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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 02:41:29 -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/2007/Oct/22/5kt9ofnarz3kdsq1193045809.htm/, Retrieved Mon, 06 May 2024 07:59:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1356, Retrieved Mon, 06 May 2024 07:59:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWerkloosheid
Estimated Impact200
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Werkloosheid] [2007-10-22 09:41:29] [a1c3b9772d97ad2d7bb67d4cdac038f3] [Current]
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Dataseries X:
542
565
555
499
511
526
532
549
561
557
566
588
620
626
620
573
573
574
580
590
593
597
595
612
628
629
621
569
567
573
584
589
591
595
594
611
613
611
594
543
537
544
555
561
562
555
547
565
578
580
569
507
501
509
510
517
519
512
509
519




Summary of compuational 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 compuational 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=1356&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1356&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 compuational 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 Mean566.24.68871707363647120.757979444656
Geometric Mean565.043409977741
Harmonic Mean563.876538953069
Quadratic Mean567.344251755493
Winsorized Mean ( 1 / 20 )566.2166666666674.67697157234382121.064808265001
Winsorized Mean ( 2 / 20 )566.354.61677272512739122.672272108515
Winsorized Mean ( 3 / 20 )566.24.54225609091784124.651712423724
Winsorized Mean ( 4 / 20 )566.1333333333334.52871981927637125.009573549594
Winsorized Mean ( 5 / 20 )566.2166666666674.51100923646251125.518844450580
Winsorized Mean ( 6 / 20 )565.6166666666674.35443093161779129.894508731253
Winsorized Mean ( 7 / 20 )565.6166666666674.30832144923997131.284694823885
Winsorized Mean ( 8 / 20 )566.154.14659515897433136.533704954220
Winsorized Mean ( 9 / 20 )566.454.0869383371604138.600084774846
Winsorized Mean ( 10 / 20 )564.1166666666673.69333585734887152.739065293563
Winsorized Mean ( 11 / 20 )565.0333333333333.37931282643494167.203618710087
Winsorized Mean ( 12 / 20 )566.2333333333333.15112451156445179.692465738910
Winsorized Mean ( 13 / 20 )567.12.92299474941108194.013348848560
Winsorized Mean ( 14 / 20 )568.2666666666672.72567481580371208.486596923377
Winsorized Mean ( 15 / 20 )568.2666666666672.64520317020755214.829119013221
Winsorized Mean ( 16 / 20 )5682.51851898009670225.529370431106
Winsorized Mean ( 17 / 20 )568.5666666666672.33946329576701243.032950205041
Winsorized Mean ( 18 / 20 )568.8666666666672.20008560011520258.565697006007
Winsorized Mean ( 19 / 20 )570.451.87104384896393304.883287644958
Winsorized Mean ( 20 / 20 )569.1166666666671.66368518633986342.081946355929
Trimmed Mean ( 1 / 20 )566.2758620689654.58051536999033123.627106630615
Trimmed Mean ( 2 / 20 )566.3392857142864.46096174955393126.954526290416
Trimmed Mean ( 3 / 20 )566.3333333333334.35224064159784130.124545026402
Trimmed Mean ( 4 / 20 )566.3846153846154.25153275937486133.218923019165
Trimmed Mean ( 5 / 20 )566.464.1289629077866137.191835492574
Trimmed Mean ( 6 / 20 )566.5208333333333.97877676230166142.385679614156
Trimmed Mean ( 7 / 20 )566.7173913043483.83659760744182147.713534045137
Trimmed Mean ( 8 / 20 )566.9318181818183.66565075851137154.660619772750
Trimmed Mean ( 9 / 20 )567.0714285714293.49105258482190162.435659387341
Trimmed Mean ( 10 / 20 )567.1753.27635027947962173.111832258083
Trimmed Mean ( 11 / 20 )567.6578947368423.10170794867071183.014617794729
Trimmed Mean ( 12 / 20 )568.0555555555562.95976844987846191.925674313773
Trimmed Mean ( 13 / 20 )568.3235294117652.83369105057633200.559453824783
Trimmed Mean ( 14 / 20 )568.52.7253292195327208.598651467685
Trimmed Mean ( 15 / 20 )568.5333333333332.62951126674059216.212548896228
Trimmed Mean ( 16 / 20 )568.5714285714292.51052207487514226.475375086955
Trimmed Mean ( 17 / 20 )568.6538461538462.37223835077747239.71193534051
Trimmed Mean ( 18 / 20 )568.6666666666672.22523949750494255.553016789558
Trimmed Mean ( 19 / 20 )568.6363636363642.04552669425425277.990194522333
Trimmed Mean ( 20 / 20 )568.351.89913415174279299.267958231618
Median568
Midrange564
Midmean - Weighted Average at Xnp567.677419354839
Midmean - Weighted Average at X(n+1)p568.533333333333
Midmean - Empirical Distribution Function567.677419354839
Midmean - Empirical Distribution Function - Averaging568.533333333333
Midmean - Empirical Distribution Function - Interpolation568.533333333333
Midmean - Closest Observation567.677419354839
Midmean - True Basic - Statistics Graphics Toolkit568.533333333333
Midmean - MS Excel (old versions)569.272727272727
