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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 02:45:10 -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/2007/Oct/22/pj85whe77uwtt8x1193046018.htm/, Retrieved Sun, 05 May 2024 22:02:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1556, Retrieved Sun, 05 May 2024 22:02:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTotale consumptiegoederen
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Totale consumptie...] [2007-10-22 09:45:10] [a1c3b9772d97ad2d7bb67d4cdac038f3] [Current]
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Dataseries X:
115,9
112,9
126,3
116,8
112,0
129,7
113,6
115,7
119,5
125,8
129,6
128,0
112,8
101,6
123,9
118,8
109,1
130,6
112,4
111,0
116,2
119,8
117,2
127,3
107,7
97,5
120,1
110,6
111,3
119,8
105,5
108,7
128,7
119,5
121,1
128,4
108,8
107,5
125,6
102,9
107,5
120,4
104,3
100,6
121,9
112,7
124,9
123,9
102,2
104,9
109,8
98,9
107,3
112,6
104,0
110,6
100,8
103,8
117,0
108,4




Summary of compuational 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 compuational 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=1556&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1556&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 compuational 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 Mean114.4451.1575261586286598.8703357992234
Geometric Mean114.099730748685
Harmonic Mean113.755068114603
Quadratic Mean114.789852193766
Winsorized Mean ( 1 / 20 )114.4533333333331.1484906987531199.6554290405595
Winsorized Mean ( 2 / 20 )114.5066666666671.1353509790256100.855743097998
Winsorized Mean ( 3 / 20 )114.4716666666671.12338042031105101.899289498896
Winsorized Mean ( 4 / 20 )114.5051.10834386809487103.311799971269
Winsorized Mean ( 5 / 20 )114.5216666666671.09159628013049104.912107847213
Winsorized Mean ( 6 / 20 )114.5216666666671.06396574980627107.636610189302
Winsorized Mean ( 7 / 20 )114.511.02161581333518112.087145192251
Winsorized Mean ( 8 / 20 )114.471.00399287592854114.014753236305
Winsorized Mean ( 9 / 20 )114.4850.990371228121822115.598067420753
Winsorized Mean ( 10 / 20 )114.4683333333330.95118270615568120.343160775043
Winsorized Mean ( 11 / 20 )114.3950.89909692607965127.233223339778
Winsorized Mean ( 12 / 20 )114.7550.841791286852905136.322389875309
Winsorized Mean ( 13 / 20 )114.3650.758674226477283150.743225496173
Winsorized Mean ( 14 / 20 )114.1783333333330.727906570596729156.858500727272
Winsorized Mean ( 15 / 20 )114.0533333333330.692422533008896164.716380383693
Winsorized Mean ( 16 / 20 )114.160.65150932977177175.223891329371
Winsorized Mean ( 17 / 20 )114.160.62579305617156182.424523369437
Winsorized Mean ( 18 / 20 )114.190.62136945531624183.771505057139
Winsorized Mean ( 19 / 20 )114.190.592994412183923192.565052307074
Winsorized Mean ( 20 / 20 )114.4233333333330.559667812424168204.448658281268
Trimmed Mean ( 1 / 20 )114.4586206896551.12645693649636101.609406432933
Trimmed Mean ( 2 / 20 )114.4642857142861.09908884510073104.144706976618
Trimmed Mean ( 3 / 20 )114.4407407407411.07368146273828106.587237194983
Trimmed Mean ( 4 / 20 )114.4288461538461.04749336847637109.240640177311
Trimmed Mean ( 5 / 20 )114.4061.02022170459690112.138370987905
Trimmed Mean ( 6 / 20 )114.3770833333330.991154314796021115.397856444657
Trimmed Mean ( 7 / 20 )114.3456521739130.962458137726887118.805844838065
Trimmed Mean ( 8 / 20 )114.3136363636360.93762435910407121.918373017598
Trimmed Mean ( 9 / 20 )114.2857142857140.909681897590243125.632613541567
Trimmed Mean ( 10 / 20 )114.25250.876041413229025130.419062700328
Trimmed Mean ( 11 / 20 )114.2184210526320.841803044097628135.683069636637
Trimmed Mean ( 12 / 20 )114.1916666666670.809941943833601140.987471430578
Trimmed Mean ( 13 / 20 )114.1088235294120.781120449046786146.083518449249
Trimmed Mean ( 14 / 20 )114.0718750.764750570434464149.162196682239
Trimmed Mean ( 15 / 20 )114.0566666666670.748618395389606152.356216957917
Trimmed Mean ( 16 / 20 )114.0571428571430.733665663720505155.462015598148
Trimmed Mean ( 17 / 20 )114.0423076923080.721540511724166158.053921906334
Trimmed Mean ( 18 / 20 )114.0250.70800930354978161.050143590356
Trimmed Mean ( 19 / 20 )1140.683826767258381166.708888066860
Trimmed Mean ( 20 / 20 )113.970.652448828402819174.680365782856
Median112.85
Midrange114.05
Midmean - Weighted Average at Xnp113.646875
Midmean - Weighted Average at X(n+1)p114.056666666667
Midmean - Empirical Distribution Function113.646875
Midmean - Empirical Distribution Function - Averaging114.056666666667
Midmean - Empirical Distribution Function - Interpolation114.056666666667
Midmean - Closest Observation113.646875
