47305555555556 & 0.0101090831735736 & 244.636977764752 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.47294117647059 & 0.00954891163049706 & 258.976234377599 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.4728125 & 0.00899411069632467 & 274.936854069462 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.473 & 0.00832044981100608 & 297.219508100244 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.4725 & 0.00762245707445125 & 324.370472126011 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.47192307692308 & 0.00690639014623928 & 357.918250284356 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.47166666666667 & 0.00638915143337887 & 386.853667883645 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.47227272727273 & 0.00595552848697986 & 415.122307395167 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.473 & 0.00567079313119797 & 436.094201072994 \tabularnewline
Median & 2.48 &  &  \tabularnewline
Midrange & 2.495 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.46969696969697 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.47612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.46969696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.47612903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.47612903225806 &  &  \tabularnewline
Midmean - Closest Observation & 2.46969696969697 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.47612903225806 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.46969696969697 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163401&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]2.4795[/C][C]0.0127102098734934[/C][C]195.079390873859[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.47758628125938[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.47568200249026[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.48142129971246[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.47933333333333[/C][C]0.0126755841342721[/C][C]195.599138238509[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.4805[/C][C]0.0124791917201676[/C][C]198.770886418169[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.47916666666667[/C][C]0.0122134770117126[/C][C]202.986149176781[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.47916666666667[/C][C]0.0122134770117126[/C][C]202.986149176781[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.47583333333333[/C][C]0.0115843545052455[/C][C]213.722165720348[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.47583333333333[/C][C]0.0115843545052455[/C][C]213.722165720348[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.47383333333333[/C][C]0.0112272158903191[/C][C]220.34254596159[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.47383333333333[/C][C]0.0104829473220769[/C][C]235.986431804679[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.4715[/C][C]0.0100895006119664[/C][C]244.957614360888[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.4765[/C][C]0.00926638112798299[/C][C]267.256436552277[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.4765[/C][C]0.00839634370250656[/C][C]294.949812411882[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.47366666666667[/C][C]0.00702685191492427[/C][C]352.03056740286[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.46766666666667[/C][C]0.00610809718522106[/C][C]403.99924752955[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.46766666666667[/C][C]0.00515503520330068[/C][C]478.690555805839[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.471[/C][C]0.00369531693250233[/C][C]668.684187347019[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.47896551724138[/C][C]0.0126536285984434[/C][C]195.909457746083[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.47857142857143[/C][C]0.0126116534736535[/C][C]196.530251465385[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.47814814814815[/C][C]0.0125450246389459[/C][C]197.540317334632[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.47769230769231[/C][C]0.0124478259097923[/C][C]199.046188920684[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.4772[/C][C]0.0123123962753323[/C][C]201.19560356931[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.47666666666667[/C][C]0.0121286445620494[/C][C]204.1997895145[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.47608695652174[/C][C]0.0118829974783101[/C][C]208.372252964062[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.47522727272727[/C][C]0.0116116176985617[/C][C]213.16816803518[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.47452380952381[/C][C]0.0113245972048799[/C][C]218.5087703126[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.47375[/C][C]0.010935050091921[/C][C]226.222100420707[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.47342105263158[/C][C]0.0105891616117632[/C][C]233.580442278257[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.47305555555556[/C][C]0.0101090831735736[/C][C]244.636977764752[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.47294