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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 computationThu, 28 Feb 2013 15:03:11 -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/Feb/28/t1362081844p77h6kxiioiwu6o.htm/, Retrieved Wed, 01 May 2024 20:11:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207207, Retrieved Wed, 01 May 2024 20:11:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid gemid...] [2013-02-28 20:03:11] [2ad6cfb061f4abd47c32d0a7b72d8383] [Current]
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Dataseries X:
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48
5,48
5,48
5,5
5,55
5,57
5,58
5,58
5,58
5,59
5,59
5,59
5,55
5,61
5,61
5,61
5,63
5,69
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,71
5,74
5,77
5,79
5,79
5,8
5,8
5,8
5,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207207&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207207&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.388055555555560.0423482464623806127.232081742557
Geometric Mean5.3757118663938
Harmonic Mean5.36283859462478
Quadratic Mean5.39985853724171
Winsorized Mean ( 1 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 2 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 3 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 4 / 24 )5.38750.0422729366582086127.445605294939
Winsorized Mean ( 5 / 24 )5.38750.0422729366582086127.445605294939
Winsorized Mean ( 6 / 24 )5.385833333333330.0420539513010525128.069614547695
Winsorized Mean ( 7 / 24 )5.386805555555560.0407940677305734132.048747654512
Winsorized Mean ( 8 / 24 )5.389027777777780.039159378865587137.617805335355
Winsorized Mean ( 9 / 24 )5.389027777777780.0387435489719437139.094840838671
Winsorized Mean ( 10 / 24 )5.389027777777780.0387435489719437139.094840838671
Winsorized Mean ( 11 / 24 )5.390555555555560.0384117838234311140.335985965518
Winsorized Mean ( 12 / 24 )5.390555555555560.0384117838234311140.335985965518
Winsorized Mean ( 13 / 24 )5.392361111111110.0380215392046152141.823851004342
Winsorized Mean ( 14 / 24 )5.460416666666670.0244840639142892223.019213059638
Winsorized Mean ( 15 / 24 )5.481250.0211281371812845259.428928966599
Winsorized Mean ( 16 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 17 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 18 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 19 / 24 )5.487916666666670.0194243622542102282.527508231431
Winsorized Mean ( 20 / 24 )5.471250.0171056478560708319.850498854871
Winsorized Mean ( 21 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 22 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 23 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 24 / 24 )5.458750.0155493277131768351.060193771216
Trimmed Mean ( 1 / 24 )5.392142857142860.0419740099301048128.463848608266
Trimmed Mean ( 2 / 24 )5.396470588235290.041506298487459130.015703276114
Trimmed Mean ( 3 / 24 )5.401060606060610.0409264100436619131.9700555289
Trimmed Mean ( 4 / 24 )5.40593750.0402107041923768134.440259343304
Trimmed Mean ( 5 / 24 )5.411290322580650.0393545786330493137.500908675372
Trimmed Mean ( 6 / 24 )5.4170.0382965679747424141.448706410785
Trimmed Mean ( 7 / 24 )5.423448275862070.0370424714335518146.411620660648
Trimmed Mean ( 8 / 24 )5.430178571428570.0358237850605822151.580257704358
Trimmed Mean ( 9 / 24 )5.437037037037040.0347152031107142156.618327125933
Trimmed Mean ( 10 / 24 )5.444423076923080.0334000991923483163.006194848976
Trimmed Mean ( 11 / 24 )5.45240.0316982713750019172.009379801698
Trimmed Mean ( 12 / 24 )5.460833333333330.0295606620750751184.733119964109
Trimmed Mean ( 13 / 24 )5.470.0266811554841805205.013609820729
Trimmed Mean ( 14 / 24 )5.479772727272730.0227693848745386240.664065255464
Trimmed Mean ( 15 / 24 )5.482142857142860.0219532173749317249.719335599661
Trimmed Mean ( 16 / 24 )5.482250.021677967959931252.895013505567
Trimmed Mean ( 17 / 24 )5.481578947368420.0214798404139563255.196446608925
Trimmed Mean ( 18 / 24 )5.480833333333330.0211621667507678258.992068150795
Trimmed Mean ( 19 / 24 )5.480.0206791980867631265.000604811063
Trimmed Mean ( 20 / 24 )5.47906250.0201624420033964271.745976954431
Trimmed Mean ( 21 / 24 )5.480.0200114909518242273.842664356823
Trimmed Mean ( 22 / 24 )5.481785714285710.0198876046279648275.638309229938
Trimmed Mean ( 23 / 24 )5.483846153846150.0195886695906425279.949903104486
Trimmed Mean ( 24 / 24 )5.486250.0190138441172726288.539759038845
Median5.48
Midrange5.245
Midmean - Weighted Average at Xnp5.51468085106383
Midmean - Weighted Average at X(n+1)p5.51468085106383
Midmean - Empirical Distribution Function5.51468085106383
Midmean - Empirical Distribution Function - Averaging5.51468085106383
Midmean - Empirical Distribution Function - Interpolation5.51468085106383
Midmean - Closest Observation5.51468085106383
Midmean - True Basic - Statistics Graphics Toolkit5.51468085106383
Midmean - MS Excel (old versions)5.51468085106383
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.38805555555556 & 0.0423482464623806 & 127.232081742557 \tabularnewline
Geometric Mean & 5.3757118663938 &  &  \tabularnewline
Harmonic Mean & 5.36283859462478 &  &  \tabularnewline
