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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 02 Nov 2009 10:50:22 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/02/t1257184285cunzxgv6r2fpgkj.htm/, Retrieved Sat, 04 May 2024 04:05:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52843, Retrieved Sat, 04 May 2024 04:05:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 3 Part 2...] [2009-11-02 17:50:22] [fd0d141bb5380cffe1d2cd25afb62297] [Current]
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Dataseries X:
3.46
3.34
3.24
3.09
2.88
2.76
2.78
2.96
2.87
2.87
3.25
3.26
3.31
3.27
3.17
3.03
2.81
2.69
2.59
2.56
2.58
2.69
3.37
3.58
3.54
3.29
3.02
2.76
2.7
2.67
2.74
2.93
2.95
3.02
3.46
3.47
3.35
3.07
2.88
2.8
2.76
2.71
2.59
2.51
2.48
2.73
3.56
3.76
3.7
3.48
3.02
2.93
3.05
3.12
3.16
3.17
3.08
3.16
3.62
3.58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52843&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52843&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.053833333333330.043178836929319270.7252337141978
Geometric Mean3.03598253461502
Harmonic Mean3.01834077529425
Quadratic Mean3.07179073723021
Winsorized Mean ( 1 / 20 )3.053333333333330.042802045113678571.3361552052932
Winsorized Mean ( 2 / 20 )3.052333333333330.041807580927094173.0090874823906
Winsorized Mean ( 3 / 20 )3.051333333333330.04116280660783874.1284082595163
Winsorized Mean ( 4 / 20 )3.0520.041034503877524574.3764323094849
Winsorized Mean ( 5 / 20 )3.050333333333330.040675765398725274.9914181929305
Winsorized Mean ( 6 / 20 )3.056333333333330.038807773892622978.7556983245134
Winsorized Mean ( 7 / 20 )3.051666666666670.03698997166485182.4998379105669
Winsorized Mean ( 8 / 20 )3.050333333333330.036730017178849483.0474246303876
Winsorized Mean ( 9 / 20 )3.050333333333330.036193115638000784.279379643422
Winsorized Mean ( 10 / 20 )3.0520.03592191783286384.96205615191
Winsorized Mean ( 11 / 20 )3.039166666666670.032300051308023494.091697802094
Winsorized Mean ( 12 / 20 )3.037166666666670.031290593220734397.0632498157348
Winsorized Mean ( 13 / 20 )3.039333333333330.0302362324898276100.519578104046
Winsorized Mean ( 14 / 20 )3.032333333333330.0290794418098056104.277563275332
Winsorized Mean ( 15 / 20 )3.027333333333330.0282811416940316107.044240507879
Winsorized Mean ( 16 / 20 )3.027333333333330.0266011200081384113.804731996515
Winsorized Mean ( 17 / 20 )3.030166666666670.0252797809682041119.865226303894
Winsorized Mean ( 18 / 20 )3.030166666666670.0243578450183092124.402083369402
Winsorized Mean ( 19 / 20 )3.0460.0210597750295150144.635923020596
Winsorized Mean ( 20 / 20 )3.022666666666670.0175648381856948172.086223323617
Trimmed Mean ( 1 / 20 )3.051551724137930.041783298391208473.0328107553139
Trimmed Mean ( 2 / 20 )3.049642857142860.040523333254230275.256466145329
Trimmed Mean ( 3 / 20 )3.048148148148150.039620027964882776.9345279324355
Trimmed Mean ( 4 / 20 )3.046923076923080.038790673162495978.5478267974205
Trimmed Mean ( 5 / 20 )3.04540.037782632874626180.6031705123763
Trimmed Mean ( 6 / 20 )3.044166666666670.036618884081779483.131060462363
Trimmed Mean ( 7 / 20 )3.041521739130430.035705406823820585.183786145837
Trimmed Mean ( 8 / 20 )3.039545454545450.035039926706240586.7452001263497
Trimmed Mean ( 9 / 20 )3.037619047619050.034210541541915488.7919018732077
Trimmed Mean ( 10 / 20 )3.03550.033231800494444591.343230124033
Trimmed Mean ( 11 / 20 )3.032894736842110.031962611280638894.8888283942954
Trimmed Mean ( 12 / 20 )3.031944444444440.031256286845563397.0027073089398
Trimmed Mean ( 13 / 20 )3.031176470588240.030511868196986899.3441781741696
Trimmed Mean ( 14 / 20 )3.030.0297096161254665101.987181093287
Trimmed Mean ( 15 / 20 )3.029666666666670.0288535076587676105.001676139229
Trimmed Mean ( 16 / 20 )3.030.0277888866675551109.036394161759
Trimmed Mean ( 17 / 20 )3.030384615384620.0267091500842848113.458668876463
Trimmed Mean ( 18 / 20 )3.030416666666670.0254629538134957119.012770036935
Trimmed Mean ( 19 / 20 )3.030454545454550.0237727086488964127.476199292723
Trimmed Mean ( 20 / 20 )3.0280.0224382192744996134.948320227944
Median3.025
Midrange3.12
Midmean - Weighted Average at Xnp3.0128125
Midmean - Weighted Average at X(n+1)p3.0128125
Midmean - Empirical Distribution Function3.0128125
Midmean - Empirical Distribution Function - Averaging3.0128125
Midmean - Empirical Distribution Function - Interpolation3.0128125
Midmean - Closest Observation3.0128125
Midmean - True Basic - Statistics Graphics Toolkit3.0128125
Midmean - MS Excel (old versions)3.02181818181818
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.05383333333333 & 0.0431788369293192 & 70.7252337141978 \tabularnewline
