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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 16 Oct 2009 10:14:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/16/t1255710287yipk8ie149it1k4.htm/, Retrieved Tue, 30 Apr 2024 01:49:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47063, Retrieved Tue, 30 Apr 2024 01:49:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [workshop 3] [2009-10-16 16:14:51] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
-  M D          [Central Tendency] [ws 2] [2009-11-14 15:18:12] [b5908418e3090fddbd22f5f0f774653d]
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Post a new message
Dataseries X:
98.3
112.3
113.9
106.2
98.6
96.5
95.9
103.7
103.1
103.7
112.1
86.9
95
111.8
108.8
109.3
101.4
100.5
100.7
113.5
106.1
111.6
114.9
88.6
99.5
115.1
118
111.4
107.3
105.3
105.3
117.9
110.2
112.4
117.5
93
103.5
116.3
120
114.3
104.7
109.8
112.6
114.4
115.7
114.7
118.4
94.9
103.8
115.1
113.7
104
94.3
92.5
93.2
104.7
94
98.1
102.7
82.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47063&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47063&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.7351.1539855402554491.6259314450291
Geometric Mean105.350840712003
Harmonic Mean104.953830385521
Quadratic Mean106.105888149527
Winsorized Mean ( 1 / 20 )105.7833333333331.1251068164397894.0207025569964
Winsorized Mean ( 2 / 20 )105.8266666666671.1070596946905395.5925567286142
Winsorized Mean ( 3 / 20 )106.0166666666671.05921345582910100.089992327073
Winsorized Mean ( 4 / 20 )106.0233333333331.04708194647627101.256003591822
Winsorized Mean ( 5 / 20 )105.941.02571512878758103.284037669624
Winsorized Mean ( 6 / 20 )105.960.999079237114804106.057653951449
Winsorized Mean ( 7 / 20 )105.9250.980676651560163108.012156536493
Winsorized Mean ( 8 / 20 )106.0050.964834885320904109.868539801753
Winsorized Mean ( 9 / 20 )105.990.9571488381151110.735128936399
Winsorized Mean ( 10 / 20 )106.1066666666670.92323083728162114.929725461824
Winsorized Mean ( 11 / 20 )106.1616666666670.894215850238255118.720403623332
Winsorized Mean ( 12 / 20 )106.4616666666670.834516984241074127.572798010199
Winsorized Mean ( 13 / 20 )106.4183333333330.81351747822791130.812596141321
Winsorized Mean ( 14 / 20 )106.4416666666670.794491244193296133.974625201495
Winsorized Mean ( 15 / 20 )106.6166666666670.749791559233332142.195074556031
Winsorized Mean ( 16 / 20 )106.6433333333330.6708387812531158.970137555446
Winsorized Mean ( 17 / 20 )106.6433333333330.653579309166836163.168160065041
Winsorized Mean ( 18 / 20 )106.8233333333330.617249076018404173.063577547013
Winsorized Mean ( 19 / 20 )107.1716666666670.548439448458291195.412031297047
Winsorized Mean ( 20 / 20 )107.2050.515036200801063208.150417064390
Trimmed Mean ( 1 / 20 )105.8913793103451.095103451628596.6953205680034
Trimmed Mean ( 2 / 20 )106.0071428571431.05787663196618100.207471886506
Trimmed Mean ( 3 / 20 )106.1074074074071.02373254067054103.647586837386
Trimmed Mean ( 4 / 20 )106.1423076923081.00435832360063105.681712590171
Trimmed Mean ( 5 / 20 )106.1780.984240264345644107.878130824683
Trimmed Mean ( 6 / 20 )106.23750.96534189456599110.051682826594
Trimmed Mean ( 7 / 20 )106.2978260869570.948650142596141112.051663004081
Trimmed Mean ( 8 / 20 )106.3704545454550.93136887790951114.208727678561
Trimmed Mean ( 9 / 20 )106.4357142857140.912316176756353116.665380925433
Trimmed Mean ( 10 / 20 )106.510.888175889256407119.919940732878
Trimmed Mean ( 11 / 20 )106.5736842105260.8645103549276123.276353606489
Trimmed Mean ( 12 / 20 )106.6361111111110.839474067948723127.027284323004
Trimmed Mean ( 13 / 20 )106.6617647058820.821025126638569129.912911609144
Trimmed Mean ( 14 / 20 )106.6968750.799426260683348133.466812697391
Trimmed Mean ( 15 / 20 )106.7333333333330.772610641309796138.146341283094
Trimmed Mean ( 16 / 20 )106.750.746428887876189143.014293436224
Trimmed Mean ( 17 / 20 )106.7653846153850.73161449091281145.931205493452
Trimmed Mean ( 18 / 20 )106.7833333333330.711414865680435150.099946577867
Trimmed Mean ( 19 / 20 )106.7772727272730.690000684427222154.749517119552
Trimmed Mean ( 20 / 20 )106.7150.678476427857221157.286230764169
Median105.7
Midrange101.2
Midmean - Weighted Average at Xnp106.470967741936
Midmean - Weighted Average at X(n+1)p106.733333333333
Midmean - Empirical Distribution Function106.470967741936
Midmean - Empirical Distribution Function - Averaging106.733333333333
Midmean - Empirical Distribution Function - Interpolation106.733333333333
Midmean - Closest Observation106.470967741936
Midmean - True Basic - Statistics Graphics Toolkit106.733333333333