Quadratic Mean & 5.39985853724171 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 5.38805555555556 & 0.0423482464623806 & 127.232081742557 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 5.38805555555556 & 0.0423482464623806 & 127.232081742557 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 5.38805555555556 & 0.0423482464623806 & 127.232081742557 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 5.3875 & 0.0422729366582086 & 127.445605294939 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 5.3875 & 0.0422729366582086 & 127.445605294939 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 5.38583333333333 & 0.0420539513010525 & 128.069614547695 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 5.38680555555556 & 0.0407940677305734 & 132.048747654512 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 5.38902777777778 & 0.039159378865587 & 137.617805335355 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 5.38902777777778 & 0.0387435489719437 & 139.094840838671 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 5.38902777777778 & 0.0387435489719437 & 139.094840838671 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 5.39055555555556 & 0.0384117838234311 & 140.335985965518 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 5.39055555555556 & 0.0384117838234311 & 140.335985965518 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 5.39236111111111 & 0.0380215392046152 & 141.823851004342 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 5.46041666666667 & 0.0244840639142892 & 223.019213059638 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 5.48125 & 0.0211281371812845 & 259.428928966599 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 5.48791666666667 & 0.0201752275896509 & 272.012627479938 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 5.48791666666667 & 0.0201752275896509 & 272.012627479938 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 5.48791666666667 & 0.0201752275896509 & 272.012627479938 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 5.48791666666667 & 0.0194243622542102 & 282.527508231431 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 5.47125 & 0.0171056478560708 & 319.850498854871 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 5.46541666666667 & 0.0163609729489797 & 334.05205691068 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 5.46541666666667 & 0.0163609729489797 & 334.05205691068 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 5.46541666666667 & 0.0163609729489797 & 334.05205691068 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 5.45875 & 0.0155493277131768 & 351.060193771216 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 5.39214285714286 & 0.0419740099301048 & 128.463848608266 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 5.39647058823529 & 0.041506298487459 & 130.015703276114 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 5.40106060606061 & 0.0409264100436619 & 131.9700555289 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 5.4059375 & 0.0402107041923768 & 134.440259343304 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 5.41129032258065 & 0.0393545786330493 & 137.500908675372 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 5.417 & 0.0382965679747424 & 141.448706410785 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 5.42344827586207 & 0.0370424714335518 & 146.411620660648 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 5.43017857142857 & 0.0358237850605822 & 151.580257704358 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 5.43703703703704 & 0.0347152031107142 & 156.618327125933 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 5.44442307692308 & 0.0334000991923483 & 163.006194848976 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 5.4524 & 0.0316982713750019 & 172.009379801698 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 5.46083333333333 & 0.0295606620750751 & 184.733119964109 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 5.47 & 0.0266811554841805 & 205.013609820729 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 5.47977272727273 & 0.0227693848745386 & 240.664065255464 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 5.48214285714286 & 0.0219532173749317 & 249.719335599661 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 5.48225 & 0.021677967959931 & 252.895013505567 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 5.48157894736842 & 0.0214798404139563 & 255.196446608925 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 5.48083333333333 & 0.0211621667507678 & 258.992068150795 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 5.48 & 0.0206791980867631 & 265.000604811063 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 5.4790625 & 0.0201624420033964 & 271.745976954431 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 5.48 & 0.0200114909518242 & 273.842664356823 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 5.48178571428571 & 0.0198876046279648 & 275.638309229938 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 5.48384615384615 & 0.0195886695906425 & 279.949903104486 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 5.48625 & 0.0190138441172726 & 288.539759038845 \tabularnewline
Median & 5.48 &  &  \tabularnewline
Midrange & 5.245 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.51468085106383 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.51468085106383 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.51468085106383 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.51468085106383 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.51468085106383 &  &  \tabularnewline
