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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, 04 Mar 2013 13:49:11 -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/2013/Mar/04/t1362423171yavtipe846w4vb9.htm/, Retrieved Sun, 28 Apr 2024 16:57:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207333, Retrieved Sun, 28 Apr 2024 16:57:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2013-03-04 18:36:16] [d55d05654abdb5022ac9ec4fde0d976a]
-    D    [Central Tendency] [] [2013-03-04 18:49:11] [54665deafd3402f8325c0d656ab7be45] [Current]
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Dataseries X:
369,82
373,1
374,55
375,01
374,81
375,31
375,31
375,39
375,59
376,26
377,18
377,26
377,26
381,87
387,09
387,14
388,78
389,16
389,16
389,42
389,49
388,97
388,97
389,09
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8
428,8
434,87
435,66
440,75
440,99
441,04
441,04
441,88
441,92
442,48
442,81
442,81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207333&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207333&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207333&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean404.348752.66420169184538151.771073202767
Geometric Mean403.73168023026
Harmonic Mean403.121368537227
Quadratic Mean404.971440404204
Winsorized Mean ( 1 / 24 )404.3943055555562.65626368597331152.24177768608
Winsorized Mean ( 2 / 24 )404.4254166666672.64786002514007152.736705425081
Winsorized Mean ( 3 / 24 )404.4129166666672.6414493952318153.102655457527
Winsorized Mean ( 4 / 24 )404.4218055555562.63925616333686153.233252297965
Winsorized Mean ( 5 / 24 )404.3843055555562.62442755384541154.084766014225
Winsorized Mean ( 6 / 24 )404.3843055555562.62442755384541154.084766014225
Winsorized Mean ( 7 / 24 )404.3872222222222.62225908935384154.213297939933
Winsorized Mean ( 8 / 24 )404.3827777777782.61357007214197154.724291530612
Winsorized Mean ( 9 / 24 )403.8302777777782.48055091920384162.798624552078
Winsorized Mean ( 10 / 24 )403.8483333333332.44098153312769165.445058822658
Winsorized Mean ( 11 / 24 )402.9331944444442.28173971002803176.590341428337
Winsorized Mean ( 12 / 24 )402.9331944444442.28173971002803176.590341428337
Winsorized Mean ( 13 / 24 )403.6734722222222.1410917932872188.536275505716
Winsorized Mean ( 14 / 24 )404.5445833333331.9815496273289204.155665724433
Winsorized Mean ( 15 / 24 )404.4695833333331.96633802495507205.696873172442
Winsorized Mean ( 16 / 24 )404.7140277777781.90274429786465212.700165877237
Winsorized Mean ( 17 / 24 )404.6927777777781.88677413492903214.489254588494
Winsorized Mean ( 18 / 24 )404.6777777777781.88435343828291214.756833594092
Winsorized Mean ( 19 / 24 )404.7094444444441.88064234906725215.197453489851
Winsorized Mean ( 20 / 24 )404.041.77393219881973227.76518756964
Winsorized Mean ( 21 / 24 )403.9029166666671.74679745457796231.224814077974
Winsorized Mean ( 22 / 24 )400.9970833333331.31644797371861304.605340536646
Winsorized Mean ( 23 / 24 )400.1761111111111.18581312203462337.469794923915
Winsorized Mean ( 24 / 24 )400.1994444444441.18283487962625338.339231736977
Trimmed Mean ( 1 / 24 )404.2925714285712.63803611066028153.255131646921
Trimmed Mean ( 2 / 24 )404.1848529411762.61503322970817154.562033227502
Trimmed Mean ( 3 / 24 )404.0536363636362.59144485116193155.918284806435
Trimmed Mean ( 4 / 24 )403.918906252.56462369525691157.496363695391
Trimmed Mean ( 5 / 24 )403.7729032258062.53174248490917159.484191473878
Trimmed Mean ( 6 / 24 )403.6261666666672.49526646892504161.756738886709
Trimmed Mean ( 7 / 24 )403.4693103448282.44962980847153164.706238040341
Trimmed Mean ( 8 / 24 )403.3007142857142.39320106851888168.519360780376
Trimmed Mean ( 9 / 24 )403.120370370372.32480757396655173.399456748402
Trimmed Mean ( 10 / 24 )403.0111538461542.2718198506759177.395735725371
Trimmed Mean ( 11 / 24 )402.89062.21354360670295182.011593889538
Trimmed Mean ( 12 / 24 )402.8847916666672.17540075360676185.200262985427
Trimmed Mean ( 13 / 24 )402.878478260872.12507384281797189.583284186789
Trimmed Mean ( 14 / 24 )402.7784090909092.08949491512575192.763526809861
Trimmed Mean ( 15 / 24 )402.5621428571432.07282187811941194.209713389542
Trimmed Mean ( 16 / 24 )402.333252.04981545096451196.277791647384
Trimmed Mean ( 17 / 24 )402.0513157894742.02739653846739198.309165553476
Trimmed Mean ( 18 / 24 )401.7405555555561.99514629071163201.358946672658
