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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, 16 Nov 2010 17:33:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289928854bnc662dmrnahlps.htm/, Retrieved Sun, 05 May 2024 01:21:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96116, Retrieved Sun, 05 May 2024 01:21:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [Blog 1 - Olie] [2010-11-15 19:55:26] [1aa8d85d6b335d32b1f6be940e33a166]
-    D      [Central Tendency] [Blog 5 - Vervoer] [2010-11-16 17:33:01] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
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Dataseries X:
115,05
114,9
114,68
114,61
114,82
114,97
114,24
112,97
111,47
111,52
110,57
110,62
109,38
110,03
110,64
109,53
109,72
108,24
108
107,1
107,03
105,95
106,62
108,9
112,12
114,11
114,51
116,86
116,21
114,74
112,86
112,38
110,76
110,78
110,76
111,69
109,55
108,65
108,39
109,02
108,43
108,12
107,9
107,01
105,68
105,16
106,52
106,25
106,15
107,2
109,21
109,09
108,49
108,5
108,03
106,61
106,35
106,34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96116&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96116&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.1032758620690.411063601169398267.849733104186
Geometric Mean110.059868986926
Harmonic Mean110.016801234123
Quadratic Mean110.147005555115
Winsorized Mean ( 1 / 19 )110.1010344827590.406166003157207271.073978685863
Winsorized Mean ( 2 / 19 )110.0703448275860.394707727681412278.865441713442
Winsorized Mean ( 3 / 19 )110.0765517241380.391940088243318280.850454000515
Winsorized Mean ( 4 / 19 )110.0786206896550.389686958321077282.479611747636
Winsorized Mean ( 5 / 19 )110.0794827586210.386870611547943284.538239589127
Winsorized Mean ( 6 / 19 )110.0722413793100.384925259918256285.95743860168
Winsorized Mean ( 7 / 19 )110.0855172413790.379957266073399289.731312100012
Winsorized Mean ( 8 / 19 )110.0882758620690.375884690484053292.877785791969
Winsorized Mean ( 9 / 19 )110.0743103448280.372373570148647295.601834203452
Winsorized Mean ( 10 / 19 )110.0950.352051136945761312.724455188911
Winsorized Mean ( 11 / 19 )110.0741379310340.346400821313722317.765233678082
Winsorized Mean ( 12 / 19 )109.8527586206900.298197224299223368.389608182466
Winsorized Mean ( 13 / 19 )109.8505172413790.290080659497920378.689559764211
Winsorized Mean ( 14 / 19 )109.9036206896550.243309593469722451.702783775896
Winsorized Mean ( 15 / 19 )109.8622413793100.227729666832592482.423932320033
Winsorized Mean ( 16 / 19 )109.7518965517240.206418404184313531.696274784325
Winsorized Mean ( 17 / 19 )109.7284482758620.194440080880671564.330398233085
Winsorized Mean ( 18 / 19 )109.7501724137930.186583653768378588.20893576259
Winsorized Mean ( 19 / 19 )109.5732758620690.144520691822500758.183997601167
Trimmed Mean ( 1 / 19 )110.0708928571430.398241938210583276.392017756150
Trimmed Mean ( 2 / 19 )110.0385185185190.388268064570828283.408625533366
Trimmed Mean ( 3 / 19 )110.0207692307690.383288329001624287.044402101539
Trimmed Mean ( 4 / 19 )109.99920.378020714258046290.987228612324
Trimmed Mean ( 5 / 19 )109.9752083333330.371885528885257295.723279857081
Trimmed Mean ( 6 / 19 )109.9489130434780.364674194906908301.499021809167
Trimmed Mean ( 7 / 19 )109.9218181818180.355673329336927309.052743388835
Trimmed Mean ( 8 / 19 )109.8895238095240.345106987801097318.421613279123
Trimmed Mean ( 9 / 19 )109.85350.332046982696649330.837217998032
Trimmed Mean ( 10 / 19 )109.8160526315790.315333944206686348.253192049632
Trimmed Mean ( 11 / 19 )109.7711111111110.298525949465719367.710449652942
Trimmed Mean ( 12 / 19 )109.7241176470590.276651778151161396.614539694395
Trimmed Mean ( 13 / 19 )109.70468750.262662769955634417.663635841997
Trimmed Mean ( 14 / 19 )109.6830.244940128738977447.795143101622
Trimmed Mean ( 15 / 19 )109.6503571428570.234896961618228466.801938975562
Trimmed Mean ( 16 / 19 )109.6188461538460.224858469622442487.501521903561
Trimmed Mean ( 17 / 19 )109.598750.217199995079003504.598307933365
Trimmed Mean ( 18 / 19 )109.5786363636360.20886344205296524.642490263333
Trimmed Mean ( 19 / 19 )109.5510.197149288878411555.675349493976
Median109.455
Midrange111.01
Midmean - Weighted Average at Xnp109.59
Midmean - Weighted Average at X(n+1)p109.683
Midmean - Empirical Distribution Function109.683
Midmean - Empirical Distribution Function - Averaging109.683
Midmean - Empirical Distribution Function - Interpolation109.650357142857
Midmean - Closest Observation109.683
