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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 computationFri, 10 Oct 2014 13:43:48 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412945066oolpxbltntk9pqh.htm/, Retrieved Mon, 13 May 2024 09:21:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240290, Retrieved Mon, 13 May 2024 09:21:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid_GCP_b...] [2014-10-10 12:43:48] [d0f5aeb11a4aa291a6c63b9267d14d48] [Current]
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Dataseries X:
39,66
40,05
39,99
40,06
40,08
40,1
40,1
40,12
40,07
40,24
40,58
40,72
40,72
40,89
40,9
41,04
41,27
41,29
41,29
41,33
41,34
41,37
41,33
41,37
41,37
41,42
41,61
41,58
41,75
41,75
41,75
41,85
41,84
41,97
42,01
42,04
42,04
42,06
41,93
41,93
41,99
42,03
42,03
42,12
42,22
42,21
42,23
42,22
42,22
42,25
42,27
42,16
42,24
42,26
42,26
42,26
42,36
42,33
42,23
42,23
40,9
40,9
40,87
40,69
40,92
41,05
41,36
41,79
41,82
41,8
41,87
41,87




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=240290&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=240290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240290&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 Mean41.45513888888890.0880989434015222470.552055317528
Geometric Mean41.4484324758706
Harmonic Mean41.4416662321328
Quadratic Mean41.461784831202
Winsorized Mean ( 1 / 24 )41.45930555555560.0868347337502729477.450713153425
Winsorized Mean ( 2 / 24 )41.45930555555560.0862161744219706480.876190964353
Winsorized Mean ( 3 / 24 )41.45930555555560.086065613138021481.717425158738
Winsorized Mean ( 4 / 24 )41.45986111111110.0859387299156389482.435115713368
Winsorized Mean ( 5 / 24 )41.46055555555560.0857809309222856483.330678622704
Winsorized Mean ( 6 / 24 )41.46138888888890.0852957447187065486.089769491113
Winsorized Mean ( 7 / 24 )41.46041666666670.0851697737229884486.797309119491
Winsorized Mean ( 8 / 24 )41.46152777777780.0845286710723869490.502538981972
Winsorized Mean ( 9 / 24 )41.47652777777780.0812430711436404510.523878454151
Winsorized Mean ( 10 / 24 )41.523750.0717658003901148578.600806711264
Winsorized Mean ( 11 / 24 )41.53902777777780.0685283372735442606.158407316475
Winsorized Mean ( 12 / 24 )41.54402777777780.0676632263175877613.982365883419
Winsorized Mean ( 13 / 24 )41.54402777777780.0676632263175877613.98236588342
Winsorized Mean ( 14 / 24 )41.571250.0625757561225081664.334761191117
Winsorized Mean ( 15 / 24 )41.5650.060447923758372687.616669286235
Winsorized Mean ( 16 / 24 )41.55833333333330.0588847180145193705.757533271812
Winsorized Mean ( 17 / 24 )41.54416666666670.0570299560248302728.462190091446
Winsorized Mean ( 18 / 24 )41.53916666666670.0563987556605871736.526297080971
Winsorized Mean ( 19 / 24 )41.54444444444440.055559780746998747.74313155815
Winsorized Mean ( 20 / 24 )41.5750.0500535706758489830.6100731403
Winsorized Mean ( 21 / 24 )41.57791666666670.0496154766211543838.002967988003
Winsorized Mean ( 22 / 24 )41.63902777777780.0392636446595221060.49828381583
Winsorized Mean ( 23 / 24 )41.63902777777780.03757733794670011108.08881238045
Winsorized Mean ( 24 / 24 )41.63236111111110.03670692042201811134.18289065019
Trimmed Mean ( 1 / 24 )41.46785714285710.0858808681474129482.853259839879
Trimmed Mean ( 2 / 24 )41.47691176470590.0847073818122819489.64931836309
Trimmed Mean ( 3 / 24 )41.48651515151510.0836516509963604495.943769876343
Trimmed Mean ( 4 / 24 )41.496718750.0824052650785956503.56877937862
Trimmed Mean ( 5 / 24 )41.50741935483870.0809034573233298513.048771067406
Trimmed Mean ( 6 / 24 )41.51866666666670.0790892604031111524.959602037617
Trimmed Mean ( 7 / 24 )41.53051724137930.0769729104435661539.54718617309
Trimmed Mean ( 8 / 24 )41.54339285714290.0743553580571006558.714179349926
Trimmed Mean ( 9 / 24 )41.5570370370370.0712299009274731583.421238776546
Trimmed Mean ( 10 / 24 )41.56942307692310.0681734399022815609.759799953
Trimmed Mean ( 11 / 24 )41.5760.0667251444206694623.093443423422
Trimmed Mean ( 12 / 24 )41.58104166666670.0655954988288645633.900837847877
Trimmed Mean ( 13 / 24 )41.58586956521740.0642921893566111646.826153866872
Trimmed Mean ( 14 / 24 )41.59113636363640.062553331080693664.890832272134
Trimmed Mean ( 15 / 24 )41.59357142857140.0614382605869142676.99786796097
Trimmed Mean ( 16 / 24 )41.5970.0603602433258762689.145664563078
Trimmed Mean ( 17 / 24 )41.60157894736840.0591758551880656703.016100319215
Trimmed Mean ( 18 / 24 )41.60833333333330.057868899452206719.010275419143
Trimmed Mean ( 19 / 24 )41.61647058823530.0560841650958568742.036018849636
Trimmed Mean ( 20 / 24 )41.6250.0537167001124208774.898679793905
Trimmed Mean ( 21 / 24 )41.6310.052028617236039800.155802933067
Trimmed Mean ( 22 / 24 )41.63750.0495632378912491840.088375407603
Trimmed Mean ( 23 / 24 )41.63730769230770.0493544719891263843.637992955961
Trimmed Mean ( 24 / 24 )41.63708333333330.049238693863972845.617136968761
Median41.75
Midrange41.01
Midmean - Weighted Average at Xnp41.5710526315789
Midmean - Weighted Average at X(n+1)p41.5710526315789
Midmean - Empirical Distribution Function41.5710526315789
Midmean - Empirical Distribution Function - Averaging41.5710526315789
Midmean - Empirical Distribution Function - Interpolation41.5710526315789
Midmean - Closest Observation41.5710526315789
Midmean - True Basic - Statistics Graphics Toolkit41.5710526315789
Midmean - MS Excel (old versions)41.5835897435897
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 41.4551388888889 & 0.0880989434015222 & 470.552055317528 \tabularnewline
Geometric Mean & 41.4484324758706 &  &  \tabularnewline
Harmonic Mean & 41.4416662321328 &  &  \tabularnewline
