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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Oct 2007 11:01:02 -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/18/t51i5fw12n5p9y31192730309.htm/, Retrieved Sun, 28 Apr 2024 21:53:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=977, Retrieved Sun, 28 Apr 2024 21:53:13 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral Tendency, Workshop 2 Question 8, investeringsgoederen, kim, wim, hoyi
Estimated Impact203
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 2 Questi...] [2007-10-18 18:01:02] [181c187d2008ac66a37ecc12859b08c5] [Current]
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Dataseries X:
101,5
126,6
93,9
89,8
93,4
101,5
110,4
105,9
108,4
113,9
86,1
69,4
101,2
100,5
98
106,6
90,1
96,9
125,9
112
100
123,9
79,8
83,4
113,6
112,9
104
109,9
99
106,3
128,9
111,1
102,9
130
87
87,5
117,6
103,4
110,8
112,6
102,5
112,4
135,6
105,1
127,7
137
91
90,5
122,4
123,3
124,3
120
118,1
119
142,7
123,6
129,6
146,9
108,7
99,4




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 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=977&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]3 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=977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=977&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.942.0704992711030952.6153288341708
Geometric Mean107.759199457392
Harmonic Mean106.552544663970
Quadratic Mean110.094753129596
Winsorized Mean ( 1 / 20 )109.0433333333331.9999807437867754.5221916121403
Winsorized Mean ( 2 / 20 )108.9733333333331.9208826635576456.7308640973963
Winsorized Mean ( 3 / 20 )109.0383333333331.874572782465658.1670310981026
Winsorized Mean ( 4 / 20 )108.7251.7792997178316361.1055006137468
Winsorized Mean ( 5 / 20 )108.7333333333331.7640183753649661.6395695486093
Winsorized Mean ( 6 / 20 )108.8933333333331.7047173940559763.8776454754458
Winsorized Mean ( 7 / 20 )108.7883333333331.6707183942600965.1147037747868
Winsorized Mean ( 8 / 20 )108.6951.6329229710487066.564683042087
Winsorized Mean ( 9 / 20 )108.6651.5994734744534667.9379819269155
Winsorized Mean ( 10 / 20 )108.7983333333331.4785786648580073.5830537253034
Winsorized Mean ( 11 / 20 )108.8166666666671.4495102751152875.0713317006409
Winsorized Mean ( 12 / 20 )109.3566666666671.3389859698649981.6712565537136
Winsorized Mean ( 13 / 20 )109.531.2903976087627384.8808144530124
Winsorized Mean ( 14 / 20 )109.5533333333331.2178068336121689.9595324230407
Winsorized Mean ( 15 / 20 )109.0533333333331.0985621487776399.2691523685544
Winsorized Mean ( 16 / 20 )108.9466666666671.03028290412078105.744418577575
Winsorized Mean ( 17 / 20 )108.8333333333330.967723949370148112.463201312904
Winsorized Mean ( 18 / 20 )108.8933333333330.913099479319592119.256812428014
Winsorized Mean ( 19 / 20 )107.8166666666670.719361638960743149.878254312294
Winsorized Mean ( 20 / 20 )107.7166666666670.705123167774666152.762909502201
Trimmed Mean ( 1 / 20 )108.9672413793101.9187557534626656.7905744035758
Trimmed Mean ( 2 / 20 )108.8857142857141.8182381020972959.8852890389423
Trimmed Mean ( 3 / 20 )108.8370370370371.7477534672727962.2725338985408
Trimmed Mean ( 4 / 20 )108.7596153846151.6826733461547564.6350140585238
Trimmed Mean ( 5 / 20 )108.771.6393384678719966.3499345203514
Trimmed Mean ( 6 / 20 )108.7791666666671.5892339425747568.4475480623271
Trimmed Mean ( 7 / 20 )108.7543478260871.5436975077323770.4505560715991
Trimmed Mean ( 8 / 20 )108.7477272727271.4945089368516472.7648557939152
Trimmed Mean ( 9 / 20 )108.7571428571431.4406982388056975.4891898440163
Trimmed Mean ( 10 / 20 )108.77251.3786373219177778.8985603905531
Trimmed Mean ( 11 / 20 )108.7684210526321.3301360119501881.7724052844493
Trimmed Mean ( 12 / 20 )108.7611111111111.2716523295564485.5273950145225
Trimmed Mean ( 13 / 20 )108.6735294117651.2223433036322488.9058982765623
Trimmed Mean ( 14 / 20 )108.551.1657321526032193.1174453390482
Trimmed Mean ( 15 / 20 )108.4066666666671.1061056603239998.007514612043
Trimmed Mean ( 16 / 20 )108.3142857142861.05950864979345102.230676205806
Trimmed Mean ( 17 / 20 )108.2230769230771.01156858685764106.985406950273
Trimmed Mean ( 18 / 20 )108.1333333333330.95906556777158112.748634678424
Trimmed Mean ( 19 / 20 )108.0181818181820.894611970919458120.743054340267
Trimmed Mean ( 20 / 20 )108.050.877571409600021123.123883501682
Median108.55
Midrange108.15
Midmean - Weighted Average at Xnp108.103225806452
Midmean - Weighted Average at X(n+1)p108.406666666667
Midmean - Empirical Distribution Function108.103225806452
Midmean - Empirical Distribution Function - Averaging108.406666666667
Midmean - Empirical Distribution Function - Interpolation108.406666666667
Midmean - Closest Observation108.103225806452