Midmean - MS Excel (old versions)106.696875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.735 & 1.15398554025544 & 91.6259314450291 \tabularnewline
Geometric Mean & 105.350840712003 &  &  \tabularnewline
Harmonic Mean & 104.953830385521 &  &  \tabularnewline
Quadratic Mean & 106.105888149527 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.783333333333 & 1.12510681643978 & 94.0207025569964 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.826666666667 & 1.10705969469053 & 95.5925567286142 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.016666666667 & 1.05921345582910 & 100.089992327073 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.023333333333 & 1.04708194647627 & 101.256003591822 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.94 & 1.02571512878758 & 103.284037669624 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.96 & 0.999079237114804 & 106.057653951449 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.925 & 0.980676651560163 & 108.012156536493 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 106.005 & 0.964834885320904 & 109.868539801753 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.99 & 0.9571488381151 & 110.735128936399 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 106.106666666667 & 0.92323083728162 & 114.929725461824 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106.161666666667 & 0.894215850238255 & 118.720403623332 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.461666666667 & 0.834516984241074 & 127.572798010199 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 106.418333333333 & 0.81351747822791 & 130.812596141321 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.441666666667 & 0.794491244193296 & 133.974625201495 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.616666666667 & 0.749791559233332 & 142.195074556031 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 106.643333333333 & 0.6708387812531 & 158.970137555446 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 106.643333333333 & 0.653579309166836 & 163.168160065041 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 106.823333333333 & 0.617249076018404 & 173.063577547013 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.171666666667 & 0.548439448458291 & 195.412031297047 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 107.205 & 0.515036200801063 & 208.150417064390 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.891379310345 & 1.0951034516285 & 96.6953205680034 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.007142857143 & 1.05787663196618 & 100.207471886506 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.107407407407 & 1.02373254067054 & 103.647586837386 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.142307692308 & 1.00435832360063 & 105.681712590171 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 106.178 & 0.984240264345644 & 107.878130824683 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 106.2375 & 0.96534189456599 & 110.051682826594 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 106.297826086957 & 0.948650142596141 & 112.051663004081 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 106.370454545455 & 0.93136887790951 & 114.208727678561 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 106.435714285714 & 0.912316176756353 & 116.665380925433 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 106.51 & 0.888175889256407 & 119.919940732878 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 106.573684210526 & 0.8645103549276 & 123.276353606489 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 106.636111111111 & 0.839474067948723 & 127.027284323004 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 106.661764705882 & 0.821025126638569 & 129.912911609144 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 106.696875 & 0.799426260683348 & 133.466812697391 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 106.733333333333 & 0.772610641309796 & 138.146341283094 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 106.75 & 0.746428887876189 & 143.014293436224 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 106.765384615385 & 0.73161449091281 & 145.931205493452 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 106.783333333333 & 0.711414865680435 & 150.099946577867 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 106.777272727273 & 0.690000684427222 & 154.749517119552 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 106.715 & 0.678476427857221 & 157.286230764169 \tabularnewline
Median & 105.7 &  &  \tabularnewline