Geometric Mean & 3.03598253461502 &  &  \tabularnewline
Harmonic Mean & 3.01834077529425 &  &  \tabularnewline
Quadratic Mean & 3.07179073723021 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.05333333333333 & 0.0428020451136785 & 71.3361552052932 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.05233333333333 & 0.0418075809270941 & 73.0090874823906 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.05133333333333 & 0.041162806607838 & 74.1284082595163 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.052 & 0.0410345038775245 & 74.3764323094849 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.05033333333333 & 0.0406757653987252 & 74.9914181929305 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.05633333333333 & 0.0388077738926229 & 78.7556983245134 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.05166666666667 & 0.036989971664851 & 82.4998379105669 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.05033333333333 & 0.0367300171788494 & 83.0474246303876 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.05033333333333 & 0.0361931156380007 & 84.279379643422 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.052 & 0.035921917832863 & 84.96205615191 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.03916666666667 & 0.0323000513080234 & 94.091697802094 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.03716666666667 & 0.0312905932207343 & 97.0632498157348 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.03933333333333 & 0.0302362324898276 & 100.519578104046 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.03233333333333 & 0.0290794418098056 & 104.277563275332 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.02733333333333 & 0.0282811416940316 & 107.044240507879 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.02733333333333 & 0.0266011200081384 & 113.804731996515 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.03016666666667 & 0.0252797809682041 & 119.865226303894 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.03016666666667 & 0.0243578450183092 & 124.402083369402 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.046 & 0.0210597750295150 & 144.635923020596 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.02266666666667 & 0.0175648381856948 & 172.086223323617 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.05155172413793 & 0.0417832983912084 & 73.0328107553139 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.04964285714286 & 0.0405233332542302 & 75.256466145329 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.04814814814815 & 0.0396200279648827 & 76.9345279324355 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.04692307692308 & 0.0387906731624959 & 78.5478267974205 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.0454 & 0.0377826328746261 & 80.6031705123763 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.04416666666667 & 0.0366188840817794 & 83.131060462363 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.04152173913043 & 0.0357054068238205 & 85.183786145837 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.03954545454545 & 0.0350399267062405 & 86.7452001263497 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.03761904761905 & 0.0342105415419154 & 88.7919018732077 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.0355 & 0.0332318004944445 & 91.343230124033 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.03289473684211 & 0.0319626112806388 & 94.8888283942954 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.03194444444444 & 0.0312562868455633 & 97.0027073089398 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.03117647058824 & 0.0305118681969868 & 99.3441781741696 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.03 & 0.0297096161254665 & 101.987181093287 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.02966666666667 & 0.0288535076587676 & 105.001676139229 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.03 & 0.0277888866675551 & 109.036394161759 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.03038461538462 & 0.0267091500842848 & 113.458668876463 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.03041666666667 & 0.0254629538134957 & 119.012770036935 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.03045454545455 & 0.0237727086488964 & 127.476199292723 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.028 & 0.0224382192744996 & 134.948320227944 \tabularnewline
Median & 3.025 &  &  \tabularnewline
