Free Statistics

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 02:46:10 -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/d8nomek25zjmdwx1193046301.htm/, Retrieved Thu, 31 Oct 2024 23:37:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1435, Retrieved Thu, 31 Oct 2024 23:37:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 2, Vraag 8: Investeringsgoederen, Wim
Estimated Impact238
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 2 - Vraa...] [2007-10-22 09:46:10] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
Feedback Forum

Post a new message
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
98,0
106,6
90,1
96,9
125,9
112,0
100,0
123,9
79,8
83,4
113,6
112,9
104,0
109,9
99,0
106,3
128,9
111,1
102,9
130,0
87,0
87,5
117,6
103,4
110,8
112,6
102,5
112,4
135,6
105,1
127,7
137,0
91,0
90,5
122,4
123,3
124,3
120,0
118,1
119,0
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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1435&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1435&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1435&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'Gwilym Jenkins' @ 72.249.127.135







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=1435&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=1435&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1435&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')