Midmean - True Basic - Statistics Graphics Toolkit109.683
Midmean - MS Excel (old versions)109.683
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.103275862069 & 0.411063601169398 & 267.849733104186 \tabularnewline
Geometric Mean & 110.059868986926 &  &  \tabularnewline
Harmonic Mean & 110.016801234123 &  &  \tabularnewline
Quadratic Mean & 110.147005555115 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 110.101034482759 & 0.406166003157207 & 271.073978685863 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 110.070344827586 & 0.394707727681412 & 278.865441713442 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 110.076551724138 & 0.391940088243318 & 280.850454000515 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 110.078620689655 & 0.389686958321077 & 282.479611747636 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 110.079482758621 & 0.386870611547943 & 284.538239589127 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 110.072241379310 & 0.384925259918256 & 285.95743860168 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 110.085517241379 & 0.379957266073399 & 289.731312100012 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 110.088275862069 & 0.375884690484053 & 292.877785791969 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 110.074310344828 & 0.372373570148647 & 295.601834203452 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 110.095 & 0.352051136945761 & 312.724455188911 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 110.074137931034 & 0.346400821313722 & 317.765233678082 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 109.852758620690 & 0.298197224299223 & 368.389608182466 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 109.850517241379 & 0.290080659497920 & 378.689559764211 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 109.903620689655 & 0.243309593469722 & 451.702783775896 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 109.862241379310 & 0.227729666832592 & 482.423932320033 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 109.751896551724 & 0.206418404184313 & 531.696274784325 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 109.728448275862 & 0.194440080880671 & 564.330398233085 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 109.750172413793 & 0.186583653768378 & 588.20893576259 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 109.573275862069 & 0.144520691822500 & 758.183997601167 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 110.070892857143 & 0.398241938210583 & 276.392017756150 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 110.038518518519 & 0.388268064570828 & 283.408625533366 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 110.020769230769 & 0.383288329001624 & 287.044402101539 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 109.9992 & 0.378020714258046 & 290.987228612324 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 109.975208333333 & 0.371885528885257 & 295.723279857081 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 109.948913043478 & 0.364674194906908 & 301.499021809167 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 109.921818181818 & 0.355673329336927 & 309.052743388835 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 109.889523809524 & 0.345106987801097 & 318.421613279123 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 109.8535 & 0.332046982696649 & 330.837217998032 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 109.816052631579 & 0.315333944206686 & 348.253192049632 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 109.771111111111 & 0.298525949465719 & 367.710449652942 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 109.724117647059 & 0.276651778151161 & 396.614539694395 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 109.7046875 & 0.262662769955634 & 417.663635841997 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 109.683 & 0.244940128738977 & 447.795143101622 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 109.650357142857 & 0.234896961618228 & 466.801938975562 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 109.618846153846 & 0.224858469622442 & 487.501521903561 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 109.59875 & 0.217199995079003 & 504.598307933365 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 109.578636363636 & 0.20886344205296 & 524.642490263333 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 109.551 & 0.197149288878411 & 555.675349493976 \tabularnewline
Median & 109.455 &  &  \tabularnewline
