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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 11:23:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318865040umo24wgdxbw6tx3.htm/, Retrieved Wed, 15 May 2024 03:59:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130594, Retrieved Wed, 15 May 2024 03:59:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde consum...] [2011-10-17 15:23:29] [ba82c27af75bb26243060ecfbd0283aa] [Current]
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Dataseries X:
6,19
6,31
6,35
6,38
6,38
6,36
6,34
6,49
6,5
6,5
6,55
6,57
6,65
6,61
6,66
6,73
6,73
6,75
6,75
6,71
6,77
6,83
6,9
6,89
7,14
7,35
7,43
7,42
7,41
7,46
7,47
7,45
7,47
7,44
7,43
7,43
7,44
7,49
7,48
7,43
7,33
7,42
7,98
7,41
7,25
7,04
6,98
6,94
6,9
6,92
6,86
6,86
6,89
6,91
6,9
6,88
6,78
6,79
6,81
6,78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130594&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130594&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.95450.0524535980034051132.583850578726
Geometric Mean6.94288339784279
Harmonic Mean6.93132814546375
Quadratic Mean6.96616118580863
Winsorized Mean ( 1 / 20 )6.948333333333330.0498688487090196139.332138463357
Winsorized Mean ( 2 / 20 )6.9490.0495953683822567140.113890201208
Winsorized Mean ( 3 / 20 )6.9490.0494019030260867140.662597477886
Winsorized Mean ( 4 / 20 )6.949666666666670.049265776770783141.064794309468
Winsorized Mean ( 5 / 20 )6.95050.0487831735601413142.477405481446
Winsorized Mean ( 6 / 20 )6.94950.0486074004502511142.972056428171
Winsorized Mean ( 7 / 20 )6.961166666666670.0460103719986059151.295596281586
Winsorized Mean ( 8 / 20 )6.96250.0457805037081727152.084390429218
Winsorized Mean ( 9 / 20 )6.9610.0455169304814371152.932105183122
Winsorized Mean ( 10 / 20 )6.969333333333330.0441299228886926157.927611859006
Winsorized Mean ( 11 / 20 )6.9730.0435470393111674160.125696495096
Winsorized Mean ( 12 / 20 )6.9810.0423248801560735164.938446943204
Winsorized Mean ( 13 / 20 )6.98750.0406810836258297171.762877908282
Winsorized Mean ( 14 / 20 )6.989833333333330.040355406716128173.206861288796
Winsorized Mean ( 15 / 20 )6.999833333333330.0382317433013049183.089567173737
Winsorized Mean ( 16 / 20 )7.005166666666670.0375578586920126186.516668165548
Winsorized Mean ( 17 / 20 )6.988166666666670.0344918656312895202.603325125079
Winsorized Mean ( 18 / 20 )6.988166666666670.0326749888511358213.868983965201
Winsorized Mean ( 19 / 20 )6.962833333333330.0282413845336352246.547166447901
Winsorized Mean ( 20 / 20 )6.932833333333330.0211639973404717327.576743740925
Trimmed Mean ( 1 / 20 )6.950.0495063348772908140.386074170642
Trimmed Mean ( 2 / 20 )6.951785714285710.0490203424132818141.814303451339
Trimmed Mean ( 3 / 20 )6.953333333333330.0485563782917982143.201234893333
Trimmed Mean ( 4 / 20 )6.9550.0480254928532848144.818919844241
Trimmed Mean ( 5 / 20 )6.95660.0473688177808902146.860325545352
Trimmed Mean ( 6 / 20 )6.9581250.0466584240282654149.129018926674
Trimmed Mean ( 7 / 20 )6.960.0457624616749441152.089720379067
Trimmed Mean ( 8 / 20 )6.959772727272730.0453066701383322153.61474824839
Trimmed Mean ( 9 / 20 )6.959285714285710.0447062847906679155.666831785996
Trimmed Mean ( 10 / 20 )6.9590.0439197987011406158.447902900322
Trimmed Mean ( 11 / 20 )6.957368421052630.0431670878041553161.17298559999
Trimmed Mean ( 12 / 20 )6.9550.0422229532100465164.720832420247
Trimmed Mean ( 13 / 20 )6.951176470588240.0411634815265573168.8675547549
Trimmed Mean ( 14 / 20 )6.94593750.0400323945814814173.50791958903
Trimmed Mean ( 15 / 20 )6.939666666666670.0383884660998836180.77478398356
Trimmed Mean ( 16 / 20 )6.931071428571430.0364798244076545189.997390094814
Trimmed Mean ( 17 / 20 )6.920384615384620.0335879134361467206.037943635315
Trimmed Mean ( 18 / 20 )6.910416666666670.0303987936370734227.325358669462
Trimmed Mean ( 19 / 20 )6.898636363636360.0257047459237918268.379869775376
Trimmed Mean ( 20 / 20 )6.88850.0203686420496647338.191421067925
Median6.89
Midrange7.085
Midmean - Weighted Average at Xnp6.93064516129032
Midmean - Weighted Average at X(n+1)p6.93966666666666
Midmean - Empirical Distribution Function6.93064516129032
Midmean - Empirical Distribution Function - Averaging6.93966666666666
Midmean - Empirical Distribution Function - Interpolation6.93966666666666
Midmean - Closest Observation6.93064516129032
Midmean - True Basic - Statistics Graphics Toolkit6.93966666666666
Midmean - MS Excel (old versions)6.96030303030303
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.9545 & 0.0524535980034051 & 132.583850578726 \tabularnewline
Geometric Mean & 6.94288339784279 &  &  \tabularnewline
