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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 16:52:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331157212u2ahlfv3r8cxism.htm/, Retrieved Mon, 29 Apr 2024 03:44:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163723, Retrieved Mon, 29 Apr 2024 03:44:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Eigen reeks centr...] [2012-03-07 21:52:36] [649f27debd29df6d3b5186bbc318d779] [Current]
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Dataseries X:
66,6
71,7
75,4
80,9
80,7
85
91,5
87,7
95,3
102,4
114,2
111,7
113,7
118,8
129
136,4
155
166
168,7
145,5
127,3
91,5
69
54
56,3
54,2
59,3
63,4
73,3
86,7
81,3
89,6
85,3
92,4
96,8
93,6
97,6
94,2
99,9
106,4
96
94,9
94,8
95,9
96,2
103,1
106,9
114,2
118,2
123,9
137,1
146,2
136,4
133,2
135,9
127,1
128,5
126,6
132,6
130,9




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=163723&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=163723&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163723&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 Mean104.1153.5790940565367529.0897635980947
Geometric Mean100.382198520893
Harmonic Mean96.5479430051576
Quadratic Mean107.683416395779
Winsorized Mean ( 1 / 20 )104.0733333333333.5647963838070429.1947483469414
Winsorized Mean ( 2 / 20 )103.7766666666673.4480546932449130.0971637340833
Winsorized Mean ( 3 / 20 )103.4866666666673.3099084824143731.2657184379853
Winsorized Mean ( 4 / 20 )103.7133333333333.2399365853690432.0109145968115
Winsorized Mean ( 5 / 20 )103.283.0417377207086633.9542753133685
Winsorized Mean ( 6 / 20 )103.452.9805380964907634.7084978117879
Winsorized Mean ( 7 / 20 )103.7652.9203569793786635.5316150500468
Winsorized Mean ( 8 / 20 )103.9116666666672.8685948957778736.2238902466181
Winsorized Mean ( 9 / 20 )103.8216666666672.7372272370538237.9295022573331
Winsorized Mean ( 10 / 20 )104.6052.5713319824250240.6812503072229
Winsorized Mean ( 11 / 20 )104.332.508802919799741.5855702241967
Winsorized Mean ( 12 / 20 )104.032.4288988693467942.8301076314375
Winsorized Mean ( 13 / 20 )104.7233333333332.2876200430564545.7782898218597
Winsorized Mean ( 14 / 20 )104.5133333333332.2284593074863246.8993680890782
Winsorized Mean ( 15 / 20 )104.8133333333332.1694247547399248.3138827951187
Winsorized Mean ( 16 / 20 )104.9466666666672.1088587250952949.7646738578586
Winsorized Mean ( 17 / 20 )104.721.9032900447252655.0205158116698
Winsorized Mean ( 18 / 20 )103.761.571812441190966.0129652119215
Winsorized Mean ( 19 / 20 )103.571.5411187146535467.2044268979524
Winsorized Mean ( 20 / 20 )102.5366666666671.2914844230829679.3944277097026
Trimmed Mean ( 1 / 20 )103.8655172413793.4196662220634130.3729985608675
Trimmed Mean ( 2 / 20 )103.6428571428573.2399002481265931.9895210362685
Trimmed Mean ( 3 / 20 )103.5685185185193.0970453493121233.4410726473611
Trimmed Mean ( 4 / 20 )103.62.9877969506646934.6743777139716
Trimmed Mean ( 5 / 20 )103.5662.8786697749949335.97703387155
Trimmed Mean ( 6 / 20 )103.63752.8098147149357636.8841046525623
Trimmed Mean ( 7 / 20 )103.6782608695652.7397625219621837.8420611416029
Trimmed Mean ( 8 / 20 )103.6613636363642.6657232614130438.8867686068114
Trimmed Mean ( 9 / 20 )103.6166666666672.5823800271693540.1244842263766
Trimmed Mean ( 10 / 20 )103.58252.5079460579301141.3017256381862
Trimmed Mean ( 11 / 20 )103.4210526315792.4508632261446142.1978066863682
Trimmed Mean ( 12 / 20 )103.2833333333332.3875487196890643.2591521511587
Trimmed Mean ( 13 / 20 )103.1735294117652.3196952164093944.4771919525984
Trimmed Mean ( 14 / 20 )102.952.25942470553945.5646960695867
Trimmed Mean ( 15 / 20 )102.7266666666672.1862208684905946.9882380811739
Trimmed Mean ( 16 / 20 )102.4285714285712.0908015800562148.9900966240029
Trimmed Mean ( 17 / 20 )102.0653846153851.9612393437093852.0412691815287
Trimmed Mean ( 18 / 20 )101.6751.837809916682155.3240022687218
Trimmed Mean ( 19 / 20 )101.3590909090911.7809800683711956.9119737548717
Trimmed Mean ( 20 / 20 )101.011.6875379138041159.8564329569934
Median97.2
Midrange111.35
Midmean - Weighted Average at Xnp102.164516129032
Midmean - Weighted Average at X(n+1)p102.726666666667
Midmean - Empirical Distribution Function102.164516129032
Midmean - Empirical Distribution Function - Averaging102.726666666667
Midmean - Empirical Distribution Function - Interpolation102.726666666667
Midmean - Closest Observation102.164516129032
Midmean - True Basic - Statistics Graphics Toolkit102.726666666667
