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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, 14 Dec 2008 03:45:26 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229251663o71zjftfxovv895.htm/, Retrieved Wed, 15 May 2024 20:40:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33272, Retrieved Wed, 15 May 2024 20:40:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsjulie govaerts
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper] [2008-12-14 10:45:26] [ff1af8c6f1c2f1c0e8def9bfc9355be9] [Current]
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Dataseries X:
878
859
845
806
786
757
769
771
726
680
661
658
642
613
612
596
592
586
619
618
593
574
564
556
564
539
512
507
491
460
478
495
461
418
409
428
420
403
385
377
376
377
374
374
363
354
342
344
362
360
349
339
346
345
363
356
337
337
344
351




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33272&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33272&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean513.3520.731929371870524.7613230197728
Geometric Mean490.378075447722
Harmonic Mean469.742389280828
Quadratic Mean537.482263273248
Winsorized Mean ( 1 / 20 )513.03333333333320.639739611344624.8565797337553
Winsorized Mean ( 2 / 20 )512.63333333333320.49971705284525.0068492170817
Winsorized Mean ( 3 / 20 )510.83333333333319.965650823502525.5856088964557
Winsorized Mean ( 4 / 20 )509.63333333333319.6202790092125.9748259998803
Winsorized Mean ( 5 / 20 )508.38333333333319.327084880580626.3041910600882
Winsorized Mean ( 6 / 20 )508.28333333333319.266728613080526.3814030674752
Winsorized Mean ( 7 / 20 )50718.932693750635926.7790736319797
Winsorized Mean ( 8 / 20 )503.26666666666717.977526250687627.9942111972952
Winsorized Mean ( 9 / 20 )496.66666666666716.558297400579229.9950323787091
Winsorized Mean ( 10 / 20 )49415.904499594285731.0603925053693
Winsorized Mean ( 11 / 20 )493.81666666666715.752436663215831.3485892515791
Winsorized Mean ( 12 / 20 )491.41666666666715.080336500364332.5865849647849
Winsorized Mean ( 13 / 20 )486.86666666666714.200530479998734.2851041622998
Winsorized Mean ( 14 / 20 )486.86666666666714.129055423357534.4585431989884
Winsorized Mean ( 15 / 20 )485.61666666666713.933885284934334.8514902151324
Winsorized Mean ( 16 / 20 )488.28333333333313.462546742107436.2697595549367
Winsorized Mean ( 17 / 20 )483.7512.771428763273437.8775162095499
Winsorized Mean ( 18 / 20 )483.4512.550585216058138.5201161282455
Winsorized Mean ( 19 / 20 )483.4512.457870813174338.8067918868405
Winsorized Mean ( 20 / 20 )481.4512.164489976327939.5783136766855
Trimmed Mean ( 1 / 20 )510.10344827586220.258891375571225.179238035254
Trimmed Mean ( 2 / 20 )506.96428571428619.776444802256525.6347534040315
Trimmed Mean ( 3 / 20 )503.81481481481519.259493091092526.1592977775635
Trimmed Mean ( 4 / 20 )501.11538461538518.864017913203926.5646156042201
Trimmed Mean ( 5 / 20 )498.5618.489338571629026.9647287851074
Trimmed Mean ( 6 / 20 )496.10416666666718.100689604808527.4080257436643
Trimmed Mean ( 7 / 20 )493.4565217391317.604311794012628.0304352429704
Trimmed Mean ( 8 / 20 )490.81818181818217.050052938584528.7869007554489
Trimmed Mean ( 9 / 20 )488.59523809523816.597687436828429.4375490534363
Trimmed Mean ( 10 / 20 )487.2516.383651560672929.7400123651060
Trimmed Mean ( 11 / 20 )486.18421052631616.238656408936929.9399284203554
Trimmed Mean ( 12 / 20 )485.02777777777816.041537654947530.2357410000648
Trimmed Mean ( 13 / 20 )484.08823529411815.907899339729230.4306825782541
Trimmed Mean ( 14 / 20 )483.687515.901120719023830.4184534251932
Trimmed Mean ( 15 / 20 )483.23333333333315.837223962401030.5125023476698
Trimmed Mean ( 16 / 20 )482.89285714285715.723835181639030.7108826545535
Trimmed Mean ( 17 / 20 )482.11538461538515.609201125083730.8866149364066
Trimmed Mean ( 18 / 20 )481.87515.563720413703930.9614274216664
Trimmed Mean ( 19 / 20 )481.63636363636415.440928556761231.1921891138774
Trimmed Mean ( 20 / 20 )481.3515.132793772744731.8084028123708
Median484.5
Midrange607.5
Midmean - Weighted Average at Xnp479.354838709677
Midmean - Weighted Average at X(n+1)p479.354838709677
Midmean - Empirical Distribution Function479.354838709677
Midmean - Empirical Distribution Function - Averaging479.354838709677
Midmean - Empirical Distribution Function - Interpolation479.354838709677
Midmean - Closest Observation479.354838709677
Midmean - True Basic - Statistics Graphics Toolkit479.354838709677
Midmean - MS Excel (old versions)483.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 513.35 & 20.7319293718705 & 24.7613230197728 \tabularnewline
