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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 29 May 2009 05:10:03 -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/May/29/t1243595430cg4f4xvl8ay5ug6.htm/, Retrieved Sat, 27 Apr 2024 16:36:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40753, Retrieved Sat, 27 Apr 2024 16:36:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2009-02-09 08:26:33] [02715571966c5d3fa10a0b3d6198f883]
-       [Histogram] [stof voor jurk: B...] [2009-02-16 20:50:18] [02715571966c5d3fa10a0b3d6198f883]
-         [Histogram] [stof voor jurk: B...] [2009-05-26 07:02:24] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [centrumaten, stof...] [2009-05-29 11:10:03] [508db52847fe44fb658c0de5bd3816a5] [Current]
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Dataseries X:
20,73
20,73
20,74
20,74
20,75
20,75
20,77
20,78
20,78
20,8
20,84
20,85
20,86
20,86
20,86
20,86
20,9
20,92
20,95
20,95
20,95
20,96
21,1
21,18
21,19
21,19
21,19
21,19
21,19
21,21
21,22
21,22
21,22
21,23
21,41
21,42
21,43
21,44
21,44
21,44
21,48
21,53
21,54
21,54
21,54
21,54
21,54
21,54
21,54
21,54
21,54
21,54
21,57
21,6
21,61
21,6
21,6
21,71
21,75
21,84
21,85
21,92
21,92
21,93
22
22
21,99
22,01
22,01
22,06
22,03
22,05
22,05
22,06
22,06
22,13
22,06
22,25
22,28
22,18




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=40753&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=40753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40753&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 Mean21.4221250.0518263573985528413.344214706438
Geometric Mean21.4171751650371
Harmonic Mean21.4122289246844
Quadratic Mean21.4270770580124
Winsorized Mean ( 1 / 26 )21.421750.0517490827289831413.954197259661
Winsorized Mean ( 2 / 26 )21.420250.051365830821173417.01359946018
Winsorized Mean ( 3 / 26 )21.4183750.0510247655648644419.764300000012
Winsorized Mean ( 4 / 26 )21.4153750.0503481372922322425.345924432124
Winsorized Mean ( 5 / 26 )21.4153750.0503481372922322425.345924432124
Winsorized Mean ( 6 / 26 )21.4168750.0501000877200526427.481786452599
Winsorized Mean ( 7 / 26 )21.417750.0499578857449078428.716101184949
Winsorized Mean ( 8 / 26 )21.416750.0497960317543578430.089491982978
Winsorized Mean ( 9 / 26 )21.4190.0494356121316955433.270654016384
Winsorized Mean ( 10 / 26 )21.42150.0482563368961312443.910611079089
Winsorized Mean ( 11 / 26 )21.4201250.0476121240775626449.888036188125
Winsorized Mean ( 12 / 26 )21.4216250.0473859202203206452.067299746428
Winsorized Mean ( 13 / 26 )21.420.0471316497171836454.47167940295
Winsorized Mean ( 14 / 26 )21.420.0471316497171836454.47167940295
Winsorized Mean ( 15 / 26 )21.4181250.0468407258663179457.254335919702
Winsorized Mean ( 16 / 26 )21.4141250.0438205827562947488.677321319374
Winsorized Mean ( 17 / 26 )21.416250.0428772810959046499.477799259188
Winsorized Mean ( 18 / 26 )21.4230.0419004244563257511.28360339953
Winsorized Mean ( 19 / 26 )21.4063750.0394676777506015542.377363453409
Winsorized Mean ( 20 / 26 )21.4038750.0391133915322093547.226260918188
Winsorized Mean ( 21 / 26 )21.3828750.0355036964335129602.271795559184
Winsorized Mean ( 22 / 26 )21.4103750.0284663046147146752.130467575083
Winsorized Mean ( 23 / 26 )21.4046250.0216976809631171986.493673512148
Winsorized Mean ( 24 / 26 )21.4046250.02094971658519511021.71429923431
Winsorized Mean ( 25 / 26 )21.4046250.02094971658519511021.71429923431
Winsorized Mean ( 26 / 26 )21.4046250.02094971658519511021.71429923431
Trimmed Mean ( 1 / 26 )21.420.0512254099450910418.1518512582
Trimmed Mean ( 2 / 26 )21.41815789473680.0506011963405886423.273745359193
Trimmed Mean ( 3 / 26 )21.41702702702700.0500912642573092427.560121401845
Trimmed Mean ( 4 / 26 )21.41652777777780.0496222663348408431.591085204845
Trimmed Mean ( 5 / 26 )21.41685714285710.0492790855805796434.60337972053
Trimmed Mean ( 6 / 26 )21.41720588235290.0488474923211855438.450468276427
Trimmed Mean ( 7 / 26 )21.41727272727270.048374291200626442.740807063145
Trimmed Mean ( 8 / 26 )21.41718750.047818724306962447.882870369292
Trimmed Mean ( 9 / 26 )21.41725806451610.0471650955442305454.091268498151
Trimmed Mean ( 10 / 26 )21.4170.0464315911354245461.259230542718
Trimmed Mean ( 11 / 26 )21.41637931034480.045761486299112468.000081342646
Trimmed Mean ( 12 / 26 )21.41589285714290.0450467122528009475.41522535446
Trimmed Mean ( 13 / 26 )21.41518518518520.0441866797272754484.652508795906
Trimmed Mean ( 14 / 26 )21.41461538461540.0431494487506595496.289431375137
Trimmed Mean ( 15 / 26 )21.4140.0418325134754472511.8984785021
Trimmed Mean ( 16 / 26 )21.41354166666670.0402160494929615532.462584879561
