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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 16:39:31 -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/20/t1255992053fwui6aku241avp7.htm/, Retrieved Thu, 02 May 2024 19:55:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48298, Retrieved Thu, 02 May 2024 19:55:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS3VR2V1
Estimated Impact118
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        [Central Tendency] [] [2009-10-19 22:39:31] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataseries X:
289,8
292,9
291,2
291,8
289,8
292,5
290,3
297,5
307,5
304,7
304,6
310,7
310,7
315,7
314,7
312,2
312,8
314,3
319,7
319,9
329,5
326,9
329,7
335,7
337,2
339,7
338,3
339,2
342,5
342,2
338,3
339
345,9
351,5
352,8
360,4
371,5
376,3
374,2
374,9
369,8
372
380,7
381,2
376,9
381,9
383,6
387,5
392,9
400,1
391,1
390,4
394,4
397,1
404,2
403,7
395,1
400,2
397,4
404,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48298&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48298&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean347.2316666666674.852921242477371.5510615806766
Geometric Mean345.218414241644
Harmonic Mean343.202623388943
Quadratic Mean349.226760381656
Winsorized Mean ( 1 / 20 )347.2233333333334.8512555114799771.5739116423917
Winsorized Mean ( 2 / 20 )347.2233333333334.8446186387763271.6719641364871
Winsorized Mean ( 3 / 20 )347.0933333333334.802004564166472.2809253292716
Winsorized Mean ( 4 / 20 )347.1266666666674.7928966193489472.4252355590803
Winsorized Mean ( 5 / 20 )346.964.7401412408335373.1961311640133
Winsorized Mean ( 6 / 20 )346.974.726967530446873.4022389121856
Winsorized Mean ( 7 / 20 )347.2733333333334.5839130809506075.7591444690563
Winsorized Mean ( 8 / 20 )348.1266666666674.4007253297036579.1066564225017
Winsorized Mean ( 9 / 20 )347.9166666666674.3584764913671879.825293851139
Winsorized Mean ( 10 / 20 )348.0833333333334.2291884375048582.3049950308426
Winsorized Mean ( 11 / 20 )348.5416666666674.1135873052471884.729371422864
Winsorized Mean ( 12 / 20 )347.9616666666674.0151500465638786.6621826410819
Winsorized Mean ( 13 / 20 )347.4416666666673.8259530710754490.8117951820576
Winsorized Mean ( 14 / 20 )347.1853.7411506319376592.8016629526043
Winsorized Mean ( 15 / 20 )347.3853.6556950578422495.0257049626679
Winsorized Mean ( 16 / 20 )347.3583333333333.6184916572824995.9953390065853
Winsorized Mean ( 17 / 20 )346.5653.40975323013198101.639320094312
Winsorized Mean ( 18 / 20 )347.5853.20177283606837108.560168942784
Winsorized Mean ( 19 / 20 )347.2053.12541741844958111.090761173347
Winsorized Mean ( 20 / 20 )349.3052.75577916120119126.753625587235
Trimmed Mean ( 1 / 20 )347.2310344827594.8188285225439172.0571468476848
Trimmed Mean ( 2 / 20 )347.2392857142864.7749751332536972.720647966532
Trimmed Mean ( 3 / 20 )347.2481481481484.7212773064286473.549619225993
Trimmed Mean ( 4 / 20 )347.3076923076924.6705092288384974.3618469187918
Trimmed Mean ( 5 / 20 )347.3624.606186514252575.4120570075027
Trimmed Mean ( 6 / 20 )347.46254.5384201341248576.5602323564964
Trimmed Mean ( 7 / 20 )347.5695652173914.4518865018945578.0724227963761
Trimmed Mean ( 8 / 20 )347.6272727272734.3777550837527579.4076566817154
Trimmed Mean ( 9 / 20 )347.5380952380954.32561980195880.3441150978598
Trimmed Mean ( 10 / 20 )347.4754.2612862961124781.5422799254297
Trimmed Mean ( 11 / 20 )347.3789473684214.202033575787482.6692459979517
Trimmed Mean ( 12 / 20 )347.2027777777784.1431325586552383.8019959203217
Trimmed Mean ( 13 / 20 )347.0911764705884.0794086802960285.083698072977
Trimmed Mean ( 14 / 20 )347.0406254.0313135700789286.0862393776048
Trimmed Mean ( 15 / 20 )347.023.9731668946086187.3409069402267
Trimmed Mean ( 16 / 20 )346.9678571428573.8993489266997188.9809718661213
Trimmed Mean ( 17 / 20 )346.9115384615383.7857560038531491.6360003413988
Trimmed Mean ( 18 / 20 )346.96253.6718267997144894.4931552945199
Trimmed Mean ( 19 / 20 )346.8681818181823.5547991240404397.577435380913
Trimmed Mean ( 20 / 20 )346.8153.3736539225999102.801000919717
Median340.95
Midrange347.25
Midmean - Weighted Average at Xnp345.916129032258
Midmean - Weighted Average at X(n+1)p347.02
Midmean - Empirical Distribution Function345.916129032258
Midmean - Empirical Distribution Function - Averaging347.02
Midmean - Empirical Distribution Function - Interpolation347.02
Midmean - Closest Observation345.916129032258
Midmean - True Basic - Statistics Graphics Toolkit347.02
Midmean - MS Excel (old versions)347.040625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 347.231666666667 & 4.8529212424773 & 71.5510615806766 \tabularnewline
Geometric Mean & 345.218414241644 &  &  \tabularnewline
