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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 computationMon, 03 Nov 2008 17:10:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/04/t12257575126azh90g7onyxpq6.htm/, Retrieved Sat, 18 May 2024 22:56:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21414, Retrieved Sat, 18 May 2024 22:56:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Explorative Data Analysis] [Investigating dis...] [2007-10-22 19:45:25] [b9964c45117f7aac638ab9056d451faa]
F R  D  [Univariate Explorative Data Analysis] [Q7] [2008-10-26 14:53:24] [4300be8b33fd3dcdacd2aa9800ceba23]
- RMPD      [Central Tendency] [central tendency] [2008-11-04 00:10:54] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataseries X:
356.2
359.5
368.4
371
397.5
416.7
413.2
424.3
415
421.7
422.1
429.2
452.1
471.5
488.3
506.2
517.3
538.6
545.3
546.7
540.3
549.2
563.9
581.7
590.7
594.1
604
628.1
662.4
688.6
705.9
701.5
686.2
645.7
668.7
696.7
715.5
741.4
754.3
771.3
797.7
809.9
790.1
830.3
847.7
834.8
824.5
764.6
780
803.2
751.1
755.2
708.2
685.4
680
710.6
702.8
656.3
575.6
567.2
545.2




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=21414&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=21414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21414&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 Mean612.64590163934418.494666277902633.1255450860086
Geometric Mean594.669775628613
Harmonic Mean575.758763137307
Quadratic Mean629.172600833304
Winsorized Mean ( 1 / 20 )612.48852459016418.438582602964433.2177661254555
Winsorized Mean ( 2 / 20 )612.63278688524618.34342480154133.3979501381759
Winsorized Mean ( 3 / 20 )612.47540983606618.259335161039033.5431385882515
Winsorized Mean ( 4 / 20 )613.25573770491817.709891886349234.6278645652048
Winsorized Mean ( 5 / 20 )613.99344262295117.354376759940735.3797460500131
Winsorized Mean ( 6 / 20 )613.62950819672117.22295430193935.6285859811889
Winsorized Mean ( 7 / 20 )612.95245901639317.032197668324635.9878666836003
Winsorized Mean ( 8 / 20 )612.28360655737716.680966736332236.7055229013666
Winsorized Mean ( 9 / 20 )611.05901639344316.45798266244137.1284275191241
Winsorized Mean ( 10 / 20 )610.3213114754116.212760796635837.6445023232598
Winsorized Mean ( 11 / 20 )609.50983606557415.779233379280638.6273414819955
Winsorized Mean ( 12 / 20 )613.83770491803314.915033338046941.1556374702956
Winsorized Mean ( 13 / 20 )617.29016393442614.076574678226443.8522991597701
Winsorized Mean ( 14 / 20 )618.91967213114813.072026575708247.3468798848135
Winsorized Mean ( 15 / 20 )616.95245901639311.388990131293354.1709538689656
Winsorized Mean ( 16 / 20 )618.5786885245910.739564286516957.5981177654655
Winsorized Mean ( 17 / 20 )623.8459016393449.7426067173533864.0327501394632
Winsorized Mean ( 18 / 20 )623.6688524590169.5720599050072365.1551346991434
Winsorized Mean ( 19 / 20 )624.2295081967219.2144242306870567.7448197053738
Winsorized Mean ( 20 / 20 )623.836065573779.1492978119846768.1840375505766
Trimmed Mean ( 1 / 20 )613.00847457627118.179008949418133.7206762085835
Trimmed Mean ( 2 / 20 )613.56491228070217.853259162600934.3671094836287
Trimmed Mean ( 3 / 20 )614.08181818181817.507283927302235.0757902100493
Trimmed Mean ( 4 / 20 )614.69811320754717.111169738797635.9237926214823
Trimmed Mean ( 5 / 20 )615.12941176470616.822566844806536.5657284907512
Trimmed Mean ( 6 / 20 )615.41224489795916.56641027070337.1481953447869
Trimmed Mean ( 7 / 20 )615.79787234042616.266967798108437.8557257863406
Trimmed Mean ( 8 / 20 )616.34888888888915.923763013411638.7062334681681
Trimmed Mean ( 9 / 20 )617.0697674418615.561988194854339.6523734445383
Trimmed Mean ( 10 / 20 )618.06341463414615.132106375751040.8445063289130
Trimmed Mean ( 11 / 20 )619.27435897435914.612720558867942.3791282724929
Trimmed Mean ( 12 / 20 )620.73783783783814.018717298846444.2792178917053
Trimmed Mean ( 13 / 20 )621.7413.45574208128246.2062958879756
Trimmed Mean ( 14 / 20 )622.37272727272712.915024777900148.1898206140275
Trimmed Mean ( 15 / 20 )622.85806451612912.442912889088850.0572550871358
Trimmed Mean ( 16 / 20 )623.68620689655212.246278940362750.9286298257453
Trimmed Mean ( 17 / 20 )624.40740740740712.106522606740551.5761154288646
Trimmed Mean ( 18 / 20 )624.48812.145396000131151.417673000803
Trimmed Mean ( 19 / 20 )624.60869565217412.157604547839251.3759674608917
Trimmed Mean ( 20 / 20 )624.66666666666712.186138365124951.2604278689614
Median628.1
Midrange601.95
Midmean - Weighted Average at Xnp619.77
Midmean - Weighted Average at X(n+1)p622.858064516129
Midmean - Empirical Distribution Function622.858064516129
Midmean - Empirical Distribution Function - Averaging622.858064516129
Midmean - Empirical Distribution Function - Interpolation622.858064516129
Midmean - Closest Observation618.653125
