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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 05:50:55 -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/t1256644542wya500czuiosvtn.htm/, Retrieved Tue, 07 May 2024 14:49:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50909, Retrieved Tue, 07 May 2024 14:49:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgemiddelde en mediaan
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Median Kleding en...] [2009-10-27 11:50:55] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
100.32
100.41
100.32
100.37
100.32
100.26
100.27
100.34
100.32
100.33
100.38
100.35
100.44
100.47
100.49
100.52
100.47
100.48
100.48
100.53
100.62
100.89
100.97
101.01
101.02
100.92
100.93
100.98
101.07
101.10
101.11
101.19
101.31
101.52
101.61
101.65
101.66
101.56
101.75
101.83
101.98
102.06
102.07
102.10
102.42
102.91
103.14
103.23
103.23
102.91
103.11
103.14
103.26
103.30
103.32
103.44
103.54




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=50909&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=50909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50909&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 Mean101.4338596491230.143415365518447707.273305635271
Geometric Mean101.428208279895
Harmonic Mean101.422583312090
Quadratic Mean101.439537111886
Winsorized Mean ( 1 / 19 )101.4322807017540.142939735610965709.615701107911
Winsorized Mean ( 2 / 19 )101.4298245614040.141659846045761716.009704885873
Winsorized Mean ( 3 / 19 )101.4287719298250.141410073574111717.266948288992
Winsorized Mean ( 4 / 19 )101.4259649122810.140751843439613720.601325238028
Winsorized Mean ( 5 / 19 )101.4233333333330.140142769427790723.714350354643
Winsorized Mean ( 6 / 19 )101.4243859649120.139995304598996724.48419791959
Winsorized Mean ( 7 / 19 )101.4145614035090.137310605533385738.577774160727
Winsorized Mean ( 8 / 19 )101.4159649122810.137115116292332739.641023211909
Winsorized Mean ( 9 / 19 )101.4143859649120.135618193220239747.793371647558
Winsorized Mean ( 10 / 19 )101.3810526315790.127702044987121793.887463914956
Winsorized Mean ( 11 / 19 )101.3868421052630.126898899503341798.957615094165
Winsorized Mean ( 12 / 19 )101.290.104928069406491965.327967749054
Winsorized Mean ( 13 / 19 )101.2238596491230.09055065268055751117.87001697512
Winsorized Mean ( 14 / 19 )101.2164912280700.08928513476486041133.63205974468
Winsorized Mean ( 15 / 19 )101.2164912280700.08844432825090461144.40906759937
Winsorized Mean ( 16 / 19 )101.1940350877190.08466980671107861195.16081373643
Winsorized Mean ( 17 / 19 )101.1522807017540.07698298218018471313.95638148961
Winsorized Mean ( 18 / 19 )101.1364912280700.07160682261045611412.38624395132
Winsorized Mean ( 19 / 19 )101.1098245614040.06658021865046111518.61658929387
Trimmed Mean ( 1 / 19 )101.4169090909090.141924452974126714.583758934045
Trimmed Mean ( 2 / 19 )101.4003773584910.1404954333158721.734329475085
Trimmed Mean ( 3 / 19 )101.3839215686270.139374816537327727.419228863882
Trimmed Mean ( 4 / 19 )101.3665306122450.137884450484487735.155633982452
Trimmed Mean ( 5 / 19 )101.3485106382980.136055159245770744.907515452775
Trimmed Mean ( 6 / 19 )101.3295555555560.133724409637449757.749133686796
Trimmed Mean ( 7 / 19 )101.3086046511630.130543451096061776.052753321302
Trimmed Mean ( 8 / 19 )101.2875609756100.127036474735199797.310860418146
Trimmed Mean ( 9 / 19 )101.2641025641030.122211801474040828.595122097216
Trimmed Mean ( 10 / 19 )101.2383783783780.115935620475858873.22927986106
Trimmed Mean ( 11 / 19 )101.2151428571430.109825967317565921.595733042589
Trimmed Mean ( 12 / 19 )101.1881818181820.1011706615319921000.17317556221
Trimmed Mean ( 13 / 19 )101.1725806451610.09685369494279571044.59185274156
Trimmed Mean ( 14 / 19 )101.1648275862070.0952603648726931061.98236508337
Trimmed Mean ( 15 / 19 )101.1570370370370.09294763837776741088.32283210795
Trimmed Mean ( 16 / 19 )101.1480.08934017386745271132.16703775466
Trimmed Mean ( 17 / 19 )101.1408695652170.0849247819794681190.94647295850
Trimmed Mean ( 18 / 19 )101.1390476190480.08092884812012261249.72800142821
Trimmed Mean ( 19 / 19 )101.1394736842110.07636276029817811324.46068331325
Median101.07
Midrange101.9
Midmean - Weighted Average at Xnp101.109655172414
Midmean - Weighted Average at X(n+1)p101.141666666667
Midmean - Empirical Distribution Function101.141666666667
Midmean - Empirical Distribution Function - Averaging101.141666666667
Midmean - Empirical Distribution Function - Interpolation101.141666666667
Midmean - Closest Observation101.141666666667
Midmean - True Basic - Statistics Graphics Toolkit101.141666666667
