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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 computationSun, 18 Oct 2009 07:59:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255874507l9hmxoeqwrx3phc.htm/, Retrieved Mon, 29 Apr 2024 14:05:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47305, Retrieved Mon, 29 Apr 2024 14:05:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Percentiles] [Percentielen] [2009-10-18 13:47:08] [03557919bc1ce1475f4920f6a43c36b0]
- RM D          [Central Tendency] [Central tendency] [2009-10-18 13:59:56] [e7a989b306049c061a54f626f1127c12] [Current]
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Post a new message
Dataseries X:
65.35
55.81
55.40
61.89
40.07
47.30
58.00
54.75
47.61
41.43
46.33
48.74
42.22
44.11
39.34
38.37
52.45
48.17
41.43
42.57
45.18
58.09
50.50
50.11
54.92
59.58
58.48
73.63
93.71
85.20
83.33
103.41
100.50
100.17
94.22
132.54
142.15
136.69
153.83
151.00
97.86
74.45
78.94
74.09
80.28
70.66
78.29
61.78
57.45
53.24
52.72
49.80
45.00
61.38
70.70
98.29
103.32
332.50
284.14
-1072.00




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=47305&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=47305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47305&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 Mean59.191166666666720.31423043993452.91377843929083
Geometric MeanNaN
Harmonic Mean64.1905418315684
Quadratic Mean166.886200013662
Winsorized Mean ( 1 / 20 )76.89133333333336.2615124094330412.2799937627682
Winsorized Mean ( 2 / 20 )72.584.2340896539563417.1418193594888
Winsorized Mean ( 3 / 20 )72.4754.1837441500400517.3230000212384
Winsorized Mean ( 4 / 20 )71.97566666666673.9899854676446018.0390799040068
Winsorized Mean ( 5 / 20 )71.52066666666673.8569718726437918.5432170698311
Winsorized Mean ( 6 / 20 )71.18466666666673.7292353502496719.0882741315591
Winsorized Mean ( 7 / 20 )67.8272.8785165798662623.5631785046558
Winsorized Mean ( 8 / 20 )68.02033333333332.8461074216803323.8994258667771
Winsorized Mean ( 9 / 20 )67.73083333333332.7398490854112124.7206438099010
Winsorized Mean ( 10 / 20 )67.70583333333332.7245092057026724.8506531714477
Winsorized Mean ( 11 / 20 )67.5722.6262997406396025.7289748593372
Winsorized Mean ( 12 / 20 )67.682.5829876058067726.2022163202989
Winsorized Mean ( 13 / 20 )66.95852.4204882757282427.6632201326629
Winsorized Mean ( 14 / 20 )66.97016666666672.3802012744458928.1363460248787
Winsorized Mean ( 15 / 20 )64.98516666666671.9716899529884632.9591204581479
Winsorized Mean ( 16 / 20 )64.76916666666671.8466953121184835.0730119049066
Winsorized Mean ( 17 / 20 )63.99283333333331.6902416016196037.8601693817116
Winsorized Mean ( 18 / 20 )63.70783333333331.6088616021573839.5980818038700
Winsorized Mean ( 19 / 20 )64.11951.4918075795892042.9810793813347
Winsorized Mean ( 20 / 20 )62.92951.2785738308601749.2185108760311
Trimmed Mean ( 1 / 20 )73.98224137931035.3284270292796913.8844430021802
Trimmed Mean ( 2 / 20 )70.86535714285713.9430130377495217.9723872237825
Trimmed Mean ( 3 / 20 )69.91277777777783.7366049364629918.7102407042142
Trimmed Mean ( 4 / 20 )68.92730769230773.4976632267726119.7066736341877
Trimmed Mean ( 5 / 20 )68.01283.2753970818942920.7647495248624
Trimmed Mean ( 6 / 20 )67.13583333333333.0381757899461122.0974156780191
Trimmed Mean ( 7 / 20 )66.2556521739132.7706095991558823.9137452617284
Trimmed Mean ( 8 / 20 )65.94954545454552.7148012583932424.2925868885068
Trimmed Mean ( 9 / 20 )65.57976190476192.6469644149819324.7754603475505
Trimmed Mean ( 10 / 20 )65.221252.5840940283038025.2395033948556
Trimmed Mean ( 11 / 20 )64.8289473684212.5000782858147725.9307669428813
Trimmed Mean ( 12 / 20 )64.41333333333332.4102918877445126.7242874860313
Trimmed Mean ( 13 / 20 )63.93294117647062.2932487727984327.8787639329918
Trimmed Mean ( 14 / 20 )63.49656252.1791600746439829.1380900553502
Trimmed Mean ( 15 / 20 )63.00033333333332.0216091509950631.1634587241177
Trimmed Mean ( 16 / 20 )62.71678571428571.9440496007435532.2608979165439
Trimmed Mean ( 17 / 20 )62.42076923076921.8659484635538733.4525687338026
Trimmed Mean ( 18 / 20 )62.18958333333331.8014469304357334.5220179860036
Trimmed Mean ( 19 / 20 )61.95954545454551.7238896266022435.9417125658252
Trimmed Mean ( 20 / 20 )61.61851.6331500519258137.7298460281342
Median59.03
Midrange-369.75
Midmean - Weighted Average at Xnp62.521935483871
Midmean - Weighted Average at X(n+1)p63.0003333333333
Midmean - Empirical Distribution Function62.521935483871
Midmean - Empirical Distribution Function - Averaging63.0003333333333
Midmean - Empirical Distribution Function - Interpolation63.0003333333333
Midmean - Closest Observation62.521935483871
Midmean - True Basic - Statistics Graphics Toolkit63.0003333333333