Trimmed Mean ( 19 / 24 )401.3951.94560999741266206.308047621974
Trimmed Mean ( 20 / 24 )401.00251.87099189882903214.326155153835
Trimmed Mean ( 21 / 24 )400.6381.79549374632814223.135280097367
Trimmed Mean ( 22 / 24 )400.2382142857141.68814133833441237.088095171347
Trimmed Mean ( 23 / 24 )400.1426923076921.68595041059405237.339538454574
Trimmed Mean ( 24 / 24 )400.1383333333331.71067171173022233.90714336921
Median394.57
Midrange406.315
Midmean - Weighted Average at Xnp401.395405405405
Midmean - Weighted Average at X(n+1)p401.395405405405
Midmean - Empirical Distribution Function401.395405405405
Midmean - Empirical Distribution Function - Averaging401.395405405405
Midmean - Empirical Distribution Function - Interpolation401.395405405405
Midmean - Closest Observation401.395405405405
Midmean - True Basic - Statistics Graphics Toolkit401.395405405405
Midmean - MS Excel (old versions)402.051315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 404.34875 & 2.66420169184538 & 151.771073202767 \tabularnewline
Geometric Mean & 403.73168023026 &  &  \tabularnewline
Harmonic Mean & 403.121368537227 &  &  \tabularnewline
Quadratic Mean & 404.971440404204 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 404.394305555556 & 2.65626368597331 & 152.24177768608 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 404.425416666667 & 2.64786002514007 & 152.736705425081 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 404.412916666667 & 2.6414493952318 & 153.102655457527 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 404.421805555556 & 2.63925616333686 & 153.233252297965 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 404.384305555556 & 2.62442755384541 & 154.084766014225 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 404.384305555556 & 2.62442755384541 & 154.084766014225 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 404.387222222222 & 2.62225908935384 & 154.213297939933 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 404.382777777778 & 2.61357007214197 & 154.724291530612 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 403.830277777778 & 2.48055091920384 & 162.798624552078 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 403.848333333333 & 2.44098153312769 & 165.445058822658 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 402.933194444444 & 2.28173971002803 & 176.590341428337 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 402.933194444444 & 2.28173971002803 & 176.590341428337 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 403.673472222222 & 2.1410917932872 & 188.536275505716 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 404.544583333333 & 1.9815496273289 & 204.155665724433 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 404.469583333333 & 1.96633802495507 & 205.696873172442 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 404.714027777778 & 1.90274429786465 & 212.700165877237 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 404.692777777778 & 1.88677413492903 & 214.489254588494 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 404.677777777778 & 1.88435343828291 & 214.756833594092 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 404.709444444444 & 1.88064234906725 & 215.197453489851 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 404.04 & 1.77393219881973 & 227.76518756964 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 403.902916666667 & 1.74679745457796 & 231.224814077974 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 400.997083333333 & 1.31644797371861 & 304.605340536646 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 400.176111111111 & 1.18581312203462 & 337.469794923915 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 400.199444444444 & 1.18283487962625 & 338.339231736977 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 404.292571428571 & 2.63803611066028 & 153.255131646921 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 404.184852941176 & 2.61503322970817 & 154.562033227502 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 404.053636363636 & 2.59144485116193 & 155.918284806435 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 403.91890625 & 2.56462369525691 & 157.496363695391 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 403.772903225806 & 2.53174248490917 & 159.484191473878 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 