Harmonic Mean & 343.202623388943 &  &  \tabularnewline
Quadratic Mean & 349.226760381656 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 347.223333333333 & 4.85125551147997 & 71.5739116423917 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 347.223333333333 & 4.84461863877632 & 71.6719641364871 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 347.093333333333 & 4.8020045641664 & 72.2809253292716 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 347.126666666667 & 4.79289661934894 & 72.4252355590803 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 346.96 & 4.74014124083353 & 73.1961311640133 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 346.97 & 4.7269675304468 & 73.4022389121856 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 347.273333333333 & 4.58391308095060 & 75.7591444690563 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 348.126666666667 & 4.40072532970365 & 79.1066564225017 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 347.916666666667 & 4.35847649136718 & 79.825293851139 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 348.083333333333 & 4.22918843750485 & 82.3049950308426 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 348.541666666667 & 4.11358730524718 & 84.729371422864 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 347.961666666667 & 4.01515004656387 & 86.6621826410819 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 347.441666666667 & 3.82595307107544 & 90.8117951820576 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 347.185 & 3.74115063193765 & 92.8016629526043 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 347.385 & 3.65569505784224 & 95.0257049626679 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 347.358333333333 & 3.61849165728249 & 95.9953390065853 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 346.565 & 3.40975323013198 & 101.639320094312 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 347.585 & 3.20177283606837 & 108.560168942784 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 347.205 & 3.12541741844958 & 111.090761173347 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 349.305 & 2.75577916120119 & 126.753625587235 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 347.231034482759 & 4.81882852254391 & 72.0571468476848 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 347.239285714286 & 4.77497513325369 & 72.720647966532 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 347.248148148148 & 4.72127730642864 & 73.549619225993 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 347.307692307692 & 4.67050922883849 & 74.3618469187918 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 347.362 & 4.6061865142525 & 75.4120570075027 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 347.4625 & 4.53842013412485 & 76.5602323564964 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 347.569565217391 & 4.45188650189455 & 78.0724227963761 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 347.627272727273 & 4.37775508375275 & 79.4076566817154 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 347.538095238095 & 4.325619801958 & 80.3441150978598 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 347.475 & 4.26128629611247 & 81.5422799254297 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 347.378947368421 & 4.2020335757874 & 82.6692459979517 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 347.202777777778 & 4.14313255865523 & 83.8019959203217 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 347.091176470588 & 4.07940868029602 & 85.083698072977 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 347.040625 & 4.03131357007892 & 86.0862393776048 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 347.02 & 3.97316689460861 & 87.3409069402267 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 346.967857142857 & 3.89934892669971 & 88.9809718661213 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 346.911538461538 & 3.78575600385314 & 91.6360003413988 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 346.9625 & 3.67182679971448 & 94.4931552945199 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 346.868181818182 & 3.55479912404043 & 97.577435380913 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 346.815 & 3.3736539225999 & 102.801000919717 \tabularnewline
Median & 340.95 &  &  \tabularnewline
Midrange & 347.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 345.916129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 347.02 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 345.916129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 347.02 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 347.02 &  &  \tabularnewline
