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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, 06 Apr 2009 14:45:53 -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/2009/Apr/06/t12390508498f1zz535vxakilt.htm/, Retrieved Fri, 10 May 2024 13:48:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39234, Retrieved Fri, 10 May 2024 13:48:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact274
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Eigen reeks centr...] [2009-04-06 20:45:53] [991c162fae1b779ae3c185368bfa1f53] [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
508
493
490
469
478
528
534
518
506
502
516




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39234&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]2 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=39234&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39234&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean556.1388888888894.82078286178211115.362775058344
Geometric Mean554.645304461316
Harmonic Mean553.143355609844
Quadratic Mean557.620390588436
Winsorized Mean ( 1 / 24 )556.254.78753393937393116.187165886231
Winsorized Mean ( 2 / 24 )556.5277777777784.70428217929852118.302379952209
Winsorized Mean ( 3 / 24 )556.4444444444444.63769042646667119.983093582291
Winsorized Mean ( 4 / 24 )556.7222222222224.56500699006428121.954297865025
Winsorized Mean ( 5 / 24 )556.8611111111114.54060559839094122.640273206827
Winsorized Mean ( 6 / 24 )556.3611111111114.41629263876248125.979222080495
Winsorized Mean ( 7 / 24 )556.6527777777784.33302453405967128.467488102645
Winsorized Mean ( 8 / 24 )556.6527777777784.29493458798972129.606811552938
Winsorized Mean ( 9 / 24 )556.7777777777784.27471284222678130.249164874369
Winsorized Mean ( 10 / 24 )554.9722222222223.93088629530251141.182466377983
Winsorized Mean ( 11 / 24 )554.8194444444443.86040280991607143.720609419126
Winsorized Mean ( 12 / 24 )554.8194444444443.86040280991607143.720609419126
Winsorized Mean ( 13 / 24 )554.8194444444443.8046655316676145.826075860409
Winsorized Mean ( 14 / 24 )555.4027777777783.71150875398622149.643396955824
Winsorized Mean ( 15 / 24 )555.6111111111113.61619961694908153.645033450855
Winsorized Mean ( 16 / 24 )555.3888888888893.51792612315322157.873948868226
Winsorized Mean ( 17 / 24 )555.1527777777783.48446472417428159.322255130401
Winsorized Mean ( 18 / 24 )555.1527777777783.41093127466588162.756952009289
Winsorized Mean ( 19 / 24 )555.1527777777783.33378281724289166.523378459579
Winsorized Mean ( 20 / 24 )555.9861111111112.88969711142141192.40290233658
Winsorized Mean ( 21 / 24 )555.1111111111112.69116937916757206.271338923609
Winsorized Mean ( 22 / 24 )555.4166666666672.64639817821957209.876454434508
Winsorized Mean ( 23 / 24 )556.0555555555562.37874068227804233.760476582525
Winsorized Mean ( 24 / 24 )555.3888888888892.11425924566634262.687222499931
Trimmed Mean ( 1 / 24 )556.3428571428574.68241438112404118.815382804566
Trimmed Mean ( 2 / 24 )556.4411764705884.55733074769347122.098045385934
Trimmed Mean ( 3 / 24 )556.3939393939394.46096139762335124.725118601198
Trimmed Mean ( 4 / 24 )556.3754.37511337721573127.168133035691
Trimmed Mean ( 5 / 24 )556.2741935483874.29720614135267129.450199792669
Trimmed Mean ( 6 / 24 )556.1333333333334.20924907528383132.121745087236
Trimmed Mean ( 7 / 24 )556.0862068965524.13609116688811134.447279921767
Trimmed Mean ( 8 / 24 )555.9821428571434.06605292759681136.737556730662
Trimmed Mean ( 9 / 24 )555.870370370373.98696743923159139.421848520916
Trimmed Mean ( 10 / 24 )555.7307692307693.89154586884606142.804630334617
Trimmed Mean ( 11 / 24 )555.843.84785760693731144.454409902766
Trimmed Mean ( 12 / 24 )555.9791666666673.80363413189782146.170516770829
Trimmed Mean ( 13 / 24 )556.1304347826093.74302684300955148.577730833332
Trimmed Mean ( 14 / 24 )556.2954545454553.67331091117582151.442518206929
Trimmed Mean ( 15 / 24 )556.4047619047623.60008057785186154.553418978407
Trimmed Mean ( 16 / 24 )556.53.52154540667617158.027211276329
Trimmed Mean ( 17 / 24 )556.6315789473683.43553123942393162.021981508951
Trimmed Mean ( 18 / 24 )556.8055555555563.32255864411189167.583364267266
Trimmed Mean ( 19 / 24 )5573.18278569451096175.003928464491
Trimmed Mean ( 20 / 24 )557.218753.00528243768234185.413105608045
Trimmed Mean ( 21 / 24 )557.3666666666672.89012720291723192.851949943267
Trimmed Mean ( 22 / 24 )557.6428571428572.77708608168063200.801430255048
Trimmed Mean ( 23 / 24 )557.9230769230772.61647036286737213.235007298784
Trimmed Mean ( 24 / 24 )558.1666666666672.47206616236522225.789533938940
Median561
Midrange549
Midmean - Weighted Average at Xnp554.71052631579
Midmean - Weighted Average at X(n+1)p556.805555555556
Midmean - Empirical Distribution Function554.71052631579
Midmean - Empirical Distribution Function - Averaging556.805555555556
Midmean - Empirical Distribution Function - Interpolation556.805555555556
Midmean - Closest Observation554.71052631579
Midmean - True Basic - Statistics Graphics Toolkit556.805555555556
Midmean - MS Excel (old versions)555.615384615385
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 556.138888888889 & 4.82078286178211 & 115.362775058344 \tabularnewline
Geometric Mean & 554.645304461316 &  &  \tabularnewline
Harmonic Mean & 553.143355609844 &  &  \tabularnewline