Quadratic Mean & 41.461784831202 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 41.4593055555556 & 0.0868347337502729 & 477.450713153425 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 41.4593055555556 & 0.0862161744219706 & 480.876190964353 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 41.4593055555556 & 0.086065613138021 & 481.717425158738 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 41.4598611111111 & 0.0859387299156389 & 482.435115713368 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 41.4605555555556 & 0.0857809309222856 & 483.330678622704 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 41.4613888888889 & 0.0852957447187065 & 486.089769491113 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 41.4604166666667 & 0.0851697737229884 & 486.797309119491 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 41.4615277777778 & 0.0845286710723869 & 490.502538981972 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 41.4765277777778 & 0.0812430711436404 & 510.523878454151 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 41.52375 & 0.0717658003901148 & 578.600806711264 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 41.5390277777778 & 0.0685283372735442 & 606.158407316475 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 41.5440277777778 & 0.0676632263175877 & 613.982365883419 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 41.5440277777778 & 0.0676632263175877 & 613.98236588342 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 41.57125 & 0.0625757561225081 & 664.334761191117 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 41.565 & 0.060447923758372 & 687.616669286235 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 41.5583333333333 & 0.0588847180145193 & 705.757533271812 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 41.5441666666667 & 0.0570299560248302 & 728.462190091446 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 41.5391666666667 & 0.0563987556605871 & 736.526297080971 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 41.5444444444444 & 0.055559780746998 & 747.74313155815 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 41.575 & 0.0500535706758489 & 830.6100731403 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 41.5779166666667 & 0.0496154766211543 & 838.002967988003 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 41.6390277777778 & 0.039263644659522 & 1060.49828381583 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 41.6390277777778 & 0.0375773379467001 & 1108.08881238045 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 41.6323611111111 & 0.0367069204220181 & 1134.18289065019 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 41.4678571428571 & 0.0858808681474129 & 482.853259839879 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 41.4769117647059 & 0.0847073818122819 & 489.64931836309 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 41.4865151515151 & 0.0836516509963604 & 495.943769876343 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 41.49671875 & 0.0824052650785956 & 503.56877937862 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 41.5074193548387 & 0.0809034573233298 & 513.048771067406 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 41.5186666666667 & 0.0790892604031111 & 524.959602037617 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 41.5305172413793 & 0.0769729104435661 & 539.54718617309 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 41.5433928571429 & 0.0743553580571006 & 558.714179349926 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 41.557037037037 & 0.0712299009274731 & 583.421238776546 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 41.5694230769231 & 0.0681734399022815 & 609.759799953 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 41.576 & 0.0667251444206694 & 623.093443423422 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 41.5810416666667 & 0.0655954988288645 & 633.900837847877 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 41.5858695652174 & 0.0642921893566111 & 646.826153866872 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 41.5911363636364 & 0.062553331080693 & 664.890832272134 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 41.5935714285714 & 0.0614382605869142 & 676.99786796097 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 41.597 & 0.0603602433258762 & 689.145664563078 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 41.6015789473684 & 0.0591758551880656 & 703.016100319215 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 41.6083333333333 & 0.057868899452206 & 719.010275419143 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 41.6164705882353 & 0.0560841650958568 & 742.036018849636 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 41.625 & 0.0537167001124208 & 774.898679793905 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 41.631 & 0.052028617236039 & 800.155802933067 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 41.6375 & 0.0495632378912491 & 840.088375407603 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 41.6373076923077 & 0.0493544719891263 & 843.637992955961 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 41.6370833333333 & 0.049238693863972 & 845.617136968761 \tabularnewline
Median & 41.75 &  &  \tabularnewline
Midrange & 41.01 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 41.5710526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 41.5710526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 41.5710526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 41.5710526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 41.5710526315789 &  &  \tabularnewline