Midmean - MS Excel (old versions)102.95
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.115 & 3.57909405653675 & 29.0897635980947 \tabularnewline
Geometric Mean & 100.382198520893 &  &  \tabularnewline
Harmonic Mean & 96.5479430051576 &  &  \tabularnewline
Quadratic Mean & 107.683416395779 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.073333333333 & 3.56479638380704 & 29.1947483469414 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.776666666667 & 3.44805469324491 & 30.0971637340833 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.486666666667 & 3.30990848241437 & 31.2657184379853 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.713333333333 & 3.23993658536904 & 32.0109145968115 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.28 & 3.04173772070866 & 33.9542753133685 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.45 & 2.98053809649076 & 34.7084978117879 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.765 & 2.92035697937866 & 35.5316150500468 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.911666666667 & 2.86859489577787 & 36.2238902466181 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.821666666667 & 2.73722723705382 & 37.9295022573331 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.605 & 2.57133198242502 & 40.6812503072229 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.33 & 2.5088029197997 & 41.5855702241967 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.03 & 2.42889886934679 & 42.8301076314375 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.723333333333 & 2.28762004305645 & 45.7782898218597 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.513333333333 & 2.22845930748632 & 46.8993680890782 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 104.813333333333 & 2.16942475473992 & 48.3138827951187 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 104.946666666667 & 2.10885872509529 & 49.7646738578586 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 104.72 & 1.90329004472526 & 55.0205158116698 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.76 & 1.5718124411909 & 66.0129652119215 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.57 & 1.54111871465354 & 67.2044268979524 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 102.536666666667 & 1.29148442308296 & 79.3944277097026 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.865517241379 & 3.41966622206341 & 30.3729985608675 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.642857142857 & 3.23990024812659 & 31.9895210362685 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.568518518519 & 3.09704534931212 & 33.4410726473611 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.6 & 2.98779695066469 & 34.6743777139716 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.566 & 2.87866977499493 & 35.97703387155 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.6375 & 2.80981471493576 & 36.8841046525623 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.678260869565 & 2.73976252196218 & 37.8420611416029 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.661363636364 & 2.66572326141304 & 38.8867686068114 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.616666666667 & 2.58238002716935 & 40.1244842263766 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.5825 & 2.50794605793011 & 41.3017256381862 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.421052631579 & 2.45086322614461 & 42.1978066863682 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.283333333333 & 2.38754871968906 & 43.2591521511587 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.173529411765 & 2.31969521640939 & 44.4771919525984 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 102.95 & 2.259424705539 & 45.5646960695867 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 102.726666666667 & 2.18622086849059 & 46.9882380811739 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 102.428571428571 & 2.09080158005621 & 48.9900966240029 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 102.065384615385 & 1.96123934370938 & 52.0412691815287 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.675 & 1.8378099166821 & 55.3240022687218 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.359090909091 & 1.78098006837119 & 56.9119737548717 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.01 & 1.68753791380411 & 59.8564329569934 \tabularnewline
Median & 97.2 &  &  \tabularnewline