Midrange & 111.01 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.59 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.683 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.683 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.683 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.650357142857 &  &  \tabularnewline
Midmean - Closest Observation & 109.683 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.683 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.683 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96116&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]110.103275862069[/C][C]0.411063601169398[/C][C]267.849733104186[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.059868986926[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.016801234123[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.147005555115[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]110.101034482759[/C][C]0.406166003157207[/C][C]271.073978685863[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]110.070344827586[/C][C]0.394707727681412[/C][C]278.865441713442[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]110.076551724138[/C][C]0.391940088243318[/C][C]280.850454000515[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]110.078620689655[/C][C]0.389686958321077[/C][C]282.479611747636[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]110.079482758621[/C][C]0.386870611547943[/C][C]284.538239589127[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]110.072241379310[/C][C]0.384925259918256[/C][C]285.95743860168[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]110.085517241379[/C][C]0.379957266073399[/C][C]289.731312100012[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]110.088275862069[/C][C]0.375884690484053[/C][C]292.877785791969[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]110.074310344828[/C][C]0.372373570148647[/C][C]295.601834203452[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]110.095[/C][C]0.352051136945761[/C][C]312.724455188911[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]110.074137931034[/C][C]0.346400821313722[/C][C]317.765233678082[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]109.852758620690[/C][C]0.298197224299223[/C][C]368.389608182466[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]109.850517241379[/C][C]0.290080659497920[/C][C]378.689559764211[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]109.903620689655[/C][C]0.243309593469722[/C][C]451.702783775896[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]109.862241379310[/C][C]0.227729666832592[/C][C]482.423932320033[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]109.751896551724[/C][C]0.206418404184313[/C][C]531.696274784325[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]109.728448275862[/C][C]0.194440080880671[/C][C]564.330398233085[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]109.750172413793[/C][C]0.186583653768378[/C][C]588.20893576259[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]109.573275862069[/C][C]0.144520691822500[/C][C]758.183997601167[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]110.070892857143[/C][C]0.398241938210583[/C][C]276.392017756150[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]110.038518518519[/C][C]0.388268064570828[/C][C]283.408625533366[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]110.020769230769[/C][C]0.383288329001624[/C][C]287.044402101539[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]109.9992[/C][C]0.378020714258046[/C][C]290.987228612324[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]109.975208333333[/C][C]0.371885528885257[/C][C]295.723279857081[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]109.948913043478[/C][C]0.364674194906908[/C][C]301.499021809167[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]109.921818181818[/C][C]0.355673329336927[/C][C]309.052743388835[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]109.889523809524[/C][C]0.345106987801097[/C][C]318.421613279123[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]109.8535[/C][C]0.332046982696649[/C][C]330.837217998032[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]109.816052631579[/C][C]0.315333944206686[/C][C]348.253192049632[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]109.771111111111[/C][C]0.298525949465719[/C][C]367.710449652942[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]109.724117647059[/C][C]0.276651778151161[/C][C]396.614539694395[