Geometric Mean & 490.378075447722 &  &  \tabularnewline
Harmonic Mean & 469.742389280828 &  &  \tabularnewline
Quadratic Mean & 537.482263273248 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 513.033333333333 & 20.6397396113446 & 24.8565797337553 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 512.633333333333 & 20.499717052845 & 25.0068492170817 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 510.833333333333 & 19.9656508235025 & 25.5856088964557 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 509.633333333333 & 19.62027900921 & 25.9748259998803 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 508.383333333333 & 19.3270848805806 & 26.3041910600882 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 508.283333333333 & 19.2667286130805 & 26.3814030674752 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 507 & 18.9326937506359 & 26.7790736319797 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 503.266666666667 & 17.9775262506876 & 27.9942111972952 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 496.666666666667 & 16.5582974005792 & 29.9950323787091 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 494 & 15.9044995942857 & 31.0603925053693 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 493.816666666667 & 15.7524366632158 & 31.3485892515791 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 491.416666666667 & 15.0803365003643 & 32.5865849647849 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 486.866666666667 & 14.2005304799987 & 34.2851041622998 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 486.866666666667 & 14.1290554233575 & 34.4585431989884 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 485.616666666667 & 13.9338852849343 & 34.8514902151324 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 488.283333333333 & 13.4625467421074 & 36.2697595549367 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 483.75 & 12.7714287632734 & 37.8775162095499 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 483.45 & 12.5505852160581 & 38.5201161282455 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 483.45 & 12.4578708131743 & 38.8067918868405 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 481.45 & 12.1644899763279 & 39.5783136766855 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 510.103448275862 & 20.2588913755712 & 25.179238035254 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 506.964285714286 & 19.7764448022565 & 25.6347534040315 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 503.814814814815 & 19.2594930910925 & 26.1592977775635 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 501.115384615385 & 18.8640179132039 & 26.5646156042201 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 498.56 & 18.4893385716290 & 26.9647287851074 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 496.104166666667 & 18.1006896048085 & 27.4080257436643 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 493.45652173913 & 17.6043117940126 & 28.0304352429704 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 490.818181818182 & 17.0500529385845 & 28.7869007554489 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 488.595238095238 & 16.5976874368284 & 29.4375490534363 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 487.25 & 16.3836515606729 & 29.7400123651060 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 486.184210526316 & 16.2386564089369 & 29.9399284203554 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 485.027777777778 & 16.0415376549475 & 30.2357410000648 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 484.088235294118 & 15.9078993397292 & 30.4306825782541 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 483.6875 & 15.9011207190238 & 30.4184534251932 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 483.233333333333 & 15.8372239624010 & 30.5125023476698 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 482.892857142857 & 15.7238351816390 & 30.7108826545535 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 482.115384615385 & 15.6092011250837 & 30.8866149364066 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 481.875 & 15.5637204137039 & 30.9614274216664 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 481.636363636364 & 15.4409285567612 & 31.1921891138774 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 481.35 & 15.1327937727447 & 31.8084028123708 \tabularnewline
Median & 484.5 &  &  \tabularnewline