Midmean - MS Excel (old versions)63.4965625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 59.1911666666667 & 20.3142304399345 & 2.91377843929083 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 64.1905418315684 &  &  \tabularnewline
Quadratic Mean & 166.886200013662 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 76.8913333333333 & 6.26151240943304 & 12.2799937627682 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 72.58 & 4.23408965395634 & 17.1418193594888 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 72.475 & 4.18374415004005 & 17.3230000212384 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 71.9756666666667 & 3.98998546764460 & 18.0390799040068 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 71.5206666666667 & 3.85697187264379 & 18.5432170698311 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 71.1846666666667 & 3.72923535024967 & 19.0882741315591 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 67.827 & 2.87851657986626 & 23.5631785046558 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 68.0203333333333 & 2.84610742168033 & 23.8994258667771 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 67.7308333333333 & 2.73984908541121 & 24.7206438099010 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 67.7058333333333 & 2.72450920570267 & 24.8506531714477 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 67.572 & 2.62629974063960 & 25.7289748593372 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 67.68 & 2.58298760580677 & 26.2022163202989 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 66.9585 & 2.42048827572824 & 27.6632201326629 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 66.9701666666667 & 2.38020127444589 & 28.1363460248787 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 64.9851666666667 & 1.97168995298846 & 32.9591204581479 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 64.7691666666667 & 1.84669531211848 & 35.0730119049066 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 63.9928333333333 & 1.69024160161960 & 37.8601693817116 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 63.7078333333333 & 1.60886160215738 & 39.5980818038700 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 64.1195 & 1.49180757958920 & 42.9810793813347 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 62.9295 & 1.27857383086017 & 49.2185108760311 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 73.9822413793103 & 5.32842702927969 & 13.8844430021802 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 70.8653571428571 & 3.94301303774952 & 17.9723872237825 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 69.9127777777778 & 3.73660493646299 & 18.7102407042142 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 68.9273076923077 & 3.49766322677261 & 19.7066736341877 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 68.0128 & 3.27539708189429 & 20.7647495248624 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 67.1358333333333 & 3.03817578994611 & 22.0974156780191 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 66.255652173913 & 2.77060959915588 & 23.9137452617284 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 65.9495454545455 & 2.71480125839324 & 24.2925868885068 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 65.5797619047619 & 2.64696441498193 & 24.7754603475505 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 65.22125 & 2.58409402830380 & 25.2395033948556 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 64.828947368421 & 2.50007828581477 & 25.9307669428813 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 64.4133333333333 & 2.41029188774451 & 26.7242874860313 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 63.9329411764706 & 2.29324877279843 & 27.8787639329918 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 63.4965625 & 2.17916007464398 & 29.1380900553502 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 63.0003333333333 & 2.02160915099506 & 31.1634587241177 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 62.7167857142857 & 1.94404960074355 & 32.2608979165439 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 62.4207692307692 & 1.86594846355387 & 33.4525687338026 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 62.1895833333333 & 1.80144693043573 & 34.5220179860036 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 61.9595454545455 & 1.72388962660224 & 35.9417125658252 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 61.6185 & 1.63315005192581 & 37.7298460281342 \tabularnewline
Median & 59.03 &  &  \tabularnewline
Midrange & -369.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 62.521935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 63.0003333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 62.521935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 63.0003333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 63.0003333333333 &  &  \tabularnewline