Midmean - Closest Observation & 5.51468085106383 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.51468085106383 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.51468085106383 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207207&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]5.38805555555556[/C][C]0.0423482464623806[/C][C]127.232081742557[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.3757118663938[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.36283859462478[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.39985853724171[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]5.38805555555556[/C][C]0.0423482464623806[/C][C]127.232081742557[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]5.38805555555556[/C][C]0.0423482464623806[/C][C]127.232081742557[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]5.38805555555556[/C][C]0.0423482464623806[/C][C]127.232081742557[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]5.3875[/C][C]0.0422729366582086[/C][C]127.445605294939[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]5.3875[/C][C]0.0422729366582086[/C][C]127.445605294939[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]5.38583333333333[/C][C]0.0420539513010525[/C][C]128.069614547695[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]5.38680555555556[/C][C]0.0407940677305734[/C][C]132.048747654512[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]5.38902777777778[/C][C]0.039159378865587[/C][C]137.617805335355[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]5.38902777777778[/C][C]0.0387435489719437[/C][C]139.094840838671[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]5.38902777777778[/C][C]0.0387435489719437[/C][C]139.094840838671[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]5.39055555555556[/C][C]0.0384117838234311[/C][C]140.335985965518[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]5.39055555555556[/C][C]0.0384117838234311[/C][C]140.335985965518[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]5.39236111111111[/C][C]0.0380215392046152[/C][C]141.823851004342[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]5.46041666666667[/C][C]0.0244840639142892[/C][C]223.019213059638[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]5.48125[/C][C]0.0211281371812845[/C][C]259.428928966599[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]5.48791666666667[/C][C]0.0201752275896509[/C][C]272.012627479938[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]5.48791666666667[/C][C]0.0201752275896509[/C][C]272.012627479938[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]5.48791666666667[/C][C]0.0201752275896509[/C][C]272.012627479938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]5.48791666666667[/C][C]0.0194243622542102[/C][C]282.527508231431[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]5.47125[/C][C]0.0171056478560708[/C][C]319.850498854871[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]5.46541666666667[/C][C]0.0163609729489797[/C][C]334.05205691068[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]5.46541666666667[/C][C]0.0163609729489797[/C][C]334.05205691068[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]5.46541666666667[/C][C]0.0163609729489797[/C][C]334.05205691068[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]5.45875[/C][C]0.0155493277131768[/C][C]351.060193771216[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]5.39214285714286[/C][C]0.0419740099301048[/C][C]128.463848608266[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]5.39647058823529[/C][C]0.041506298487459[/C][C]130.015703276114[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]5.40106060606061[/C][C]0.0409264100436619[/C][C]131.9700555289[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]5.4059375[/C][C]0.0402107041923768[/C][C]134.440259343304[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]5.41129032258065[/C][C]0.0393545786330493[/C][C]137.500908675372[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]5.417[/C][C]0.0382965679747424[/C][C]141.448706410785[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]5.42344827586207[/C][C]0.0370424714335518[/C][C]146.411620660648[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]5.43017857142857[/C][C]0.0358237850605822[/C][C]151.580257704358[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]5.43703703703704[/C][C]0.0347152031107142[/C][C]156.618327125933[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]5.44442307692308[/C][C]0.0334000991923483[/C][C]163.006194848976[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]5.4524[/C][C]0.0316982713750019[/C][C]172.009379801698[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]5.46083333333333[/C][C]0.0295606620750751[/C][C]184.733119964109[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]5.47[/C][C]0.0266811554841805[/C][C]205.013609820729[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]5.47977272727273[/C][C]0.0227693848745386[/C][C]240.664065255464[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]5.48214285714286[/C][C]0.0219532173749317[/C][C]249.719335599661[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]5.48225[/C][C]0.021677967959931[/C][C]252.895013