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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 computationSat, 13 Dec 2008 04:33:43 -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/13/t1229168056wc3a2q49z3dbkz5.htm/, Retrieved Fri, 17 May 2024 01:41:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32976, Retrieved Fri, 17 May 2024 01:41:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - central t...] [2008-12-13 11:33:43] [73ec5abea95a9c3c8c3a1ac44cab1f72] [Current]
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Dataseries X:
458
582
597
729
812
697
545
677
598
701
956
971
967
683
611
955
782
877
399
615
906
1324
952
710
288
312
313
387
540
465
282
389
488
803
1050
1027
332
466
353
345
341
354
287
379
533
534
578
991
366
254
449
349
532
590
469
362
424
372
253
462




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=32976&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=32976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32976&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 Mean580.38333333333332.117730918601618.0704961631394
Geometric Mean532.094589335622
Harmonic Mean489.392755584765
Quadratic Mean630.639503467182
Winsorized Mean ( 1 / 20 )575.83333333333330.612210615940918.8105766211302
Winsorized Mean ( 2 / 20 )57630.254644318267219.0383993260903
Winsorized Mean ( 3 / 20 )574.4529.772673788556119.2945384777905
Winsorized Mean ( 4 / 20 )573.18333333333329.450998195764619.4622718565703
Winsorized Mean ( 5 / 20 )574.8529.05719885131319.7833935384320
Winsorized Mean ( 6 / 20 )573.8528.792309325081719.9306694548501
Winsorized Mean ( 7 / 20 )575.9528.434595633023520.2552555145571
Winsorized Mean ( 8 / 20 )576.7528.171895930856020.4725305465969
Winsorized Mean ( 9 / 20 )570.4526.567613615459321.4716311467306
Winsorized Mean ( 10 / 20 )566.28333333333325.45373660499222.247552181485
Winsorized Mean ( 11 / 20 )555.122.978996796755724.1568422202997
Winsorized Mean ( 12 / 20 )553.522.610250912532724.4800467779506
Winsorized Mean ( 13 / 20 )550.68333333333321.511375149641825.5996341239255
Winsorized Mean ( 14 / 20 )539.2519.203028024526128.0815087761821
Winsorized Mean ( 15 / 20 )53618.190579296472229.4658015703738
Winsorized Mean ( 16 / 20 )535.46666666666717.519891304945430.5633555223896
Winsorized Mean ( 17 / 20 )536.616.997859619329131.5686805290359
Winsorized Mean ( 18 / 20 )53316.243312400496232.8135042199717
Winsorized Mean ( 19 / 20 )534.26666666666715.473503262077034.5278414084849
Winsorized Mean ( 20 / 20 )521.93333333333311.130805897358546.8908844648164
Trimmed Mean ( 1 / 20 )573.20689655172430.066218093234519.0648153610217
Trimmed Mean ( 2 / 20 )570.39285714285729.381510647063819.4133264281242
Trimmed Mean ( 3 / 20 )567.27777777777828.756531378139719.7269194367793
Trimmed Mean ( 4 / 20 )564.51923076923128.194841509950120.0220749802764
Trimmed Mean ( 5 / 20 )561.9227.599006784850120.3601529714632
Trimmed Mean ( 6 / 20 )558.687526.954834107853720.7268016476947
Trimmed Mean ( 7 / 20 )555.39130434782626.195170079954621.2020499448038
Trimmed Mean ( 8 / 20 )551.38636363636425.290180930343821.8023890439944
Trimmed Mean ( 9 / 20 )546.85714285714324.152236184106922.6420915516302
Trimmed Mean ( 10 / 20 )542.92523.123785830911123.4790705972651
Trimmed Mean ( 11 / 20 )539.23684210526322.063158861829924.4406000737349
Trimmed Mean ( 12 / 20 )536.83333333333321.364653348426125.1271726518737
Trimmed Mean ( 13 / 20 )534.38235294117620.481025291234426.0915821030642
Trimmed Mean ( 14 / 20 )532.0312519.557632181900227.2032547218253
Trimmed Mean ( 15 / 20 )53118.969000725018427.9930402079462
Trimmed Mean ( 16 / 20 )530.28571428571418.391312155792228.8334899540435
Trimmed Mean ( 17 / 20 )529.53846153846217.701128236030729.9155203260200
Trimmed Mean ( 18 / 20 )528.516.772022079572931.5108099364879
Trimmed Mean ( 19 / 20 )527.81818181818215.565618172968633.9092335397765
Trimmed Mean ( 20 / 20 )526.813.866582320931137.9906156980596
Median533.5
Midrange788.5
Midmean - Weighted Average at Xnp525.677419354839
Midmean - Weighted Average at X(n+1)p531
Midmean - Empirical Distribution Function525.677419354839
Midmean - Empirical Distribution Function - Averaging531
Midmean - Empirical Distribution Function - Interpolation531
Midmean - Closest Observation525.677419354839
Midmean - True Basic - Statistics Graphics Toolkit531
Midmean - MS Excel (old versions)532.03125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 580.383333333333 & 32.1177309186016 & 18.0704961631394 \tabularnewline
Geometric Mean & 532.094589335622 &  &  \tabularnewline
