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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 computationFri, 23 Dec 2011 08:59:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324648751844ajerkxpm6940.htm/, Retrieved Mon, 29 Apr 2024 18:27:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160417, Retrieved Mon, 29 Apr 2024 18:27:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [paper : central t...] [2010-12-18 10:58:46] [2c786c21adba4dd4c8af44dce5258f06]
- R  D    [Central Tendency] [] [2011-12-23 13:59:00] [c80accbb627afb8a1e74b91ef6a0d2c4] [Current]
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Dataseries X:
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
707
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160417&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160417&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean659.35416666666721.018471477432331.3702243940345
Geometric Mean640.5166421256
Harmonic Mean617.960995153039
Quadratic Mean674.915843519274
Winsorized Mean ( 1 / 16 )659.60416666666720.924567739659731.5229530604102
Winsorized Mean ( 2 / 16 )657.72916666666720.180518210230732.5922833008929
Winsorized Mean ( 3 / 16 )658.10416666666719.931781696989133.0178293476935
Winsorized Mean ( 4 / 16 )659.52083333333319.413336919237633.9725641231612
Winsorized Mean ( 5 / 16 )657.64583333333318.719194305477435.1321655516392
Winsorized Mean ( 6 / 16 )660.39583333333317.655734095163737.4040427757819
Winsorized Mean ( 7 / 16 )672.20833333333312.210112304728855.0534111854972
Winsorized Mean ( 8 / 16 )677.7083333333338.7822838237417877.1676646911861
Winsorized Mean ( 9 / 16 )674.8958333333337.721104883598187.4092300917982
Winsorized Mean ( 10 / 16 )676.3541666666676.73705019836542100.393220586477
Winsorized Mean ( 11 / 16 )679.1041666666676.24366626469904108.766890777978
Winsorized Mean ( 12 / 16 )678.6041666666676.15590441812434110.236306572387
Winsorized Mean ( 13 / 16 )677.255.64936605996041119.880707465564
Winsorized Mean ( 14 / 16 )677.255.35847079117337126.388670647526
Winsorized Mean ( 15 / 16 )677.255.05190259784925134.058404112606
Winsorized Mean ( 16 / 16 )678.5833333333334.83429618680418140.368588748371
Trimmed Mean ( 1 / 16 )660.89130434782619.931530824926533.1580805384658
Trimmed Mean ( 2 / 16 )662.29545454545518.631186758414235.547679443788
Trimmed Mean ( 3 / 16 )664.90476190476217.460119134480638.0813416439808
Trimmed Mean ( 4 / 16 )667.62516.016045139892641.6847601370133
Trimmed Mean ( 5 / 16 )670.18421052631614.277420786991546.9401455994725
Trimmed Mean ( 6 / 16 )673.52777777777812.081435720362755.7489849192822
Trimmed Mean ( 7 / 16 )676.6176470588249.2330699434638573.2819800133547
Trimmed Mean ( 8 / 16 )677.56257.8483532148778786.3318050869023
Trimmed Mean ( 9 / 16 )677.5333333333337.3493659642603492.1893584600562
Trimmed Mean ( 10 / 16 )678.0357142857147.0170770801167196.6265165031416
Trimmed Mean ( 11 / 16 )678.3461538461546.8715561573539398.7179815332207
Trimmed Mean ( 12 / 16 )678.2083333333336.7946001489105299.8157828966699
Trimmed Mean ( 13 / 16 )678.1363636363646.65842416472093101.84637488693
Trimmed Mean ( 14 / 16 )678.36.59269931139941102.886536752428
Trimmed Mean ( 15 / 16 )678.56.53409859463755103.839877861169
Trimmed Mean ( 16 / 16 )678.756.48427585265566104.676299315985
Median684
Midrange624
Midmean - Weighted Average at Xnp676.24
Midmean - Weighted Average at X(n+1)p676.24
Midmean - Empirical Distribution Function676.24
Midmean - Empirical Distribution Function - Averaging676.24
Midmean - Empirical Distribution Function - Interpolation676.24
Midmean - Closest Observation676.24
Midmean - True Basic - Statistics Graphics Toolkit676.24
Midmean - MS Excel (old versions)680.296296296296
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 659.354166666667 & 21.0184714774323 & 31.3702243940345 \tabularnewline
Geometric Mean & 640.5166421256 &  &  \tabularnewline
Harmonic Mean & 617.960995153039 &  &  \tabularnewline
Quadratic Mean & 674.915843519274 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 659.604166666667 & 20.9245677396597 & 31.5229530604102 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 657.729166666667 & 20.1805182102307 & 32.5922833008929 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 658.104166666667 & 19.9317816969891 & 33.0178293476935 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 659.520833333333 & 19.4133369192376 & 33.9725641231612 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 657.645833333333 & 18.7191943054774 & 35.1321655516392 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 660.395833333333 & 17.6557340951637 & 37.4040427757819 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 672.208333333333 & 12.2101123047288 & 55.0534111854972 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 677.708333333333 & 8.78228382374178 & 77.1676646911861 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 674.895833333333 & 7.7211048835981 & 87.4092300917982 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 676.354166666667 & 6.73705019836542 & 100.393220586477 