Midmean - MS Excel (old versions)101.141666666667
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.433859649123 & 0.143415365518447 & 707.273305635271 \tabularnewline
Geometric Mean & 101.428208279895 &  &  \tabularnewline
Harmonic Mean & 101.422583312090 &  &  \tabularnewline
Quadratic Mean & 101.439537111886 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 101.432280701754 & 0.142939735610965 & 709.615701107911 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 101.429824561404 & 0.141659846045761 & 716.009704885873 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 101.428771929825 & 0.141410073574111 & 717.266948288992 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 101.425964912281 & 0.140751843439613 & 720.601325238028 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 101.423333333333 & 0.140142769427790 & 723.714350354643 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 101.424385964912 & 0.139995304598996 & 724.48419791959 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 101.414561403509 & 0.137310605533385 & 738.577774160727 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 101.415964912281 & 0.137115116292332 & 739.641023211909 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 101.414385964912 & 0.135618193220239 & 747.793371647558 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 101.381052631579 & 0.127702044987121 & 793.887463914956 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 101.386842105263 & 0.126898899503341 & 798.957615094165 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 101.29 & 0.104928069406491 & 965.327967749054 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 101.223859649123 & 0.0905506526805575 & 1117.87001697512 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 101.216491228070 & 0.0892851347648604 & 1133.63205974468 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 101.216491228070 & 0.0884443282509046 & 1144.40906759937 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 101.194035087719 & 0.0846698067110786 & 1195.16081373643 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 101.152280701754 & 0.0769829821801847 & 1313.95638148961 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 101.136491228070 & 0.0716068226104561 & 1412.38624395132 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 101.109824561404 & 0.0665802186504611 & 1518.61658929387 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 101.416909090909 & 0.141924452974126 & 714.583758934045 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 101.400377358491 & 0.1404954333158 & 721.734329475085 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 101.383921568627 & 0.139374816537327 & 727.419228863882 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 101.366530612245 & 0.137884450484487 & 735.155633982452 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 101.348510638298 & 0.136055159245770 & 744.907515452775 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 101.329555555556 & 0.133724409637449 & 757.749133686796 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 101.308604651163 & 0.130543451096061 & 776.052753321302 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 101.287560975610 & 0.127036474735199 & 797.310860418146 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 101.264102564103 & 0.122211801474040 & 828.595122097216 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 101.238378378378 & 0.115935620475858 & 873.22927986106 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 101.215142857143 & 0.109825967317565 & 921.595733042589 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 101.188181818182 & 0.101170661531992 & 1000.17317556221 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 101.172580645161 & 0.0968536949427957 & 1044.59185274156 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 101.164827586207 & 0.095260364872693 & 1061.98236508337 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 101.157037037037 & 0.0929476383777674 & 1088.32283210795 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 101.148 & 0.0893401738674527 & 1132.16703775466 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 101.140869565217 & 0.084924781979468 & 1190.94647295850 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 101.139047619048 & 0.0809288481201226 & 1249.72800142821 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 101.139473684211 & 0.0763627602981781 & 1324.46068331325 \tabularnewline
Median & 101.07 &  &  \tabularnewline
