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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 computationWed, 07 Mar 2012 05:13:40 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331115237j7a6kh7i90j7not.htm/, Retrieved Mon, 29 Apr 2024 07:20:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163577, Retrieved Mon, 29 Apr 2024 07:20:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [werkloosheid] [2012-03-07 10:13:40] [d08a5fa9e4c562ec79e796d78c067f4f] [Current]
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Dataseries X:
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
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163577&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163577&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean549.554.66755994275478117.73817727891
Geometric Mean548.375870158593
Harmonic Mean547.1971839604
Quadratic Mean550.718243145561
Winsorized Mean ( 1 / 20 )549.64.59895591196806119.505385683249
Winsorized Mean ( 2 / 20 )5504.50091014022669122.197507362877
Winsorized Mean ( 3 / 20 )549.354.27460144506178128.514905321673
Winsorized Mean ( 4 / 20 )549.554.1458184637612132.555249296042
Winsorized Mean ( 5 / 20 )549.4666666666674.0265690114248136.46026309437
Winsorized Mean ( 6 / 20 )549.4666666666673.87031777748052141.969393279214
Winsorized Mean ( 7 / 20 )549.353.76092194791451146.067907711997
Winsorized Mean ( 8 / 20 )549.353.6635188079901149.951461638978
Winsorized Mean ( 9 / 20 )549.353.6096876087507152.187684792515
Winsorized Mean ( 10 / 20 )549.6833333333333.49191897339569157.415832818938
Winsorized Mean ( 11 / 20 )549.1333333333333.27207554050171167.824161311733
Winsorized Mean ( 12 / 20 )549.1333333333333.20508658816962171.331824656549
Winsorized Mean ( 13 / 20 )549.353.16850897940062173.378078954953
Winsorized Mean ( 14 / 20 )549.5833333333332.75314834332926199.619949526129
Winsorized Mean ( 15 / 20 )550.0833333333332.67561616185401205.591273208697
Winsorized Mean ( 16 / 20 )550.0833333333332.59326503475631212.11998232376
Winsorized Mean ( 17 / 20 )550.0833333333332.50663432332782219.450969857877
Winsorized Mean ( 18 / 20 )550.0833333333332.50663432332782219.450969857877
Winsorized Mean ( 19 / 20 )549.1333333333331.98660296413244276.418259334039
Winsorized Mean ( 20 / 20 )549.1333333333331.89042587296292290.48128317915
Trimmed Mean ( 1 / 20 )549.6206896551724.42691730732122124.154270680912
Trimmed Mean ( 2 / 20 )549.6428571428574.21449482201886130.417257667804
Trimmed Mean ( 3 / 20 )549.4444444444444.01766423468067136.757183365801
Trimmed Mean ( 4 / 20 )549.4807692307693.88537599142381141.422804496563
Trimmed Mean ( 5 / 20 )549.463.77058540358315145.722730342576
Trimmed Mean ( 6 / 20 )549.4583333333333.66601682668294149.87883561639
Trimmed Mean ( 7 / 20 )549.456521739133.58036871252422153.463669765943
Trimmed Mean ( 8 / 20 )549.4772727272733.4996962472184157.007132594437
Trimmed Mean ( 9 / 20 )549.53.41909137497519160.715213410752
Trimmed Mean ( 10 / 20 )549.5253.32453727260247165.293679974244
Trimmed Mean ( 11 / 20 )549.53.22789010619872170.235039583523
Trimmed Mean ( 12 / 20 )549.5555555555563.15409646570792174.23549391417
Trimmed Mean ( 13 / 20 )549.6176470588243.066120632397179.255062978115
Trimmed Mean ( 14 / 20 )549.656252.94869072059547186.406884303214
Trimmed Mean ( 15 / 20 )549.6666666666672.90157837876605189.43712521749
Trimmed Mean ( 16 / 20 )549.6071428571432.84583576109696193.126796131513
Trimmed Mean ( 17 / 20 )549.5384615384622.77806283875917197.813546141351
Trimmed Mean ( 18 / 20 )549.4583333333332.69256838667251204.064764353992
Trimmed Mean ( 19 / 20 )549.3636363636362.54274747827857216.051197005042
Trimmed Mean ( 20 / 20 )549.42.51772662702309218.212729731345
Median550
Midrange547.5
Midmean - Weighted Average at Xnp549.65625
Midmean - Weighted Average at X(n+1)p550.483870967742
Midmean - Empirical Distribution Function549.65625
Midmean - Empirical Distribution Function - Averaging550.483870967742
Midmean - Empirical Distribution Function - Interpolation550.483870967742
Midmean - Closest Observation549.65625
Midmean - True Basic - Statistics Graphics Toolkit550.483870967742
Midmean - MS Excel (old versions)549.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 549.55 & 4.66755994275478 & 117.73817727891 \tabularnewline
Geometric Mean & 548.375870158593 &  &  \tabularnewline
Harmonic Mean & 547.1971839604 &  &  \tabularnewline
