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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 11:16:52 -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/y4m7rs27ouwv0y41192731215.htm/, Retrieved Sun, 28 Apr 2024 22:20:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=991, Retrieved Sun, 28 Apr 2024 22:20:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 2 Question 8, Niet-duurzame consumptiegoederen, central tendency, kim, wim, hoyi
Estimated Impact173
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 18:16:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
112,7
118,4
108,1
105,4
114,6
106,9
115,9
109,8
101,8
114,2
110,8
108,4
127,5
128,6
116,6
127,4
105
108,3
125
111,6
106,5
130,3
115
116,1
134
126,5
125,8
136,4
114,9
110,9
125,5
116,8
116,8
125,5
104,2
115,1
132,8
123,3
124,8
122
117,4
117,9
137,4
114,6
124,7
129,6
109,4
120,9
134,9
136,3
133,2
127,2
122,7
120,5
137,8
119,1
124,3
134,3
121,7
125




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=991&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=991&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=991&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 Mean120.1516666666671.2309439941609297.6093690993384
Geometric Mean119.779315324743
Harmonic Mean119.407115861814
Quadratic Mean120.523114657175
Winsorized Mean ( 1 / 20 )120.1851.2198379650662498.525380781597
Winsorized Mean ( 2 / 20 )120.1783333333331.2062457322114599.6300588877576
Winsorized Mean ( 3 / 20 )120.1933333333331.20088683488793100.087143801980
Winsorized Mean ( 4 / 20 )120.1733333333331.16532012688221103.124738482682
Winsorized Mean ( 5 / 20 )120.1566666666671.14816819637034104.650753301227
Winsorized Mean ( 6 / 20 )120.2466666666671.11912361461254107.447171247743
Winsorized Mean ( 7 / 20 )120.1766666666671.09570905935359109.679358439881
Winsorized Mean ( 8 / 20 )120.1366666666671.08259983860434110.970519653452
Winsorized Mean ( 9 / 20 )119.9116666666670.984349541939057121.818176935862
Winsorized Mean ( 10 / 20 )119.8616666666670.951787173151392125.933265385161
Winsorized Mean ( 11 / 20 )119.8616666666670.88829199297496134.934984908780
Winsorized Mean ( 12 / 20 )119.6616666666670.849240576891374140.904320781145
Winsorized Mean ( 13 / 20 )119.7916666666670.819729498123718146.135605636809
Winsorized Mean ( 14 / 20 )120.0016666666670.7699640158393155.853603802327
Winsorized Mean ( 15 / 20 )120.2016666666670.684293076880012175.658165671817
Winsorized Mean ( 16 / 20 )120.1216666666670.639946553500447187.705779505511
Winsorized Mean ( 17 / 20 )120.0366666666670.627279871879198191.360622343998
Winsorized Mean ( 18 / 20 )120.1266666666670.614177446647032195.589511341506
Winsorized Mean ( 19 / 20 )1200.586418797149032204.631912522926
Winsorized Mean ( 20 / 20 )120.0333333333330.581614092778898206.379685127341
Trimmed Mean ( 1 / 20 )120.1637931034481.19431426326683100.613211111422
Trimmed Mean ( 2 / 20 )120.1410714285711.16268770802858103.330473521802
Trimmed Mean ( 3 / 20 )120.1203703703701.13240305767992106.075632307523
Trimmed Mean ( 4 / 20 )120.0923076923081.09701654284604109.471738120509
Trimmed Mean ( 5 / 20 )120.0681.06665389448136112.565097845896
Trimmed Mean ( 6 / 20 )120.0458333333331.03389351522651116.110442289633
Trimmed Mean ( 7 / 20 )120.0021739130431.00096807793639119.886114810416
Trimmed Mean ( 8 / 20 )119.9681818181820.965262250770156124.285583241717
Trimmed Mean ( 9 / 20 )119.9380952380950.922149387784242130.063628330638
Trimmed Mean ( 10 / 20 )119.94250.893673544336048134.212879815202
Trimmed Mean ( 11 / 20 )119.9552631578950.864074319221605138.825168726176
Trimmed Mean ( 12 / 20 )119.9694444444440.841010535808196142.649157574650
Trimmed Mean ( 13 / 20 )120.0147058823530.818765345372693146.580099610498
Trimmed Mean ( 14 / 20 )120.0468750.7948800930953151.025137052473
Trimmed Mean ( 15 / 20 )120.0533333333330.774325562427299155.042451339200
Trimmed Mean ( 16 / 20 )120.0321428571430.76790882070471156.310410325785
Trimmed Mean ( 17 / 20 )120.0192307692310.767634112176833156.349527548853
Trimmed Mean ( 18 / 20 )120.0166666666670.765673584922024156.746515786997
Trimmed Mean ( 19 / 20 )1200.760724193582207157.744424342450
Trimmed Mean ( 20 / 20 )1200.756306816047562158.665765604384
Median119.8
Midrange119.8
Midmean - Weighted Average at Xnp119.816129032258
Midmean - Weighted Average at X(n+1)p120.053333333333
Midmean - Empirical Distribution Function119.816129032258
Midmean - Empirical Distribution Function - Averaging120.053333333333
Midmean - Empirical Distribution Function - Interpolation120.053333333333
Midmean - Closest Observation119.816129032258
Midmean - True Basic - Statistics Graphics Toolkit120.053333333333
Midmean - MS Excel (old versions)120.046875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.151666666667 & 1.23094399416092 & 97.6093690993384 \tabularnewline
