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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 03:06:57 -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/balbzi4f5puvb0e1193047651.htm/, Retrieved Mon, 06 May 2024 02:29:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1417, Retrieved Mon, 06 May 2024 02:29:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 2, Vraag 8, niet-duurzame consumptiegoederen
Estimated Impact210
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 10:06:57] [014bfc073eb4f6c1ae65a07cc44c50c0] [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
105,0
108,3
125,0
111,6
106,5
130,3
115,0
116,1
134,0
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
122,0
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
125,0




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1417&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]1 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=1417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1417&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 time1 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=1417&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=1417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1417&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')