Quadratic Mean & 550.718243145561 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 549.6 & 4.59895591196806 & 119.505385683249 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 550 & 4.50091014022669 & 122.197507362877 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 549.35 & 4.27460144506178 & 128.514905321673 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 549.55 & 4.1458184637612 & 132.555249296042 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 549.466666666667 & 4.0265690114248 & 136.46026309437 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 549.466666666667 & 3.87031777748052 & 141.969393279214 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 549.35 & 3.76092194791451 & 146.067907711997 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 549.35 & 3.6635188079901 & 149.951461638978 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 549.35 & 3.6096876087507 & 152.187684792515 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 549.683333333333 & 3.49191897339569 & 157.415832818938 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 549.133333333333 & 3.27207554050171 & 167.824161311733 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 549.133333333333 & 3.20508658816962 & 171.331824656549 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 549.35 & 3.16850897940062 & 173.378078954953 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 549.583333333333 & 2.75314834332926 & 199.619949526129 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 550.083333333333 & 2.67561616185401 & 205.591273208697 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 550.083333333333 & 2.59326503475631 & 212.11998232376 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 550.083333333333 & 2.50663432332782 & 219.450969857877 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 550.083333333333 & 2.50663432332782 & 219.450969857877 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 549.133333333333 & 1.98660296413244 & 276.418259334039 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 549.133333333333 & 1.89042587296292 & 290.48128317915 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 549.620689655172 & 4.42691730732122 & 124.154270680912 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 549.642857142857 & 4.21449482201886 & 130.417257667804 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 549.444444444444 & 4.01766423468067 & 136.757183365801 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 549.480769230769 & 3.88537599142381 & 141.422804496563 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 549.46 & 3.77058540358315 & 145.722730342576 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 549.458333333333 & 3.66601682668294 & 149.87883561639 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 549.45652173913 & 3.58036871252422 & 153.463669765943 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 549.477272727273 & 3.4996962472184 & 157.007132594437 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 549.5 & 3.41909137497519 & 160.715213410752 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 549.525 & 3.32453727260247 & 165.293679974244 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 549.5 & 3.22789010619872 & 170.235039583523 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 549.555555555556 & 3.15409646570792 & 174.23549391417 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 549.617647058824 & 3.066120632397 & 179.255062978115 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 549.65625 & 2.94869072059547 & 186.406884303214 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 549.666666666667 & 2.90157837876605 & 189.43712521749 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 549.607142857143 & 2.84583576109696 & 193.126796131513 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 549.538461538462 & 2.77806283875917 & 197.813546141351 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 549.458333333333 & 2.69256838667251 & 204.064764353992 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 549.363636363636 & 2.54274747827857 & 216.051197005042 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 549.4 & 2.51772662702309 & 218.212729731345 \tabularnewline
Median & 550 &  &  \tabularnewline
Midrange & 547.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 549.65625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 550.483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 549.65625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 550.483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 550.483870967742 &  &  \tabularnewline
