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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 27 Oct 2009 05:38:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/27/t1256643987jrwaq2cebnwosjz.htm/, Retrieved Tue, 07 May 2024 08:46:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50902, Retrieved Tue, 07 May 2024 08:46:55 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmediaan, getrimd gemiddelde
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [mediaan voedingsm...] [2009-10-27 11:38:41] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
100.29
101.12
102.65
102.71
103.39
102.80
102.07
102.15
101.21
101.27
101.86
101.65
101.94
102.62
102.71
103.39
104.51
104.09
104.29
104.57
105.39
105.15
106.13
105.46
106.47
106.62
106.52
108.04
107.15
107.32
107.76
107.26
107.89
109.08
110.40
111.03
112.05
112.28
112.80
114.17
114.92
114.65
115.49
114.67
114.71
115.15
115.03
115.07
116.46
116.37
116.20
116.50
116.38
115.44
114.96
114.48
114.30




Summary of computational 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 computational 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=50902&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]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=50902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50902&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.4392982456140.724939192837129149.583991756915
Geometric Mean108.304188528773
Harmonic Mean108.169838333139
Quadratic Mean108.574911773700
Winsorized Mean ( 1 / 19 )108.4531578947370.722017769182976150.208433259836
Winsorized Mean ( 2 / 19 )108.4535087719300.720894585365835150.442950985535
Winsorized Mean ( 3 / 19 )108.4561403508770.720226648849795150.586125248326
Winsorized Mean ( 4 / 19 )108.4708771929820.713248871309953152.079984359127
Winsorized Mean ( 5 / 19 )108.4270175438600.698476141401613155.233673875076
Winsorized Mean ( 6 / 19 )108.4301754385960.696119817418137155.763667008874
Winsorized Mean ( 7 / 19 )108.4105263157890.687154170073509157.767399278377
Winsorized Mean ( 8 / 19 )108.4105263157890.683350437819395158.645579655634
Winsorized Mean ( 9 / 19 )108.4784210526320.67038643278729161.814761974831
Winsorized Mean ( 10 / 19 )108.4714035087720.667428313601373162.521429340436
Winsorized Mean ( 11 / 19 )108.4752631578950.66429061722961163.294889833437
Winsorized Mean ( 12 / 19 )108.4310526315790.656686386556688165.118471847929
Winsorized Mean ( 13 / 19 )108.4424561403510.651946635917442166.336399585446
Winsorized Mean ( 14 / 19 )108.5824561403510.629220301654273172.566676337172
Winsorized Mean ( 15 / 19 )108.5377192982460.621549574273598174.624396493382
Winsorized Mean ( 16 / 19 )108.6836842105260.584563684491904185.922743909405
Winsorized Mean ( 17 / 19 )108.7045614035090.56960243523138190.842866321931
Winsorized Mean ( 18 / 19 )108.3414035087720.487389177596688222.289309013800
Winsorized Mean ( 19 / 19 )108.1880701754390.456532331095641236.977893582686
Trimmed Mean ( 1 / 19 )108.4409090909090.72151343336565150.296451980199
Trimmed Mean ( 2 / 19 )108.4277358490570.719875596085589150.620102193554
Trimmed Mean ( 3 / 19 )108.4133333333330.717531698646193151.092047275239
Trimmed Mean ( 4 / 19 )108.3967346938780.71384589957954151.848928119814
Trimmed Mean ( 5 / 19 )108.3742553191490.710724490277744152.484199998226
Trimmed Mean ( 6 / 19 )108.3608888888890.710317955710163152.552653382599
Trimmed Mean ( 7 / 19 )108.3455813953490.708929152238218152.829914037647
Trimmed Mean ( 8 / 19 )108.3326829268290.707955922597074153.021790579024
Trimmed Mean ( 9 / 19 )108.3184615384620.705839202332561153.460534893083
Trimmed Mean ( 10 / 19 )108.2910810810810.704341298116048153.748021549688
Trimmed Mean ( 11 / 19 )108.2617142857140.70082442276837154.477656269545
Trimmed Mean ( 12 / 19 )108.2281818181820.69446055674605155.844965947805
Trimmed Mean ( 13 / 19 )108.1970967741940.68532124067012157.877926953492
Trimmed Mean ( 14 / 19 )108.160.671115533357186161.164500930176
Trimmed Mean ( 15 / 19 )108.0962962962960.654525153153478165.152241706056
Trimmed Mean ( 16 / 19 )108.02920.629451591996292171.624317697550
Trimmed Mean ( 17 / 19 )107.9278260869570.600804781919195179.638760101400
Trimmed Mean ( 18 / 19 )107.8038095238100.556621388031858193.67529139509
Trimmed Mean ( 19 / 19 )107.7142105263160.524721767425575205.278715717838
Median107.26
Midrange108.395
Midmean - Weighted Average at Xnp107.928214285714
Midmean - Weighted Average at X(n+1)p108.16
Midmean - Empirical Distribution Function108.16
Midmean - Empirical Distribution Function - Averaging108.16