Harmonic Mean & 6.93132814546375 &  &  \tabularnewline
Quadratic Mean & 6.96616118580863 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.94833333333333 & 0.0498688487090196 & 139.332138463357 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.949 & 0.0495953683822567 & 140.113890201208 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.949 & 0.0494019030260867 & 140.662597477886 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.94966666666667 & 0.049265776770783 & 141.064794309468 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.9505 & 0.0487831735601413 & 142.477405481446 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.9495 & 0.0486074004502511 & 142.972056428171 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.96116666666667 & 0.0460103719986059 & 151.295596281586 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.9625 & 0.0457805037081727 & 152.084390429218 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.961 & 0.0455169304814371 & 152.932105183122 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.96933333333333 & 0.0441299228886926 & 157.927611859006 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.973 & 0.0435470393111674 & 160.125696495096 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.981 & 0.0423248801560735 & 164.938446943204 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.9875 & 0.0406810836258297 & 171.762877908282 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.98983333333333 & 0.040355406716128 & 173.206861288796 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.99983333333333 & 0.0382317433013049 & 183.089567173737 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.00516666666667 & 0.0375578586920126 & 186.516668165548 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6.98816666666667 & 0.0344918656312895 & 202.603325125079 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6.98816666666667 & 0.0326749888511358 & 213.868983965201 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.96283333333333 & 0.0282413845336352 & 246.547166447901 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6.93283333333333 & 0.0211639973404717 & 327.576743740925 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.95 & 0.0495063348772908 & 140.386074170642 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.95178571428571 & 0.0490203424132818 & 141.814303451339 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.95333333333333 & 0.0485563782917982 & 143.201234893333 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.955 & 0.0480254928532848 & 144.818919844241 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.9566 & 0.0473688177808902 & 146.860325545352 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.958125 & 0.0466584240282654 & 149.129018926674 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.96 & 0.0457624616749441 & 152.089720379067 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.95977272727273 & 0.0453066701383322 & 153.61474824839 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.95928571428571 & 0.0447062847906679 & 155.666831785996 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.959 & 0.0439197987011406 & 158.447902900322 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.95736842105263 & 0.0431670878041553 & 161.17298559999 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.955 & 0.0422229532100465 & 164.720832420247 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.95117647058824 & 0.0411634815265573 & 168.8675547549 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6.9459375 & 0.0400323945814814 & 173.50791958903 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6.93966666666667 & 0.0383884660998836 & 180.77478398356 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6.93107142857143 & 0.0364798244076545 & 189.997390094814 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6.92038461538462 & 0.0335879134361467 & 206.037943635315 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6.91041666666667 & 0.0303987936370734 & 227.325358669462 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6.89863636363636 & 0.0257047459237918 & 268.379869775376 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6.8885 & 0.0203686420496647 & 338.191421067925 \tabularnewline
Median & 6.89 &  &  \tabularnewline
Midrange & 7.085 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.93064516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.93966666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.93064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.93966666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.93966666666666 &  &  \tabularnewline