Trimmed Mean ( 17 / 26 )21.41347826086960.0388123410217029551.718285915701
Trimmed Mean ( 18 / 26 )21.41318181818180.0371994974949476575.63094289352
Trimmed Mean ( 19 / 26 )21.41214285714290.0353077324599266606.443443555745
Trimmed Mean ( 20 / 26 )21.412750.0334107834196977640.893382565099
Trimmed Mean ( 21 / 26 )21.41368421052630.0309255542862768692.426852314451
Trimmed Mean ( 22 / 26 )21.41694444444440.0285268446239245750.764577253062
Trimmed Mean ( 23 / 26 )21.41764705882350.0273456088153974783.22070660076
Trimmed Mean ( 24 / 26 )21.41906250.0274132038433977781.341087395687
Trimmed Mean ( 25 / 26 )21.42066666666670.0275469644251802777.605341047539
Trimmed Mean ( 26 / 26 )21.42250.0275720556717894776.964193566411
Median21.46
Midrange21.505
Midmean - Weighted Average at Xnp21.3907142857143
Midmean - Weighted Average at X(n+1)p21.3907142857143
Midmean - Empirical Distribution Function21.3907142857143
Midmean - Empirical Distribution Function - Averaging21.3907142857143
Midmean - Empirical Distribution Function - Interpolation21.3907142857143
Midmean - Closest Observation21.3907142857143
Midmean - True Basic - Statistics Graphics Toolkit21.3907142857143
Midmean - MS Excel (old versions)21.4013953488372
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.422125 & 0.0518263573985528 & 413.344214706438 \tabularnewline
Geometric Mean & 21.4171751650371 &  &  \tabularnewline
Harmonic Mean & 21.4122289246844 &  &  \tabularnewline
Quadratic Mean & 21.4270770580124 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 21.42175 & 0.0517490827289831 & 413.954197259661 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 21.42025 & 0.051365830821173 & 417.01359946018 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 21.418375 & 0.0510247655648644 & 419.764300000012 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 21.415375 & 0.0503481372922322 & 425.345924432124 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 21.415375 & 0.0503481372922322 & 425.345924432124 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 21.416875 & 0.0501000877200526 & 427.481786452599 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 21.41775 & 0.0499578857449078 & 428.716101184949 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 21.41675 & 0.0497960317543578 & 430.089491982978 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 21.419 & 0.0494356121316955 & 433.270654016384 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 21.4215 & 0.0482563368961312 & 443.910611079089 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 21.420125 & 0.0476121240775626 & 449.888036188125 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 21.421625 & 0.0473859202203206 & 452.067299746428 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 21.42 & 0.0471316497171836 & 454.47167940295 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 21.42 & 0.0471316497171836 & 454.47167940295 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 21.418125 & 0.0468407258663179 & 457.254335919702 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 21.414125 & 0.0438205827562947 & 488.677321319374 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 21.41625 & 0.0428772810959046 & 499.477799259188 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 21.423 & 0.0419004244563257 & 511.28360339953 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 21.406375 & 0.0394676777506015 & 542.377363453409 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 21.403875 & 0.0391133915322093 & 547.226260918188 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 21.382875 & 0.0355036964335129 & 602.271795559184 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 21.410375 & 0.0284663046147146 & 752.130467575083 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 21.404625 & 0.0216976809631171 & 986.493673512148 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 21.404625 & 0.0209497165851951 & 1021.71429923431 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 21.404625 & 0.0209497165851951 & 1021.71429923431 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 21.404625 & 0.0209497165851951 & 1021.71429923431 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 21.42 & 0.0512254099450910 & 418.1518512582 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 21.4181578947368 & 0.0506011963405886 & 423.273745359193 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 21.4170270270270 & 0.0500912642573092 & 427.560121401845 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 21.4165277777778 & 0.0496222663348408 & 431.591085204845 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 