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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Dec 2008 13:29:01 -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/2008/Dec/22/t1229977836gilq5wy1sy80eoj.htm/, Retrieved Tue, 02 Sep 2025 10:50:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36216, Retrieved Tue, 02 Sep 2025 10:50:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact300

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-    D  [Central Tendency] [Arithmetic mean -...] [2008-12-21 10:09:47] [33f4701c7363e8b81858dafbf0350eed]
-    D    [Central Tendency] [Arithmetic Mean -...] [2008-12-22 12:34:15] [33f4701c7363e8b81858dafbf0350eed]
-             [Central Tendency] [arithmetic mean -...] [2008-12-22 20:29:01] [77ff908fa699164c8765f2430a4f222b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103
102.4
102
101.8
101.6
101.4
101.3
101.4
101.7
102.4
103.1
103.8
104.4
105
105.7
106.4
107.1
107.9
108.8
109.6
110.3
110.8
111.2
111.7
112.3
112.8
113.1
113.1
113.1
113.2
113.1
112.8
112.5
112.3
112.5
112.9
113.5
114.1
114.6
114.9
115.4
115.7
116.1
116.5
117.1
117.5
117.7
117.7
117.7
117.6
117.5
117.6
117.9
118.2
118.5
118.7
118.8
118.9
119
119

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36216&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]3 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=36216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36216&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.4783333333330.767408478014193145.265965293742
Geometric Mean111.319596350128
Harmonic Mean111.158106057296
Quadratic Mean111.634066634399
Winsorized Mean ( 1 / 20 )111.480.767035529049899145.338769558806
Winsorized Mean ( 2 / 20 )111.4766666666670.766484994441725145.438811555419
Winsorized Mean ( 3 / 20 )111.4816666666670.763457388828898146.022120288433
Winsorized Mean ( 4 / 20 )111.4816666666670.76092232046233146.508603662633
Winsorized Mean ( 5 / 20 )111.4733333333330.756459440500554147.361943502973
Winsorized Mean ( 6 / 20 )111.4633333333330.747492859088264149.116251718161
Winsorized Mean ( 7 / 20 )111.4750.732307802439742152.224241812817
Winsorized Mean ( 8 / 20 )111.4483333333330.728385303708918153.007388762296
Winsorized Mean ( 9 / 20 )111.5383333333330.709730957486755157.155795667001
Winsorized Mean ( 10 / 20 )111.5550.70634103333109157.933625169571
Winsorized Mean ( 11 / 20 )111.6650.67798648804095164.700922466253
Winsorized Mean ( 12 / 20 )111.7850.654712707081174170.739010853108
Winsorized Mean ( 13 / 20 )111.8933333333330.626892013816428178.489007464209
Winsorized Mean ( 14 / 20 )112.0566666666670.596919430096194187.724944132927
Winsorized Mean ( 15 / 20 )112.1316666666670.550282370590134203.771141253198
Winsorized Mean ( 16 / 20 )112.1583333333330.493381573072844227.325744321574
Winsorized Mean ( 17 / 20 )112.2716666666670.437610949074093256.555890350124
Winsorized Mean ( 18 / 20 )112.4216666666670.374792535203737299.957059191572
Winsorized Mean ( 19 / 20 )112.580.319849894172658351.977605905439
Winsorized Mean ( 20 / 20 )112.6466666666670.258663084604472435.495721544176
Trimmed Mean ( 1 / 20 )111.5241379310340.762963426534222146.172324979764
Trimmed Mean ( 2 / 20 )111.5714285714290.757206564337676147.346092633282
Trimmed Mean ( 3 / 20 )111.6240740740740.749711965120073148.889279172964
Trimmed Mean ( 4 / 20 )111.6788461538460.741087500092821150.695897771664
Trimmed Mean ( 5 / 20 )111.7380.730517792321282152.957260144128
Trimmed Mean ( 6 / 20 )111.8041666666670.717918819946306155.733717462691
Trimmed Mean ( 7 / 20 )111.8782608695650.703846663715858158.952605215062
Trimmed Mean ( 8 / 20 )111.9568181818180.689358847622698162.407168005327
Trimmed Mean ( 9 / 20 )112.0476190476190.670623317586732167.079813822799
Trimmed Mean ( 10 / 20 )112.13250.650614970426895172.348478127433
Trimmed Mean ( 11 / 20 )112.2236842105260.623992037400029179.847942736779
Trimmed Mean ( 12 / 20 )112.3083333333330.595837079575302188.488325388181
Trimmed Mean ( 13 / 20 )112.3852941176470.563746260176934199.354394089239
Trimmed Mean ( 14 / 20 )112.456250.527202321985072213.307577205975
Trimmed Mean ( 15 / 20 )112.5133333333330.484868351212639232.049241927095
Trimmed Mean ( 16 / 20 )112.5678571428570.439517940940030256.116637473546
Trimmed Mean ( 17 / 20 )112.6269230769230.39338991001521286.298454051779
Trimmed Mean ( 18 / 20 )112.6791666666670.346095151460887325.572797512596
Trimmed Mean ( 19 / 20 )112.7181818181820.301197923136942374.232931768702
Trimmed Mean ( 20 / 20 )112.740.256433021931346439.646965710148
Median112.85
Midrange110.15
Midmean - Weighted Average at Xnp112.293548387097
Midmean - Weighted Average at X(n+1)p112.513333333333
Midmean - Empirical Distribution Function112.293548387097
Midmean - Empirical Distribution Function - Averaging112.513333333333