Midrange & 101.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.470967741936 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.470967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.733333333333 &  &  \tabularnewline
Midmean - Closest Observation & 106.470967741936 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.733333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.696875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47063&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]105.735[/C][C]1.15398554025544[/C][C]91.6259314450291[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.350840712003[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.953830385521[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.105888149527[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.783333333333[/C][C]1.12510681643978[/C][C]94.0207025569964[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.826666666667[/C][C]1.10705969469053[/C][C]95.5925567286142[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.016666666667[/C][C]1.05921345582910[/C][C]100.089992327073[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.023333333333[/C][C]1.04708194647627[/C][C]101.256003591822[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.94[/C][C]1.02571512878758[/C][C]103.284037669624[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.96[/C][C]0.999079237114804[/C][C]106.057653951449[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.925[/C][C]0.980676651560163[/C][C]108.012156536493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]106.005[/C][C]0.964834885320904[/C][C]109.868539801753[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.99[/C][C]0.9571488381151[/C][C]110.735128936399[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]106.106666666667[/C][C]0.92323083728162[/C][C]114.929725461824[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106.161666666667[/C][C]0.894215850238255[/C][C]118.720403623332[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.461666666667[/C][C]0.834516984241074[/C][C]127.572798010199[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]106.418333333333[/C][C]0.81351747822791[/C][C]130.812596141321[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.441666666667[/C][C]0.794491244193296[/C][C]133.974625201495[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.616666666667[/C][C]0.749791559233332[/C][C]142.195074556031[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]106.643333333333[/C][C]0.6708387812531[/C][C]158.970137555446[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]106.643333333333[/C][C]0.653579309166836[/C][C]163.168160065041[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]106.823333333333[/C][C]0.617249076018404[/C][C]173.063577547013[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.171666666667[/C][C]0.548439448458291[/C][C]195.412031297047[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]107.205[/C][C]0.515036200801063[/C][C]208.150417064390[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.891379310345[/C][C]1.0951034516285[/C][C]96.6953205680034[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.007142857143[/C][C]1.05787663196618[/C][C]100.207471886506[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.107407407407[/C][C]1.02373254067054[/C][C]103.647586837386[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.142307692308[/C][C]1.00435832360063[/C][C]105.681712590171[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]106.178[/C][C]0.984240264345644[/C][C]107.878130824683[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]106.2375[/C][C]0.96534189456599[/C][C]110.051682826594[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]106.297826086957[/C][C]0.948650142596141[/C][C]112.051663004081[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]106.370454545455[/C][C]0.93136887790951[/C][C]114.208727678561[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]106.435714285714[/C][C]0.912316176756353[/C][C]116.665380925433[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]106.51[/C][C]0.888175889256407[/C][C]119.919940732878[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]106.573684210526[/C][C]0.8645103549276[/C][C]123.276353606489[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]106.636111111111[/C][C]0.839474067948723[/C][C]127.027284323004[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]106.661764705882[/C][C]0.821025126638569[/C][C]129.912911609144[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]106.696875[/C][C]0.799426260683348[/C][C]133.466812697391[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]106.733333333333[/C][C]0.772610641309796[/C][C]138.146341283094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]106.75[/C][C]0.746428887876189[/C][C]143.014293436224[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]106.765384615385[/C][C]0.73161449091281[/C][C]145.931205493452[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]106.783333333333[/C][C]0.711414865680435[/C][C]150.099946577867[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]106.777272727273[/C][C]0.690000684427222[/C][C]154.749517119552[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]106.715[/C][C]0.678476427857221[/C][C]157.286230764169[/C][/ROW]