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 679.104166666667 & 6.24366626469904 & 108.766890777978 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 678.604166666667 & 6.15590441812434 & 110.236306572387 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 677.25 & 5.64936605996041 & 119.880707465564 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 677.25 & 5.35847079117337 & 126.388670647526 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 677.25 & 5.05190259784925 & 134.058404112606 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 678.583333333333 & 4.83429618680418 & 140.368588748371 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 660.891304347826 & 19.9315308249265 & 33.1580805384658 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 662.295454545455 & 18.6311867584142 & 35.547679443788 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 664.904761904762 & 17.4601191344806 & 38.0813416439808 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 667.625 & 16.0160451398926 & 41.6847601370133 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 670.184210526316 & 14.2774207869915 & 46.9401455994725 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 673.527777777778 & 12.0814357203627 & 55.7489849192822 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 676.617647058824 & 9.23306994346385 & 73.2819800133547 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 677.5625 & 7.84835321487787 & 86.3318050869023 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 677.533333333333 & 7.34936596426034 & 92.1893584600562 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 678.035714285714 & 7.01707708011671 & 96.6265165031416 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 678.346153846154 & 6.87155615735393 & 98.7179815332207 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 678.208333333333 & 6.79460014891052 & 99.8157828966699 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 678.136363636364 & 6.65842416472093 & 101.84637488693 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 678.3 & 6.59269931139941 & 102.886536752428 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 678.5 & 6.53409859463755 & 103.839877861169 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 678.75 & 6.48427585265566 & 104.676299315985 \tabularnewline
Median & 684 &  &  \tabularnewline
Midrange & 624 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 676.24 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 676.24 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 676.24 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 676.24 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 676.24 &  &  \tabularnewline
Midmean - Closest Observation & 676.24 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 676.24 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 680.296296296296 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160417&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]659.354166666667[/C][C]21.0184714774323[/C][C]31.3702243940345[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]640.5166421256[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]617.960995153039[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]674.915843519274[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]659.604166666667[/C][C]20.9245677396597[/C][C]31.5229530604102[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]657.729166666667[/C][C]20.1805182102307[/C][C]32.5922833008929[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]658.104166666667[/C][C]19.9317816969891[/C][C]33.0178293476935[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]659.520833333333[/C][C]19.4133369192376[/C][C]33.9725641231612[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]657.645833333333[/C][C]18.7191943054774[/C][C]35.1321655516392[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]660.395833333333[/C][C]17.6557340951637[/C][C]37.4040427757819[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]672.208333333333[/C][C]12.2101123047288[/C][C]55.0534111854972[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]677.708333333333[/C][C]8.78228382374178[/C][C]77.1676646911861[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]674.895833333333[/C][C]7.7211048835981[/C][C]87.4092300917982[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]676.354166666667[/C][C]6.73705019836542[/C][C]100.393220586477[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]679.104166666667[/C][C]6.24366626469904[/C][C]108.766890777978[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]678.604166666667[/C][C]6.15590441812434[/C][C]110.236306572387[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]677.25[/C][C]5.64936605996041[/C][C]119.880707465564[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]677.25[/C][C]5.35847079117337[/C][C]126.388670647526[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]677.25[/C][C]5.05190259784925[/C][C]134.058404112606[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]678.583333333333[/C][C]4.83429618680418[/C][C]140.368588