Midmean - Empirical Distribution Function - Interpolation112.513333333333
Midmean - Closest Observation112.293548387097
Midmean - True Basic - Statistics Graphics Toolkit112.513333333333
Midmean - MS Excel (old versions)112.609090909091
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.478333333333 & 0.767408478014193 & 145.265965293742 \tabularnewline
Geometric Mean & 111.319596350128 &  &  \tabularnewline
Harmonic Mean & 111.158106057296 &  &  \tabularnewline
Quadratic Mean & 111.634066634399 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.48 & 0.767035529049899 & 145.338769558806 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.476666666667 & 0.766484994441725 & 145.438811555419 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.481666666667 & 0.763457388828898 & 146.022120288433 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.481666666667 & 0.76092232046233 & 146.508603662633 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.473333333333 & 0.756459440500554 & 147.361943502973 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.463333333333 & 0.747492859088264 & 149.116251718161 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.475 & 0.732307802439742 & 152.224241812817 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.448333333333 & 0.728385303708918 & 153.007388762296 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.538333333333 & 0.709730957486755 & 157.155795667001 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.555 & 0.70634103333109 & 157.933625169571 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.665 & 0.67798648804095 & 164.700922466253 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.785 & 0.654712707081174 & 170.739010853108 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.893333333333 & 0.626892013816428 & 178.489007464209 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 112.056666666667 & 0.596919430096194 & 187.724944132927 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 112.131666666667 & 0.550282370590134 & 203.771141253198 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 112.158333333333 & 0.493381573072844 & 227.325744321574 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 112.271666666667 & 0.437610949074093 & 256.555890350124 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 112.421666666667 & 0.374792535203737 & 299.957059191572 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 112.58 & 0.319849894172658 & 351.977605905439 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 112.646666666667 & 0.258663084604472 & 435.495721544176 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.524137931034 & 0.762963426534222 & 146.172324979764 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.571428571429 & 0.757206564337676 & 147.346092633282 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.624074074074 & 0.749711965120073 & 148.889279172964 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.678846153846 & 0.741087500092821 & 150.695897771664 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.738 & 0.730517792321282 & 152.957260144128 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.804166666667 & 0.717918819946306 & 155.733717462691 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.878260869565 & 0.703846663715858 & 158.952605215062 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.956818181818 & 0.689358847622698 & 162.407168005327 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 112.047619047619 & 0.670623317586732 & 167.079813822799 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 112.1325 & 0.650614970426895 & 172.348478127433 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 112.223684210526 & 0.623992037400029 & 179.847942736779 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 112.308333333333 & 0.595837079575302 & 188.488325388181 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 112.385294117647 & 0.563746260176934 & 199.354394089239 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 112.45625 & 0.527202321985072 & 213.307577205975 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 112.513333333333 & 0.484868351212639 & 232.049241927095 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 112.567857142857 & 0.439517940940030 & 256.116637473546 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 112.626923076923 & 0.39338991001521 & 286.298454051779 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 112.679166666667 & 0.346095151460887 & 325.572797512596 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 112.718181818182 & 0.301197923136942 & 374.232931768702 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 112.74 & 0.256433021931346 & 439.646965710148 \tabularnewline