Midmean - Closest Observation & 345.916129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 347.02 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 347.040625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48298&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]347.231666666667[/C][C]4.8529212424773[/C][C]71.5510615806766[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]345.218414241644[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]343.202623388943[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]349.226760381656[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]347.223333333333[/C][C]4.85125551147997[/C][C]71.5739116423917[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]347.223333333333[/C][C]4.84461863877632[/C][C]71.6719641364871[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]347.093333333333[/C][C]4.8020045641664[/C][C]72.2809253292716[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]347.126666666667[/C][C]4.79289661934894[/C][C]72.4252355590803[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]346.96[/C][C]4.74014124083353[/C][C]73.1961311640133[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]346.97[/C][C]4.7269675304468[/C][C]73.4022389121856[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]347.273333333333[/C][C]4.58391308095060[/C][C]75.7591444690563[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]348.126666666667[/C][C]4.40072532970365[/C][C]79.1066564225017[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]347.916666666667[/C][C]4.35847649136718[/C][C]79.825293851139[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]348.083333333333[/C][C]4.22918843750485[/C][C]82.3049950308426[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]348.541666666667[/C][C]4.11358730524718[/C][C]84.729371422864[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]347.961666666667[/C][C]4.01515004656387[/C][C]86.6621826410819[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]347.441666666667[/C][C]3.82595307107544[/C][C]90.8117951820576[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]347.185[/C][C]3.74115063193765[/C][C]92.8016629526043[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]347.385[/C][C]3.65569505784224[/C][C]95.0257049626679[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]347.358333333333[/C][C]3.61849165728249[/C][C]95.9953390065853[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]346.565[/C][C]3.40975323013198[/C][C]101.639320094312[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]347.585[/C][C]3.20177283606837[/C][C]108.560168942784[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]347.205[/C][C]3.12541741844958[/C][C]111.090761173347[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]349.305[/C][C]2.75577916120119[/C][C]126.753625587235[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]347.231034482759[/C][C]4.81882852254391[/C][C]72.0571468476848[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]347.239285714286[/C][C]4.77497513325369[/C][C]72.720647966532[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]347.248148148148[/C][C]4.72127730642864[/C][C]73.549619225993[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]347.307692307692[/C][C]4.67050922883849[/C][C]74.3618469187918[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]347.362[/C][C]4.6061865142525[/C][C]75.4120570075027[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]347.4625[/C][C]4.53842013412485[/C][C]76.5602323564964[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]347.569565217391[/C][C]4.45188650189455[/C][C]78.0724227963761[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]347.627272727273[/C][C]4.37775508375275[/C][C]79.4076566817154[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]347.538095238095[/C][C]4.325619801958[/C][C]80.3441150978598[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]347.475[/C][C]4.26128629611247[/C][C]81.5422799254297[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]347.378947368421[/C][C]4.2020335757874[/C][C]82.6692459979517[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]347.202777777778[/C][C]4.14313255865523[/C][C]83.8019959203217[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]347.091176470588[/C][C]4.07940868029602[/C][C]85.083698072977[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]347.040625[/C][C]4.03131357007892[/C][C]86.0862393776048[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]347.02[/C][C]3.97316689460861[/C][C]87.3409069402267[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]346.967857142857[/C][C]3.89934892669971[/C][C]88.9809718661213[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]346.911538461538[/C][C]3.78575600385314[/C][C]91.6360003413988[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]346.9625[/C][C]3.67182679971448[/C][C]94.4931552945199[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]346.868181818182[/C][C]3.55479912404043[/C][C]97.577435380913[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]346.815[/C][C]3.3736539225999[/C][C]102.801000919717[/C][/ROW]