Midmean - Empirical Distribution Function - Interpolation108.16
Midmean - Closest Observation107.981333333333
Midmean - True Basic - Statistics Graphics Toolkit108.16
Midmean - MS Excel (old versions)108.16
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.439298245614 & 0.724939192837129 & 149.583991756915 \tabularnewline
Geometric Mean & 108.304188528773 &  &  \tabularnewline
Harmonic Mean & 108.169838333139 &  &  \tabularnewline
Quadratic Mean & 108.574911773700 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 108.453157894737 & 0.722017769182976 & 150.208433259836 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 108.453508771930 & 0.720894585365835 & 150.442950985535 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 108.456140350877 & 0.720226648849795 & 150.586125248326 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 108.470877192982 & 0.713248871309953 & 152.079984359127 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 108.427017543860 & 0.698476141401613 & 155.233673875076 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 108.430175438596 & 0.696119817418137 & 155.763667008874 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 108.410526315789 & 0.687154170073509 & 157.767399278377 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 108.410526315789 & 0.683350437819395 & 158.645579655634 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 108.478421052632 & 0.67038643278729 & 161.814761974831 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 108.471403508772 & 0.667428313601373 & 162.521429340436 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 108.475263157895 & 0.66429061722961 & 163.294889833437 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 108.431052631579 & 0.656686386556688 & 165.118471847929 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 108.442456140351 & 0.651946635917442 & 166.336399585446 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 108.582456140351 & 0.629220301654273 & 172.566676337172 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 108.537719298246 & 0.621549574273598 & 174.624396493382 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 108.683684210526 & 0.584563684491904 & 185.922743909405 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 108.704561403509 & 0.56960243523138 & 190.842866321931 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 108.341403508772 & 0.487389177596688 & 222.289309013800 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 108.188070175439 & 0.456532331095641 & 236.977893582686 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 108.440909090909 & 0.72151343336565 & 150.296451980199 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 108.427735849057 & 0.719875596085589 & 150.620102193554 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 108.413333333333 & 0.717531698646193 & 151.092047275239 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 108.396734693878 & 0.71384589957954 & 151.848928119814 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 108.374255319149 & 0.710724490277744 & 152.484199998226 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 108.360888888889 & 0.710317955710163 & 152.552653382599 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 108.345581395349 & 0.708929152238218 & 152.829914037647 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 108.332682926829 & 0.707955922597074 & 153.021790579024 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 108.318461538462 & 0.705839202332561 & 153.460534893083 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 108.291081081081 & 0.704341298116048 & 153.748021549688 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 108.261714285714 & 0.70082442276837 & 154.477656269545 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 108.228181818182 & 0.69446055674605 & 155.844965947805 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 108.197096774194 & 0.68532124067012 & 157.877926953492 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 108.16 & 0.671115533357186 & 161.164500930176 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 108.096296296296 & 0.654525153153478 & 165.152241706056 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 108.0292 & 0.629451591996292 & 171.624317697550 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 107.927826086957 & 0.600804781919195 & 179.638760101400 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 107.803809523810 & 0.556621388031858 & 193.67529139509 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 107.714210526316 & 0.524721767425575 & 205.278715717838 \tabularnewline