Median & 112.85 &  &  \tabularnewline
Midrange & 110.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.293548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.513333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.293548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.513333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.513333333333 &  &  \tabularnewline
Midmean - Closest Observation & 112.293548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.513333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.609090909091 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36216&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]111.478333333333[/C][C]0.767408478014193[/C][C]145.265965293742[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.319596350128[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.158106057296[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.634066634399[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.48[/C][C]0.767035529049899[/C][C]145.338769558806[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.476666666667[/C][C]0.766484994441725[/C][C]145.438811555419[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.481666666667[/C][C]0.763457388828898[/C][C]146.022120288433[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.481666666667[/C][C]0.76092232046233[/C][C]146.508603662633[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.473333333333[/C][C]0.756459440500554[/C][C]147.361943502973[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.463333333333[/C][C]0.747492859088264[/C][C]149.116251718161[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.475[/C][C]0.732307802439742[/C][C]152.224241812817[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.448333333333[/C][C]0.728385303708918[/C][C]153.007388762296[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.538333333333[/C][C]0.709730957486755[/C][C]157.155795667001[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.555[/C][C]0.70634103333109[/C][C]157.933625169571[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.665[/C][C]0.67798648804095[/C][C]164.700922466253[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.785[/C][C]0.654712707081174[/C][C]170.739010853108[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.893333333333[/C][C]0.626892013816428[/C][C]178.489007464209[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]112.056666666667[/C][C]0.596919430096194[/C][C]187.724944132927[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]112.131666666667[/C][C]0.550282370590134[/C][C]203.771141253198[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]112.158333333333[/C][C]0.493381573072844[/C][C]227.325744321574[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]112.271666666667[/C][C]0.437610949074093[/C][C]256.555890350124[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]112.421666666667[/C][C]0.374792535203737[/C][C]299.957059191572[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]112.58[/C][C]0.319849894172658[/C][C]351.977605905439[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]112.646666666667[/C][C]0.258663084604472[/C][C]435.495721544176[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.524137931034[/C][C]0.762963426534222[/C][C]146.172324979764[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.571428571429[/C][C]0.757206564337676[/C][C]147.346092633282[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.624074074074[/C][C]0.749711965120073[/C][C]148.889279172964[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.678846153846[/C][C]0.741087500092821[/C][C]150.695897771664[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.738[/C][C]0.730517792321282[/C][C]152.957260144128[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.804166666667[/C][C]0.717918819946306[/C][C]155.733717462691[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.878260869565[/C][C]0.703846663715858[/C][C]158.952605215062[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.956818181818[/C][C]0.689358847622698[/C][C]162.407168005327[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]112.047619047619[/C][C]0.670623317586732[/C][C]167.079813822799[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]112.1325[/C][C]0.650614970426895[/C][C]172.348478127433[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]112.223684210526[/C][C]0.623992037400029[/C][C]179.847942736779[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]112.308333333333[/C][C]0.595837079575302[/C][C]188.488325388181[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]112.385294117647[/C][C]0.563746260176934[/C][C]199.354394089239[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]112.45625[/C][C]0.527202321985072[/C][C]213