Midmean - True Basic - Statistics Graphics Toolkit114.056666666667
Midmean - MS Excel (old versions)113.872727272727
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.445 & 1.15752615862865 & 98.8703357992234 \tabularnewline
Geometric Mean & 114.099730748685 &  &  \tabularnewline
Harmonic Mean & 113.755068114603 &  &  \tabularnewline
Quadratic Mean & 114.789852193766 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.453333333333 & 1.14849069875311 & 99.6554290405595 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.506666666667 & 1.1353509790256 & 100.855743097998 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.471666666667 & 1.12338042031105 & 101.899289498896 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.505 & 1.10834386809487 & 103.311799971269 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.521666666667 & 1.09159628013049 & 104.912107847213 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.521666666667 & 1.06396574980627 & 107.636610189302 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.51 & 1.02161581333518 & 112.087145192251 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.47 & 1.00399287592854 & 114.014753236305 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.485 & 0.990371228121822 & 115.598067420753 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.468333333333 & 0.95118270615568 & 120.343160775043 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.395 & 0.89909692607965 & 127.233223339778 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 114.755 & 0.841791286852905 & 136.322389875309 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 114.365 & 0.758674226477283 & 150.743225496173 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.178333333333 & 0.727906570596729 & 156.858500727272 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.053333333333 & 0.692422533008896 & 164.716380383693 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.16 & 0.65150932977177 & 175.223891329371 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.16 & 0.62579305617156 & 182.424523369437 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.19 & 0.62136945531624 & 183.771505057139 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.19 & 0.592994412183923 & 192.565052307074 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.423333333333 & 0.559667812424168 & 204.448658281268 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 114.458620689655 & 1.12645693649636 & 101.609406432933 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.464285714286 & 1.09908884510073 & 104.144706976618 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.440740740741 & 1.07368146273828 & 106.587237194983 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.428846153846 & 1.04749336847637 & 109.240640177311 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.406 & 1.02022170459690 & 112.138370987905 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.377083333333 & 0.991154314796021 & 115.397856444657 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.345652173913 & 0.962458137726887 & 118.805844838065 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.313636363636 & 0.93762435910407 & 121.918373017598 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.285714285714 & 0.909681897590243 & 125.632613541567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.2525 & 0.876041413229025 & 130.419062700328 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.218421052632 & 0.841803044097628 & 135.683069636637 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.191666666667 & 0.809941943833601 & 140.987471430578 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.108823529412 & 0.781120449046786 & 146.083518449249 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.071875 & 0.764750570434464 & 149.162196682239 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.056666666667 & 0.748618395389606 & 152.356216957917 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.057142857143 & 0.733665663720505 & 155.462015598148 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.042307692308 & 0.721540511724166 & 158.053921906334 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.025 & 0.70800930354978 & 161.050143590356 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114 & 0.683826767258381 & 166.708888066860 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 113.97 & 0.652448828402819 & 174.680365782856 \tabularnewline
Median & 112.85 &  &  \tabularnewline