21.4168571428571 & 0.0492790855805796 & 434.60337972053 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 21.4172058823529 & 0.0488474923211855 & 438.450468276427 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 21.4172727272727 & 0.048374291200626 & 442.740807063145 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 21.4171875 & 0.047818724306962 & 447.882870369292 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 21.4172580645161 & 0.0471650955442305 & 454.091268498151 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 21.417 & 0.0464315911354245 & 461.259230542718 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 21.4163793103448 & 0.045761486299112 & 468.000081342646 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 21.4158928571429 & 0.0450467122528009 & 475.41522535446 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 21.4151851851852 & 0.0441866797272754 & 484.652508795906 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 21.4146153846154 & 0.0431494487506595 & 496.289431375137 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 21.414 & 0.0418325134754472 & 511.8984785021 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 21.4135416666667 & 0.0402160494929615 & 532.462584879561 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 21.4134782608696 & 0.0388123410217029 & 551.718285915701 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 21.4131818181818 & 0.0371994974949476 & 575.63094289352 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 21.4121428571429 & 0.0353077324599266 & 606.443443555745 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 21.41275 & 0.0334107834196977 & 640.893382565099 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 21.4136842105263 & 0.0309255542862768 & 692.426852314451 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 21.4169444444444 & 0.0285268446239245 & 750.764577253062 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 21.4176470588235 & 0.0273456088153974 & 783.22070660076 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 21.4190625 & 0.0274132038433977 & 781.341087395687 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 21.4206666666667 & 0.0275469644251802 & 777.605341047539 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 21.4225 & 0.0275720556717894 & 776.964193566411 \tabularnewline
Median & 21.46 &  &  \tabularnewline
Midrange & 21.505 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.3907142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.3907142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.3907142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.3907142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.3907142857143 &  &  \tabularnewline
Midmean - Closest Observation & 21.3907142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.3907142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.4013953488372 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40753&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]21.422125[/C][C]0.0518263573985528[/C][C]413.344214706438[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.4171751650371[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.4122289246844[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.4270770580124[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]21.42175[/C][C]0.0517490827289831[/C][C]413.954197259661[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]21.42025[/C][C]0.051365830821173[/C][C]417.01359946018[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]21.418375[/C][C]0.0510247655648644[/C][C]419.764300000012[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]21.415375[/C][C]0.0503481372922322[/C][C]425.345924432124[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]21.415375[/C][C]0.0503481372922322[/C][C]425.345924432124[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]21.416875[/C][C]0.0501000877200526[/C][C]427.481786452599[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]21.41775[/C][C]0.0499578857449078[/C][C]428.716101184949[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]21.41675[/C][C]0.0497960317543578[/C][C]430.089491982978[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]21.419[/C][C]0.0494356121316955[/C][C]433.270654016384[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]21.4215[/C][C]0.0482563368961312[/C][C]443.910611079089[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]21.420125[/C][C]0.0476121240775626[/C][C]449.888036188125[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]21.421625[/C][C]0.0473859202203206[/C][C]452.067299