Midrange & 111.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.164516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.726666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.164516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.726666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.726666666667 &  &  \tabularnewline
Midmean - Closest Observation & 102.164516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.726666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.95 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163723&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]104.115[/C][C]3.57909405653675[/C][C]29.0897635980947[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.382198520893[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.5479430051576[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.683416395779[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.073333333333[/C][C]3.56479638380704[/C][C]29.1947483469414[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.776666666667[/C][C]3.44805469324491[/C][C]30.0971637340833[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.486666666667[/C][C]3.30990848241437[/C][C]31.2657184379853[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.713333333333[/C][C]3.23993658536904[/C][C]32.0109145968115[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.28[/C][C]3.04173772070866[/C][C]33.9542753133685[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.45[/C][C]2.98053809649076[/C][C]34.7084978117879[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.765[/C][C]2.92035697937866[/C][C]35.5316150500468[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.911666666667[/C][C]2.86859489577787[/C][C]36.2238902466181[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.821666666667[/C][C]2.73722723705382[/C][C]37.9295022573331[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.605[/C][C]2.57133198242502[/C][C]40.6812503072229[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.33[/C][C]2.5088029197997[/C][C]41.5855702241967[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.03[/C][C]2.42889886934679[/C][C]42.8301076314375[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.723333333333[/C][C]2.28762004305645[/C][C]45.7782898218597[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.513333333333[/C][C]2.22845930748632[/C][C]46.8993680890782[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]104.813333333333[/C][C]2.16942475473992[/C][C]48.3138827951187[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]104.946666666667[/C][C]2.10885872509529[/C][C]49.7646738578586[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]104.72[/C][C]1.90329004472526[/C][C]55.0205158116698[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.76[/C][C]1.5718124411909[/C][C]66.0129652119215[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.57[/C][C]1.54111871465354[/C][C]67.2044268979524[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]102.536666666667[/C][C]1.29148442308296[/C][C]79.3944277097026[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.865517241379[/C][C]3.41966622206341[/C][C]30.3729985608675[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.642857142857[/C][C]3.23990024812659[/C][C]31.9895210362685[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.568518518519[/C][C]3.09704534931212[/C][C]33.4410726473611[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.6[/C][C]2.98779695066469[/C][C]34.6743777139716[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.566[/C][C]2.87866977499493[/C][C]35.97703387155[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.6375[/C][C]2.80981471493576[/C][C]36.8841046525623[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.678260869565[/C][C]2.73976252196218[/C][C]37.8420611416029[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.661363636364[/C][C]2.66572326141304[/C][C]38.8867686068114[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.616666666667[/C][C]2.58238002716935[/C][C]40.1244842263766[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.5825[/C][C]2.50794605793011[/C][C]41.3017256381862[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.421052631579[/C][C]2.45086322614461[/C][C]42.1978066863682[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.283333333333[/C][C]2.38754871968906[/C][C]43.2591521511587[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.173529411765[/C][C]2.31969521640939[/C][C]44.4771919525984[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