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]109.7046875[/C][C]0.262662769955634[/C][C]417.663635841997[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]109.683[/C][C]0.244940128738977[/C][C]447.795143101622[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]109.650357142857[/C][C]0.234896961618228[/C][C]466.801938975562[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]109.618846153846[/C][C]0.224858469622442[/C][C]487.501521903561[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]109.59875[/C][C]0.217199995079003[/C][C]504.598307933365[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]109.578636363636[/C][C]0.20886344205296[/C][C]524.642490263333[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]109.551[/C][C]0.197149288878411[/C][C]555.675349493976[/C][/ROW]
[ROW][C]Median[/C][C]109.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.650357142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.683[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96116&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 Mean110.1032758620690.411063601169398267.849733104186
Geometric Mean110.059868986926
Harmonic Mean110.016801234123
Quadratic Mean110.147005555115
Winsorized Mean ( 1 / 19 )110.1010344827590.406166003157207271.073978685863
Winsorized Mean ( 2 / 19 )110.0703448275860.394707727681412278.865441713442
Winsorized Mean ( 3 / 19 )110.0765517241380.391940088243318280.850454000515
Winsorized Mean ( 4 / 19 )110.0786206896550.389686958321077282.479611747636
Winsorized Mean ( 5 / 19 )110.0794827586210.386870611547943284.538239589127
Winsorized Mean ( 6 / 19 )110.0722413793100.384925259918256285.95743860168
Winsorized Mean ( 7 / 19 )110.0855172413790.379957266073399289.731312100012
Winsorized Mean ( 8 / 19 )110.0882758620690.375884690484053292.877785791969
Winsorized Mean ( 9 / 19 )110.0743103448280.372373570148647295.601834203452
Winsorized Mean ( 10 / 19 )110.0950.352051136945761312.724455188911
Winsorized Mean ( 11 / 19 )110.0741379310340.346400821313722317.765233678082
Winsorized Mean ( 12 / 19 )109.8527586206900.298197224299223368.389608182466
Winsorized Mean ( 13 / 19 )109.8505172413790.290080659497920378.689559764211
Winsorized Mean ( 14 / 19 )109.9036206896550.243309593469722451.702783775896
Winsorized Mean ( 15 / 19 )109.8622413793100.227729666832592482.423932320033
Winsorized Mean ( 16 / 19 )109.7518965517240.206418404184313531.696274784325
Winsorized Mean ( 17 / 19 )109.7284482758620.194440080880671564.330398233085
Winsorized Mean ( 18 / 19 )109.7501724137930.186583653768378588.20893576259
Winsorized Mean ( 19 / 19 )109.5732758620690.144520691822500758.183997601167
Trimmed Mean ( 1 / 19 )110.0708928571430.398241938210583276.392017756150
Trimmed Mean ( 2 / 19 )110.0385185185190.388268064570828283.408625533366
Trimmed Mean ( 3 / 19 )110.0207692307690.383288329001624287.044402101539
Trimmed Mean ( 4 / 19 )109.99920.378020714258046290.987228612324
Trimmed Mean ( 5 / 19 )109.9752083333330.371885528885257295.723279857081
Trimmed Mean ( 6 / 19 )109.9489130434780.364674194906908301.499021809167
Trimmed Mean ( 7 / 19 )109.9218181818180.355673329336927309.052743388835
Trimmed Mean ( 8 / 19 )109.8895238095240.345106987801097318.421613279123
Trimmed Mean ( 9 / 19 )109.85350.332046982696649330.837217998032
Trimmed Mean ( 10 / 19 )109.8160526315790.315333944206686348.253192049632
Trimmed Mean ( 11 / 19 )109.7711111111110.298525949465719367.710449652942
Trimmed Mean ( 12 / 19 )109.7241176470590.276651778151161396.614539694395
Trimmed Mean ( 13 / 19 )109.70468750.262662769955634417.663635841997
Trimmed Mean ( 14 / 19 )109.6830.244940128738977447.795143101622
Trimmed Mean ( 15 / 19 )109.6503571428570.234896961618228466.801938975562
Trimmed Mean ( 16 / 19 )109.6188461538460.224858469622442487.501521903561
Trimmed Mean ( 17 / 19 )109.598750.217199995079003504.598307933365
Trimmed Mean ( 18 / 19 )109.5786363636360.20886344205296524.642490263333
Trimmed Mean ( 19 / 19 )109.5510.197149288878411555.675349493976
Median109.455
Midrange111.01
Midmean - Weighted Average at Xnp109.59
Midmean - Weighted Average at X(n+1)p109.683
Midmean - Empirical Distribution Function109.683
Midmean - Empirical Distribution Function - Averaging109.683
Midmean - Empirical Distribution Function - Interpolation109.650357142857
Midmean - Closest Observation109.683
Midmean - True Basic - Statistics Graphics Toolkit109.683
Midmean - MS Excel (old versions)109.683
Number of observations58



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')