Midmean - True Basic - Statistics Graphics Toolkit108.406666666667
Midmean - MS Excel (old versions)108.55
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.94 & 2.07049927110309 & 52.6153288341708 \tabularnewline
Geometric Mean & 107.759199457392 &  &  \tabularnewline
Harmonic Mean & 106.552544663970 &  &  \tabularnewline
Quadratic Mean & 110.094753129596 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.043333333333 & 1.99998074378677 & 54.5221916121403 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 108.973333333333 & 1.92088266355764 & 56.7308640973963 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.038333333333 & 1.8745727824656 & 58.1670310981026 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 108.725 & 1.77929971783163 & 61.1055006137468 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 108.733333333333 & 1.76401837536496 & 61.6395695486093 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 108.893333333333 & 1.70471739405597 & 63.8776454754458 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 108.788333333333 & 1.67071839426009 & 65.1147037747868 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 108.695 & 1.63292297104870 & 66.564683042087 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 108.665 & 1.59947347445346 & 67.9379819269155 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 108.798333333333 & 1.47857866485800 & 73.5830537253034 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108.816666666667 & 1.44951027511528 & 75.0713317006409 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 109.356666666667 & 1.33898596986499 & 81.6712565537136 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109.53 & 1.29039760876273 & 84.8808144530124 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109.553333333333 & 1.21780683361216 & 89.9595324230407 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 109.053333333333 & 1.09856214877763 & 99.2691523685544 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 108.946666666667 & 1.03028290412078 & 105.744418577575 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 108.833333333333 & 0.967723949370148 & 112.463201312904 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 108.893333333333 & 0.913099479319592 & 119.256812428014 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.816666666667 & 0.719361638960743 & 149.878254312294 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 107.716666666667 & 0.705123167774666 & 152.762909502201 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 108.967241379310 & 1.91875575346266 & 56.7905744035758 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 108.885714285714 & 1.81823810209729 & 59.8852890389423 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 108.837037037037 & 1.74775346727279 & 62.2725338985408 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 108.759615384615 & 1.68267334615475 & 64.6350140585238 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 108.77 & 1.63933846787199 & 66.3499345203514 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108.779166666667 & 1.58923394257475 & 68.4475480623271 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 108.754347826087 & 1.54369750773237 & 70.4505560715991 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 108.747727272727 & 1.49450893685164 & 72.7648557939152 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 108.757142857143 & 1.44069823880569 & 75.4891898440163 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 108.7725 & 1.37863732191777 & 78.8985603905531 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 108.768421052632 & 1.33013601195018 & 81.7724052844493 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 108.761111111111 & 1.27165232955644 & 85.5273950145225 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 108.673529411765 & 1.22234330363224 & 88.9058982765623 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 108.55 & 1.16573215260321 & 93.1174453390482 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 108.406666666667 & 1.10610566032399 & 98.007514612043 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 108.314285714286 & 1.05950864979345 & 102.230676205806 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 108.223076923077 & 1.01156858685764 & 106.985406950273 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.133333333333 & 0.95906556777158 & 112.748634678424 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.018181818182 & 0.894611970919458 & 120.743054340267 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.05 & 0.877571409600021 & 123.123883501682 \tabularnewline
Median & 108.55 &  &  \tabularnewline