Midrange & 101.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.109655172414 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.141666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.141666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.141666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.141666666667 &  &  \tabularnewline
Midmean - Closest Observation & 101.141666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.141666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.141666666667 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50909&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]101.433859649123[/C][C]0.143415365518447[/C][C]707.273305635271[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.428208279895[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.422583312090[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.439537111886[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]101.432280701754[/C][C]0.142939735610965[/C][C]709.615701107911[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]101.429824561404[/C][C]0.141659846045761[/C][C]716.009704885873[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]101.428771929825[/C][C]0.141410073574111[/C][C]717.266948288992[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]101.425964912281[/C][C]0.140751843439613[/C][C]720.601325238028[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]101.423333333333[/C][C]0.140142769427790[/C][C]723.714350354643[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]101.424385964912[/C][C]0.139995304598996[/C][C]724.48419791959[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]101.414561403509[/C][C]0.137310605533385[/C][C]738.577774160727[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]101.415964912281[/C][C]0.137115116292332[/C][C]739.641023211909[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]101.414385964912[/C][C]0.135618193220239[/C][C]747.793371647558[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]101.381052631579[/C][C]0.127702044987121[/C][C]793.887463914956[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]101.386842105263[/C][C]0.126898899503341[/C][C]798.957615094165[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]101.29[/C][C]0.104928069406491[/C][C]965.327967749054[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]101.223859649123[/C][C]0.0905506526805575[/C][C]1117.87001697512[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]101.216491228070[/C][C]0.0892851347648604[/C][C]1133.63205974468[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]101.216491228070[/C][C]0.0884443282509046[/C][C]1144.40906759937[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]101.194035087719[/C][C]0.0846698067110786[/C][C]1195.16081373643[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]101.152280701754[/C][C]0.0769829821801847[/C][C]1313.95638148961[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]101.136491228070[/C][C]0.0716068226104561[/C][C]1412.38624395132[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]101.109824561404[/C][C]0.0665802186504611[/C][C]1518.61658929387[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]101.416909090909[/C][C]0.141924452974126[/C][C]714.583758934045[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]101.400377358491[/C][C]0.1404954333158[/C][C]721.734329475085[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]101.383921568627[/C][C]0.139374816537327[/C][C]727.419228863882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]101.366530612245[/C][C]0.137884450484487[/C][C]735.155633982452[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]101.348510638298[/C][C]0.136055159245770[/C][C]744.907515452775[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]101.329555555556[/C][C]0.133724409637449[/C][C]757.749133686796[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]101.308604651163[/C][C]0.130543451096061[/C][C]776.052753321302[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]101.287560975610[/C][C]0.127036474735199[/C][C]797.310860418146[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]101.264102564103[/C][C]0.122211801474040[/C][C]828.595122097216[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]101.238378378378[/C][C]0.115935620475858[/C][C]873.22927986106[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]101.215142857143[/C][C]0.109825967317565[/C][C]921.595733042589[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]101.188181818182[/C][C]0.101170661531992[/C][C]1000.17317556221[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]101.172580645161[/C][C]0.0968536949427957[/C