748371[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]660.891304347826[/C][C]19.9315308249265[/C][C]33.1580805384658[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]662.295454545455[/C][C]18.6311867584142[/C][C]35.547679443788[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]664.904761904762[/C][C]17.4601191344806[/C][C]38.0813416439808[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]667.625[/C][C]16.0160451398926[/C][C]41.6847601370133[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]670.184210526316[/C][C]14.2774207869915[/C][C]46.9401455994725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]673.527777777778[/C][C]12.0814357203627[/C][C]55.7489849192822[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]676.617647058824[/C][C]9.23306994346385[/C][C]73.2819800133547[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]677.5625[/C][C]7.84835321487787[/C][C]86.3318050869023[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]677.533333333333[/C][C]7.34936596426034[/C][C]92.1893584600562[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]678.035714285714[/C][C]7.01707708011671[/C][C]96.6265165031416[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]678.346153846154[/C][C]6.87155615735393[/C][C]98.7179815332207[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]678.208333333333[/C][C]6.79460014891052[/C][C]99.8157828966699[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]678.136363636364[/C][C]6.65842416472093[/C][C]101.84637488693[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]678.3[/C][C]6.59269931139941[/C][C]102.886536752428[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]678.5[/C][C]6.53409859463755[/C][C]103.839877861169[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]678.75[/C][C]6.48427585265566[/C][C]104.676299315985[/C][/ROW]
[ROW][C]Median[/C][C]684[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]624[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]676.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]680.296296296296[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160417&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 Mean659.35416666666721.018471477432331.3702243940345
Geometric Mean640.5166421256
Harmonic Mean617.960995153039
Quadratic Mean674.915843519274
Winsorized Mean ( 1 / 16 )659.60416666666720.924567739659731.5229530604102
Winsorized Mean ( 2 / 16 )657.72916666666720.180518210230732.5922833008929
Winsorized Mean ( 3 / 16 )658.10416666666719.931781696989133.0178293476935
Winsorized Mean ( 4 / 16 )659.52083333333319.413336919237633.9725641231612
Winsorized Mean ( 5 / 16 )657.64583333333318.719194305477435.1321655516392
Winsorized Mean ( 6 / 16 )660.39583333333317.655734095163737.4040427757819
Winsorized Mean ( 7 / 16 )672.20833333333312.210112304728855.0534111854972
Winsorized Mean ( 8 / 16 )677.7083333333338.7822838237417877.1676646911861
Winsorized Mean ( 9 / 16 )674.8958333333337.721104883598187.4092300917982
Winsorized Mean ( 10 / 16 )676.3541666666676.73705019836542100.393220586477
Winsorized Mean ( 11 / 16 )679.1041666666676.24366626469904108.766890777978
Winsorized Mean ( 12 / 16 )678.6041666666676.15590441812434110.236306572387
Winsorized Mean ( 13 / 16 )677.255.64936605996041119.880707465564
Winsorized Mean ( 14 / 16 )677.255.35847079117337126.388670647526
Winsorized Mean ( 15 / 16 )677.255.05190259784925134.058404112606
Winsorized Mean ( 16 / 16 )678.5833333333334.83429618680418140.368588748371
Trimmed Mean ( 1 / 16 )660.89130434782619.931530824926533.1580805384658
Trimmed Mean ( 2 / 16 )662.29545454545518.631186758414235.547679443788
Trimmed Mean ( 3 / 16 )664.90476190476217.460119134480638.0813416439808
Trimmed Mean ( 4 / 16 )667.62516.016045139892641.6847601370133
Trimmed Mean ( 5 / 16 )670.18421052631614.277420786991546.9401455994725
Trimmed Mean ( 6 / 16 )673.52777777777812.081435720362755.7489849192822
Trimmed Mean ( 7 / 16 )676.6176470588249.2330699434638573.2819800133547
Trimmed Mean ( 8 / 16 )677.56257.8483532148778786.3318050869023
Trimmed Mean ( 9 / 16 )677.5333333333337.3493659642603492.1893584600562
Trimmed Mean ( 10 / 16 )678.0357142857147.0170770801167196.6265165031416
Trimmed Mean ( 11 / 16 )678.3461538461546.8715561573539398.7179815332207
Trimmed Mean ( 12 / 16 )678.2083333333336.7946001489105299.8157828966699
Trimmed Mean ( 13 / 16 )678.1363636363646.65842416472093101.84637488693
Trimmed Mean ( 14 / 16 )678.36.59269931139941102.886536752428
Trimmed Mean ( 15 / 16 )678.56.53409859463755103.839877861169
Trimmed Mean ( 16 / 16 )678.756.48427585265566104.676299315985
Median684
Midrange624
Midmean - Weighted Average at Xnp676.24
Midmean - Weighted Average at X(n+1)p676.24
Midmean - Empirical Distribution Function676.24
Midmean - Empirical Distribution Function - Averaging676.24
Midmean - Empirical Distribution Function - Interpolation676.24
Midmean - Closest Observation676.24
Midmean - True Basic - Statistics Graphics Toolkit676.24
Midmean - MS Excel (old versions)680.296296296296
Number of observations48



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')