]102.95[/C][C]2.259424705539[/C][C]45.5646960695867[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]102.726666666667[/C][C]2.18622086849059[/C][C]46.9882380811739[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]102.428571428571[/C][C]2.09080158005621[/C][C]48.9900966240029[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]102.065384615385[/C][C]1.96123934370938[/C][C]52.0412691815287[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.675[/C][C]1.8378099166821[/C][C]55.3240022687218[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.359090909091[/C][C]1.78098006837119[/C][C]56.9119737548717[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.01[/C][C]1.68753791380411[/C][C]59.8564329569934[/C][/ROW]
[ROW][C]Median[/C][C]97.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.95[/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=163723&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163723&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 Mean104.1153.5790940565367529.0897635980947
Geometric Mean100.382198520893
Harmonic Mean96.5479430051576
Quadratic Mean107.683416395779
Winsorized Mean ( 1 / 20 )104.0733333333333.5647963838070429.1947483469414
Winsorized Mean ( 2 / 20 )103.7766666666673.4480546932449130.0971637340833
Winsorized Mean ( 3 / 20 )103.4866666666673.3099084824143731.2657184379853
Winsorized Mean ( 4 / 20 )103.7133333333333.2399365853690432.0109145968115
Winsorized Mean ( 5 / 20 )103.283.0417377207086633.9542753133685
Winsorized Mean ( 6 / 20 )103.452.9805380964907634.7084978117879
Winsorized Mean ( 7 / 20 )103.7652.9203569793786635.5316150500468
Winsorized Mean ( 8 / 20 )103.9116666666672.8685948957778736.2238902466181
Winsorized Mean ( 9 / 20 )103.8216666666672.7372272370538237.9295022573331
Winsorized Mean ( 10 / 20 )104.6052.5713319824250240.6812503072229
Winsorized Mean ( 11 / 20 )104.332.508802919799741.5855702241967
Winsorized Mean ( 12 / 20 )104.032.4288988693467942.8301076314375
Winsorized Mean ( 13 / 20 )104.7233333333332.2876200430564545.7782898218597
Winsorized Mean ( 14 / 20 )104.5133333333332.2284593074863246.8993680890782
Winsorized Mean ( 15 / 20 )104.8133333333332.1694247547399248.3138827951187
Winsorized Mean ( 16 / 20 )104.9466666666672.1088587250952949.7646738578586
Winsorized Mean ( 17 / 20 )104.721.9032900447252655.0205158116698
Winsorized Mean ( 18 / 20 )103.761.571812441190966.0129652119215
Winsorized Mean ( 19 / 20 )103.571.5411187146535467.2044268979524
Winsorized Mean ( 20 / 20 )102.5366666666671.2914844230829679.3944277097026
Trimmed Mean ( 1 / 20 )103.8655172413793.4196662220634130.3729985608675
Trimmed Mean ( 2 / 20 )103.6428571428573.2399002481265931.9895210362685
Trimmed Mean ( 3 / 20 )103.5685185185193.0970453493121233.4410726473611
Trimmed Mean ( 4 / 20 )103.62.9877969506646934.6743777139716
Trimmed Mean ( 5 / 20 )103.5662.8786697749949335.97703387155
Trimmed Mean ( 6 / 20 )103.63752.8098147149357636.8841046525623
Trimmed Mean ( 7 / 20 )103.6782608695652.7397625219621837.8420611416029
Trimmed Mean ( 8 / 20 )103.6613636363642.6657232614130438.8867686068114
Trimmed Mean ( 9 / 20 )103.6166666666672.5823800271693540.1244842263766
Trimmed Mean ( 10 / 20 )103.58252.5079460579301141.3017256381862
Trimmed Mean ( 11 / 20 )103.4210526315792.4508632261446142.1978066863682
Trimmed Mean ( 12 / 20 )103.2833333333332.3875487196890643.2591521511587
Trimmed Mean ( 13 / 20 )103.1735294117652.3196952164093944.4771919525984
Trimmed Mean ( 14 / 20 )102.952.25942470553945.5646960695867
Trimmed Mean ( 15 / 20 )102.7266666666672.1862208684905946.9882380811739
Trimmed Mean ( 16 / 20 )102.4285714285712.0908015800562148.9900966240029
Trimmed Mean ( 17 / 20 )102.0653846153851.9612393437093852.0412691815287
Trimmed Mean ( 18 / 20 )101.6751.837809916682155.3240022687218
Trimmed Mean ( 19 / 20 )101.3590909090911.7809800683711956.9119737548717
Trimmed Mean ( 20 / 20 )101.011.6875379138041159.8564329569934
Median97.2
Midrange111.35
Midmean - Weighted Average at Xnp102.164516129032
Midmean - Weighted Average at X(n+1)p102.726666666667
Midmean - Empirical Distribution Function102.164516129032
Midmean - Empirical Distribution Function - Averaging102.726666666667
Midmean - Empirical Distribution Function - Interpolation102.726666666667
Midmean - Closest Observation102.164516129032
Midmean - True Basic - Statistics Graphics Toolkit102.726666666667
Midmean - MS Excel (old versions)102.95
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')