Quadratic Mean & 557.620390588436 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 556.25 & 4.78753393937393 & 116.187165886231 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 556.527777777778 & 4.70428217929852 & 118.302379952209 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 556.444444444444 & 4.63769042646667 & 119.983093582291 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 556.722222222222 & 4.56500699006428 & 121.954297865025 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 556.861111111111 & 4.54060559839094 & 122.640273206827 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 556.361111111111 & 4.41629263876248 & 125.979222080495 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 556.652777777778 & 4.33302453405967 & 128.467488102645 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 556.652777777778 & 4.29493458798972 & 129.606811552938 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 556.777777777778 & 4.27471284222678 & 130.249164874369 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 554.972222222222 & 3.93088629530251 & 141.182466377983 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 554.819444444444 & 3.86040280991607 & 143.720609419126 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 554.819444444444 & 3.86040280991607 & 143.720609419126 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 554.819444444444 & 3.8046655316676 & 145.826075860409 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 555.402777777778 & 3.71150875398622 & 149.643396955824 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 555.611111111111 & 3.61619961694908 & 153.645033450855 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 555.388888888889 & 3.51792612315322 & 157.873948868226 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 555.152777777778 & 3.48446472417428 & 159.322255130401 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 555.152777777778 & 3.41093127466588 & 162.756952009289 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 555.152777777778 & 3.33378281724289 & 166.523378459579 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 555.986111111111 & 2.88969711142141 & 192.40290233658 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 555.111111111111 & 2.69116937916757 & 206.271338923609 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 555.416666666667 & 2.64639817821957 & 209.876454434508 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 556.055555555556 & 2.37874068227804 & 233.760476582525 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 555.388888888889 & 2.11425924566634 & 262.687222499931 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 556.342857142857 & 4.68241438112404 & 118.815382804566 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 556.441176470588 & 4.55733074769347 & 122.098045385934 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 556.393939393939 & 4.46096139762335 & 124.725118601198 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 556.375 & 4.37511337721573 & 127.168133035691 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 556.274193548387 & 4.29720614135267 & 129.450199792669 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 556.133333333333 & 4.20924907528383 & 132.121745087236 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 556.086206896552 & 4.13609116688811 & 134.447279921767 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 555.982142857143 & 4.06605292759681 & 136.737556730662 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 555.87037037037 & 3.98696743923159 & 139.421848520916 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 555.730769230769 & 3.89154586884606 & 142.804630334617 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 555.84 & 3.84785760693731 & 144.454409902766 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 555.979166666667 & 3.80363413189782 & 146.170516770829 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 556.130434782609 & 3.74302684300955 & 148.577730833332 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 556.295454545455 & 3.67331091117582 & 151.442518206929 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 556.404761904762 & 3.60008057785186 & 154.553418978407 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 556.5 & 3.52154540667617 & 158.027211276329 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 556.631578947368 & 3.43553123942393 & 162.021981508951 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 556.805555555556 & 3.32255864411189 & 167.583364267266 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 557 & 3.18278569451096 & 175.003928464491 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 557.21875 & 3.00528243768234 & 185.413105608045 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 557.366666666667 & 2.89012720291723 & 192.851949943267 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 557.642857142857 & 2.77708608168063 & 200.801430255048 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 557.923076923077 & 2.61647036286737 & 213.235007298784 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 558.166666666667 & 2.47206616236522 & 225.789533938940 \tabularnewline
Median & 561 &  &  \tabularnewline
Midrange & 549 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 554.71052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 556.805555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 554.71052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 556.805555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 556.805555555556 &  &  \tabularnewline