746428[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]21.42[/C][C]0.0471316497171836[/C][C]454.47167940295[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]21.42[/C][C]0.0471316497171836[/C][C]454.47167940295[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]21.418125[/C][C]0.0468407258663179[/C][C]457.254335919702[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]21.414125[/C][C]0.0438205827562947[/C][C]488.677321319374[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]21.41625[/C][C]0.0428772810959046[/C][C]499.477799259188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]21.423[/C][C]0.0419004244563257[/C][C]511.28360339953[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]21.406375[/C][C]0.0394676777506015[/C][C]542.377363453409[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]21.403875[/C][C]0.0391133915322093[/C][C]547.226260918188[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]21.382875[/C][C]0.0355036964335129[/C][C]602.271795559184[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]21.410375[/C][C]0.0284663046147146[/C][C]752.130467575083[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]21.404625[/C][C]0.0216976809631171[/C][C]986.493673512148[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]21.404625[/C][C]0.0209497165851951[/C][C]1021.71429923431[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]21.404625[/C][C]0.0209497165851951[/C][C]1021.71429923431[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]21.404625[/C][C]0.0209497165851951[/C][C]1021.71429923431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]21.42[/C][C]0.0512254099450910[/C][C]418.1518512582[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]21.4181578947368[/C][C]0.0506011963405886[/C][C]423.273745359193[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]21.4170270270270[/C][C]0.0500912642573092[/C][C]427.560121401845[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]21.4165277777778[/C][C]0.0496222663348408[/C][C]431.591085204845[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]21.4168571428571[/C][C]0.0492790855805796[/C][C]434.60337972053[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]21.4172058823529[/C][C]0.0488474923211855[/C][C]438.450468276427[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]21.4172727272727[/C][C]0.048374291200626[/C][C]442.740807063145[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]21.4171875[/C][C]0.047818724306962[/C][C]447.882870369292[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]21.4172580645161[/C][C]0.0471650955442305[/C][C]454.091268498151[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]21.417[/C][C]0.0464315911354245[/C][C]461.259230542718[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]21.4163793103448[/C][C]0.045761486299112[/C][C]468.000081342646[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]21.4158928571429[/C][C]0.0450467122528009[/C][C]475.41522535446[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]21.4151851851852[/C][C]0.0441866797272754[/C][C]484.652508795906[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]21.4146153846154[/C][C]0.0431494487506595[/C][C]496.289431375137[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]21.414[/C][C]0.0418325134754472[/C][C]511.8984785021[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]21.4135416666667[/C][C]0.0402160494929615[/C][C]532.462584879561[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]21.4134782608696[/C][C]0.0388123410217029[/C][C]551.718285915701[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]21.4131818181818[/C][C]0.0371994974949476[/C][C]575.63094289352[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]21.4121428571429[/C][C]0.0353077324599266[/C][C]606.443443555745[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]21.41275[/C][C]0.0334107834196977[/C][C]640.893382565099[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]21.4136842105263[/C][C]0.0309255542862768[/C][C]692.426852314451[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]21.4169444444444[/C][C]0.0285268446239245[/C][C]750.764577253062[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]21.4176470588235[/C][C]0.0273456088153974[/C][C]783.22070660076[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]21.4190625[/C][C]0.0274132038433977[/C][C]781.341087395687[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]21.4206666666667[/C][C]0.0275469644251802[/C][C]777.605341047539[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]21.4225[/C][C]0.0275720556717894[/C][C]776.964193566411[/C][/ROW]