403.626166666667 & 2.49526646892504 & 161.756738886709 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 403.469310344828 & 2.44962980847153 & 164.706238040341 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 403.300714285714 & 2.39320106851888 & 168.519360780376 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 403.12037037037 & 2.32480757396655 & 173.399456748402 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 403.011153846154 & 2.2718198506759 & 177.395735725371 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 402.8906 & 2.21354360670295 & 182.011593889538 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 402.884791666667 & 2.17540075360676 & 185.200262985427 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 402.87847826087 & 2.12507384281797 & 189.583284186789 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 402.778409090909 & 2.08949491512575 & 192.763526809861 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 402.562142857143 & 2.07282187811941 & 194.209713389542 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 402.33325 & 2.04981545096451 & 196.277791647384 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 402.051315789474 & 2.02739653846739 & 198.309165553476 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 401.740555555556 & 1.99514629071163 & 201.358946672658 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 401.395 & 1.94560999741266 & 206.308047621974 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 401.0025 & 1.87099189882903 & 214.326155153835 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 400.638 & 1.79549374632814 & 223.135280097367 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 400.238214285714 & 1.68814133833441 & 237.088095171347 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 400.142692307692 & 1.68595041059405 & 237.339538454574 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 400.138333333333 & 1.71067171173022 & 233.90714336921 \tabularnewline
Median & 394.57 &  &  \tabularnewline
Midrange & 406.315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 401.395405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 401.395405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 401.395405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 401.395405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 401.395405405405 &  &  \tabularnewline
Midmean - Closest Observation & 401.395405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 401.395405405405 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 402.051315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207333&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]404.34875[/C][C]2.66420169184538[/C][C]151.771073202767[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]403.73168023026[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]403.121368537227[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]404.971440404204[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]404.394305555556[/C][C]2.65626368597331[/C][C]152.24177768608[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]404.425416666667[/C][C]2.64786002514007[/C][C]152.736705425081[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]404.412916666667[/C][C]2.6414493952318[/C][C]153.102655457527[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]404.421805555556[/C][C]2.63925616333686[/C][C]153.233252297965[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]404.384305555556[/C][C]2.62442755384541[/C][C]154.084766014225[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]404.384305555556[/C][C]2.62442755384541[/C][C]154.084766014225[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]404.387222222222[/C][C]2.62225908935384[/C][C]154.213297939933[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]404.382777777778[/C][C]2.61357007214197[/C][C]154.724291530612[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]403.830277777778[/C][C]2.48055091920384[/C][C]162.798624552078[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]403.848333333333[/C][C]2.44098153312769[/C][C]165.445058822658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]402.933194444444[/C][C]2.28173971002803[/C][C]176.590341428337[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]402.933194444444[/C][C]2.28173971002803[/C][C]176.590341428337[