Geometric Mean & 119.779315324743 &  &  \tabularnewline
Harmonic Mean & 119.407115861814 &  &  \tabularnewline
Quadratic Mean & 120.523114657175 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 120.185 & 1.21983796506624 & 98.525380781597 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 120.178333333333 & 1.20624573221145 & 99.6300588877576 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 120.193333333333 & 1.20088683488793 & 100.087143801980 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 120.173333333333 & 1.16532012688221 & 103.124738482682 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 120.156666666667 & 1.14816819637034 & 104.650753301227 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 120.246666666667 & 1.11912361461254 & 107.447171247743 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 120.176666666667 & 1.09570905935359 & 109.679358439881 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 120.136666666667 & 1.08259983860434 & 110.970519653452 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 119.911666666667 & 0.984349541939057 & 121.818176935862 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 119.861666666667 & 0.951787173151392 & 125.933265385161 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 119.861666666667 & 0.88829199297496 & 134.934984908780 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 119.661666666667 & 0.849240576891374 & 140.904320781145 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 119.791666666667 & 0.819729498123718 & 146.135605636809 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 120.001666666667 & 0.7699640158393 & 155.853603802327 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 120.201666666667 & 0.684293076880012 & 175.658165671817 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 120.121666666667 & 0.639946553500447 & 187.705779505511 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 120.036666666667 & 0.627279871879198 & 191.360622343998 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 120.126666666667 & 0.614177446647032 & 195.589511341506 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 120 & 0.586418797149032 & 204.631912522926 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 120.033333333333 & 0.581614092778898 & 206.379685127341 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 120.163793103448 & 1.19431426326683 & 100.613211111422 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 120.141071428571 & 1.16268770802858 & 103.330473521802 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 120.120370370370 & 1.13240305767992 & 106.075632307523 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 120.092307692308 & 1.09701654284604 & 109.471738120509 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 120.068 & 1.06665389448136 & 112.565097845896 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 120.045833333333 & 1.03389351522651 & 116.110442289633 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 120.002173913043 & 1.00096807793639 & 119.886114810416 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 119.968181818182 & 0.965262250770156 & 124.285583241717 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 119.938095238095 & 0.922149387784242 & 130.063628330638 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 119.9425 & 0.893673544336048 & 134.212879815202 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 119.955263157895 & 0.864074319221605 & 138.825168726176 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 119.969444444444 & 0.841010535808196 & 142.649157574650 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 120.014705882353 & 0.818765345372693 & 146.580099610498 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 120.046875 & 0.7948800930953 & 151.025137052473 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 120.053333333333 & 0.774325562427299 & 155.042451339200 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 120.032142857143 & 0.76790882070471 & 156.310410325785 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 120.019230769231 & 0.767634112176833 & 156.349527548853 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 120.016666666667 & 0.765673584922024 & 156.746515786997 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 120 & 0.760724193582207 & 157.744424342450 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 120 & 0.756306816047562 & 158.665765604384 \tabularnewline
Median & 119.8 &  &  \tabularnewline
Midrange & 119.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 119.816129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 120.053333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 119.816129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 120.053333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 120.053333333333 &  &  \tabularnewline