Midmean - Closest Observation & 6.93064516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.93966666666666 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.96030303030303 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130594&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]6.9545[/C][C]0.0524535980034051[/C][C]132.583850578726[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.94288339784279[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.93132814546375[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.96616118580863[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.94833333333333[/C][C]0.0498688487090196[/C][C]139.332138463357[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.949[/C][C]0.0495953683822567[/C][C]140.113890201208[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.949[/C][C]0.0494019030260867[/C][C]140.662597477886[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.94966666666667[/C][C]0.049265776770783[/C][C]141.064794309468[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.9505[/C][C]0.0487831735601413[/C][C]142.477405481446[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.9495[/C][C]0.0486074004502511[/C][C]142.972056428171[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.96116666666667[/C][C]0.0460103719986059[/C][C]151.295596281586[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.9625[/C][C]0.0457805037081727[/C][C]152.084390429218[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.961[/C][C]0.0455169304814371[/C][C]152.932105183122[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.96933333333333[/C][C]0.0441299228886926[/C][C]157.927611859006[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.973[/C][C]0.0435470393111674[/C][C]160.125696495096[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.981[/C][C]0.0423248801560735[/C][C]164.938446943204[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.9875[/C][C]0.0406810836258297[/C][C]171.762877908282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.98983333333333[/C][C]0.040355406716128[/C][C]173.206861288796[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.99983333333333[/C][C]0.0382317433013049[/C][C]183.089567173737[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.00516666666667[/C][C]0.0375578586920126[/C][C]186.516668165548[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6.98816666666667[/C][C]0.0344918656312895[/C][C]202.603325125079[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6.98816666666667[/C][C]0.0326749888511358[/C][C]213.868983965201[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.96283333333333[/C][C]0.0282413845336352[/C][C]246.547166447901[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6.93283333333333[/C][C]0.0211639973404717[/C][C]327.576743740925[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.95[/C][C]0.0495063348772908[/C][C]140.386074170642[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.95178571428571[/C][C]0.0490203424132818[/C][C]141.814303451339[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.95333333333333[/C][C]0.0485563782917982[/C][C]143.201234893333[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.955[/C][C]0.0480254928532848[/C][C]144.818919844241[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.9566[/C][C]0.0473688177808902[/C][C]146.860325545352[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.958125[/C][C]0.0466584240282654[/C][C]149.129018926674[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.96[/C][C]0.0457624616749441[/C][C]152.089720379067[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.95977272727273[/C][C]0.0453066701383322[/C][C]153.61474824839[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.95928571428571[/C][C]0.0447062847906679[/C][C]155.666831785996[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.959[/C][C]0.0439197987011406[/C][C]158.447902900322[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.95736842105263[/C][C]0.0431670878041553[/C][C]161.17298559999[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.955[/C][C]0.0422229532100465[/C][C]164.720832420247[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.95117647058824[/C][C]0.0411634815265573[/C][C]168.8675547549[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6.9459375[/C][C]0.0400323945814814[/C][C]173.50791958903[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6.93966666666667[/C][C]0.0383884660998836[/C][C]180.77478398356[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6.93107142857143[/C][C]0.0364798244076545[/C][C]189.997390094814[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6.92038461538462[/C][C]0.0335879134361467[/C][C]206.037943635315[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6.91041666666667[/C][C]0.0303987936370734[/C][C]227.325358669462[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6.89863636363636[/C][C]0.0257047459237918[/C][C]268.379869775376[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6.8885[/C][C]0.0203686420496647[/C][C]338.191421067925[/C][/ROW]