Midmean - Closest Observation & 549.65625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 550.483870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 549.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163577&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]549.55[/C][C]4.66755994275478[/C][C]117.73817727891[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]548.375870158593[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]547.1971839604[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]550.718243145561[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]549.6[/C][C]4.59895591196806[/C][C]119.505385683249[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]550[/C][C]4.50091014022669[/C][C]122.197507362877[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]549.35[/C][C]4.27460144506178[/C][C]128.514905321673[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]549.55[/C][C]4.1458184637612[/C][C]132.555249296042[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]549.466666666667[/C][C]4.0265690114248[/C][C]136.46026309437[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]549.466666666667[/C][C]3.87031777748052[/C][C]141.969393279214[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]549.35[/C][C]3.76092194791451[/C][C]146.067907711997[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]549.35[/C][C]3.6635188079901[/C][C]149.951461638978[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]549.35[/C][C]3.6096876087507[/C][C]152.187684792515[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]549.683333333333[/C][C]3.49191897339569[/C][C]157.415832818938[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]549.133333333333[/C][C]3.27207554050171[/C][C]167.824161311733[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]549.133333333333[/C][C]3.20508658816962[/C][C]171.331824656549[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]549.35[/C][C]3.16850897940062[/C][C]173.378078954953[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]549.583333333333[/C][C]2.75314834332926[/C][C]199.619949526129[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]550.083333333333[/C][C]2.67561616185401[/C][C]205.591273208697[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]550.083333333333[/C][C]2.59326503475631[/C][C]212.11998232376[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]550.083333333333[/C][C]2.50663432332782[/C][C]219.450969857877[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]550.083333333333[/C][C]2.50663432332782[/C][C]219.450969857877[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]549.133333333333[/C][C]1.98660296413244[/C][C]276.418259334039[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]549.133333333333[/C][C]1.89042587296292[/C][C]290.48128317915[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]549.620689655172[/C][C]4.42691730732122[/C][C]124.154270680912[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]549.642857142857[/C][C]4.21449482201886[/C][C]130.417257667804[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]549.444444444444[/C][C]4.01766423468067[/C][C]136.757183365801[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]549.480769230769[/C][C]3.88537599142381[/C][C]141.422804496563[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]549.46[/C][C]3.77058540358315[/C][C]145.722730342576[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]549.458333333333[/C][C]3.66601682668294[/C][C]149.87883561639[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]549.45652173913[/C][C]3.58036871252422[/C][C]153.463669765943[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]549.477272727273[/C][C]3.4996962472184[/C][C]157.007132594437[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]549.5[/C][C]3.41909137497519[/C][C]160.715213410752[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]549.525[/C][C]3.32453727260247[/C][C]165.293679974244[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]549.5[/C][C]3.22789010619872[/C][C]170.235039583523[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]549.555555555556[/C][C]3.15409646570792[/C][C]174.23549391417[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]549.617647058824[/C][C]3.066120632397[/C][C]179.255062978115[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]549.65625[/C][C]2.94869072059547[/C][C]186.406884303214[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]549.666666666667[/C][C]2.90157837876605[/C][C]189.43712521749[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]549.607142857143[/C][C]2.84583576109696[/C][C]193.126796131513[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]549.538461538462[/C][C]2.77806283875917[/C][C]197.813546141351[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]549.458333333333[/C][C]2.69256838667251[/C][C]204.064764353992[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]549.363636363636[/C][C]2.54274747827857[/C][C]216.051197005042[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]549.4[/C][C]2.51772662702309[/C][C]218.212729731345[/C][/ROW]