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 566.2 & 4.68871707363647 & 120.757979444656 \tabularnewline
Geometric Mean & 565.043409977741 &  &  \tabularnewline
Harmonic Mean & 563.876538953069 &  &  \tabularnewline
Quadratic Mean & 567.344251755493 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 566.216666666667 & 4.67697157234382 & 121.064808265001 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 566.35 & 4.61677272512739 & 122.672272108515 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 566.2 & 4.54225609091784 & 124.651712423724 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 566.133333333333 & 4.52871981927637 & 125.009573549594 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 566.216666666667 & 4.51100923646251 & 125.518844450580 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 565.616666666667 & 4.35443093161779 & 129.894508731253 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 565.616666666667 & 4.30832144923997 & 131.284694823885 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 566.15 & 4.14659515897433 & 136.533704954220 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 566.45 & 4.0869383371604 & 138.600084774846 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 564.116666666667 & 3.69333585734887 & 152.739065293563 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 565.033333333333 & 3.37931282643494 & 167.203618710087 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 566.233333333333 & 3.15112451156445 & 179.692465738910 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 567.1 & 2.92299474941108 & 194.013348848560 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 568.266666666667 & 2.72567481580371 & 208.486596923377 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 568.266666666667 & 2.64520317020755 & 214.829119013221 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 568 & 2.51851898009670 & 225.529370431106 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 568.566666666667 & 2.33946329576701 & 243.032950205041 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 568.866666666667 & 2.20008560011520 & 258.565697006007 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 570.45 & 1.87104384896393 & 304.883287644958 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 569.116666666667 & 1.66368518633986 & 342.081946355929 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 566.275862068965 & 4.58051536999033 & 123.627106630615 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 566.339285714286 & 4.46096174955393 & 126.954526290416 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 566.333333333333 & 4.35224064159784 & 130.124545026402 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 566.384615384615 & 4.25153275937486 & 133.218923019165 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 566.46 & 4.1289629077866 & 137.191835492574 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 566.520833333333 & 3.97877676230166 & 142.385679614156 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 566.717391304348 & 3.83659760744182 & 147.713534045137 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 566.931818181818 & 3.66565075851137 & 154.660619772750 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 567.071428571429 & 3.49105258482190 & 162.435659387341 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 567.175 & 3.27635027947962 & 173.111832258083 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 567.657894736842 & 3.10170794867071 & 183.014617794729 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 568.055555555556 & 2.95976844987846 & 191.925674313773 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 568.323529411765 & 2.83369105057633 & 200.559453824783 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 568.5 & 2.7253292195327 & 208.598651467685 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 568.533333333333 & 2.62951126674059 & 216.212548896228 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 568.571428571429 & 2.51052207487514 & 226.475375086955 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 568.653846153846 & 2.37223835077747 & 239.71193534051 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 568.666666666667 & 2.22523949750494 & 255.553016789558 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 568.636363636364 & 2.04552669425425 & 277.990194522333 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 568.35 & 1.89913415174279 & 299.267958231618 \tabularnewline
Median & 568 &  &  \tabularnewline
Midrange & 564 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 567.677419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 568.533333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 567.677419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 568.533333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 568.533333333333 &  &  \tabularnewline