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]403.673472222222[/C][C]2.1410917932872[/C][C]188.536275505716[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]404.544583333333[/C][C]1.9815496273289[/C][C]204.155665724433[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]404.469583333333[/C][C]1.96633802495507[/C][C]205.696873172442[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]404.714027777778[/C][C]1.90274429786465[/C][C]212.700165877237[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]404.692777777778[/C][C]1.88677413492903[/C][C]214.489254588494[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]404.677777777778[/C][C]1.88435343828291[/C][C]214.756833594092[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]404.709444444444[/C][C]1.88064234906725[/C][C]215.197453489851[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]404.04[/C][C]1.77393219881973[/C][C]227.76518756964[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]403.902916666667[/C][C]1.74679745457796[/C][C]231.224814077974[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]400.997083333333[/C][C]1.31644797371861[/C][C]304.605340536646[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]400.176111111111[/C][C]1.18581312203462[/C][C]337.469794923915[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]400.199444444444[/C][C]1.18283487962625[/C][C]338.339231736977[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]404.292571428571[/C][C]2.63803611066028[/C][C]153.255131646921[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]404.184852941176[/C][C]2.61503322970817[/C][C]154.562033227502[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]404.053636363636[/C][C]2.59144485116193[/C][C]155.918284806435[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]403.91890625[/C][C]2.56462369525691[/C][C]157.496363695391[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]403.772903225806[/C][C]2.53174248490917[/C][C]159.484191473878[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]403.626166666667[/C][C]2.49526646892504[/C][C]161.756738886709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]403.469310344828[/C][C]2.44962980847153[/C][C]164.706238040341[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]403.300714285714[/C][C]2.39320106851888[/C][C]168.519360780376[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]403.12037037037[/C][C]2.32480757396655[/C][C]173.399456748402[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]403.011153846154[/C][C]2.2718198506759[/C][C]177.395735725371[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]402.8906[/C][C]2.21354360670295[/C][C]182.011593889538[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]402.884791666667[/C][C]2.17540075360676[/C][C]185.200262985427[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]402.87847826087[/C][C]2.12507384281797[/C][C]189.583284186789[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]402.778409090909[/C][C]2.08949491512575[/C][C]192.763526809861[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]402.562142857143[/C][C]2.07282187811941[/C][C]194.209713389542[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]402.33325[/C][C]2.04981545096451[/C][C]196.277791647384[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]402.051315789474[/C][C]2.02739653846739[/C][C]198.309165553476[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]401.740555555556[/C][C]1.99514629071163[/C][C]201.358946672658[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]401.395[/C][C]1.94560999741266[/C][C]206.308047621974[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]401.0025[/C][C]1.87099189882903[/C][C]214.326155153835[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]400.638[/C][C]1.79549374632814[/C][C]223.135280097367[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]400.238214285714[/C][C]1.68814133833441[/C][C]237.088095171347[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]400.142692307692[/C][C]1.68595041059405[/C][C]237.339538454574[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]400.138333333333[/C][C]1.71067171173022[/C][C]233.90714336921[/C][/ROW]