505567[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]5.48157894736842[/C][C]0.0214798404139563[/C][C]255.196446608925[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]5.48083333333333[/C][C]0.0211621667507678[/C][C]258.992068150795[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]5.48[/C][C]0.0206791980867631[/C][C]265.000604811063[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]5.4790625[/C][C]0.0201624420033964[/C][C]271.745976954431[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]5.48[/C][C]0.0200114909518242[/C][C]273.842664356823[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]5.48178571428571[/C][C]0.0198876046279648[/C][C]275.638309229938[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]5.48384615384615[/C][C]0.0195886695906425[/C][C]279.949903104486[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]5.48625[/C][C]0.0190138441172726[/C][C]288.539759038845[/C][/ROW]
[ROW][C]Median[/C][C]5.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.51468085106383[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.51468085106383[/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=207207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207207&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 Mean5.388055555555560.0423482464623806127.232081742557
Geometric Mean5.3757118663938
Harmonic Mean5.36283859462478
Quadratic Mean5.39985853724171
Winsorized Mean ( 1 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 2 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 3 / 24 )5.388055555555560.0423482464623806127.232081742557
Winsorized Mean ( 4 / 24 )5.38750.0422729366582086127.445605294939
Winsorized Mean ( 5 / 24 )5.38750.0422729366582086127.445605294939
Winsorized Mean ( 6 / 24 )5.385833333333330.0420539513010525128.069614547695
Winsorized Mean ( 7 / 24 )5.386805555555560.0407940677305734132.048747654512
Winsorized Mean ( 8 / 24 )5.389027777777780.039159378865587137.617805335355
Winsorized Mean ( 9 / 24 )5.389027777777780.0387435489719437139.094840838671
Winsorized Mean ( 10 / 24 )5.389027777777780.0387435489719437139.094840838671
Winsorized Mean ( 11 / 24 )5.390555555555560.0384117838234311140.335985965518
Winsorized Mean ( 12 / 24 )5.390555555555560.0384117838234311140.335985965518
Winsorized Mean ( 13 / 24 )5.392361111111110.0380215392046152141.823851004342
Winsorized Mean ( 14 / 24 )5.460416666666670.0244840639142892223.019213059638
Winsorized Mean ( 15 / 24 )5.481250.0211281371812845259.428928966599
Winsorized Mean ( 16 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 17 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 18 / 24 )5.487916666666670.0201752275896509272.012627479938
Winsorized Mean ( 19 / 24 )5.487916666666670.0194243622542102282.527508231431
Winsorized Mean ( 20 / 24 )5.471250.0171056478560708319.850498854871
Winsorized Mean ( 21 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 22 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 23 / 24 )5.465416666666670.0163609729489797334.05205691068
Winsorized Mean ( 24 / 24 )5.458750.0155493277131768351.060193771216
Trimmed Mean ( 1 / 24 )5.392142857142860.0419740099301048128.463848608266
Trimmed Mean ( 2 / 24 )5.396470588235290.041506298487459130.015703276114
Trimmed Mean ( 3 / 24 )5.401060606060610.0409264100436619131.9700555289
Trimmed Mean ( 4 / 24 )5.40593750.0402107041923768134.440259343304
Trimmed Mean ( 5 / 24 )5.411290322580650.0393545786330493137.500908675372
Trimmed Mean ( 6 / 24 )5.4170.0382965679747424141.448706410785
Trimmed Mean ( 7 / 24 )5.423448275862070.0370424714335518146.411620660648
Trimmed Mean ( 8 / 24 )5.430178571428570.0358237850605822151.580257704358
Trimmed Mean ( 9 / 24 )5.437037037037040.0347152031107142156.618327125933
Trimmed Mean ( 10 / 24 )5.444423076923080.0334000991923483163.006194848976
Trimmed Mean ( 11 / 24 )5.45240.0316982713750019172.009379801698
Trimmed Mean ( 12 / 24 )5.460833333333330.0295606620750751184.733119964109
Trimmed Mean ( 13 / 24 )5.470.0266811554841805205.013609820729
Trimmed Mean ( 14 / 24 )5.479772727272730.0227693848745386240.664065255464
Trimmed Mean ( 15 / 24 )5.482142857142860.0219532173749317249.719335599661
Trimmed Mean ( 16 / 24 )5.482250.021677967959931252.895013505567
Trimmed Mean ( 17 / 24 )5.481578947368420.0214798404139563255.196446608925
Trimmed Mean ( 18 / 24 )5.480833333333330.0211621667507678258.992068150795
Trimmed Mean ( 19 / 24 )5.480.0206791980867631265.000604811063
Trimmed Mean ( 20 / 24 )5.47906250.0201624420033964271.745976954431
Trimmed Mean ( 21 / 24 )5.480.0200114909518242273.842664356823
Trimmed Mean ( 22 / 24 )5.481785714285710.0198876046279648275.638309229938
Trimmed Mean ( 23 / 24 )5.483846153846150.0195886695906425279.949903104486
Trimmed Mean ( 24 / 24 )5.486250.0190138441172726288.539759038845
Median5.48
Midrange5.245
Midmean - Weighted Average at Xnp5.51468085106383
Midmean - Weighted Average at X(n+1)p5.51468085106383
Midmean - Empirical Distribution Function5.51468085106383
Midmean - Empirical Distribution Function - Averaging5.51468085106383
Midmean - Empirical Distribution Function - Interpolation5.51468085106383
Midmean - Closest Observation5.51468085106383
Midmean - True Basic - Statistics Graphics Toolkit5.51468085106383
Midmean - MS Excel (old versions)5.51468085106383
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')