[ROW][C]Median[/C][C]21.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.3907142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.4013953488372[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40753&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 Mean21.4221250.0518263573985528413.344214706438
Geometric Mean21.4171751650371
Harmonic Mean21.4122289246844
Quadratic Mean21.4270770580124
Winsorized Mean ( 1 / 26 )21.421750.0517490827289831413.954197259661
Winsorized Mean ( 2 / 26 )21.420250.051365830821173417.01359946018
Winsorized Mean ( 3 / 26 )21.4183750.0510247655648644419.764300000012
Winsorized Mean ( 4 / 26 )21.4153750.0503481372922322425.345924432124
Winsorized Mean ( 5 / 26 )21.4153750.0503481372922322425.345924432124
Winsorized Mean ( 6 / 26 )21.4168750.0501000877200526427.481786452599
Winsorized Mean ( 7 / 26 )21.417750.0499578857449078428.716101184949
Winsorized Mean ( 8 / 26 )21.416750.0497960317543578430.089491982978
Winsorized Mean ( 9 / 26 )21.4190.0494356121316955433.270654016384
Winsorized Mean ( 10 / 26 )21.42150.0482563368961312443.910611079089
Winsorized Mean ( 11 / 26 )21.4201250.0476121240775626449.888036188125
Winsorized Mean ( 12 / 26 )21.4216250.0473859202203206452.067299746428
Winsorized Mean ( 13 / 26 )21.420.0471316497171836454.47167940295
Winsorized Mean ( 14 / 26 )21.420.0471316497171836454.47167940295
Winsorized Mean ( 15 / 26 )21.4181250.0468407258663179457.254335919702
Winsorized Mean ( 16 / 26 )21.4141250.0438205827562947488.677321319374
Winsorized Mean ( 17 / 26 )21.416250.0428772810959046499.477799259188
Winsorized Mean ( 18 / 26 )21.4230.0419004244563257511.28360339953
Winsorized Mean ( 19 / 26 )21.4063750.0394676777506015542.377363453409
Winsorized Mean ( 20 / 26 )21.4038750.0391133915322093547.226260918188
Winsorized Mean ( 21 / 26 )21.3828750.0355036964335129602.271795559184
Winsorized Mean ( 22 / 26 )21.4103750.0284663046147146752.130467575083
Winsorized Mean ( 23 / 26 )21.4046250.0216976809631171986.493673512148
Winsorized Mean ( 24 / 26 )21.4046250.02094971658519511021.71429923431
Winsorized Mean ( 25 / 26 )21.4046250.02094971658519511021.71429923431
Winsorized Mean ( 26 / 26 )21.4046250.02094971658519511021.71429923431
Trimmed Mean ( 1 / 26 )21.420.0512254099450910418.1518512582
Trimmed Mean ( 2 / 26 )21.41815789473680.0506011963405886423.273745359193
Trimmed Mean ( 3 / 26 )21.41702702702700.0500912642573092427.560121401845
Trimmed Mean ( 4 / 26 )21.41652777777780.0496222663348408431.591085204845
Trimmed Mean ( 5 / 26 )21.41685714285710.0492790855805796434.60337972053
Trimmed Mean ( 6 / 26 )21.41720588235290.0488474923211855438.450468276427
Trimmed Mean ( 7 / 26 )21.41727272727270.048374291200626442.740807063145
Trimmed Mean ( 8 / 26 )21.41718750.047818724306962447.882870369292
Trimmed Mean ( 9 / 26 )21.41725806451610.0471650955442305454.091268498151
Trimmed Mean ( 10 / 26 )21.4170.0464315911354245461.259230542718
Trimmed Mean ( 11 / 26 )21.41637931034480.045761486299112468.000081342646
Trimmed Mean ( 12 / 26 )21.41589285714290.0450467122528009475.41522535446
Trimmed Mean ( 13 / 26 )21.41518518518520.0441866797272754484.652508795906
Trimmed Mean ( 14 / 26 )21.41461538461540.0431494487506595496.289431375137
Trimmed Mean ( 15 / 26 )21.4140.0418325134754472511.8984785021
Trimmed Mean ( 16 / 26 )21.41354166666670.0402160494929615532.462584879561
Trimmed Mean ( 17 / 26 )21.41347826086960.0388123410217029551.718285915701
Trimmed Mean ( 18 / 26 )21.41318181818180.0371994974949476575.63094289352
Trimmed Mean ( 19 / 26 )21.41214285714290.0353077324599266606.443443555745
Trimmed Mean ( 20 / 26 )21.412750.0334107834196977640.893382565099
Trimmed Mean ( 21 / 26 )21.41368421052630.0309255542862768692.426852314451
Trimmed Mean ( 22 / 26 )21.41694444444440.0285268446239245750.764577253062
Trimmed Mean ( 23 / 26 )21.41764705882350.0273456088153974783.22070660076
Trimmed Mean ( 24 / 26 )21.41906250.0274132038433977781.341087395687
Trimmed Mean ( 25 / 26 )21.42066666666670.0275469644251802777.605341047539
Trimmed Mean ( 26 / 26 )21.42250.0275720556717894776.964193566411
Median21.46
Midrange21.505
Midmean - Weighted Average at Xnp21.3907142857143
Midmean - Weighted Average at X(n+1)p21.3907142857143
Midmean - Empirical Distribution Function21.3907142857143
Midmean - Empirical Distribution Function - Averaging21.3907142857143
Midmean - Empirical Distribution Function - Interpolation21.3907142857143
Midmean - Closest Observation21.3907142857143
Midmean - True Basic - Statistics Graphics Toolkit21.3907142857143
Midmean - MS Excel (old versions)21.4013953488372
Number of observations80



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')