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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 11 Nov 2007 03:43:24 -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/Nov/11/t1194777581rl2k0569zq3vo03.htm/, Retrieved Sun, 05 May 2024 18:33:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5077, Retrieved Sun, 05 May 2024 18:33:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency, consumptiegoederen
Estimated Impact235
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [PAPER_Central Ten...] [2007-11-11 10:43:24] [ca5e0f9f346e091f4d0fe7e17f7dba21] [Current]
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Dataseries X:
108,4
117
103,8
100,8
110,6
104
112,6
107,3
98,9
109,8
104,9
102,2
123,9
124,9
112,7
121,9
100,6
104,3
120,4
107,5
102,9
125,6
107,5
108,8
128,4
121,1
119,5
128,7
108,7
105,5
119,8
111,3
110,6
120,1
97,5
107,7
127,3
117,2
119,8
116,2
111
112,4
130,6
109,1
118,8
123,9
101,6
112,8
128
129,6
125,8
119,5
115,7
113,6
129,7
112
116,8
126,3
112,9
115,9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5077&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5077&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5077&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







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 )114.160.625793056171561182.424523369437
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 & 0.625793056171561 & 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=5077&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]0.625793056171561[/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=5077&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5077&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 )114.160.625793056171561182.424523369437
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')