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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, 18 Oct 2008 08:05:41 -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/2008/Oct/18/t1224338779td4srojex2th07y.htm/, Retrieved Wed, 22 May 2024 09:54:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16628, Retrieved Wed, 22 May 2024 09:54:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-10-18 14:05:41] [bda7fba231d49184c6a1b627868bbb81] [Current]
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Dataseries X:
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517




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=16628&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=16628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16628&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 Mean565.5737704918034.65189655291396121.579180460822
Geometric Mean564.416636829091
Harmonic Mean563.251238230372
Quadratic Mean566.720476390836
Winsorized Mean ( 1 / 20 )565.5901639344264.64048336051582121.881735154322
Winsorized Mean ( 2 / 20 )565.721311475414.58210651127006123.463151736864
Winsorized Mean ( 3 / 20 )565.5737704918034.5091563807201125.427845640936
Winsorized Mean ( 4 / 20 )565.5737704918034.48217227635988126.182961211639
Winsorized Mean ( 5 / 20 )565.5737704918034.48217227635988126.182961211639
Winsorized Mean ( 6 / 20 )564.9836065573774.32835938601097130.530659811515
Winsorized Mean ( 7 / 20 )565.2131147540984.23671918860737133.408208000655
Winsorized Mean ( 8 / 20 )565.4754098360664.13452784766977136.769041271488
Winsorized Mean ( 9 / 20 )565.4754098360664.13452784766977136.769041271488
Winsorized Mean ( 10 / 20 )563.5081967213113.68289673876774153.006786964615
Winsorized Mean ( 11 / 20 )564.4098360655743.38143250993188166.91441701344
Winsorized Mean ( 12 / 20 )564.6065573770493.34437613649589168.822684510787
Winsorized Mean ( 13 / 20 )565.4590163934433.11663733692039181.432407837411
Winsorized Mean ( 14 / 20 )566.6065573770492.91672009523503194.261546832245
Winsorized Mean ( 15 / 20 )567.5901639344262.67577444477921212.121827025394
Winsorized Mean ( 16 / 20 )567.3278688524592.55194357641380222.31207386243
Winsorized Mean ( 17 / 20 )567.3278688524592.46491460203832230.161267405903
Winsorized Mean ( 18 / 20 )567.9180327868852.28206299654516248.861680701481
Winsorized Mean ( 19 / 20 )568.2295081967212.1398372649711265.548001008570
Winsorized Mean ( 20 / 20 )568.885245901641.6524693164741344.263727156810
Trimmed Mean ( 1 / 20 )565.6271186440684.54691103327594124.398105550033
Trimmed Mean ( 2 / 20 )565.6666666666674.43134294928397127.651295135726
Trimmed Mean ( 3 / 20 )565.6363636363644.32667426470233130.732366023232
Trimmed Mean ( 4 / 20 )565.6603773584914.23055985859383133.708160684555
Trimmed Mean ( 5 / 20 )565.6862745098044.11953644794458137.317943816725
Trimmed Mean ( 6 / 20 )565.7142857142863.97825723304123142.201535138495
Trimmed Mean ( 7 / 20 )565.8723404255323.84681434348284147.101546864152
Trimmed Mean ( 8 / 20 )5663.70462446467148152.782017556047
Trimmed Mean ( 9 / 20 )566.0930232558143.54902603167683159.506585244276
Trimmed Mean ( 10 / 20 )566.195121951223.34230450514551169.402614597071
Trimmed Mean ( 11 / 20 )566.6153846153853.19594365558647177.292044440442
Trimmed Mean ( 12 / 20 )566.9459459459463.0851153715501183.768150512014
Trimmed Mean ( 13 / 20 )567.2857142857142.94075146989389192.905017677738
Trimmed Mean ( 14 / 20 )567.5454545454552.80863485559553202.071641108760
Trimmed Mean ( 15 / 20 )567.6774193548392.68343668943038211.54865385527
Trimmed Mean ( 16 / 20 )567.6896551724142.57790127734818220.213884899573
Trimmed Mean ( 17 / 20 )567.7407407407412.45854089669455230.925888401554
Trimmed Mean ( 18 / 20 )567.82.30362033908947246.481588291771
Trimmed Mean ( 19 / 20 )567.7826086956522.13289363630516266.202964381867
Trimmed Mean ( 20 / 20 )567.7142857142861.91503183753574296.451617454475
Median567
Midrange564
Midmean - Weighted Average at Xnp566.833333333333
Midmean - Weighted Average at X(n+1)p567.677419354839
Midmean - Empirical Distribution Function567.677419354839
Midmean - Empirical Distribution Function - Averaging567.677419354839
Midmean - Empirical Distribution Function - Interpolation567.677419354839
Midmean - Closest Observation566.71875
Midmean - True Basic - Statistics Graphics Toolkit567.677419354839
Midmean - MS Excel (old versions)567.677419354839
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 565.573770491803 & 4.65189655291396 & 121.579180460822 \tabularnewline
Geometric Mean & 564.416636829091 &  &  \tabularnewline
Harmonic Mean & 563.251238230372 &  &  \tabularnewline