Midmean - Closest Observation & 567.677419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 568.533333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 569.272727272727 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1356&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]566.2[/C][C]4.68871707363647[/C][C]120.757979444656[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]565.043409977741[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]563.876538953069[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]567.344251755493[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]566.216666666667[/C][C]4.67697157234382[/C][C]121.064808265001[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]566.35[/C][C]4.61677272512739[/C][C]122.672272108515[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]566.2[/C][C]4.54225609091784[/C][C]124.651712423724[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]566.133333333333[/C][C]4.52871981927637[/C][C]125.009573549594[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]566.216666666667[/C][C]4.51100923646251[/C][C]125.518844450580[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]565.616666666667[/C][C]4.35443093161779[/C][C]129.894508731253[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]565.616666666667[/C][C]4.30832144923997[/C][C]131.284694823885[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]566.15[/C][C]4.14659515897433[/C][C]136.533704954220[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]566.45[/C][C]4.0869383371604[/C][C]138.600084774846[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]564.116666666667[/C][C]3.69333585734887[/C][C]152.739065293563[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]565.033333333333[/C][C]3.37931282643494[/C][C]167.203618710087[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]566.233333333333[/C][C]3.15112451156445[/C][C]179.692465738910[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]567.1[/C][C]2.92299474941108[/C][C]194.013348848560[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]568.266666666667[/C][C]2.72567481580371[/C][C]208.486596923377[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]568.266666666667[/C][C]2.64520317020755[/C][C]214.829119013221[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]568[/C][C]2.51851898009670[/C][C]225.529370431106[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]568.566666666667[/C][C]2.33946329576701[/C][C]243.032950205041[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]568.866666666667[/C][C]2.20008560011520[/C][C]258.565697006007[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]570.45[/C][C]1.87104384896393[/C][C]304.883287644958[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]569.116666666667[/C][C]1.66368518633986[/C][C]342.081946355929[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]566.275862068965[/C][C]4.58051536999033[/C][C]123.627106630615[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]566.339285714286[/C][C]4.46096174955393[/C][C]126.954526290416[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]566.333333333333[/C][C]4.35224064159784[/C][C]130.124545026402[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]566.384615384615[/C][C]4.25153275937486[/C][C]133.218923019165[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]566.46[/C][C]4.1289629077866[/C][C]137.191835492574[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]566.520833333333[/C][C]3.97877676230166[/C][C]142.385679614156[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]566.717391304348[/C][C]3.83659760744182[/C][C]147.713534045137[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]566.931818181818[/C][C]3.66565075851137[/C][C]154.660619772750[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]567.071428571429[/C][C]3.49105258482190[/C][C]162.435659387341[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]567.175[/C][C]3.27635027947962[/C][C]173.111832258083[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]567.657894736842[/C][C]3.10170794867071[/C][C]183.014617794729[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]568.055555555556[/C][C]2.95976844987846[/C][C]191.925674313773[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]568.323529411765[/C][C]2.83369105057633[/C][C]200.559453824783[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]568.5[/C][C]2.7253292195327[/C][C]208.598651467685[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]568.533333333333[/C][C]2.62951126674059[/C][C]216.212548896228[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]568.571428571429[/C][C]2.51052207487514[/C][C]226.475375086955[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]568.653846153846[/C][C]2.37223835077747[/C][C]239.71193534051[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]568.666666666667[/C][C]2.22523949750494[/C][C]255.553016789558[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]568.636363636364[/C][C]2.04552669425425[/C][C]277.990194522333[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]568.35[/C][C]1.89913415174279[/C][C]299.267958231618[/C][/ROW]