Harmonic Mean & 489.392755584765 &  &  \tabularnewline
Quadratic Mean & 630.639503467182 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 575.833333333333 & 30.6122106159409 & 18.8105766211302 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 576 & 30.2546443182672 & 19.0383993260903 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 574.45 & 29.7726737885561 & 19.2945384777905 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 573.183333333333 & 29.4509981957646 & 19.4622718565703 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 574.85 & 29.057198851313 & 19.7833935384320 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 573.85 & 28.7923093250817 & 19.9306694548501 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 575.95 & 28.4345956330235 & 20.2552555145571 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 576.75 & 28.1718959308560 & 20.4725305465969 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 570.45 & 26.5676136154593 & 21.4716311467306 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 566.283333333333 & 25.453736604992 & 22.247552181485 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 555.1 & 22.9789967967557 & 24.1568422202997 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 553.5 & 22.6102509125327 & 24.4800467779506 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 550.683333333333 & 21.5113751496418 & 25.5996341239255 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 539.25 & 19.2030280245261 & 28.0815087761821 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 536 & 18.1905792964722 & 29.4658015703738 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 535.466666666667 & 17.5198913049454 & 30.5633555223896 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 536.6 & 16.9978596193291 & 31.5686805290359 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 533 & 16.2433124004962 & 32.8135042199717 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 534.266666666667 & 15.4735032620770 & 34.5278414084849 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 521.933333333333 & 11.1308058973585 & 46.8908844648164 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 573.206896551724 & 30.0662180932345 & 19.0648153610217 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 570.392857142857 & 29.3815106470638 & 19.4133264281242 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 567.277777777778 & 28.7565313781397 & 19.7269194367793 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 564.519230769231 & 28.1948415099501 & 20.0220749802764 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 561.92 & 27.5990067848501 & 20.3601529714632 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 558.6875 & 26.9548341078537 & 20.7268016476947 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 555.391304347826 & 26.1951700799546 & 21.2020499448038 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 551.386363636364 & 25.2901809303438 & 21.8023890439944 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 546.857142857143 & 24.1522361841069 & 22.6420915516302 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 542.925 & 23.1237858309111 & 23.4790705972651 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 539.236842105263 & 22.0631588618299 & 24.4406000737349 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 536.833333333333 & 21.3646533484261 & 25.1271726518737 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 534.382352941176 & 20.4810252912344 & 26.0915821030642 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 532.03125 & 19.5576321819002 & 27.2032547218253 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 531 & 18.9690007250184 & 27.9930402079462 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 530.285714285714 & 18.3913121557922 & 28.8334899540435 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 529.538461538462 & 17.7011282360307 & 29.9155203260200 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 528.5 & 16.7720220795729 & 31.5108099364879 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 527.818181818182 & 15.5656181729686 & 33.9092335397765 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 526.8 & 13.8665823209311 & 37.9906156980596 \tabularnewline
Median & 533.5 &  &  \tabularnewline
Midrange & 788.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 525.677419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 531 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 525.677419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 531 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 531 &  &  \tabularnewline