Midmean - Closest Observation & 554.71052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 556.805555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 555.615384615385 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39234&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]556.138888888889[/C][C]4.82078286178211[/C][C]115.362775058344[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]554.645304461316[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]553.143355609844[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]557.620390588436[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]556.25[/C][C]4.78753393937393[/C][C]116.187165886231[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]556.527777777778[/C][C]4.70428217929852[/C][C]118.302379952209[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]556.444444444444[/C][C]4.63769042646667[/C][C]119.983093582291[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]556.722222222222[/C][C]4.56500699006428[/C][C]121.954297865025[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]556.861111111111[/C][C]4.54060559839094[/C][C]122.640273206827[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]556.361111111111[/C][C]4.41629263876248[/C][C]125.979222080495[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]556.652777777778[/C][C]4.33302453405967[/C][C]128.467488102645[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]556.652777777778[/C][C]4.29493458798972[/C][C]129.606811552938[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]556.777777777778[/C][C]4.27471284222678[/C][C]130.249164874369[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]554.972222222222[/C][C]3.93088629530251[/C][C]141.182466377983[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]554.819444444444[/C][C]3.86040280991607[/C][C]143.720609419126[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]554.819444444444[/C][C]3.86040280991607[/C][C]143.720609419126[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]554.819444444444[/C][C]3.8046655316676[/C][C]145.826075860409[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]555.402777777778[/C][C]3.71150875398622[/C][C]149.643396955824[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]555.611111111111[/C][C]3.61619961694908[/C][C]153.645033450855[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]555.388888888889[/C][C]3.51792612315322[/C][C]157.873948868226[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]555.152777777778[/C][C]3.48446472417428[/C][C]159.322255130401[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]555.152777777778[/C][C]3.41093127466588[/C][C]162.756952009289[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]555.152777777778[/C][C]3.33378281724289[/C][C]166.523378459579[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]555.986111111111[/C][C]2.88969711142141[/C][C]192.40290233658[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]555.111111111111[/C][C]2.69116937916757[/C][C]206.271338923609[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]555.416666666667[/C][C]2.64639817821957[/C][C]209.876454434508[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]556.055555555556[/C][C]2.37874068227804[/C][C]233.760476582525[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]555.388888888889[/C][C]2.11425924566634[/C][C]262.687222499931[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]556.342857142857[/C][C]4.68241438112404[/C][C]118.815382804566[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]556.441176470588[/C][C]4.55733074769347[/C][C]122.098045385934[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]556.393939393939[/C][C]4.46096139762335[/C][C]124.725118601198[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]556.375[/C][C]4.37511337721573[/C][C]127.168133035691[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]556.274193548387[/C][C]4.29720614135267[/C][C]129.450199792669[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]556.133333333333[/C][C]4.20924907528383[/C][C]132.121745087236[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]556.086206896552[/C][C]4.13609116688811[/C][C]134.447279921767[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]555.982142857143[/C][C]4.06605292759681[/C][C]136.737556730662[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]555.87037037037[/C][C]3.98696743923159[/C][C]139.421848520916[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]555.730769230769[/C][C]3.89154586884606[/C][C]142.804630334617[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]555.84[/C][C]3.84785760693731[/C][C]144.454409902766[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]555.979166666667[/C][C]3.80363413189782[/C][C]146.170516770829[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]556.130434782609[/C][C]3.74302684300955[/C][C]148.577730833332[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]556.295454545455[/C][C]3.67331091117582[/C][C]151.442518206929[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]556.404761904762[/C][C]3.60008057785186[/C][C]154.553418978407[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]556.5[/C][C]3.52154540667617[/C][C]158.027211276329[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]556.631578947368[/C][C]3.43553123942393[/C][C]162.021981508951[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]556.805555555556[/C][C]3.32255864411189[/C][C]167.583364267266[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]557[/C][C]3.18278569451096[/C][C]175.003928464491[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]557.21875[/C][C]3.00528243768234[/C][C]185.413105608045[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]557.366666666667[/C][C]2.89012720291723[/C][C]192.851949943267[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]557.642857142857[/C][C]2.77708608168063[/C][C]200.801430255048[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]557.923076923077[/C][C]2.61647036286737[/C][C]213.235007298784[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]558.166666666667[/C][C]2.47206616236522[/C][C]225.789533938940[/C][/ROW]