[ROW][C]Median[/C][C]568[/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]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]568.533333333333[/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]568.533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]568.533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]567.677419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]568.533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]569.272727272727[/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=1356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1356&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 Mean566.24.68871707363647120.757979444656
Geometric Mean565.043409977741
Harmonic Mean563.876538953069
Quadratic Mean567.344251755493
Winsorized Mean ( 1 / 20 )566.2166666666674.67697157234382121.064808265001
Winsorized Mean ( 2 / 20 )566.354.61677272512739122.672272108515
Winsorized Mean ( 3 / 20 )566.24.54225609091784124.651712423724
Winsorized Mean ( 4 / 20 )566.1333333333334.52871981927637125.009573549594
Winsorized Mean ( 5 / 20 )566.2166666666674.51100923646251125.518844450580
Winsorized Mean ( 6 / 20 )565.6166666666674.35443093161779129.894508731253
Winsorized Mean ( 7 / 20 )565.6166666666674.30832144923997131.284694823885
Winsorized Mean ( 8 / 20 )566.154.14659515897433136.533704954220
Winsorized Mean ( 9 / 20 )566.454.0869383371604138.600084774846
Winsorized Mean ( 10 / 20 )564.1166666666673.69333585734887152.739065293563
Winsorized Mean ( 11 / 20 )565.0333333333333.37931282643494167.203618710087
Winsorized Mean ( 12 / 20 )566.2333333333333.15112451156445179.692465738910
Winsorized Mean ( 13 / 20 )567.12.92299474941108194.013348848560
Winsorized Mean ( 14 / 20 )568.2666666666672.72567481580371208.486596923377
Winsorized Mean ( 15 / 20 )568.2666666666672.64520317020755214.829119013221
Winsorized Mean ( 16 / 20 )5682.51851898009670225.529370431106
Winsorized Mean ( 17 / 20 )568.5666666666672.33946329576701243.032950205041
Winsorized Mean ( 18 / 20 )568.8666666666672.20008560011520258.565697006007
Winsorized Mean ( 19 / 20 )570.451.87104384896393304.883287644958
Winsorized Mean ( 20 / 20 )569.1166666666671.66368518633986342.081946355929
Trimmed Mean ( 1 / 20 )566.2758620689654.58051536999033123.627106630615
Trimmed Mean ( 2 / 20 )566.3392857142864.46096174955393126.954526290416
Trimmed Mean ( 3 / 20 )566.3333333333334.35224064159784130.124545026402
Trimmed Mean ( 4 / 20 )566.3846153846154.25153275937486133.218923019165
Trimmed Mean ( 5 / 20 )566.464.1289629077866137.191835492574
Trimmed Mean ( 6 / 20 )566.5208333333333.97877676230166142.385679614156
Trimmed Mean ( 7 / 20 )566.7173913043483.83659760744182147.713534045137
Trimmed Mean ( 8 / 20 )566.9318181818183.66565075851137154.660619772750
Trimmed Mean ( 9 / 20 )567.0714285714293.49105258482190162.435659387341
Trimmed Mean ( 10 / 20 )567.1753.27635027947962173.111832258083
Trimmed Mean ( 11 / 20 )567.6578947368423.10170794867071183.014617794729
Trimmed Mean ( 12 / 20 )568.0555555555562.95976844987846191.925674313773
Trimmed Mean ( 13 / 20 )568.3235294117652.83369105057633200.559453824783
Trimmed Mean ( 14 / 20 )568.52.7253292195327208.598651467685
Trimmed Mean ( 15 / 20 )568.5333333333332.62951126674059216.212548896228
Trimmed Mean ( 16 / 20 )568.5714285714292.51052207487514226.475375086955
Trimmed Mean ( 17 / 20 )568.6538461538462.37223835077747239.71193534051
Trimmed Mean ( 18 / 20 )568.6666666666672.22523949750494255.553016789558
Trimmed Mean ( 19 / 20 )568.6363636363642.04552669425425277.990194522333
Trimmed Mean ( 20 / 20 )568.351.89913415174279299.267958231618
Median568
Midrange564
Midmean - Weighted Average at Xnp567.677419354839
Midmean - Weighted Average at X(n+1)p568.533333333333
Midmean - Empirical Distribution Function567.677419354839
Midmean - Empirical Distribution Function - Averaging568.533333333333
Midmean - Empirical Distribution Function - Interpolation568.533333333333
Midmean - Closest Observation567.677419354839
Midmean - True Basic - Statistics Graphics Toolkit568.533333333333
Midmean - MS Excel (old versions)569.272727272727
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')