Midmean - Closest Observation & 525.677419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 531 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 532.03125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32976&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]580.383333333333[/C][C]32.1177309186016[/C][C]18.0704961631394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]532.094589335622[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]489.392755584765[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]630.639503467182[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]575.833333333333[/C][C]30.6122106159409[/C][C]18.8105766211302[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]576[/C][C]30.2546443182672[/C][C]19.0383993260903[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]574.45[/C][C]29.7726737885561[/C][C]19.2945384777905[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]573.183333333333[/C][C]29.4509981957646[/C][C]19.4622718565703[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]574.85[/C][C]29.057198851313[/C][C]19.7833935384320[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]573.85[/C][C]28.7923093250817[/C][C]19.9306694548501[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]575.95[/C][C]28.4345956330235[/C][C]20.2552555145571[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]576.75[/C][C]28.1718959308560[/C][C]20.4725305465969[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]570.45[/C][C]26.5676136154593[/C][C]21.4716311467306[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]566.283333333333[/C][C]25.453736604992[/C][C]22.247552181485[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]555.1[/C][C]22.9789967967557[/C][C]24.1568422202997[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]553.5[/C][C]22.6102509125327[/C][C]24.4800467779506[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]550.683333333333[/C][C]21.5113751496418[/C][C]25.5996341239255[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]539.25[/C][C]19.2030280245261[/C][C]28.0815087761821[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]536[/C][C]18.1905792964722[/C][C]29.4658015703738[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]535.466666666667[/C][C]17.5198913049454[/C][C]30.5633555223896[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]536.6[/C][C]16.9978596193291[/C][C]31.5686805290359[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]533[/C][C]16.2433124004962[/C][C]32.8135042199717[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]534.266666666667[/C][C]15.4735032620770[/C][C]34.5278414084849[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]521.933333333333[/C][C]11.1308058973585[/C][C]46.8908844648164[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]573.206896551724[/C][C]30.0662180932345[/C][C]19.0648153610217[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]570.392857142857[/C][C]29.3815106470638[/C][C]19.4133264281242[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]567.277777777778[/C][C]28.7565313781397[/C][C]19.7269194367793[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]564.519230769231[/C][C]28.1948415099501[/C][C]20.0220749802764[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]561.92[/C][C]27.5990067848501[/C][C]20.3601529714632[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]558.6875[/C][C]26.9548341078537[/C][C]20.7268016476947[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]555.391304347826[/C][C]26.1951700799546[/C][C]21.2020499448038[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]551.386363636364[/C][C]25.2901809303438[/C][C]21.8023890439944[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]546.857142857143[/C][C]24.1522361841069[/C][C]22.6420915516302[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]542.925[/C][C]23.1237858309111[/C][C]23.4790705972651[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]539.236842105263[/C][C]22.0631588618299[/C][C]24.4406000737349[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]536.833333333333[/C][C]21.3646533484261[/C][C]25.1271726518737[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]534.382352941176[/C][C]20.4810252912344[/C][C]26.0915821030642[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]532.03125[/C][C]19.5576321819002[/C][C]27.2032547218253[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]531[/C][C]18.9690007250184[/C][C]27.9930402079462[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]530.285714285714[/C][C]18.3913121557922[/C][C]28.8334899540435[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]529.538461538462[/C][C]17.7011282360307[/C][C]29.9155203260200[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]528.5[/C][C]16.7720220795729[/C][C]31.5108099364879[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]527.818181818182[/C][C]15.5656181729686[/C][C]33.9092335397765[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]526.8[/C][C]13.8665823209311[/C][C]37.9906156980596[/C][/ROW]