Midrange & 3.12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.0128125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.0128125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.0128125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.0128125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.0128125 &  &  \tabularnewline
Midmean - Closest Observation & 3.0128125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.0128125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.02181818181818 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52843&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]3.05383333333333[/C][C]0.0431788369293192[/C][C]70.7252337141978[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.03598253461502[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.01834077529425[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.07179073723021[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.05333333333333[/C][C]0.0428020451136785[/C][C]71.3361552052932[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.05233333333333[/C][C]0.0418075809270941[/C][C]73.0090874823906[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.05133333333333[/C][C]0.041162806607838[/C][C]74.1284082595163[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.052[/C][C]0.0410345038775245[/C][C]74.3764323094849[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.05033333333333[/C][C]0.0406757653987252[/C][C]74.9914181929305[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.05633333333333[/C][C]0.0388077738926229[/C][C]78.7556983245134[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.05166666666667[/C][C]0.036989971664851[/C][C]82.4998379105669[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.05033333333333[/C][C]0.0367300171788494[/C][C]83.0474246303876[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.05033333333333[/C][C]0.0361931156380007[/C][C]84.279379643422[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.052[/C][C]0.035921917832863[/C][C]84.96205615191[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.03916666666667[/C][C]0.0323000513080234[/C][C]94.091697802094[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.03716666666667[/C][C]0.0312905932207343[/C][C]97.0632498157348[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.03933333333333[/C][C]0.0302362324898276[/C][C]100.519578104046[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.03233333333333[/C][C]0.0290794418098056[/C][C]104.277563275332[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.02733333333333[/C][C]0.0282811416940316[/C][C]107.044240507879[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.02733333333333[/C][C]0.0266011200081384[/C][C]113.804731996515[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.03016666666667[/C][C]0.0252797809682041[/C][C]119.865226303894[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.03016666666667[/C][C]0.0243578450183092[/C][C]124.402083369402[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.046[/C][C]0.0210597750295150[/C][C]144.635923020596[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.02266666666667[/C][C]0.0175648381856948[/C][C]172.086223323617[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.05155172413793[/C][C]0.0417832983912084[/C][C]73.0328107553139[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.04964285714286[/C][C]0.0405233332542302[/C][C]75.256466145329[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.04814814814815[/C][C]0.0396200279648827[/C][C]76.9345279324355[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.04692307692308[/C][C]0.0387906731624959[/C][C]78.5478267974205[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.0454[/C][C]0.0377826328746261[/C][C]80.6031705123763[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.04416666666667[/C][C]0.0366188840817794[/C][C]83.131060462363[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.04152173913043[/C][C]0.0357054068238205[/C][C]85.183786145837[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.03954545454545[/C][C]0.0350399267062405[/C][C]86.7452001263497[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.03761904761905[/C][C]0.0342105415419154[/C][C]88.7919018732077[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.0355[/C][C]0.0332318004944445[/C][C]91.343230124033[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.03289473684211[/C][C]0.0319626112806388[/C][C]94.8888283942954[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.03194444444444[/C][C]0.0312562868455633[/C][C]97.0027073089398[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.03117647058824[/C][C]0.0305118681969868[/C][C]99.3441781741696[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.03[/C][C]0.0297096161254