[ROW][C]Median[/C][C]105.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.470967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.470967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.470967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.696875[/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=47063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47063&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 Mean105.7351.1539855402554491.6259314450291
Geometric Mean105.350840712003
Harmonic Mean104.953830385521
Quadratic Mean106.105888149527
Winsorized Mean ( 1 / 20 )105.7833333333331.1251068164397894.0207025569964
Winsorized Mean ( 2 / 20 )105.8266666666671.1070596946905395.5925567286142
Winsorized Mean ( 3 / 20 )106.0166666666671.05921345582910100.089992327073
Winsorized Mean ( 4 / 20 )106.0233333333331.04708194647627101.256003591822
Winsorized Mean ( 5 / 20 )105.941.02571512878758103.284037669624
Winsorized Mean ( 6 / 20 )105.960.999079237114804106.057653951449
Winsorized Mean ( 7 / 20 )105.9250.980676651560163108.012156536493
Winsorized Mean ( 8 / 20 )106.0050.964834885320904109.868539801753
Winsorized Mean ( 9 / 20 )105.990.9571488381151110.735128936399
Winsorized Mean ( 10 / 20 )106.1066666666670.92323083728162114.929725461824
Winsorized Mean ( 11 / 20 )106.1616666666670.894215850238255118.720403623332
Winsorized Mean ( 12 / 20 )106.4616666666670.834516984241074127.572798010199
Winsorized Mean ( 13 / 20 )106.4183333333330.81351747822791130.812596141321
Winsorized Mean ( 14 / 20 )106.4416666666670.794491244193296133.974625201495
Winsorized Mean ( 15 / 20 )106.6166666666670.749791559233332142.195074556031
Winsorized Mean ( 16 / 20 )106.6433333333330.6708387812531158.970137555446
Winsorized Mean ( 17 / 20 )106.6433333333330.653579309166836163.168160065041
Winsorized Mean ( 18 / 20 )106.8233333333330.617249076018404173.063577547013
Winsorized Mean ( 19 / 20 )107.1716666666670.548439448458291195.412031297047
Winsorized Mean ( 20 / 20 )107.2050.515036200801063208.150417064390
Trimmed Mean ( 1 / 20 )105.8913793103451.095103451628596.6953205680034
Trimmed Mean ( 2 / 20 )106.0071428571431.05787663196618100.207471886506
Trimmed Mean ( 3 / 20 )106.1074074074071.02373254067054103.647586837386
Trimmed Mean ( 4 / 20 )106.1423076923081.00435832360063105.681712590171
Trimmed Mean ( 5 / 20 )106.1780.984240264345644107.878130824683
Trimmed Mean ( 6 / 20 )106.23750.96534189456599110.051682826594
Trimmed Mean ( 7 / 20 )106.2978260869570.948650142596141112.051663004081
Trimmed Mean ( 8 / 20 )106.3704545454550.93136887790951114.208727678561
Trimmed Mean ( 9 / 20 )106.4357142857140.912316176756353116.665380925433
Trimmed Mean ( 10 / 20 )106.510.888175889256407119.919940732878
Trimmed Mean ( 11 / 20 )106.5736842105260.8645103549276123.276353606489
Trimmed Mean ( 12 / 20 )106.6361111111110.839474067948723127.027284323004
Trimmed Mean ( 13 / 20 )106.6617647058820.821025126638569129.912911609144
Trimmed Mean ( 14 / 20 )106.6968750.799426260683348133.466812697391
Trimmed Mean ( 15 / 20 )106.7333333333330.772610641309796138.146341283094
Trimmed Mean ( 16 / 20 )106.750.746428887876189143.014293436224
Trimmed Mean ( 17 / 20 )106.7653846153850.73161449091281145.931205493452
Trimmed Mean ( 18 / 20 )106.7833333333330.711414865680435150.099946577867
Trimmed Mean ( 19 / 20 )106.7772727272730.690000684427222154.749517119552
Trimmed Mean ( 20 / 20 )106.7150.678476427857221157.286230764169
Median105.7
Midrange101.2
Midmean - Weighted Average at Xnp106.470967741936
Midmean - Weighted Average at X(n+1)p106.733333333333
Midmean - Empirical Distribution Function106.470967741936
Midmean - Empirical Distribution Function - Averaging106.733333333333
Midmean - Empirical Distribution Function - Interpolation106.733333333333
Midmean - Closest Observation106.470967741936
Midmean - True Basic - Statistics Graphics Toolkit106.733333333333
Midmean - MS Excel (old versions)106.696875
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')