Midrange & 607.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 479.354838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 479.354838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 479.354838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 479.354838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 479.354838709677 &  &  \tabularnewline
Midmean - Closest Observation & 479.354838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 479.354838709677 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 483.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33272&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]513.35[/C][C]20.7319293718705[/C][C]24.7613230197728[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]490.378075447722[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]469.742389280828[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]537.482263273248[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]513.033333333333[/C][C]20.6397396113446[/C][C]24.8565797337553[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]512.633333333333[/C][C]20.499717052845[/C][C]25.0068492170817[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]510.833333333333[/C][C]19.9656508235025[/C][C]25.5856088964557[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]509.633333333333[/C][C]19.62027900921[/C][C]25.9748259998803[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]508.383333333333[/C][C]19.3270848805806[/C][C]26.3041910600882[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]508.283333333333[/C][C]19.2667286130805[/C][C]26.3814030674752[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]507[/C][C]18.9326937506359[/C][C]26.7790736319797[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]503.266666666667[/C][C]17.9775262506876[/C][C]27.9942111972952[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]496.666666666667[/C][C]16.5582974005792[/C][C]29.9950323787091[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]494[/C][C]15.9044995942857[/C][C]31.0603925053693[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]493.816666666667[/C][C]15.7524366632158[/C][C]31.3485892515791[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]491.416666666667[/C][C]15.0803365003643[/C][C]32.5865849647849[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]486.866666666667[/C][C]14.2005304799987[/C][C]34.2851041622998[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]486.866666666667[/C][C]14.1290554233575[/C][C]34.4585431989884[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]485.616666666667[/C][C]13.9338852849343[/C][C]34.8514902151324[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]488.283333333333[/C][C]13.4625467421074[/C][C]36.2697595549367[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]483.75[/C][C]12.7714287632734[/C][C]37.8775162095499[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]483.45[/C][C]12.5505852160581[/C][C]38.5201161282455[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]483.45[/C][C]12.4578708131743[/C][C]38.8067918868405[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]481.45[/C][C]12.1644899763279[/C][C]39.5783136766855[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]510.103448275862[/C][C]20.2588913755712[/C][C]25.179238035254[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]506.964285714286[/C][C]19.7764448022565[/C][C]25.6347534040315[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]503.814814814815[/C][C]19.2594930910925[/C][C]26.1592977775635[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]501.115384615385[/C][C]18.8640179132039[/C][C]26.5646156042201[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]498.56[/C][C]18.4893385716290[/C][C]26.9647287851074[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]496.104166666667[/C][C]18.1006896048085[/C][C]27.4080257436643[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]493.45652173913[/C][C]17.6043117940126[/C][C]28.0304352429704[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]490.818181818182[/C][C]17.0500529385845[/C][C]28.7869007554489[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]488.595238095238[/C][C]16.5976874368284[/C][C]29.4375490534363[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]487.25[/C][C]16.3836515606729[/C][C]29.7400123651060[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]486.184210526316[/C][C]16.2386564089369[/C][C]29.9399284203554[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]485.027777777778[/C][C]16.0415376549475[/C][C]30.2357410000648[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]484.088235294118[/C][C]15.9078993397292[/C][C]30.4306825782541[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]483.6875[/C][C]15.9011207190238[/C][C]30.4