Midmean - Closest Observation & 119.816129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 120.053333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 120.046875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=991&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]120.151666666667[/C][C]1.23094399416092[/C][C]97.6093690993384[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.779315324743[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]119.407115861814[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.523114657175[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]120.185[/C][C]1.21983796506624[/C][C]98.525380781597[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]120.178333333333[/C][C]1.20624573221145[/C][C]99.6300588877576[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]120.193333333333[/C][C]1.20088683488793[/C][C]100.087143801980[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]120.173333333333[/C][C]1.16532012688221[/C][C]103.124738482682[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]120.156666666667[/C][C]1.14816819637034[/C][C]104.650753301227[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]120.246666666667[/C][C]1.11912361461254[/C][C]107.447171247743[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]120.176666666667[/C][C]1.09570905935359[/C][C]109.679358439881[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]120.136666666667[/C][C]1.08259983860434[/C][C]110.970519653452[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]119.911666666667[/C][C]0.984349541939057[/C][C]121.818176935862[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]119.861666666667[/C][C]0.951787173151392[/C][C]125.933265385161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]119.861666666667[/C][C]0.88829199297496[/C][C]134.934984908780[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]119.661666666667[/C][C]0.849240576891374[/C][C]140.904320781145[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]119.791666666667[/C][C]0.819729498123718[/C][C]146.135605636809[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]120.001666666667[/C][C]0.7699640158393[/C][C]155.853603802327[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]120.201666666667[/C][C]0.684293076880012[/C][C]175.658165671817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]120.121666666667[/C][C]0.639946553500447[/C][C]187.705779505511[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]120.036666666667[/C][C]0.627279871879198[/C][C]191.360622343998[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]120.126666666667[/C][C]0.614177446647032[/C][C]195.589511341506[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]120[/C][C]0.586418797149032[/C][C]204.631912522926[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]120.033333333333[/C][C]0.581614092778898[/C][C]206.379685127341[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]120.163793103448[/C][C]1.19431426326683[/C][C]100.613211111422[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]120.141071428571[/C][C]1.16268770802858[/C][C]103.330473521802[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]120.120370370370[/C][C]1.13240305767992[/C][C]106.075632307523[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]120.092307692308[/C][C]1.09701654284604[/C][C]109.471738120509[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]120.068[/C][C]1.06665389448136[/C][C]112.565097845896[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]120.045833333333[/C][C]1.03389351522651[/C][C]116.110442289633[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]120.002173913043[/C][C]1.00096807793639[/C][C]119.886114810416[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]119.968181818182[/C][C]0.965262250770156[/C][C]124.285583241717[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]119.938095238095[/C][C]0.922149387784242[/C][C]130.063628330638[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]119.9425[/C][C]0.893673544336048[/C][C]134.212879815202[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]119.955263157895[/C][C]0.864074319221605[/C][C]138.825168726176[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]119.969444444444[/C][C]0.841010535808196[/C][C]142.649157574650[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]120.014705882353[/C][C]0.818765345372693[/C][C]146.580099610498[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]120.046875[/C][C]0.7948800930953[/C][C]151.025137052473[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]120.053333333333[/C][C]0.774325562427299[/C][C]155.042451339200[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]120.032142857143[/C][C]0.76790882070471[/C][C]156.310410325785[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]120.019230769231[/C][C]0.767634112176833[/C][C]156.349527548853[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]120.016666666667[/C][C]0.765673584922024[/C][C]156.746515786997[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]120[/C][C]0.760724193582207[/C][C]157.744424342450[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]120[/C][C]0.756306816047562[/C][C]158.665765604384[/C][/ROW]