Midmean - True Basic - Statistics Graphics Toolkit622.858064516129
Midmean - MS Excel (old versions)622.858064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 612.645901639344 & 18.4946662779026 & 33.1255450860086 \tabularnewline
Geometric Mean & 594.669775628613 &  &  \tabularnewline
Harmonic Mean & 575.758763137307 &  &  \tabularnewline
Quadratic Mean & 629.172600833304 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 612.488524590164 & 18.4385826029644 & 33.2177661254555 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 612.632786885246 & 18.343424801541 & 33.3979501381759 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 612.475409836066 & 18.2593351610390 & 33.5431385882515 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 613.255737704918 & 17.7098918863492 & 34.6278645652048 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 613.993442622951 & 17.3543767599407 & 35.3797460500131 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 613.629508196721 & 17.222954301939 & 35.6285859811889 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 612.952459016393 & 17.0321976683246 & 35.9878666836003 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 612.283606557377 & 16.6809667363322 & 36.7055229013666 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 611.059016393443 & 16.457982662441 & 37.1284275191241 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 610.32131147541 & 16.2127607966358 & 37.6445023232598 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 609.509836065574 & 15.7792333792806 & 38.6273414819955 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 613.837704918033 & 14.9150333380469 & 41.1556374702956 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 617.290163934426 & 14.0765746782264 & 43.8522991597701 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 618.919672131148 & 13.0720265757082 & 47.3468798848135 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 616.952459016393 & 11.3889901312933 & 54.1709538689656 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 618.57868852459 & 10.7395642865169 & 57.5981177654655 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 623.845901639344 & 9.74260671735338 & 64.0327501394632 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 623.668852459016 & 9.57205990500723 & 65.1551346991434 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 624.229508196721 & 9.21442423068705 & 67.7448197053738 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 623.83606557377 & 9.14929781198467 & 68.1840375505766 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 613.008474576271 & 18.1790089494181 & 33.7206762085835 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 613.564912280702 & 17.8532591626009 & 34.3671094836287 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 614.081818181818 & 17.5072839273022 & 35.0757902100493 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 614.698113207547 & 17.1111697387976 & 35.9237926214823 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 615.129411764706 & 16.8225668448065 & 36.5657284907512 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 615.412244897959 & 16.566410270703 & 37.1481953447869 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 615.797872340426 & 16.2669677981084 & 37.8557257863406 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 616.348888888889 & 15.9237630134116 & 38.7062334681681 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 617.06976744186 & 15.5619881948543 & 39.6523734445383 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 618.063414634146 & 15.1321063757510 & 40.8445063289130 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 619.274358974359 & 14.6127205588679 & 42.3791282724929 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 620.737837837838 & 14.0187172988464 & 44.2792178917053 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 621.74 & 13.455742081282 & 46.2062958879756 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 622.372727272727 & 12.9150247779001 & 48.1898206140275 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 622.858064516129 & 12.4429128890888 & 50.0572550871358 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 623.686206896552 & 12.2462789403627 & 50.9286298257453 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 624.407407407407 & 12.1065226067405 & 51.5761154288646 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 624.488 & 12.1453960001311 & 51.417673000803 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 624.608695652174 & 12.1576045478392 & 51.3759674608917 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 624.666666666667 & 12.1861383651249 & 51.2604278689614 \tabularnewline
Median & 628.1 &  &  \tabularnewline