[ROW][C]Median[/C][C]550[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]547.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]549.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]550.483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]549.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]550.483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]550.483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]549.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]550.483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]549.65625[/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=163577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163577&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 Mean549.554.66755994275478117.73817727891
Geometric Mean548.375870158593
Harmonic Mean547.1971839604
Quadratic Mean550.718243145561
Winsorized Mean ( 1 / 20 )549.64.59895591196806119.505385683249
Winsorized Mean ( 2 / 20 )5504.50091014022669122.197507362877
Winsorized Mean ( 3 / 20 )549.354.27460144506178128.514905321673
Winsorized Mean ( 4 / 20 )549.554.1458184637612132.555249296042
Winsorized Mean ( 5 / 20 )549.4666666666674.0265690114248136.46026309437
Winsorized Mean ( 6 / 20 )549.4666666666673.87031777748052141.969393279214
Winsorized Mean ( 7 / 20 )549.353.76092194791451146.067907711997
Winsorized Mean ( 8 / 20 )549.353.6635188079901149.951461638978
Winsorized Mean ( 9 / 20 )549.353.6096876087507152.187684792515
Winsorized Mean ( 10 / 20 )549.6833333333333.49191897339569157.415832818938
Winsorized Mean ( 11 / 20 )549.1333333333333.27207554050171167.824161311733
Winsorized Mean ( 12 / 20 )549.1333333333333.20508658816962171.331824656549
Winsorized Mean ( 13 / 20 )549.353.16850897940062173.378078954953
Winsorized Mean ( 14 / 20 )549.5833333333332.75314834332926199.619949526129
Winsorized Mean ( 15 / 20 )550.0833333333332.67561616185401205.591273208697
Winsorized Mean ( 16 / 20 )550.0833333333332.59326503475631212.11998232376
Winsorized Mean ( 17 / 20 )550.0833333333332.50663432332782219.450969857877
Winsorized Mean ( 18 / 20 )550.0833333333332.50663432332782219.450969857877
Winsorized Mean ( 19 / 20 )549.1333333333331.98660296413244276.418259334039
Winsorized Mean ( 20 / 20 )549.1333333333331.89042587296292290.48128317915
Trimmed Mean ( 1 / 20 )549.6206896551724.42691730732122124.154270680912
Trimmed Mean ( 2 / 20 )549.6428571428574.21449482201886130.417257667804
Trimmed Mean ( 3 / 20 )549.4444444444444.01766423468067136.757183365801
Trimmed Mean ( 4 / 20 )549.4807692307693.88537599142381141.422804496563
Trimmed Mean ( 5 / 20 )549.463.77058540358315145.722730342576
Trimmed Mean ( 6 / 20 )549.4583333333333.66601682668294149.87883561639
Trimmed Mean ( 7 / 20 )549.456521739133.58036871252422153.463669765943
Trimmed Mean ( 8 / 20 )549.4772727272733.4996962472184157.007132594437
Trimmed Mean ( 9 / 20 )549.53.41909137497519160.715213410752
Trimmed Mean ( 10 / 20 )549.5253.32453727260247165.293679974244
Trimmed Mean ( 11 / 20 )549.53.22789010619872170.235039583523
Trimmed Mean ( 12 / 20 )549.5555555555563.15409646570792174.23549391417
Trimmed Mean ( 13 / 20 )549.6176470588243.066120632397179.255062978115
Trimmed Mean ( 14 / 20 )549.656252.94869072059547186.406884303214
Trimmed Mean ( 15 / 20 )549.6666666666672.90157837876605189.43712521749
Trimmed Mean ( 16 / 20 )549.6071428571432.84583576109696193.126796131513
Trimmed Mean ( 17 / 20 )549.5384615384622.77806283875917197.813546141351
Trimmed Mean ( 18 / 20 )549.4583333333332.69256838667251204.064764353992
Trimmed Mean ( 19 / 20 )549.3636363636362.54274747827857216.051197005042
Trimmed Mean ( 20 / 20 )549.42.51772662702309218.212729731345
Median550
Midrange547.5
Midmean - Weighted Average at Xnp549.65625
Midmean - Weighted Average at X(n+1)p550.483870967742
Midmean - Empirical Distribution Function549.65625
Midmean - Empirical Distribution Function - Averaging550.483870967742
Midmean - Empirical Distribution Function - Interpolation550.483870967742
Midmean - Closest Observation549.65625
Midmean - True Basic - Statistics Graphics Toolkit550.483870967742
Midmean - MS Excel (old versions)549.65625
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')