Median & 107.26 &  &  \tabularnewline
Midrange & 108.395 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.928214285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.16 &  &  \tabularnewline
Midmean - Closest Observation & 107.981333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.16 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.16 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50902&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]108.439298245614[/C][C]0.724939192837129[/C][C]149.583991756915[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.304188528773[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.169838333139[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.574911773700[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]108.453157894737[/C][C]0.722017769182976[/C][C]150.208433259836[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]108.453508771930[/C][C]0.720894585365835[/C][C]150.442950985535[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]108.456140350877[/C][C]0.720226648849795[/C][C]150.586125248326[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]108.470877192982[/C][C]0.713248871309953[/C][C]152.079984359127[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]108.427017543860[/C][C]0.698476141401613[/C][C]155.233673875076[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]108.430175438596[/C][C]0.696119817418137[/C][C]155.763667008874[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]108.410526315789[/C][C]0.687154170073509[/C][C]157.767399278377[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]108.410526315789[/C][C]0.683350437819395[/C][C]158.645579655634[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]108.478421052632[/C][C]0.67038643278729[/C][C]161.814761974831[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]108.471403508772[/C][C]0.667428313601373[/C][C]162.521429340436[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]108.475263157895[/C][C]0.66429061722961[/C][C]163.294889833437[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]108.431052631579[/C][C]0.656686386556688[/C][C]165.118471847929[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]108.442456140351[/C][C]0.651946635917442[/C][C]166.336399585446[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]108.582456140351[/C][C]0.629220301654273[/C][C]172.566676337172[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]108.537719298246[/C][C]0.621549574273598[/C][C]174.624396493382[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]108.683684210526[/C][C]0.584563684491904[/C][C]185.922743909405[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]108.704561403509[/C][C]0.56960243523138[/C][C]190.842866321931[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]108.341403508772[/C][C]0.487389177596688[/C][C]222.289309013800[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]108.188070175439[/C][C]0.456532331095641[/C][C]236.977893582686[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]108.440909090909[/C][C]0.72151343336565[/C][C]150.296451980199[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]108.427735849057[/C][C]0.719875596085589[/C][C]150.620102193554[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]108.413333333333[/C][C]0.717531698646193[/C][C]151.092047275239[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]108.396734693878[/C][C]0.71384589957954[/C][C]151.848928119814[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]108.374255319149[/C][C]0.710724490277744[/C][C]152.484199998226[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]108.360888888889[/C][C]0.710317955710163[/C][C]152.552653382599[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]108.345581395349[/C][C]0.708929152238218[/C][C]152.829914037647[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]108.332682926829[/C][C]0.707955922597074[/C][C]153.021790579024[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]108.318461538462[/C][C]0.705839202332561[/C][C]153.460534893083[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]108.291081081081[/C][C]0.704341298116048[/C][C]153.748021549688[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]108.261714285714[/C][C]0.70082442276837[/C][C]154.477656269545[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]108.228181818182[/C][C]0.69446055674605[/C][C]155.844965947805[