[ROW][C]Median[/C][C]6.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.93064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.93966666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.93064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.93966666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.93966666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.93064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.93966666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.96030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130594&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 Mean6.95450.0524535980034051132.583850578726
Geometric Mean6.94288339784279
Harmonic Mean6.93132814546375
Quadratic Mean6.96616118580863
Winsorized Mean ( 1 / 20 )6.948333333333330.0498688487090196139.332138463357
Winsorized Mean ( 2 / 20 )6.9490.0495953683822567140.113890201208
Winsorized Mean ( 3 / 20 )6.9490.0494019030260867140.662597477886
Winsorized Mean ( 4 / 20 )6.949666666666670.049265776770783141.064794309468
Winsorized Mean ( 5 / 20 )6.95050.0487831735601413142.477405481446
Winsorized Mean ( 6 / 20 )6.94950.0486074004502511142.972056428171
Winsorized Mean ( 7 / 20 )6.961166666666670.0460103719986059151.295596281586
Winsorized Mean ( 8 / 20 )6.96250.0457805037081727152.084390429218
Winsorized Mean ( 9 / 20 )6.9610.0455169304814371152.932105183122
Winsorized Mean ( 10 / 20 )6.969333333333330.0441299228886926157.927611859006
Winsorized Mean ( 11 / 20 )6.9730.0435470393111674160.125696495096
Winsorized Mean ( 12 / 20 )6.9810.0423248801560735164.938446943204
Winsorized Mean ( 13 / 20 )6.98750.0406810836258297171.762877908282
Winsorized Mean ( 14 / 20 )6.989833333333330.040355406716128173.206861288796
Winsorized Mean ( 15 / 20 )6.999833333333330.0382317433013049183.089567173737
Winsorized Mean ( 16 / 20 )7.005166666666670.0375578586920126186.516668165548
Winsorized Mean ( 17 / 20 )6.988166666666670.0344918656312895202.603325125079
Winsorized Mean ( 18 / 20 )6.988166666666670.0326749888511358213.868983965201
Winsorized Mean ( 19 / 20 )6.962833333333330.0282413845336352246.547166447901
Winsorized Mean ( 20 / 20 )6.932833333333330.0211639973404717327.576743740925
Trimmed Mean ( 1 / 20 )6.950.0495063348772908140.386074170642
Trimmed Mean ( 2 / 20 )6.951785714285710.0490203424132818141.814303451339
Trimmed Mean ( 3 / 20 )6.953333333333330.0485563782917982143.201234893333
Trimmed Mean ( 4 / 20 )6.9550.0480254928532848144.818919844241
Trimmed Mean ( 5 / 20 )6.95660.0473688177808902146.860325545352
Trimmed Mean ( 6 / 20 )6.9581250.0466584240282654149.129018926674
Trimmed Mean ( 7 / 20 )6.960.0457624616749441152.089720379067
Trimmed Mean ( 8 / 20 )6.959772727272730.0453066701383322153.61474824839
Trimmed Mean ( 9 / 20 )6.959285714285710.0447062847906679155.666831785996
Trimmed Mean ( 10 / 20 )6.9590.0439197987011406158.447902900322
Trimmed Mean ( 11 / 20 )6.957368421052630.0431670878041553161.17298559999
Trimmed Mean ( 12 / 20 )6.9550.0422229532100465164.720832420247
Trimmed Mean ( 13 / 20 )6.951176470588240.0411634815265573168.8675547549
Trimmed Mean ( 14 / 20 )6.94593750.0400323945814814173.50791958903
Trimmed Mean ( 15 / 20 )6.939666666666670.0383884660998836180.77478398356
Trimmed Mean ( 16 / 20 )6.931071428571430.0364798244076545189.997390094814
Trimmed Mean ( 17 / 20 )6.920384615384620.0335879134361467206.037943635315
Trimmed Mean ( 18 / 20 )6.910416666666670.0303987936370734227.325358669462
Trimmed Mean ( 19 / 20 )6.898636363636360.0257047459237918268.379869775376
Trimmed Mean ( 20 / 20 )6.88850.0203686420496647338.191421067925
Median6.89
Midrange7.085
Midmean - Weighted Average at Xnp6.93064516129032
Midmean - Weighted Average at X(n+1)p6.93966666666666
Midmean - Empirical Distribution Function6.93064516129032
Midmean - Empirical Distribution Function - Averaging6.93966666666666
Midmean - Empirical Distribution Function - Interpolation6.93966666666666
Midmean - Closest Observation6.93064516129032
Midmean - True Basic - Statistics Graphics Toolkit6.93966666666666
Midmean - MS Excel (old versions)6.96030303030303
Number of observations60



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')