[ROW][C]Median[/C][C]340.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]347.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]345.916129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]347.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]345.916129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]347.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]347.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]345.916129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]347.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]347.040625[/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=48298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48298&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 Mean347.2316666666674.852921242477371.5510615806766
Geometric Mean345.218414241644
Harmonic Mean343.202623388943
Quadratic Mean349.226760381656
Winsorized Mean ( 1 / 20 )347.2233333333334.8512555114799771.5739116423917
Winsorized Mean ( 2 / 20 )347.2233333333334.8446186387763271.6719641364871
Winsorized Mean ( 3 / 20 )347.0933333333334.802004564166472.2809253292716
Winsorized Mean ( 4 / 20 )347.1266666666674.7928966193489472.4252355590803
Winsorized Mean ( 5 / 20 )346.964.7401412408335373.1961311640133
Winsorized Mean ( 6 / 20 )346.974.726967530446873.4022389121856
Winsorized Mean ( 7 / 20 )347.2733333333334.5839130809506075.7591444690563
Winsorized Mean ( 8 / 20 )348.1266666666674.4007253297036579.1066564225017
Winsorized Mean ( 9 / 20 )347.9166666666674.3584764913671879.825293851139
Winsorized Mean ( 10 / 20 )348.0833333333334.2291884375048582.3049950308426
Winsorized Mean ( 11 / 20 )348.5416666666674.1135873052471884.729371422864
Winsorized Mean ( 12 / 20 )347.9616666666674.0151500465638786.6621826410819
Winsorized Mean ( 13 / 20 )347.4416666666673.8259530710754490.8117951820576
Winsorized Mean ( 14 / 20 )347.1853.7411506319376592.8016629526043
Winsorized Mean ( 15 / 20 )347.3853.6556950578422495.0257049626679
Winsorized Mean ( 16 / 20 )347.3583333333333.6184916572824995.9953390065853
Winsorized Mean ( 17 / 20 )346.5653.40975323013198101.639320094312
Winsorized Mean ( 18 / 20 )347.5853.20177283606837108.560168942784
Winsorized Mean ( 19 / 20 )347.2053.12541741844958111.090761173347
Winsorized Mean ( 20 / 20 )349.3052.75577916120119126.753625587235
Trimmed Mean ( 1 / 20 )347.2310344827594.8188285225439172.0571468476848
Trimmed Mean ( 2 / 20 )347.2392857142864.7749751332536972.720647966532
Trimmed Mean ( 3 / 20 )347.2481481481484.7212773064286473.549619225993
Trimmed Mean ( 4 / 20 )347.3076923076924.6705092288384974.3618469187918
Trimmed Mean ( 5 / 20 )347.3624.606186514252575.4120570075027
Trimmed Mean ( 6 / 20 )347.46254.5384201341248576.5602323564964
Trimmed Mean ( 7 / 20 )347.5695652173914.4518865018945578.0724227963761
Trimmed Mean ( 8 / 20 )347.6272727272734.3777550837527579.4076566817154
Trimmed Mean ( 9 / 20 )347.5380952380954.32561980195880.3441150978598
Trimmed Mean ( 10 / 20 )347.4754.2612862961124781.5422799254297
Trimmed Mean ( 11 / 20 )347.3789473684214.202033575787482.6692459979517
Trimmed Mean ( 12 / 20 )347.2027777777784.1431325586552383.8019959203217
Trimmed Mean ( 13 / 20 )347.0911764705884.0794086802960285.083698072977
Trimmed Mean ( 14 / 20 )347.0406254.0313135700789286.0862393776048
Trimmed Mean ( 15 / 20 )347.023.9731668946086187.3409069402267
Trimmed Mean ( 16 / 20 )346.9678571428573.8993489266997188.9809718661213
Trimmed Mean ( 17 / 20 )346.9115384615383.7857560038531491.6360003413988
Trimmed Mean ( 18 / 20 )346.96253.6718267997144894.4931552945199
Trimmed Mean ( 19 / 20 )346.8681818181823.5547991240404397.577435380913
Trimmed Mean ( 20 / 20 )346.8153.3736539225999102.801000919717
Median340.95
Midrange347.25
Midmean - Weighted Average at Xnp345.916129032258
Midmean - Weighted Average at X(n+1)p347.02
Midmean - Empirical Distribution Function345.916129032258
Midmean - Empirical Distribution Function - Averaging347.02
Midmean - Empirical Distribution Function - Interpolation347.02
Midmean - Closest Observation345.916129032258
Midmean - True Basic - Statistics Graphics Toolkit347.02
Midmean - MS Excel (old versions)347.040625
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')