117647059[/C][C]0.00954891163049706[/C][C]258.976234377599[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.4728125[/C][C]0.00899411069632467[/C][C]274.936854069462[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.473[/C][C]0.00832044981100608[/C][C]297.219508100244[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.4725[/C][C]0.00762245707445125[/C][C]324.370472126011[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.47192307692308[/C][C]0.00690639014623928[/C][C]357.918250284356[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.47166666666667[/C][C]0.00638915143337887[/C][C]386.853667883645[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.47227272727273[/C][C]0.00595552848697986[/C][C]415.122307395167[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.473[/C][C]0.00567079313119797[/C][C]436.094201072994[/C][/ROW]
[ROW][C]Median[/C][C]2.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.46969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.47612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.46969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.47612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.47612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.46969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.47612903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.46969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163401&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 Mean2.47950.0127102098734934195.079390873859
Geometric Mean2.47758628125938
Harmonic Mean2.47568200249026
Quadratic Mean2.48142129971246
Winsorized Mean ( 1 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 2 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 3 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 4 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 5 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 6 / 20 )2.479333333333330.0126755841342721195.599138238509
Winsorized Mean ( 7 / 20 )2.48050.0124791917201676198.770886418169
Winsorized Mean ( 8 / 20 )2.479166666666670.0122134770117126202.986149176781
Winsorized Mean ( 9 / 20 )2.479166666666670.0122134770117126202.986149176781
Winsorized Mean ( 10 / 20 )2.475833333333330.0115843545052455213.722165720348
Winsorized Mean ( 11 / 20 )2.475833333333330.0115843545052455213.722165720348
Winsorized Mean ( 12 / 20 )2.473833333333330.0112272158903191220.34254596159
Winsorized Mean ( 13 / 20 )2.473833333333330.0104829473220769235.986431804679
Winsorized Mean ( 14 / 20 )2.47150.0100895006119664244.957614360888
Winsorized Mean ( 15 / 20 )2.47650.00926638112798299267.256436552277
Winsorized Mean ( 16 / 20 )2.47650.00839634370250656294.949812411882
Winsorized Mean ( 17 / 20 )2.473666666666670.00702685191492427352.03056740286
Winsorized Mean ( 18 / 20 )2.467666666666670.00610809718522106403.99924752955
Winsorized Mean ( 19 / 20 )2.467666666666670.00515503520330068478.690555805839
Winsorized Mean ( 20 / 20 )2.4710.00369531693250233668.684187347019
Trimmed Mean ( 1 / 20 )2.478965517241380.0126536285984434195.909457746083
Trimmed Mean ( 2 / 20 )2.478571428571430.0126116534736535196.530251465385
Trimmed Mean ( 3 / 20 )2.478148148148150.0125450246389459197.540317334632
Trimmed Mean ( 4 / 20 )2.477692307692310.0124478259097923199.046188920684
Trimmed Mean ( 5 / 20 )2.47720.0123123962753323201.19560356931
Trimmed Mean ( 6 / 20 )2.476666666666670.0121286445620494204.1997895145
Trimmed Mean ( 7 / 20 )2.476086956521740.0118829974783101208.372252964062
Trimmed Mean ( 8 / 20 )2.475227272727270.0116116176985617213.16816803518
Trimmed Mean ( 9 / 20 )2.474523809523810.0113245972048799218.5087703126
Trimmed Mean ( 10 / 20 )2.473750.010935050091921226.222100420707
Trimmed Mean ( 11 / 20 )2.473421052631580.0105891616117632233.580442278257
Trimmed Mean ( 12 / 20 )2.473055555555560.0101090831735736244.636977764752
Trimmed Mean ( 13 / 20 )2.472941176470590.00954891163049706258.976234377599
Trimmed Mean ( 14 / 20 )2.47281250.00899411069632467274.936854069462
Trimmed Mean ( 15 / 20 )2.4730.00832044981100608297.219508100244
Trimmed Mean ( 16 / 20 )2.47250.00762245707445125324.370472126011
Trimmed Mean ( 17 / 20 )2.471923076923080.00690639014623928357.918250284356
Trimmed Mean ( 18 / 20 )2.471666666666670.00638915143337887386.853667883645
Trimmed Mean ( 19 / 20 )2.472272727272730.00595552848697986415.122307395167
Trimmed Mean ( 20 / 20 )2.4730.00567079313119797436.094201072994
Median2.48
Midrange2.495
Midmean - Weighted Average at Xnp2.46969696969697
Midmean - Weighted Average at X(n+1)p2.47612903225806
Midmean - Empirical Distribution Function2.46969696969697
Midmean - Empirical Distribution Function - Averaging2.47612903225806
Midmean - Empirical Distribution Function - Interpolation2.47612903225806
Midmean - Closest Observation2.46969696969697
Midmean - True Basic - Statistics Graphics Toolkit2.47612903225806
Midmean - MS Excel (old versions)2.46969696969697
Number of observations60



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')