184534251932[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]483.233333333333[/C][C]15.8372239624010[/C][C]30.5125023476698[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]482.892857142857[/C][C]15.7238351816390[/C][C]30.7108826545535[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]482.115384615385[/C][C]15.6092011250837[/C][C]30.8866149364066[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]481.875[/C][C]15.5637204137039[/C][C]30.9614274216664[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]481.636363636364[/C][C]15.4409285567612[/C][C]31.1921891138774[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]481.35[/C][C]15.1327937727447[/C][C]31.8084028123708[/C][/ROW]
[ROW][C]Median[/C][C]484.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]607.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]479.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]483.6875[/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=33272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33272&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 Mean513.3520.731929371870524.7613230197728
Geometric Mean490.378075447722
Harmonic Mean469.742389280828
Quadratic Mean537.482263273248
Winsorized Mean ( 1 / 20 )513.03333333333320.639739611344624.8565797337553
Winsorized Mean ( 2 / 20 )512.63333333333320.49971705284525.0068492170817
Winsorized Mean ( 3 / 20 )510.83333333333319.965650823502525.5856088964557
Winsorized Mean ( 4 / 20 )509.63333333333319.6202790092125.9748259998803
Winsorized Mean ( 5 / 20 )508.38333333333319.327084880580626.3041910600882
Winsorized Mean ( 6 / 20 )508.28333333333319.266728613080526.3814030674752
Winsorized Mean ( 7 / 20 )50718.932693750635926.7790736319797
Winsorized Mean ( 8 / 20 )503.26666666666717.977526250687627.9942111972952
Winsorized Mean ( 9 / 20 )496.66666666666716.558297400579229.9950323787091
Winsorized Mean ( 10 / 20 )49415.904499594285731.0603925053693
Winsorized Mean ( 11 / 20 )493.81666666666715.752436663215831.3485892515791
Winsorized Mean ( 12 / 20 )491.41666666666715.080336500364332.5865849647849
Winsorized Mean ( 13 / 20 )486.86666666666714.200530479998734.2851041622998
Winsorized Mean ( 14 / 20 )486.86666666666714.129055423357534.4585431989884
Winsorized Mean ( 15 / 20 )485.61666666666713.933885284934334.8514902151324
Winsorized Mean ( 16 / 20 )488.28333333333313.462546742107436.2697595549367
Winsorized Mean ( 17 / 20 )483.7512.771428763273437.8775162095499
Winsorized Mean ( 18 / 20 )483.4512.550585216058138.5201161282455
Winsorized Mean ( 19 / 20 )483.4512.457870813174338.8067918868405
Winsorized Mean ( 20 / 20 )481.4512.164489976327939.5783136766855
Trimmed Mean ( 1 / 20 )510.10344827586220.258891375571225.179238035254
Trimmed Mean ( 2 / 20 )506.96428571428619.776444802256525.6347534040315
Trimmed Mean ( 3 / 20 )503.81481481481519.259493091092526.1592977775635
Trimmed Mean ( 4 / 20 )501.11538461538518.864017913203926.5646156042201
Trimmed Mean ( 5 / 20 )498.5618.489338571629026.9647287851074
Trimmed Mean ( 6 / 20 )496.10416666666718.100689604808527.4080257436643
Trimmed Mean ( 7 / 20 )493.4565217391317.604311794012628.0304352429704
Trimmed Mean ( 8 / 20 )490.81818181818217.050052938584528.7869007554489
Trimmed Mean ( 9 / 20 )488.59523809523816.597687436828429.4375490534363
Trimmed Mean ( 10 / 20 )487.2516.383651560672929.7400123651060
Trimmed Mean ( 11 / 20 )486.18421052631616.238656408936929.9399284203554
Trimmed Mean ( 12 / 20 )485.02777777777816.041537654947530.2357410000648
Trimmed Mean ( 13 / 20 )484.08823529411815.907899339729230.4306825782541
Trimmed Mean ( 14 / 20 )483.687515.901120719023830.4184534251932
Trimmed Mean ( 15 / 20 )483.23333333333315.837223962401030.5125023476698
Trimmed Mean ( 16 / 20 )482.89285714285715.723835181639030.7108826545535
Trimmed Mean ( 17 / 20 )482.11538461538515.609201125083730.8866149364066
Trimmed Mean ( 18 / 20 )481.87515.563720413703930.9614274216664
Trimmed Mean ( 19 / 20 )481.63636363636415.440928556761231.1921891138774
Trimmed Mean ( 20 / 20 )481.3515.132793772744731.8084028123708
Median484.5
Midrange607.5
Midmean - Weighted Average at Xnp479.354838709677
Midmean - Weighted Average at X(n+1)p479.354838709677
Midmean - Empirical Distribution Function479.354838709677
Midmean - Empirical Distribution Function - Averaging479.354838709677
Midmean - Empirical Distribution Function - Interpolation479.354838709677
Midmean - Closest Observation479.354838709677
Midmean - True Basic - Statistics Graphics Toolkit479.354838709677
Midmean - MS Excel (old versions)483.6875
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')