[ROW][C]Median[/C][C]561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]554.71052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]556.805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]554.71052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]556.805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]556.805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]554.71052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]556.805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]555.615384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39234&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39234&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 Mean556.1388888888894.82078286178211115.362775058344
Geometric Mean554.645304461316
Harmonic Mean553.143355609844
Quadratic Mean557.620390588436
Winsorized Mean ( 1 / 24 )556.254.78753393937393116.187165886231
Winsorized Mean ( 2 / 24 )556.5277777777784.70428217929852118.302379952209
Winsorized Mean ( 3 / 24 )556.4444444444444.63769042646667119.983093582291
Winsorized Mean ( 4 / 24 )556.7222222222224.56500699006428121.954297865025
Winsorized Mean ( 5 / 24 )556.8611111111114.54060559839094122.640273206827
Winsorized Mean ( 6 / 24 )556.3611111111114.41629263876248125.979222080495
Winsorized Mean ( 7 / 24 )556.6527777777784.33302453405967128.467488102645
Winsorized Mean ( 8 / 24 )556.6527777777784.29493458798972129.606811552938
Winsorized Mean ( 9 / 24 )556.7777777777784.27471284222678130.249164874369
Winsorized Mean ( 10 / 24 )554.9722222222223.93088629530251141.182466377983
Winsorized Mean ( 11 / 24 )554.8194444444443.86040280991607143.720609419126
Winsorized Mean ( 12 / 24 )554.8194444444443.86040280991607143.720609419126
Winsorized Mean ( 13 / 24 )554.8194444444443.8046655316676145.826075860409
Winsorized Mean ( 14 / 24 )555.4027777777783.71150875398622149.643396955824
Winsorized Mean ( 15 / 24 )555.6111111111113.61619961694908153.645033450855
Winsorized Mean ( 16 / 24 )555.3888888888893.51792612315322157.873948868226
Winsorized Mean ( 17 / 24 )555.1527777777783.48446472417428159.322255130401
Winsorized Mean ( 18 / 24 )555.1527777777783.41093127466588162.756952009289
Winsorized Mean ( 19 / 24 )555.1527777777783.33378281724289166.523378459579
Winsorized Mean ( 20 / 24 )555.9861111111112.88969711142141192.40290233658
Winsorized Mean ( 21 / 24 )555.1111111111112.69116937916757206.271338923609
Winsorized Mean ( 22 / 24 )555.4166666666672.64639817821957209.876454434508
Winsorized Mean ( 23 / 24 )556.0555555555562.37874068227804233.760476582525
Winsorized Mean ( 24 / 24 )555.3888888888892.11425924566634262.687222499931
Trimmed Mean ( 1 / 24 )556.3428571428574.68241438112404118.815382804566
Trimmed Mean ( 2 / 24 )556.4411764705884.55733074769347122.098045385934
Trimmed Mean ( 3 / 24 )556.3939393939394.46096139762335124.725118601198
Trimmed Mean ( 4 / 24 )556.3754.37511337721573127.168133035691
Trimmed Mean ( 5 / 24 )556.2741935483874.29720614135267129.450199792669
Trimmed Mean ( 6 / 24 )556.1333333333334.20924907528383132.121745087236
Trimmed Mean ( 7 / 24 )556.0862068965524.13609116688811134.447279921767
Trimmed Mean ( 8 / 24 )555.9821428571434.06605292759681136.737556730662
Trimmed Mean ( 9 / 24 )555.870370370373.98696743923159139.421848520916
Trimmed Mean ( 10 / 24 )555.7307692307693.89154586884606142.804630334617
Trimmed Mean ( 11 / 24 )555.843.84785760693731144.454409902766
Trimmed Mean ( 12 / 24 )555.9791666666673.80363413189782146.170516770829
Trimmed Mean ( 13 / 24 )556.1304347826093.74302684300955148.577730833332
Trimmed Mean ( 14 / 24 )556.2954545454553.67331091117582151.442518206929
Trimmed Mean ( 15 / 24 )556.4047619047623.60008057785186154.553418978407
Trimmed Mean ( 16 / 24 )556.53.52154540667617158.027211276329
Trimmed Mean ( 17 / 24 )556.6315789473683.43553123942393162.021981508951
Trimmed Mean ( 18 / 24 )556.8055555555563.32255864411189167.583364267266
Trimmed Mean ( 19 / 24 )5573.18278569451096175.003928464491
Trimmed Mean ( 20 / 24 )557.218753.00528243768234185.413105608045
Trimmed Mean ( 21 / 24 )557.3666666666672.89012720291723192.851949943267
Trimmed Mean ( 22 / 24 )557.6428571428572.77708608168063200.801430255048
Trimmed Mean ( 23 / 24 )557.9230769230772.61647036286737213.235007298784
Trimmed Mean ( 24 / 24 )558.1666666666672.47206616236522225.789533938940
Median561
Midrange549
Midmean - Weighted Average at Xnp554.71052631579
Midmean - Weighted Average at X(n+1)p556.805555555556
Midmean - Empirical Distribution Function554.71052631579
Midmean - Empirical Distribution Function - Averaging556.805555555556
Midmean - Empirical Distribution Function - Interpolation556.805555555556
Midmean - Closest Observation554.71052631579
Midmean - True Basic - Statistics Graphics Toolkit556.805555555556
Midmean - MS Excel (old versions)555.615384615385
Number of observations72



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')