Midrange & 114.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.646875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.056666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.646875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.056666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.056666666667 &  &  \tabularnewline
Midmean - Closest Observation & 113.646875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.056666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.872727272727 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1556&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]114.445[/C][C]1.15752615862865[/C][C]98.8703357992234[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.099730748685[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.755068114603[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.789852193766[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.453333333333[/C][C]1.14849069875311[/C][C]99.6554290405595[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.506666666667[/C][C]1.1353509790256[/C][C]100.855743097998[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.471666666667[/C][C]1.12338042031105[/C][C]101.899289498896[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.505[/C][C]1.10834386809487[/C][C]103.311799971269[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.521666666667[/C][C]1.09159628013049[/C][C]104.912107847213[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.521666666667[/C][C]1.06396574980627[/C][C]107.636610189302[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.51[/C][C]1.02161581333518[/C][C]112.087145192251[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.47[/C][C]1.00399287592854[/C][C]114.014753236305[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.485[/C][C]0.990371228121822[/C][C]115.598067420753[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.468333333333[/C][C]0.95118270615568[/C][C]120.343160775043[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.395[/C][C]0.89909692607965[/C][C]127.233223339778[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]114.755[/C][C]0.841791286852905[/C][C]136.322389875309[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]114.365[/C][C]0.758674226477283[/C][C]150.743225496173[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.178333333333[/C][C]0.727906570596729[/C][C]156.858500727272[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.053333333333[/C][C]0.692422533008896[/C][C]164.716380383693[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.16[/C][C]0.65150932977177[/C][C]175.223891329371[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.16[/C][C]0.62579305617156[/C][C]182.424523369437[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.19[/C][C]0.62136945531624[/C][C]183.771505057139[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.19[/C][C]0.592994412183923[/C][C]192.565052307074[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.423333333333[/C][C]0.559667812424168[/C][C]204.448658281268[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]114.458620689655[/C][C]1.12645693649636[/C][C]101.609406432933[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.464285714286[/C][C]1.09908884510073[/C][C]104.144706976618[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.440740740741[/C][C]1.07368146273828[/C][C]106.587237194983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.428846153846[/C][C]1.04749336847637[/C][C]109.240640177311[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.406[/C][C]1.02022170459690[/C][C]112.138370987905[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.377083333333[/C][C]0.991154314796021[/C][C]115.397856444657[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.345652173913[/C][C]0.962458137726887[/C][C]118.805844838065[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.313636363636[/C][C]0.93762435910407[/C][C]121.918373017598[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.285714285714[/C][C]0.909681897590243[/C][C]125.632613541567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.2525[/C][C]0.876041413229025[/C][C]130.419062700328[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.218421052632[/C][C]0.841803044097628[/C][C]135.683069636637[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.191666666667[/C][C]0.809941943833601[/C][C]140.987471430578[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.108823529412[/C][C]0.781120449046786[/C][C]146.083518449249[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.071875[/C][C]0.764750570434464[/C][C]149.162196682239[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.056666666667[/C][C]0.748618395389606[/C][C]152.356216957917[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.057142857143[/C][C]0.733665663720505[/C][C]155.462015598148[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.042307692308[/C][C]0.721540511724166[/C][C]158.053921906334[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.025[/C][C]0.70800930354978[/C][C]161.050143590356[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114[/C][C]0.683826767258381[/C][C]166.708888066860[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]113.97[/C][C]0.652448828402819[/C][C]174.680365782856[/C][/ROW]