Quadratic Mean & 566.720476390836 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 565.590163934426 & 4.64048336051582 & 121.881735154322 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 565.72131147541 & 4.58210651127006 & 123.463151736864 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 565.573770491803 & 4.5091563807201 & 125.427845640936 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 565.573770491803 & 4.48217227635988 & 126.182961211639 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 565.573770491803 & 4.48217227635988 & 126.182961211639 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 564.983606557377 & 4.32835938601097 & 130.530659811515 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 565.213114754098 & 4.23671918860737 & 133.408208000655 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 565.475409836066 & 4.13452784766977 & 136.769041271488 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 565.475409836066 & 4.13452784766977 & 136.769041271488 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 563.508196721311 & 3.68289673876774 & 153.006786964615 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 564.409836065574 & 3.38143250993188 & 166.91441701344 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 564.606557377049 & 3.34437613649589 & 168.822684510787 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 565.459016393443 & 3.11663733692039 & 181.432407837411 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 566.606557377049 & 2.91672009523503 & 194.261546832245 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 567.590163934426 & 2.67577444477921 & 212.121827025394 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 567.327868852459 & 2.55194357641380 & 222.31207386243 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 567.327868852459 & 2.46491460203832 & 230.161267405903 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 567.918032786885 & 2.28206299654516 & 248.861680701481 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 568.229508196721 & 2.1398372649711 & 265.548001008570 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 568.88524590164 & 1.6524693164741 & 344.263727156810 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 565.627118644068 & 4.54691103327594 & 124.398105550033 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 565.666666666667 & 4.43134294928397 & 127.651295135726 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 565.636363636364 & 4.32667426470233 & 130.732366023232 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 565.660377358491 & 4.23055985859383 & 133.708160684555 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 565.686274509804 & 4.11953644794458 & 137.317943816725 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 565.714285714286 & 3.97825723304123 & 142.201535138495 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 565.872340425532 & 3.84681434348284 & 147.101546864152 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 566 & 3.70462446467148 & 152.782017556047 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 566.093023255814 & 3.54902603167683 & 159.506585244276 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 566.19512195122 & 3.34230450514551 & 169.402614597071 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 566.615384615385 & 3.19594365558647 & 177.292044440442 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 566.945945945946 & 3.0851153715501 & 183.768150512014 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 567.285714285714 & 2.94075146989389 & 192.905017677738 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 567.545454545455 & 2.80863485559553 & 202.071641108760 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 567.677419354839 & 2.68343668943038 & 211.54865385527 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 567.689655172414 & 2.57790127734818 & 220.213884899573 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 567.740740740741 & 2.45854089669455 & 230.925888401554 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 567.8 & 2.30362033908947 & 246.481588291771 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 567.782608695652 & 2.13289363630516 & 266.202964381867 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 567.714285714286 & 1.91503183753574 & 296.451617454475 \tabularnewline
Median & 567 &  &  \tabularnewline
Midrange & 564 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 566.833333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 567.677419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 567.677419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 567.677419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 567.677419354839 &  &  \tabularnewline