[ROW][C]Median[/C][C]394.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]406.315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]401.395405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]402.051315789474[/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=207333&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207333&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 Mean404.348752.66420169184538151.771073202767
Geometric Mean403.73168023026
Harmonic Mean403.121368537227
Quadratic Mean404.971440404204
Winsorized Mean ( 1 / 24 )404.3943055555562.65626368597331152.24177768608
Winsorized Mean ( 2 / 24 )404.4254166666672.64786002514007152.736705425081
Winsorized Mean ( 3 / 24 )404.4129166666672.6414493952318153.102655457527
Winsorized Mean ( 4 / 24 )404.4218055555562.63925616333686153.233252297965
Winsorized Mean ( 5 / 24 )404.3843055555562.62442755384541154.084766014225
Winsorized Mean ( 6 / 24 )404.3843055555562.62442755384541154.084766014225
Winsorized Mean ( 7 / 24 )404.3872222222222.62225908935384154.213297939933
Winsorized Mean ( 8 / 24 )404.3827777777782.61357007214197154.724291530612
Winsorized Mean ( 9 / 24 )403.8302777777782.48055091920384162.798624552078
Winsorized Mean ( 10 / 24 )403.8483333333332.44098153312769165.445058822658
Winsorized Mean ( 11 / 24 )402.9331944444442.28173971002803176.590341428337
Winsorized Mean ( 12 / 24 )402.9331944444442.28173971002803176.590341428337
Winsorized Mean ( 13 / 24 )403.6734722222222.1410917932872188.536275505716
Winsorized Mean ( 14 / 24 )404.5445833333331.9815496273289204.155665724433
Winsorized Mean ( 15 / 24 )404.4695833333331.96633802495507205.696873172442
Winsorized Mean ( 16 / 24 )404.7140277777781.90274429786465212.700165877237
Winsorized Mean ( 17 / 24 )404.6927777777781.88677413492903214.489254588494
Winsorized Mean ( 18 / 24 )404.6777777777781.88435343828291214.756833594092
Winsorized Mean ( 19 / 24 )404.7094444444441.88064234906725215.197453489851
Winsorized Mean ( 20 / 24 )404.041.77393219881973227.76518756964
Winsorized Mean ( 21 / 24 )403.9029166666671.74679745457796231.224814077974
Winsorized Mean ( 22 / 24 )400.9970833333331.31644797371861304.605340536646
Winsorized Mean ( 23 / 24 )400.1761111111111.18581312203462337.469794923915
Winsorized Mean ( 24 / 24 )400.1994444444441.18283487962625338.339231736977
Trimmed Mean ( 1 / 24 )404.2925714285712.63803611066028153.255131646921
Trimmed Mean ( 2 / 24 )404.1848529411762.61503322970817154.562033227502
Trimmed Mean ( 3 / 24 )404.0536363636362.59144485116193155.918284806435
Trimmed Mean ( 4 / 24 )403.918906252.56462369525691157.496363695391
Trimmed Mean ( 5 / 24 )403.7729032258062.53174248490917159.484191473878
Trimmed Mean ( 6 / 24 )403.6261666666672.49526646892504161.756738886709
Trimmed Mean ( 7 / 24 )403.4693103448282.44962980847153164.706238040341
Trimmed Mean ( 8 / 24 )403.3007142857142.39320106851888168.519360780376
Trimmed Mean ( 9 / 24 )403.120370370372.32480757396655173.399456748402
Trimmed Mean ( 10 / 24 )403.0111538461542.2718198506759177.395735725371
Trimmed Mean ( 11 / 24 )402.89062.21354360670295182.011593889538
Trimmed Mean ( 12 / 24 )402.8847916666672.17540075360676185.200262985427
Trimmed Mean ( 13 / 24 )402.878478260872.12507384281797189.583284186789
Trimmed Mean ( 14 / 24 )402.7784090909092.08949491512575192.763526809861
Trimmed Mean ( 15 / 24 )402.5621428571432.07282187811941194.209713389542
Trimmed Mean ( 16 / 24 )402.333252.04981545096451196.277791647384
Trimmed Mean ( 17 / 24 )402.0513157894742.02739653846739198.309165553476
Trimmed Mean ( 18 / 24 )401.7405555555561.99514629071163201.358946672658
Trimmed Mean ( 19 / 24 )401.3951.94560999741266206.308047621974
Trimmed Mean ( 20 / 24 )401.00251.87099189882903214.326155153835
Trimmed Mean ( 21 / 24 )400.6381.79549374632814223.135280097367
Trimmed Mean ( 22 / 24 )400.2382142857141.68814133833441237.088095171347
Trimmed Mean ( 23 / 24 )400.1426923076921.68595041059405237.339538454574
Trimmed Mean ( 24 / 24 )400.1383333333331.71067171173022233.90714336921
Median394.57
Midrange406.315
Midmean - Weighted Average at Xnp401.395405405405
Midmean - Weighted Average at X(n+1)p401.395405405405
Midmean - Empirical Distribution Function401.395405405405
Midmean - Empirical Distribution Function - Averaging401.395405405405
Midmean - Empirical Distribution Function - Interpolation401.395405405405
Midmean - Closest Observation401.395405405405
Midmean - True Basic - Statistics Graphics Toolkit401.395405405405
Midmean - MS Excel (old versions)402.051315789474
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')