665[/C][C]101.987181093287[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.02966666666667[/C][C]0.0288535076587676[/C][C]105.001676139229[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.03[/C][C]0.0277888866675551[/C][C]109.036394161759[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.03038461538462[/C][C]0.0267091500842848[/C][C]113.458668876463[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.03041666666667[/C][C]0.0254629538134957[/C][C]119.012770036935[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.03045454545455[/C][C]0.0237727086488964[/C][C]127.476199292723[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.028[/C][C]0.0224382192744996[/C][C]134.948320227944[/C][/ROW]
[ROW][C]Median[/C][C]3.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.0128125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.02181818181818[/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=52843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52843&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 Mean3.053833333333330.043178836929319270.7252337141978
Geometric Mean3.03598253461502
Harmonic Mean3.01834077529425
Quadratic Mean3.07179073723021
Winsorized Mean ( 1 / 20 )3.053333333333330.042802045113678571.3361552052932
Winsorized Mean ( 2 / 20 )3.052333333333330.041807580927094173.0090874823906
Winsorized Mean ( 3 / 20 )3.051333333333330.04116280660783874.1284082595163
Winsorized Mean ( 4 / 20 )3.0520.041034503877524574.3764323094849
Winsorized Mean ( 5 / 20 )3.050333333333330.040675765398725274.9914181929305
Winsorized Mean ( 6 / 20 )3.056333333333330.038807773892622978.7556983245134
Winsorized Mean ( 7 / 20 )3.051666666666670.03698997166485182.4998379105669
Winsorized Mean ( 8 / 20 )3.050333333333330.036730017178849483.0474246303876
Winsorized Mean ( 9 / 20 )3.050333333333330.036193115638000784.279379643422
Winsorized Mean ( 10 / 20 )3.0520.03592191783286384.96205615191
Winsorized Mean ( 11 / 20 )3.039166666666670.032300051308023494.091697802094
Winsorized Mean ( 12 / 20 )3.037166666666670.031290593220734397.0632498157348
Winsorized Mean ( 13 / 20 )3.039333333333330.0302362324898276100.519578104046
Winsorized Mean ( 14 / 20 )3.032333333333330.0290794418098056104.277563275332
Winsorized Mean ( 15 / 20 )3.027333333333330.0282811416940316107.044240507879
Winsorized Mean ( 16 / 20 )3.027333333333330.0266011200081384113.804731996515
Winsorized Mean ( 17 / 20 )3.030166666666670.0252797809682041119.865226303894
Winsorized Mean ( 18 / 20 )3.030166666666670.0243578450183092124.402083369402
Winsorized Mean ( 19 / 20 )3.0460.0210597750295150144.635923020596
Winsorized Mean ( 20 / 20 )3.022666666666670.0175648381856948172.086223323617
Trimmed Mean ( 1 / 20 )3.051551724137930.041783298391208473.0328107553139
Trimmed Mean ( 2 / 20 )3.049642857142860.040523333254230275.256466145329
Trimmed Mean ( 3 / 20 )3.048148148148150.039620027964882776.9345279324355
Trimmed Mean ( 4 / 20 )3.046923076923080.038790673162495978.5478267974205
Trimmed Mean ( 5 / 20 )3.04540.037782632874626180.6031705123763
Trimmed Mean ( 6 / 20 )3.044166666666670.036618884081779483.131060462363
Trimmed Mean ( 7 / 20 )3.041521739130430.035705406823820585.183786145837
Trimmed Mean ( 8 / 20 )3.039545454545450.035039926706240586.7452001263497
Trimmed Mean ( 9 / 20 )3.037619047619050.034210541541915488.7919018732077
Trimmed Mean ( 10 / 20 )3.03550.033231800494444591.343230124033
Trimmed Mean ( 11 / 20 )3.032894736842110.031962611280638894.8888283942954
Trimmed Mean ( 12 / 20 )3.031944444444440.031256286845563397.0027073089398
Trimmed Mean ( 13 / 20 )3.031176470588240.030511868196986899.3441781741696
Trimmed Mean ( 14 / 20 )3.030.0297096161254665101.987181093287
Trimmed Mean ( 15 / 20 )3.029666666666670.0288535076587676105.001676139229
Trimmed Mean ( 16 / 20 )3.030.0277888866675551109.036394161759
Trimmed Mean ( 17 / 20 )3.030384615384620.0267091500842848113.458668876463
Trimmed Mean ( 18 / 20 )3.030416666666670.0254629538134957119.012770036935
Trimmed Mean ( 19 / 20 )3.030454545454550.0237727086488964127.476199292723
Trimmed Mean ( 20 / 20 )3.0280.0224382192744996134.948320227944
Median3.025
Midrange3.12
Midmean - Weighted Average at Xnp3.0128125
Midmean - Weighted Average at X(n+1)p3.0128125
Midmean - Empirical Distribution Function3.0128125
Midmean - Empirical Distribution Function - Averaging3.0128125
Midmean - Empirical Distribution Function - Interpolation3.0128125
Midmean - Closest Observation3.0128125
Midmean - True Basic - Statistics Graphics Toolkit3.0128125
Midmean - MS Excel (old versions)3.02181818181818
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')