Midmean - Closest Observation & 566.71875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 567.677419354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 567.677419354839 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16628&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]565.573770491803[/C][C]4.65189655291396[/C][C]121.579180460822[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]564.416636829091[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]563.251238230372[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]566.720476390836[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]565.590163934426[/C][C]4.64048336051582[/C][C]121.881735154322[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]565.72131147541[/C][C]4.58210651127006[/C][C]123.463151736864[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]565.573770491803[/C][C]4.5091563807201[/C][C]125.427845640936[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]565.573770491803[/C][C]4.48217227635988[/C][C]126.182961211639[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]565.573770491803[/C][C]4.48217227635988[/C][C]126.182961211639[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]564.983606557377[/C][C]4.32835938601097[/C][C]130.530659811515[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]565.213114754098[/C][C]4.23671918860737[/C][C]133.408208000655[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]565.475409836066[/C][C]4.13452784766977[/C][C]136.769041271488[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]565.475409836066[/C][C]4.13452784766977[/C][C]136.769041271488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]563.508196721311[/C][C]3.68289673876774[/C][C]153.006786964615[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]564.409836065574[/C][C]3.38143250993188[/C][C]166.91441701344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]564.606557377049[/C][C]3.34437613649589[/C][C]168.822684510787[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]565.459016393443[/C][C]3.11663733692039[/C][C]181.432407837411[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]566.606557377049[/C][C]2.91672009523503[/C][C]194.261546832245[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]567.590163934426[/C][C]2.67577444477921[/C][C]212.121827025394[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]567.327868852459[/C][C]2.55194357641380[/C][C]222.31207386243[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]567.327868852459[/C][C]2.46491460203832[/C][C]230.161267405903[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]567.918032786885[/C][C]2.28206299654516[/C][C]248.861680701481[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]568.229508196721[/C][C]2.1398372649711[/C][C]265.548001008570[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]568.88524590164[/C][C]1.6524693164741[/C][C]344.263727156810[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]565.627118644068[/C][C]4.54691103327594[/C][C]124.398105550033[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]565.666666666667[/C][C]4.43134294928397[/C][C]127.651295135726[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]565.636363636364[/C][C]4.32667426470233[/C][C]130.732366023232[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]565.660377358491[/C][C]4.23055985859383[/C][C]133.708160684555[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]565.686274509804[/C][C]4.11953644794458[/C][C]137.317943816725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]565.714285714286[/C][C]3.97825723304123[/C][C]142.201535138495[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]565.872340425532[/C][C]3.84681434348284[/C][C]147.101546864152[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]566[/C][C]3.70462446467148[/C][C]152.782017556047[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]566.093023255814[/C][C]3.54902603167683[/C][C]159.506585244276[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]566.19512195122[/C][C]3.34230450514551[/C][C]169.402614597071[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]566.615384615385[/C][C]3.19594365558647[/C][C]177.292044440442[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]566.945945945946[/C][C]3.0851153715501[/C][C]183.768150512014[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]567.285714285714[/C][C]2.94075146989389[/C][C]192.905017677738[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]567.545454545455[/C][C]2.80863485559