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]108.197096774194[/C][C]0.68532124067012[/C][C]157.877926953492[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]108.16[/C][C]0.671115533357186[/C][C]161.164500930176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]108.096296296296[/C][C]0.654525153153478[/C][C]165.152241706056[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]108.0292[/C][C]0.629451591996292[/C][C]171.624317697550[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]107.927826086957[/C][C]0.600804781919195[/C][C]179.638760101400[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]107.803809523810[/C][C]0.556621388031858[/C][C]193.67529139509[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]107.714210526316[/C][C]0.524721767425575[/C][C]205.278715717838[/C][/ROW]
[ROW][C]Median[/C][C]107.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.928214285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.981333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50902&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.4392982456140.724939192837129149.583991756915
Geometric Mean108.304188528773
Harmonic Mean108.169838333139
Quadratic Mean108.574911773700
Winsorized Mean ( 1 / 19 )108.4531578947370.722017769182976150.208433259836
Winsorized Mean ( 2 / 19 )108.4535087719300.720894585365835150.442950985535
Winsorized Mean ( 3 / 19 )108.4561403508770.720226648849795150.586125248326
Winsorized Mean ( 4 / 19 )108.4708771929820.713248871309953152.079984359127
Winsorized Mean ( 5 / 19 )108.4270175438600.698476141401613155.233673875076
Winsorized Mean ( 6 / 19 )108.4301754385960.696119817418137155.763667008874
Winsorized Mean ( 7 / 19 )108.4105263157890.687154170073509157.767399278377
Winsorized Mean ( 8 / 19 )108.4105263157890.683350437819395158.645579655634
Winsorized Mean ( 9 / 19 )108.4784210526320.67038643278729161.814761974831
Winsorized Mean ( 10 / 19 )108.4714035087720.667428313601373162.521429340436
Winsorized Mean ( 11 / 19 )108.4752631578950.66429061722961163.294889833437
Winsorized Mean ( 12 / 19 )108.4310526315790.656686386556688165.118471847929
Winsorized Mean ( 13 / 19 )108.4424561403510.651946635917442166.336399585446
Winsorized Mean ( 14 / 19 )108.5824561403510.629220301654273172.566676337172
Winsorized Mean ( 15 / 19 )108.5377192982460.621549574273598174.624396493382
Winsorized Mean ( 16 / 19 )108.6836842105260.584563684491904185.922743909405
Winsorized Mean ( 17 / 19 )108.7045614035090.56960243523138190.842866321931
Winsorized Mean ( 18 / 19 )108.3414035087720.487389177596688222.289309013800
Winsorized Mean ( 19 / 19 )108.1880701754390.456532331095641236.977893582686
Trimmed Mean ( 1 / 19 )108.4409090909090.72151343336565150.296451980199
Trimmed Mean ( 2 / 19 )108.4277358490570.719875596085589150.620102193554
Trimmed Mean ( 3 / 19 )108.4133333333330.717531698646193151.092047275239
Trimmed Mean ( 4 / 19 )108.3967346938780.71384589957954151.848928119814
Trimmed Mean ( 5 / 19 )108.3742553191490.710724490277744152.484199998226
Trimmed Mean ( 6 / 19 )108.3608888888890.710317955710163152.552653382599
Trimmed Mean ( 7 / 19 )108.3455813953490.708929152238218152.829914037647
Trimmed Mean ( 8 / 19 )108.3326829268290.707955922597074153.021790579024
Trimmed Mean ( 9 / 19 )108.3184615384620.705839202332561153.460534893083
Trimmed Mean ( 10 / 19 )108.2910810810810.704341298116048153.748021549688
Trimmed Mean ( 11 / 19 )108.2617142857140.70082442276837154.477656269545
Trimmed Mean ( 12 / 19 )108.2281818181820.69446055674605155.844965947805
Trimmed Mean ( 13 / 19 )108.1970967741940.68532124067012157.877926953492
Trimmed Mean ( 14 / 19 )108.160.671115533357186161.164500930176
Trimmed Mean ( 15 / 19 )108.0962962962960.654525153153478165.152241706056
Trimmed Mean ( 16 / 19 )108.02920.629451591996292171.624317697550
Trimmed Mean ( 17 / 19 )107.9278260869570.600804781919195179.638760101400
Trimmed Mean ( 18 / 19 )107.8038095238100.556621388031858193.67529139509
Trimmed Mean ( 19 / 19 )107.7142105263160.524721767425575205.278715717838
Median107.26
Midrange108.395
Midmean - Weighted Average at Xnp107.928214285714
Midmean - Weighted Average at X(n+1)p108.16
Midmean - Empirical Distribution Function108.16
Midmean - Empirical Distribution Function - Averaging108.16
Midmean - Empirical Distribution Function - Interpolation108.16
Midmean - Closest Observation107.981333333333
Midmean - True Basic - Statistics Graphics Toolkit108.16
Midmean - MS Excel (old versions)108.16
Number of observations57



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')