Midrange & 601.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 619.77 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 622.858064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 622.858064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 622.858064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 622.858064516129 &  &  \tabularnewline
Midmean - Closest Observation & 618.653125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 622.858064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 622.858064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21414&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]612.645901639344[/C][C]18.4946662779026[/C][C]33.1255450860086[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]594.669775628613[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]575.758763137307[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]629.172600833304[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]612.488524590164[/C][C]18.4385826029644[/C][C]33.2177661254555[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]612.632786885246[/C][C]18.343424801541[/C][C]33.3979501381759[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]612.475409836066[/C][C]18.2593351610390[/C][C]33.5431385882515[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]613.255737704918[/C][C]17.7098918863492[/C][C]34.6278645652048[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]613.993442622951[/C][C]17.3543767599407[/C][C]35.3797460500131[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]613.629508196721[/C][C]17.222954301939[/C][C]35.6285859811889[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]612.952459016393[/C][C]17.0321976683246[/C][C]35.9878666836003[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]612.283606557377[/C][C]16.6809667363322[/C][C]36.7055229013666[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]611.059016393443[/C][C]16.457982662441[/C][C]37.1284275191241[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]610.32131147541[/C][C]16.2127607966358[/C][C]37.6445023232598[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]609.509836065574[/C][C]15.7792333792806[/C][C]38.6273414819955[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]613.837704918033[/C][C]14.9150333380469[/C][C]41.1556374702956[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]617.290163934426[/C][C]14.0765746782264[/C][C]43.8522991597701[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]618.919672131148[/C][C]13.0720265757082[/C][C]47.3468798848135[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]616.952459016393[/C][C]11.3889901312933[/C][C]54.1709538689656[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]618.57868852459[/C][C]10.7395642865169[/C][C]57.5981177654655[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]623.845901639344[/C][C]9.74260671735338[/C][C]64.0327501394632[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]623.668852459016[/C][C]9.57205990500723[/C][C]65.1551346991434[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]624.229508196721[/C][C]9.21442423068705[/C][C]67.7448197053738[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]623.83606557377[/C][C]9.14929781198467[/C][C]68.1840375505766[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]613.008474576271[/C][C]18.1790089494181[/C][C]33.7206762085835[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]613.564912280702[/C][C]17.8532591626009[/C][C]34.3671094836287[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]614.081818181818[/C][C]17.5072839273022[/C][C]35.0757902100493[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]614.698113207547[/C][C]17.1111697387976[/C][C]35.9237926214823[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]615.129411764706[/C][C]16.8225668448065[/C][C]36.5657284907512[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]615.412244897959[/C][C]16.566410270703[/C][C]37.1481953447869[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]615.797872340426[/C][C]16.2669677981084[/C][C]37.8557257863406[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]616.348888888889[/C][C]15.9237630134116[/C][C]38.7062334681681[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]617.06976744186[/C][C]15.5619881948543[/C][C]39.6523734445383[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]618.063414634146[/C][C]15.1321063757510[/C][C]40.8445063289130[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]619.274358974359[/C][C]14.6127205588679[/C][C]42.3791282724929[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]620.737837837838[/C][C]14.0187172988464[/C][C]44.2792178917053[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]621.74[/C][C]13.455742081282[/C][C]46.2062958879756[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