[ROW][C]Median[/C][C]533.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]788.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]525.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]531[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]525.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]531[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]531[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]525.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]531[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]532.03125[/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=32976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32976&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 Mean580.38333333333332.117730918601618.0704961631394
Geometric Mean532.094589335622
Harmonic Mean489.392755584765
Quadratic Mean630.639503467182
Winsorized Mean ( 1 / 20 )575.83333333333330.612210615940918.8105766211302
Winsorized Mean ( 2 / 20 )57630.254644318267219.0383993260903
Winsorized Mean ( 3 / 20 )574.4529.772673788556119.2945384777905
Winsorized Mean ( 4 / 20 )573.18333333333329.450998195764619.4622718565703
Winsorized Mean ( 5 / 20 )574.8529.05719885131319.7833935384320
Winsorized Mean ( 6 / 20 )573.8528.792309325081719.9306694548501
Winsorized Mean ( 7 / 20 )575.9528.434595633023520.2552555145571
Winsorized Mean ( 8 / 20 )576.7528.171895930856020.4725305465969
Winsorized Mean ( 9 / 20 )570.4526.567613615459321.4716311467306
Winsorized Mean ( 10 / 20 )566.28333333333325.45373660499222.247552181485
Winsorized Mean ( 11 / 20 )555.122.978996796755724.1568422202997
Winsorized Mean ( 12 / 20 )553.522.610250912532724.4800467779506
Winsorized Mean ( 13 / 20 )550.68333333333321.511375149641825.5996341239255
Winsorized Mean ( 14 / 20 )539.2519.203028024526128.0815087761821
Winsorized Mean ( 15 / 20 )53618.190579296472229.4658015703738
Winsorized Mean ( 16 / 20 )535.46666666666717.519891304945430.5633555223896
Winsorized Mean ( 17 / 20 )536.616.997859619329131.5686805290359
Winsorized Mean ( 18 / 20 )53316.243312400496232.8135042199717
Winsorized Mean ( 19 / 20 )534.26666666666715.473503262077034.5278414084849
Winsorized Mean ( 20 / 20 )521.93333333333311.130805897358546.8908844648164
Trimmed Mean ( 1 / 20 )573.20689655172430.066218093234519.0648153610217
Trimmed Mean ( 2 / 20 )570.39285714285729.381510647063819.4133264281242
Trimmed Mean ( 3 / 20 )567.27777777777828.756531378139719.7269194367793
Trimmed Mean ( 4 / 20 )564.51923076923128.194841509950120.0220749802764
Trimmed Mean ( 5 / 20 )561.9227.599006784850120.3601529714632
Trimmed Mean ( 6 / 20 )558.687526.954834107853720.7268016476947
Trimmed Mean ( 7 / 20 )555.39130434782626.195170079954621.2020499448038
Trimmed Mean ( 8 / 20 )551.38636363636425.290180930343821.8023890439944
Trimmed Mean ( 9 / 20 )546.85714285714324.152236184106922.6420915516302
Trimmed Mean ( 10 / 20 )542.92523.123785830911123.4790705972651
Trimmed Mean ( 11 / 20 )539.23684210526322.063158861829924.4406000737349
Trimmed Mean ( 12 / 20 )536.83333333333321.364653348426125.1271726518737
Trimmed Mean ( 13 / 20 )534.38235294117620.481025291234426.0915821030642
Trimmed Mean ( 14 / 20 )532.0312519.557632181900227.2032547218253
Trimmed Mean ( 15 / 20 )53118.969000725018427.9930402079462
Trimmed Mean ( 16 / 20 )530.28571428571418.391312155792228.8334899540435
Trimmed Mean ( 17 / 20 )529.53846153846217.701128236030729.9155203260200
Trimmed Mean ( 18 / 20 )528.516.772022079572931.5108099364879
Trimmed Mean ( 19 / 20 )527.81818181818215.565618172968633.9092335397765
Trimmed Mean ( 20 / 20 )526.813.866582320931137.9906156980596
Median533.5
Midrange788.5
Midmean - Weighted Average at Xnp525.677419354839
Midmean - Weighted Average at X(n+1)p531
Midmean - Empirical Distribution Function525.677419354839
Midmean - Empirical Distribution Function - Averaging531
Midmean - Empirical Distribution Function - Interpolation531
Midmean - Closest Observation525.677419354839
Midmean - True Basic - Statistics Graphics Toolkit531
Midmean - MS Excel (old versions)532.03125
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')