Midrange & 108.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.103225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.406666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.103225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.406666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.406666666667 &  &  \tabularnewline
Midmean - Closest Observation & 108.103225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.406666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.55 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=977&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]108.94[/C][C]2.07049927110309[/C][C]52.6153288341708[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.759199457392[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.552544663970[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.094753129596[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.043333333333[/C][C]1.99998074378677[/C][C]54.5221916121403[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]108.973333333333[/C][C]1.92088266355764[/C][C]56.7308640973963[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.038333333333[/C][C]1.8745727824656[/C][C]58.1670310981026[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]108.725[/C][C]1.77929971783163[/C][C]61.1055006137468[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]108.733333333333[/C][C]1.76401837536496[/C][C]61.6395695486093[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]108.893333333333[/C][C]1.70471739405597[/C][C]63.8776454754458[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]108.788333333333[/C][C]1.67071839426009[/C][C]65.1147037747868[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]108.695[/C][C]1.63292297104870[/C][C]66.564683042087[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]108.665[/C][C]1.59947347445346[/C][C]67.9379819269155[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]108.798333333333[/C][C]1.47857866485800[/C][C]73.5830537253034[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108.816666666667[/C][C]1.44951027511528[/C][C]75.0713317006409[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]109.356666666667[/C][C]1.33898596986499[/C][C]81.6712565537136[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109.53[/C][C]1.29039760876273[/C][C]84.8808144530124[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109.553333333333[/C][C]1.21780683361216[/C][C]89.9595324230407[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]109.053333333333[/C][C]1.09856214877763[/C][C]99.2691523685544[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]108.946666666667[/C][C]1.03028290412078[/C][C]105.744418577575[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]108.833333333333[/C][C]0.967723949370148[/C][C]112.463201312904[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]108.893333333333[/C][C]0.913099479319592[/C][C]119.256812428014[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.816666666667[/C][C]0.719361638960743[/C][C]149.878254312294[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]107.716666666667[/C][C]0.705123167774666[/C][C]152.762909502201[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]108.967241379310[/C][C]1.91875575346266[/C][C]56.7905744035758[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]108.885714285714[/C][C]1.81823810209729[/C][C]59.8852890389423[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]108.837037037037[/C][C]1.74775346727279[/C][C]62.2725338985408[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]108.759615384615[/C][C]1.68267334615475[/C][C]64.6350140585238[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]108.77[/C][C]1.63933846787199[/C][C]66.3499345203514[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108.779166666667[/C][C]1.58923394257475[/C][C]68.4475480623271[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]108.754347826087[/C][C]1.54369750773237[/C][C]70.4505560715991[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]108.747727272727[/C][C]1.49450893685164[/C][C]72.7648557939152[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]108.757142857143[/C][C]1.44069823880569[/C][C]75.4891898440163[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]108.7725[/C][C]1.37863732191777[/C][C]78.8985603905531[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]108.768421052632[/C][C]1.33013601195018[/C][C]81.7724052844493[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]108.761111111111[/C][C]1.27165232955644[/C][C]85.5273950145225[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]108.673529411765[/C][C]1.22234330363224[/C][C]88.9058982765623[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]108.55[/C][C]1.16573215260321[/C][C]93.1174453390482[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]108.406666666667[/C][C]1.10610566032399[/C][C]98.007514612043[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]108.314285714286[/C][C]1.05950864979345[/C][C]102.230676205806[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]108.223076923077[/C][C]1.01156858685764[/C][C]106.985406950273[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.133333333333[/C][C]0.95906556777158[/C][C]112.748634678424[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.018181818182[/C][C]0.894611970919458[/C][C]120.743054340267[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.05[/C][C]0.877571409600021[/C][C]123.123883501682[/C][/ROW]