Midmean - Closest Observation & 62.521935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 63.0003333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 63.4965625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47305&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]59.1911666666667[/C][C]20.3142304399345[/C][C]2.91377843929083[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.1905418315684[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]166.886200013662[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]76.8913333333333[/C][C]6.26151240943304[/C][C]12.2799937627682[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]72.58[/C][C]4.23408965395634[/C][C]17.1418193594888[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]72.475[/C][C]4.18374415004005[/C][C]17.3230000212384[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]71.9756666666667[/C][C]3.98998546764460[/C][C]18.0390799040068[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]71.5206666666667[/C][C]3.85697187264379[/C][C]18.5432170698311[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]71.1846666666667[/C][C]3.72923535024967[/C][C]19.0882741315591[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]67.827[/C][C]2.87851657986626[/C][C]23.5631785046558[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]68.0203333333333[/C][C]2.84610742168033[/C][C]23.8994258667771[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]67.7308333333333[/C][C]2.73984908541121[/C][C]24.7206438099010[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]67.7058333333333[/C][C]2.72450920570267[/C][C]24.8506531714477[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]67.572[/C][C]2.62629974063960[/C][C]25.7289748593372[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]67.68[/C][C]2.58298760580677[/C][C]26.2022163202989[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]66.9585[/C][C]2.42048827572824[/C][C]27.6632201326629[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]66.9701666666667[/C][C]2.38020127444589[/C][C]28.1363460248787[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]64.9851666666667[/C][C]1.97168995298846[/C][C]32.9591204581479[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]64.7691666666667[/C][C]1.84669531211848[/C][C]35.0730119049066[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]63.9928333333333[/C][C]1.69024160161960[/C][C]37.8601693817116[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]63.7078333333333[/C][C]1.60886160215738[/C][C]39.5980818038700[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]64.1195[/C][C]1.49180757958920[/C][C]42.9810793813347[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]62.9295[/C][C]1.27857383086017[/C][C]49.2185108760311[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]73.9822413793103[/C][C]5.32842702927969[/C][C]13.8844430021802[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]70.8653571428571[/C][C]3.94301303774952[/C][C]17.9723872237825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]69.9127777777778[/C][C]3.73660493646299[/C][C]18.7102407042142[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]68.9273076923077[/C][C]3.49766322677261[/C][C]19.7066736341877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]68.0128[/C][C]3.27539708189429[/C][C]20.7647495248624[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]67.1358333333333[/C][C]3.03817578994611[/C][C]22.0974156780191[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]66.255652173913[/C][C]2.77060959915588[/C][C]23.9137452617284[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]65.9495454545455[/C][C]2.71480125839324[/C][C]24.2925868885068[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]65.5797619047619[/C][C]2.64696441498193[/C][C]24.7754603475505[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]65.22125[/C][C]2.58409402830380[/C][C]25.2395033948556[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]64.828947368421[/C][C]2.50007828581477[/C][C]25.9307669428813[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]64.4133333333333[/C][C]2.41029188774451[/C][C]26.7242874860313[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]63.9329411764706[/C][C]2.29324877279843[/C][C]27.8787639329918[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]63.4965625[/C][C]2.17916007464398[/C][C]29.1380900553502[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]63.0003333333333[/C][C]2.02160915099506[/C][C]31.1634587241177[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]62.7167857142857[/C][C]1.94404960074355[/C][C]32.2608979165439[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]62.4207692307692[/C][C]1.86594846355387[/C][C]33.4525687338026[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]62.1895833333333[/C][C]1.80144693043573[/C][C]34.5220179860036[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]61.9595454545455[/C][C]1.72388962660224[/C][C]35.9417125658252[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]61.6185[/C][C]1.63315005192581[/C][C]37.7298460281342[/C][/ROW]