.307577205975[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]112.513333333333[/C][C]0.484868351212639[/C][C]232.049241927095[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]112.567857142857[/C][C]0.439517940940030[/C][C]256.116637473546[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]112.626923076923[/C][C]0.39338991001521[/C][C]286.298454051779[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]112.679166666667[/C][C]0.346095151460887[/C][C]325.572797512596[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]112.718181818182[/C][C]0.301197923136942[/C][C]374.232931768702[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]112.74[/C][C]0.256433021931346[/C][C]439.646965710148[/C][/ROW]
[ROW][C]Median[/C][C]112.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.293548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.293548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.293548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.609090909091[/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=36216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36216&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.4783333333330.767408478014193145.265965293742
Geometric Mean111.319596350128
Harmonic Mean111.158106057296
Quadratic Mean111.634066634399
Winsorized Mean ( 1 / 20 )111.480.767035529049899145.338769558806
Winsorized Mean ( 2 / 20 )111.4766666666670.766484994441725145.438811555419
Winsorized Mean ( 3 / 20 )111.4816666666670.763457388828898146.022120288433
Winsorized Mean ( 4 / 20 )111.4816666666670.76092232046233146.508603662633
Winsorized Mean ( 5 / 20 )111.4733333333330.756459440500554147.361943502973
Winsorized Mean ( 6 / 20 )111.4633333333330.747492859088264149.116251718161
Winsorized Mean ( 7 / 20 )111.4750.732307802439742152.224241812817
Winsorized Mean ( 8 / 20 )111.4483333333330.728385303708918153.007388762296
Winsorized Mean ( 9 / 20 )111.5383333333330.709730957486755157.155795667001
Winsorized Mean ( 10 / 20 )111.5550.70634103333109157.933625169571
Winsorized Mean ( 11 / 20 )111.6650.67798648804095164.700922466253
Winsorized Mean ( 12 / 20 )111.7850.654712707081174170.739010853108
Winsorized Mean ( 13 / 20 )111.8933333333330.626892013816428178.489007464209
Winsorized Mean ( 14 / 20 )112.0566666666670.596919430096194187.724944132927
Winsorized Mean ( 15 / 20 )112.1316666666670.550282370590134203.771141253198
Winsorized Mean ( 16 / 20 )112.1583333333330.493381573072844227.325744321574
Winsorized Mean ( 17 / 20 )112.2716666666670.437610949074093256.555890350124
Winsorized Mean ( 18 / 20 )112.4216666666670.374792535203737299.957059191572
Winsorized Mean ( 19 / 20 )112.580.319849894172658351.977605905439
Winsorized Mean ( 20 / 20 )112.6466666666670.258663084604472435.495721544176
Trimmed Mean ( 1 / 20 )111.5241379310340.762963426534222146.172324979764
Trimmed Mean ( 2 / 20 )111.5714285714290.757206564337676147.346092633282
Trimmed Mean ( 3 / 20 )111.6240740740740.749711965120073148.889279172964
Trimmed Mean ( 4 / 20 )111.6788461538460.741087500092821150.695897771664
Trimmed Mean ( 5 / 20 )111.7380.730517792321282152.957260144128
Trimmed Mean ( 6 / 20 )111.8041666666670.717918819946306155.733717462691
Trimmed Mean ( 7 / 20 )111.8782608695650.703846663715858158.952605215062
Trimmed Mean ( 8 / 20 )111.9568181818180.689358847622698162.407168005327
Trimmed Mean ( 9 / 20 )112.0476190476190.670623317586732167.079813822799
Trimmed Mean ( 10 / 20 )112.13250.650614970426895172.348478127433
Trimmed Mean ( 11 / 20 )112.2236842105260.623992037400029179.847942736779
Trimmed Mean ( 12 / 20 )112.3083333333330.595837079575302188.488325388181
Trimmed Mean ( 13 / 20 )112.3852941176470.563746260176934199.354394089239
Trimmed Mean ( 14 / 20 )112.456250.527202321985072213.307577205975
Trimmed Mean ( 15 / 20 )112.5133333333330.484868351212639232.049241927095
Trimmed Mean ( 16 / 20 )112.5678571428570.439517940940030256.116637473546
Trimmed Mean ( 17 / 20 )112.6269230769230.39338991001521286.298454051779
Trimmed Mean ( 18 / 20 )112.6791666666670.346095151460887325.572797512596
Trimmed Mean ( 19 / 20 )112.7181818181820.301197923136942374.232931768702
Trimmed Mean ( 20 / 20 )112.740.256433021931346439.646965710148
Median112.85
Midrange110.15
Midmean - Weighted Average at Xnp112.293548387097
Midmean - Weighted Average at X(n+1)p112.513333333333
Midmean - Empirical Distribution Function112.293548387097
Midmean - Empirical Distribution Function - Averaging112.513333333333
Midmean - Empirical Distribution Function - Interpolation112.513333333333
Midmean - Closest Observation112.293548387097
Midmean - True Basic - Statistics Graphics Toolkit112.513333333333
Midmean - MS Excel (old versions)112.609090909091
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')