][C]1044.59185274156[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]101.164827586207[/C][C]0.095260364872693[/C][C]1061.98236508337[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]101.157037037037[/C][C]0.0929476383777674[/C][C]1088.32283210795[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]101.148[/C][C]0.0893401738674527[/C][C]1132.16703775466[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]101.140869565217[/C][C]0.084924781979468[/C][C]1190.94647295850[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]101.139047619048[/C][C]0.0809288481201226[/C][C]1249.72800142821[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]101.139473684211[/C][C]0.0763627602981781[/C][C]1324.46068331325[/C][/ROW]
[ROW][C]Median[/C][C]101.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.109655172414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.141666666667[/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=50909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50909&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 Mean101.4338596491230.143415365518447707.273305635271
Geometric Mean101.428208279895
Harmonic Mean101.422583312090
Quadratic Mean101.439537111886
Winsorized Mean ( 1 / 19 )101.4322807017540.142939735610965709.615701107911
Winsorized Mean ( 2 / 19 )101.4298245614040.141659846045761716.009704885873
Winsorized Mean ( 3 / 19 )101.4287719298250.141410073574111717.266948288992
Winsorized Mean ( 4 / 19 )101.4259649122810.140751843439613720.601325238028
Winsorized Mean ( 5 / 19 )101.4233333333330.140142769427790723.714350354643
Winsorized Mean ( 6 / 19 )101.4243859649120.139995304598996724.48419791959
Winsorized Mean ( 7 / 19 )101.4145614035090.137310605533385738.577774160727
Winsorized Mean ( 8 / 19 )101.4159649122810.137115116292332739.641023211909
Winsorized Mean ( 9 / 19 )101.4143859649120.135618193220239747.793371647558
Winsorized Mean ( 10 / 19 )101.3810526315790.127702044987121793.887463914956
Winsorized Mean ( 11 / 19 )101.3868421052630.126898899503341798.957615094165
Winsorized Mean ( 12 / 19 )101.290.104928069406491965.327967749054
Winsorized Mean ( 13 / 19 )101.2238596491230.09055065268055751117.87001697512
Winsorized Mean ( 14 / 19 )101.2164912280700.08928513476486041133.63205974468
Winsorized Mean ( 15 / 19 )101.2164912280700.08844432825090461144.40906759937
Winsorized Mean ( 16 / 19 )101.1940350877190.08466980671107861195.16081373643
Winsorized Mean ( 17 / 19 )101.1522807017540.07698298218018471313.95638148961
Winsorized Mean ( 18 / 19 )101.1364912280700.07160682261045611412.38624395132
Winsorized Mean ( 19 / 19 )101.1098245614040.06658021865046111518.61658929387
Trimmed Mean ( 1 / 19 )101.4169090909090.141924452974126714.583758934045
Trimmed Mean ( 2 / 19 )101.4003773584910.1404954333158721.734329475085
Trimmed Mean ( 3 / 19 )101.3839215686270.139374816537327727.419228863882
Trimmed Mean ( 4 / 19 )101.3665306122450.137884450484487735.155633982452
Trimmed Mean ( 5 / 19 )101.3485106382980.136055159245770744.907515452775
Trimmed Mean ( 6 / 19 )101.3295555555560.133724409637449757.749133686796
Trimmed Mean ( 7 / 19 )101.3086046511630.130543451096061776.052753321302
Trimmed Mean ( 8 / 19 )101.2875609756100.127036474735199797.310860418146
Trimmed Mean ( 9 / 19 )101.2641025641030.122211801474040828.595122097216
Trimmed Mean ( 10 / 19 )101.2383783783780.115935620475858873.22927986106
Trimmed Mean ( 11 / 19 )101.2151428571430.109825967317565921.595733042589
Trimmed Mean ( 12 / 19 )101.1881818181820.1011706615319921000.17317556221
Trimmed Mean ( 13 / 19 )101.1725806451610.09685369494279571044.59185274156
Trimmed Mean ( 14 / 19 )101.1648275862070.0952603648726931061.98236508337
Trimmed Mean ( 15 / 19 )101.1570370370370.09294763837776741088.32283210795
Trimmed Mean ( 16 / 19 )101.1480.08934017386745271132.16703775466
Trimmed Mean ( 17 / 19 )101.1408695652170.0849247819794681190.94647295850
Trimmed Mean ( 18 / 19 )101.1390476190480.08092884812012261249.72800142821
Trimmed Mean ( 19 / 19 )101.1394736842110.07636276029817811324.46068331325
Median101.07
Midrange101.9
Midmean - Weighted Average at Xnp101.109655172414
Midmean - Weighted Average at X(n+1)p101.141666666667
Midmean - Empirical Distribution Function101.141666666667
Midmean - Empirical Distribution Function - Averaging101.141666666667
Midmean - Empirical Distribution Function - Interpolation101.141666666667
Midmean - Closest Observation101.141666666667
Midmean - True Basic - Statistics Graphics Toolkit101.141666666667
Midmean - MS Excel (old versions)101.141666666667
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')