]622.372727272727[/C][C]12.9150247779001[/C][C]48.1898206140275[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]622.858064516129[/C][C]12.4429128890888[/C][C]50.0572550871358[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]623.686206896552[/C][C]12.2462789403627[/C][C]50.9286298257453[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]624.407407407407[/C][C]12.1065226067405[/C][C]51.5761154288646[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]624.488[/C][C]12.1453960001311[/C][C]51.417673000803[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]624.608695652174[/C][C]12.1576045478392[/C][C]51.3759674608917[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]624.666666666667[/C][C]12.1861383651249[/C][C]51.2604278689614[/C][/ROW]
[ROW][C]Median[/C][C]628.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]601.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]619.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]618.653125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]622.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21414&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 Mean612.64590163934418.494666277902633.1255450860086
Geometric Mean594.669775628613
Harmonic Mean575.758763137307
Quadratic Mean629.172600833304
Winsorized Mean ( 1 / 20 )612.48852459016418.438582602964433.2177661254555
Winsorized Mean ( 2 / 20 )612.63278688524618.34342480154133.3979501381759
Winsorized Mean ( 3 / 20 )612.47540983606618.259335161039033.5431385882515
Winsorized Mean ( 4 / 20 )613.25573770491817.709891886349234.6278645652048
Winsorized Mean ( 5 / 20 )613.99344262295117.354376759940735.3797460500131
Winsorized Mean ( 6 / 20 )613.62950819672117.22295430193935.6285859811889
Winsorized Mean ( 7 / 20 )612.95245901639317.032197668324635.9878666836003
Winsorized Mean ( 8 / 20 )612.28360655737716.680966736332236.7055229013666
Winsorized Mean ( 9 / 20 )611.05901639344316.45798266244137.1284275191241
Winsorized Mean ( 10 / 20 )610.3213114754116.212760796635837.6445023232598
Winsorized Mean ( 11 / 20 )609.50983606557415.779233379280638.6273414819955
Winsorized Mean ( 12 / 20 )613.83770491803314.915033338046941.1556374702956
Winsorized Mean ( 13 / 20 )617.29016393442614.076574678226443.8522991597701
Winsorized Mean ( 14 / 20 )618.91967213114813.072026575708247.3468798848135
Winsorized Mean ( 15 / 20 )616.95245901639311.388990131293354.1709538689656
Winsorized Mean ( 16 / 20 )618.5786885245910.739564286516957.5981177654655
Winsorized Mean ( 17 / 20 )623.8459016393449.7426067173533864.0327501394632
Winsorized Mean ( 18 / 20 )623.6688524590169.5720599050072365.1551346991434
Winsorized Mean ( 19 / 20 )624.2295081967219.2144242306870567.7448197053738
Winsorized Mean ( 20 / 20 )623.836065573779.1492978119846768.1840375505766
Trimmed Mean ( 1 / 20 )613.00847457627118.179008949418133.7206762085835
Trimmed Mean ( 2 / 20 )613.56491228070217.853259162600934.3671094836287
Trimmed Mean ( 3 / 20 )614.08181818181817.507283927302235.0757902100493
Trimmed Mean ( 4 / 20 )614.69811320754717.111169738797635.9237926214823
Trimmed Mean ( 5 / 20 )615.12941176470616.822566844806536.5657284907512
Trimmed Mean ( 6 / 20 )615.41224489795916.56641027070337.1481953447869
Trimmed Mean ( 7 / 20 )615.79787234042616.266967798108437.8557257863406
Trimmed Mean ( 8 / 20 )616.34888888888915.923763013411638.7062334681681
Trimmed Mean ( 9 / 20 )617.0697674418615.561988194854339.6523734445383
Trimmed Mean ( 10 / 20 )618.06341463414615.132106375751040.8445063289130
Trimmed Mean ( 11 / 20 )619.27435897435914.612720558867942.3791282724929
Trimmed Mean ( 12 / 20 )620.73783783783814.018717298846444.2792178917053
Trimmed Mean ( 13 / 20 )621.7413.45574208128246.2062958879756
Trimmed Mean ( 14 / 20 )622.37272727272712.915024777900148.1898206140275
Trimmed Mean ( 15 / 20 )622.85806451612912.442912889088850.0572550871358
Trimmed Mean ( 16 / 20 )623.68620689655212.246278940362750.9286298257453
Trimmed Mean ( 17 / 20 )624.40740740740712.106522606740551.5761154288646
Trimmed Mean ( 18 / 20 )624.48812.145396000131151.417673000803
Trimmed Mean ( 19 / 20 )624.60869565217412.157604547839251.3759674608917
Trimmed Mean ( 20 / 20 )624.66666666666712.186138365124951.2604278689614
Median628.1
Midrange601.95
Midmean - Weighted Average at Xnp619.77
Midmean - Weighted Average at X(n+1)p622.858064516129
Midmean - Empirical Distribution Function622.858064516129
Midmean - Empirical Distribution Function - Averaging622.858064516129
Midmean - Empirical Distribution Function - Interpolation622.858064516129
Midmean - Closest Observation618.653125
Midmean - True Basic - Statistics Graphics Toolkit622.858064516129
Midmean - MS Excel (old versions)622.858064516129
Number of observations61



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')