[ROW][C]Median[/C][C]119.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]119.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]119.816129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]120.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]119.816129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]120.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]120.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]119.816129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]120.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]120.046875[/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=991&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=991&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 Mean120.1516666666671.2309439941609297.6093690993384
Geometric Mean119.779315324743
Harmonic Mean119.407115861814
Quadratic Mean120.523114657175
Winsorized Mean ( 1 / 20 )120.1851.2198379650662498.525380781597
Winsorized Mean ( 2 / 20 )120.1783333333331.2062457322114599.6300588877576
Winsorized Mean ( 3 / 20 )120.1933333333331.20088683488793100.087143801980
Winsorized Mean ( 4 / 20 )120.1733333333331.16532012688221103.124738482682
Winsorized Mean ( 5 / 20 )120.1566666666671.14816819637034104.650753301227
Winsorized Mean ( 6 / 20 )120.2466666666671.11912361461254107.447171247743
Winsorized Mean ( 7 / 20 )120.1766666666671.09570905935359109.679358439881
Winsorized Mean ( 8 / 20 )120.1366666666671.08259983860434110.970519653452
Winsorized Mean ( 9 / 20 )119.9116666666670.984349541939057121.818176935862
Winsorized Mean ( 10 / 20 )119.8616666666670.951787173151392125.933265385161
Winsorized Mean ( 11 / 20 )119.8616666666670.88829199297496134.934984908780
Winsorized Mean ( 12 / 20 )119.6616666666670.849240576891374140.904320781145
Winsorized Mean ( 13 / 20 )119.7916666666670.819729498123718146.135605636809
Winsorized Mean ( 14 / 20 )120.0016666666670.7699640158393155.853603802327
Winsorized Mean ( 15 / 20 )120.2016666666670.684293076880012175.658165671817
Winsorized Mean ( 16 / 20 )120.1216666666670.639946553500447187.705779505511
Winsorized Mean ( 17 / 20 )120.0366666666670.627279871879198191.360622343998
Winsorized Mean ( 18 / 20 )120.1266666666670.614177446647032195.589511341506
Winsorized Mean ( 19 / 20 )1200.586418797149032204.631912522926
Winsorized Mean ( 20 / 20 )120.0333333333330.581614092778898206.379685127341
Trimmed Mean ( 1 / 20 )120.1637931034481.19431426326683100.613211111422
Trimmed Mean ( 2 / 20 )120.1410714285711.16268770802858103.330473521802
Trimmed Mean ( 3 / 20 )120.1203703703701.13240305767992106.075632307523
Trimmed Mean ( 4 / 20 )120.0923076923081.09701654284604109.471738120509
Trimmed Mean ( 5 / 20 )120.0681.06665389448136112.565097845896
Trimmed Mean ( 6 / 20 )120.0458333333331.03389351522651116.110442289633
Trimmed Mean ( 7 / 20 )120.0021739130431.00096807793639119.886114810416
Trimmed Mean ( 8 / 20 )119.9681818181820.965262250770156124.285583241717
Trimmed Mean ( 9 / 20 )119.9380952380950.922149387784242130.063628330638
Trimmed Mean ( 10 / 20 )119.94250.893673544336048134.212879815202
Trimmed Mean ( 11 / 20 )119.9552631578950.864074319221605138.825168726176
Trimmed Mean ( 12 / 20 )119.9694444444440.841010535808196142.649157574650
Trimmed Mean ( 13 / 20 )120.0147058823530.818765345372693146.580099610498
Trimmed Mean ( 14 / 20 )120.0468750.7948800930953151.025137052473
Trimmed Mean ( 15 / 20 )120.0533333333330.774325562427299155.042451339200
Trimmed Mean ( 16 / 20 )120.0321428571430.76790882070471156.310410325785
Trimmed Mean ( 17 / 20 )120.0192307692310.767634112176833156.349527548853
Trimmed Mean ( 18 / 20 )120.0166666666670.765673584922024156.746515786997
Trimmed Mean ( 19 / 20 )1200.760724193582207157.744424342450
Trimmed Mean ( 20 / 20 )1200.756306816047562158.665765604384
Median119.8
Midrange119.8
Midmean - Weighted Average at Xnp119.816129032258
Midmean - Weighted Average at X(n+1)p120.053333333333
Midmean - Empirical Distribution Function119.816129032258
Midmean - Empirical Distribution Function - Averaging120.053333333333
Midmean - Empirical Distribution Function - Interpolation120.053333333333
Midmean - Closest Observation119.816129032258
Midmean - True Basic - Statistics Graphics Toolkit120.053333333333
Midmean - MS Excel (old versions)120.046875
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')