553[/C][C]202.071641108760[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]567.677419354839[/C][C]2.68343668943038[/C][C]211.54865385527[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]567.689655172414[/C][C]2.57790127734818[/C][C]220.213884899573[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]567.740740740741[/C][C]2.45854089669455[/C][C]230.925888401554[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]567.8[/C][C]2.30362033908947[/C][C]246.481588291771[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]567.782608695652[/C][C]2.13289363630516[/C][C]266.202964381867[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]567.714285714286[/C][C]1.91503183753574[/C][C]296.451617454475[/C][/ROW]
[ROW][C]Median[/C][C]567[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]566.833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]566.71875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16628&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 Mean565.5737704918034.65189655291396121.579180460822
Geometric Mean564.416636829091
Harmonic Mean563.251238230372
Quadratic Mean566.720476390836
Winsorized Mean ( 1 / 20 )565.5901639344264.64048336051582121.881735154322
Winsorized Mean ( 2 / 20 )565.721311475414.58210651127006123.463151736864
Winsorized Mean ( 3 / 20 )565.5737704918034.5091563807201125.427845640936
Winsorized Mean ( 4 / 20 )565.5737704918034.48217227635988126.182961211639
Winsorized Mean ( 5 / 20 )565.5737704918034.48217227635988126.182961211639
Winsorized Mean ( 6 / 20 )564.9836065573774.32835938601097130.530659811515
Winsorized Mean ( 7 / 20 )565.2131147540984.23671918860737133.408208000655
Winsorized Mean ( 8 / 20 )565.4754098360664.13452784766977136.769041271488
Winsorized Mean ( 9 / 20 )565.4754098360664.13452784766977136.769041271488
Winsorized Mean ( 10 / 20 )563.5081967213113.68289673876774153.006786964615
Winsorized Mean ( 11 / 20 )564.4098360655743.38143250993188166.91441701344
Winsorized Mean ( 12 / 20 )564.6065573770493.34437613649589168.822684510787
Winsorized Mean ( 13 / 20 )565.4590163934433.11663733692039181.432407837411
Winsorized Mean ( 14 / 20 )566.6065573770492.91672009523503194.261546832245
Winsorized Mean ( 15 / 20 )567.5901639344262.67577444477921212.121827025394
Winsorized Mean ( 16 / 20 )567.3278688524592.55194357641380222.31207386243
Winsorized Mean ( 17 / 20 )567.3278688524592.46491460203832230.161267405903
Winsorized Mean ( 18 / 20 )567.9180327868852.28206299654516248.861680701481
Winsorized Mean ( 19 / 20 )568.2295081967212.1398372649711265.548001008570
Winsorized Mean ( 20 / 20 )568.885245901641.6524693164741344.263727156810
Trimmed Mean ( 1 / 20 )565.6271186440684.54691103327594124.398105550033
Trimmed Mean ( 2 / 20 )565.6666666666674.43134294928397127.651295135726
Trimmed Mean ( 3 / 20 )565.6363636363644.32667426470233130.732366023232
Trimmed Mean ( 4 / 20 )565.6603773584914.23055985859383133.708160684555
Trimmed Mean ( 5 / 20 )565.6862745098044.11953644794458137.317943816725
Trimmed Mean ( 6 / 20 )565.7142857142863.97825723304123142.201535138495
Trimmed Mean ( 7 / 20 )565.8723404255323.84681434348284147.101546864152
Trimmed Mean ( 8 / 20 )5663.70462446467148152.782017556047
Trimmed Mean ( 9 / 20 )566.0930232558143.54902603167683159.506585244276
Trimmed Mean ( 10 / 20 )566.195121951223.34230450514551169.402614597071
Trimmed Mean ( 11 / 20 )566.6153846153853.19594365558647177.292044440442
Trimmed Mean ( 12 / 20 )566.9459459459463.0851153715501183.768150512014
Trimmed Mean ( 13 / 20 )567.2857142857142.94075146989389192.905017677738
Trimmed Mean ( 14 / 20 )567.5454545454552.80863485559553202.071641108760
Trimmed Mean ( 15 / 20 )567.6774193548392.68343668943038211.54865385527
Trimmed Mean ( 16 / 20 )567.6896551724142.57790127734818220.213884899573
Trimmed Mean ( 17 / 20 )567.7407407407412.45854089669455230.925888401554
Trimmed Mean ( 18 / 20 )567.82.30362033908947246.481588291771
Trimmed Mean ( 19 / 20 )567.7826086956522.13289363630516266.202964381867
Trimmed Mean ( 20 / 20 )567.7142857142861.91503183753574296.451617454475
Median567
Midrange564
Midmean - Weighted Average at Xnp566.833333333333
Midmean - Weighted Average at X(n+1)p567.677419354839
Midmean - Empirical Distribution Function567.677419354839
Midmean - Empirical Distribution Function - Averaging567.677419354839
Midmean - Empirical Distribution Function - Interpolation567.677419354839
Midmean - Closest Observation566.71875
Midmean - True Basic - Statistics Graphics Toolkit567.677419354839
Midmean - MS Excel (old versions)567.677419354839
Number of observations61



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')