[ROW][C]Median[/C][C]112.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.646875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.056666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.646875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.056666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.056666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.646875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.056666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.872727272727[/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=1556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1556&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 Mean114.4451.1575261586286598.8703357992234
Geometric Mean114.099730748685
Harmonic Mean113.755068114603
Quadratic Mean114.789852193766
Winsorized Mean ( 1 / 20 )114.4533333333331.1484906987531199.6554290405595
Winsorized Mean ( 2 / 20 )114.5066666666671.1353509790256100.855743097998
Winsorized Mean ( 3 / 20 )114.4716666666671.12338042031105101.899289498896
Winsorized Mean ( 4 / 20 )114.5051.10834386809487103.311799971269
Winsorized Mean ( 5 / 20 )114.5216666666671.09159628013049104.912107847213
Winsorized Mean ( 6 / 20 )114.5216666666671.06396574980627107.636610189302
Winsorized Mean ( 7 / 20 )114.511.02161581333518112.087145192251
Winsorized Mean ( 8 / 20 )114.471.00399287592854114.014753236305
Winsorized Mean ( 9 / 20 )114.4850.990371228121822115.598067420753
Winsorized Mean ( 10 / 20 )114.4683333333330.95118270615568120.343160775043
Winsorized Mean ( 11 / 20 )114.3950.89909692607965127.233223339778
Winsorized Mean ( 12 / 20 )114.7550.841791286852905136.322389875309
Winsorized Mean ( 13 / 20 )114.3650.758674226477283150.743225496173
Winsorized Mean ( 14 / 20 )114.1783333333330.727906570596729156.858500727272
Winsorized Mean ( 15 / 20 )114.0533333333330.692422533008896164.716380383693
Winsorized Mean ( 16 / 20 )114.160.65150932977177175.223891329371
Winsorized Mean ( 17 / 20 )114.160.62579305617156182.424523369437
Winsorized Mean ( 18 / 20 )114.190.62136945531624183.771505057139
Winsorized Mean ( 19 / 20 )114.190.592994412183923192.565052307074
Winsorized Mean ( 20 / 20 )114.4233333333330.559667812424168204.448658281268
Trimmed Mean ( 1 / 20 )114.4586206896551.12645693649636101.609406432933
Trimmed Mean ( 2 / 20 )114.4642857142861.09908884510073104.144706976618
Trimmed Mean ( 3 / 20 )114.4407407407411.07368146273828106.587237194983
Trimmed Mean ( 4 / 20 )114.4288461538461.04749336847637109.240640177311
Trimmed Mean ( 5 / 20 )114.4061.02022170459690112.138370987905
Trimmed Mean ( 6 / 20 )114.3770833333330.991154314796021115.397856444657
Trimmed Mean ( 7 / 20 )114.3456521739130.962458137726887118.805844838065
Trimmed Mean ( 8 / 20 )114.3136363636360.93762435910407121.918373017598
Trimmed Mean ( 9 / 20 )114.2857142857140.909681897590243125.632613541567
Trimmed Mean ( 10 / 20 )114.25250.876041413229025130.419062700328
Trimmed Mean ( 11 / 20 )114.2184210526320.841803044097628135.683069636637
Trimmed Mean ( 12 / 20 )114.1916666666670.809941943833601140.987471430578
Trimmed Mean ( 13 / 20 )114.1088235294120.781120449046786146.083518449249
Trimmed Mean ( 14 / 20 )114.0718750.764750570434464149.162196682239
Trimmed Mean ( 15 / 20 )114.0566666666670.748618395389606152.356216957917
Trimmed Mean ( 16 / 20 )114.0571428571430.733665663720505155.462015598148
Trimmed Mean ( 17 / 20 )114.0423076923080.721540511724166158.053921906334
Trimmed Mean ( 18 / 20 )114.0250.70800930354978161.050143590356
Trimmed Mean ( 19 / 20 )1140.683826767258381166.708888066860
Trimmed Mean ( 20 / 20 )113.970.652448828402819174.680365782856
Median112.85
Midrange114.05
Midmean - Weighted Average at Xnp113.646875
Midmean - Weighted Average at X(n+1)p114.056666666667
Midmean - Empirical Distribution Function113.646875
Midmean - Empirical Distribution Function - Averaging114.056666666667
Midmean - Empirical Distribution Function - Interpolation114.056666666667
Midmean - Closest Observation113.646875
Midmean - True Basic - Statistics Graphics Toolkit114.056666666667
Midmean - MS Excel (old versions)113.872727272727
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')