[ROW][C]Median[/C][C]108.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.103225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.103225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.103225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.406666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.55[/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=977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=977&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 Mean108.942.0704992711030952.6153288341708
Geometric Mean107.759199457392
Harmonic Mean106.552544663970
Quadratic Mean110.094753129596
Winsorized Mean ( 1 / 20 )109.0433333333331.9999807437867754.5221916121403
Winsorized Mean ( 2 / 20 )108.9733333333331.9208826635576456.7308640973963
Winsorized Mean ( 3 / 20 )109.0383333333331.874572782465658.1670310981026
Winsorized Mean ( 4 / 20 )108.7251.7792997178316361.1055006137468
Winsorized Mean ( 5 / 20 )108.7333333333331.7640183753649661.6395695486093
Winsorized Mean ( 6 / 20 )108.8933333333331.7047173940559763.8776454754458
Winsorized Mean ( 7 / 20 )108.7883333333331.6707183942600965.1147037747868
Winsorized Mean ( 8 / 20 )108.6951.6329229710487066.564683042087
Winsorized Mean ( 9 / 20 )108.6651.5994734744534667.9379819269155
Winsorized Mean ( 10 / 20 )108.7983333333331.4785786648580073.5830537253034
Winsorized Mean ( 11 / 20 )108.8166666666671.4495102751152875.0713317006409
Winsorized Mean ( 12 / 20 )109.3566666666671.3389859698649981.6712565537136
Winsorized Mean ( 13 / 20 )109.531.2903976087627384.8808144530124
Winsorized Mean ( 14 / 20 )109.5533333333331.2178068336121689.9595324230407
Winsorized Mean ( 15 / 20 )109.0533333333331.0985621487776399.2691523685544
Winsorized Mean ( 16 / 20 )108.9466666666671.03028290412078105.744418577575
Winsorized Mean ( 17 / 20 )108.8333333333330.967723949370148112.463201312904
Winsorized Mean ( 18 / 20 )108.8933333333330.913099479319592119.256812428014
Winsorized Mean ( 19 / 20 )107.8166666666670.719361638960743149.878254312294
Winsorized Mean ( 20 / 20 )107.7166666666670.705123167774666152.762909502201
Trimmed Mean ( 1 / 20 )108.9672413793101.9187557534626656.7905744035758
Trimmed Mean ( 2 / 20 )108.8857142857141.8182381020972959.8852890389423
Trimmed Mean ( 3 / 20 )108.8370370370371.7477534672727962.2725338985408
Trimmed Mean ( 4 / 20 )108.7596153846151.6826733461547564.6350140585238
Trimmed Mean ( 5 / 20 )108.771.6393384678719966.3499345203514
Trimmed Mean ( 6 / 20 )108.7791666666671.5892339425747568.4475480623271
Trimmed Mean ( 7 / 20 )108.7543478260871.5436975077323770.4505560715991
Trimmed Mean ( 8 / 20 )108.7477272727271.4945089368516472.7648557939152
Trimmed Mean ( 9 / 20 )108.7571428571431.4406982388056975.4891898440163
Trimmed Mean ( 10 / 20 )108.77251.3786373219177778.8985603905531
Trimmed Mean ( 11 / 20 )108.7684210526321.3301360119501881.7724052844493
Trimmed Mean ( 12 / 20 )108.7611111111111.2716523295564485.5273950145225
Trimmed Mean ( 13 / 20 )108.6735294117651.2223433036322488.9058982765623
Trimmed Mean ( 14 / 20 )108.551.1657321526032193.1174453390482
Trimmed Mean ( 15 / 20 )108.4066666666671.1061056603239998.007514612043
Trimmed Mean ( 16 / 20 )108.3142857142861.05950864979345102.230676205806
Trimmed Mean ( 17 / 20 )108.2230769230771.01156858685764106.985406950273
Trimmed Mean ( 18 / 20 )108.1333333333330.95906556777158112.748634678424
Trimmed Mean ( 19 / 20 )108.0181818181820.894611970919458120.743054340267
Trimmed Mean ( 20 / 20 )108.050.877571409600021123.123883501682
Median108.55
Midrange108.15
Midmean - Weighted Average at Xnp108.103225806452
Midmean - Weighted Average at X(n+1)p108.406666666667
Midmean - Empirical Distribution Function108.103225806452
Midmean - Empirical Distribution Function - Averaging108.406666666667
Midmean - Empirical Distribution Function - Interpolation108.406666666667
Midmean - Closest Observation108.103225806452
Midmean - True Basic - Statistics Graphics Toolkit108.406666666667
Midmean - MS Excel (old versions)108.55
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')