[ROW][C]Median[/C][C]59.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-369.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]62.521935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]63.0003333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]62.521935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]63.0003333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]63.0003333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]62.521935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]63.0003333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]63.4965625[/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=47305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47305&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 Mean59.191166666666720.31423043993452.91377843929083
Geometric MeanNaN
Harmonic Mean64.1905418315684
Quadratic Mean166.886200013662
Winsorized Mean ( 1 / 20 )76.89133333333336.2615124094330412.2799937627682
Winsorized Mean ( 2 / 20 )72.584.2340896539563417.1418193594888
Winsorized Mean ( 3 / 20 )72.4754.1837441500400517.3230000212384
Winsorized Mean ( 4 / 20 )71.97566666666673.9899854676446018.0390799040068
Winsorized Mean ( 5 / 20 )71.52066666666673.8569718726437918.5432170698311
Winsorized Mean ( 6 / 20 )71.18466666666673.7292353502496719.0882741315591
Winsorized Mean ( 7 / 20 )67.8272.8785165798662623.5631785046558
Winsorized Mean ( 8 / 20 )68.02033333333332.8461074216803323.8994258667771
Winsorized Mean ( 9 / 20 )67.73083333333332.7398490854112124.7206438099010
Winsorized Mean ( 10 / 20 )67.70583333333332.7245092057026724.8506531714477
Winsorized Mean ( 11 / 20 )67.5722.6262997406396025.7289748593372
Winsorized Mean ( 12 / 20 )67.682.5829876058067726.2022163202989
Winsorized Mean ( 13 / 20 )66.95852.4204882757282427.6632201326629
Winsorized Mean ( 14 / 20 )66.97016666666672.3802012744458928.1363460248787
Winsorized Mean ( 15 / 20 )64.98516666666671.9716899529884632.9591204581479
Winsorized Mean ( 16 / 20 )64.76916666666671.8466953121184835.0730119049066
Winsorized Mean ( 17 / 20 )63.99283333333331.6902416016196037.8601693817116
Winsorized Mean ( 18 / 20 )63.70783333333331.6088616021573839.5980818038700
Winsorized Mean ( 19 / 20 )64.11951.4918075795892042.9810793813347
Winsorized Mean ( 20 / 20 )62.92951.2785738308601749.2185108760311
Trimmed Mean ( 1 / 20 )73.98224137931035.3284270292796913.8844430021802
Trimmed Mean ( 2 / 20 )70.86535714285713.9430130377495217.9723872237825
Trimmed Mean ( 3 / 20 )69.91277777777783.7366049364629918.7102407042142
Trimmed Mean ( 4 / 20 )68.92730769230773.4976632267726119.7066736341877
Trimmed Mean ( 5 / 20 )68.01283.2753970818942920.7647495248624
Trimmed Mean ( 6 / 20 )67.13583333333333.0381757899461122.0974156780191
Trimmed Mean ( 7 / 20 )66.2556521739132.7706095991558823.9137452617284
Trimmed Mean ( 8 / 20 )65.94954545454552.7148012583932424.2925868885068
Trimmed Mean ( 9 / 20 )65.57976190476192.6469644149819324.7754603475505
Trimmed Mean ( 10 / 20 )65.221252.5840940283038025.2395033948556
Trimmed Mean ( 11 / 20 )64.8289473684212.5000782858147725.9307669428813
Trimmed Mean ( 12 / 20 )64.41333333333332.4102918877445126.7242874860313
Trimmed Mean ( 13 / 20 )63.93294117647062.2932487727984327.8787639329918
Trimmed Mean ( 14 / 20 )63.49656252.1791600746439829.1380900553502
Trimmed Mean ( 15 / 20 )63.00033333333332.0216091509950631.1634587241177
Trimmed Mean ( 16 / 20 )62.71678571428571.9440496007435532.2608979165439
Trimmed Mean ( 17 / 20 )62.42076923076921.8659484635538733.4525687338026
Trimmed Mean ( 18 / 20 )62.18958333333331.8014469304357334.5220179860036
Trimmed Mean ( 19 / 20 )61.95954545454551.7238896266022435.9417125658252
Trimmed Mean ( 20 / 20 )61.61851.6331500519258137.7298460281342
Median59.03
Midrange-369.75
Midmean - Weighted Average at Xnp62.521935483871
Midmean - Weighted Average at X(n+1)p63.0003333333333
Midmean - Empirical Distribution Function62.521935483871
Midmean - Empirical Distribution Function - Averaging63.0003333333333
Midmean - Empirical Distribution Function - Interpolation63.0003333333333
Midmean - Closest Observation62.521935483871
Midmean - True Basic - Statistics Graphics Toolkit63.0003333333333
Midmean - MS Excel (old versions)63.4965625
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')