Midmean - Closest Observation & 41.5710526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 41.5710526315789 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 41.5835897435897 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240290&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]41.4551388888889[/C][C]0.0880989434015222[/C][C]470.552055317528[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]41.4484324758706[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]41.4416662321328[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]41.461784831202[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]41.4593055555556[/C][C]0.0868347337502729[/C][C]477.450713153425[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]41.4593055555556[/C][C]0.0862161744219706[/C][C]480.876190964353[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]41.4593055555556[/C][C]0.086065613138021[/C][C]481.717425158738[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]41.4598611111111[/C][C]0.0859387299156389[/C][C]482.435115713368[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]41.4605555555556[/C][C]0.0857809309222856[/C][C]483.330678622704[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]41.4613888888889[/C][C]0.0852957447187065[/C][C]486.089769491113[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]41.4604166666667[/C][C]0.0851697737229884[/C][C]486.797309119491[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]41.4615277777778[/C][C]0.0845286710723869[/C][C]490.502538981972[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]41.4765277777778[/C][C]0.0812430711436404[/C][C]510.523878454151[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]41.52375[/C][C]0.0717658003901148[/C][C]578.600806711264[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]41.5390277777778[/C][C]0.0685283372735442[/C][C]606.158407316475[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]41.5440277777778[/C][C]0.0676632263175877[/C][C]613.982365883419[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]41.5440277777778[/C][C]0.0676632263175877[/C][C]613.98236588342[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]41.57125[/C][C]0.0625757561225081[/C][C]664.334761191117[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]41.565[/C][C]0.060447923758372[/C][C]687.616669286235[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]41.5583333333333[/C][C]0.0588847180145193[/C][C]705.757533271812[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]41.5441666666667[/C][C]0.0570299560248302[/C][C]728.462190091446[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]41.5391666666667[/C][C]0.0563987556605871[/C][C]736.526297080971[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]41.5444444444444[/C][C]0.055559780746998[/C][C]747.74313155815[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]41.575[/C][C]0.0500535706758489[/C][C]830.6100731403[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]41.5779166666667[/C][C]0.0496154766211543[/C][C]838.002967988003[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]41.6390277777778[/C][C]0.039263644659522[/C][C]1060.49828381583[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]41.6390277777778[/C][C]0.0375773379467001[/C][C]1108.08881238045[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]41.6323611111111[/C][C]0.0367069204220181[/C][C]1134.18289065019[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]41.4678571428571[/C][C]0.0858808681474129[/C][C]482.853259839879[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]41.4769117647059[/C][C]0.0847073818122819[/C][C]489.64931836309[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]41.4865151515151[/C][C]0.0836516509963604[/C][C]495.943769876343[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]41.49671875[/C][C]0.0824052650785956[/C][C]503.56877937862[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]41.5074193548387[/C][C]0.0809034573233298[/C][C]513.048771067406[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]41.5186666666667[/C][C]0.0790892604031111[/C][C]524.959602037617[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]41.5305172413793[/C][C]0.0769729104435661[/C][C]539.54718617309[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]41.5433928571429[/C][C]0.0743553580571006[/C][C]558.714179349926[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]41.557037037037[/C][C]0.0712299009274731[/C][C]583.421238776546[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]41.5694230769231[/C][C]0.0681734399022815[/C][C]609.759799953[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]41.576[/C][C]0.0667251444206694[/C][C]623.093443423422[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]41.5810416666667[/C][C]0.0655954988288645[/C][C]633.900837847877[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]41.5858695652174[/C][C]0.0642921893566111[/C][C]646.826153866872[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]41.5911363636364[/C][C]0.062553331080693[/C][C]664.890832272134[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]41.5935714285714[/C][C]0.0614382605869142[/C][C]676.99786796097[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]41.597[/C][C]0.0603602433258762[/C][C]689.145664563078[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]41.6015789473684[/C][C]0.0591758551880656[/C][C]703.016100319215[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]41.6083333333333[/C][C]0.057868899452206[/C][C]719.010275419143[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]41.6164705882353[/C][C]0.0560841650958568[/C][C]742.036018849636[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]41.625[/C][C]0.0537167001124208[/C][C]774.898679793905[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]41.631[/C][C]0.052028617236039[/C][C]800.155802933067[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]41.6375[/C][C]0.0495632378912491[/C][C]840.088375407603[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]41.6373076923077[/C][C]0.0493544719891263[/C][C]843.637992955961[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]41.6370833333333[/C][C]0.049238693863972[/C][C]845.617136968761[/C][/ROW]
[ROW][C]Median[/C][C]41.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]41.5710526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]41.5835897435897[/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=240290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240290&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 Mean41.45513888888890.0880989434015222470.552055317528
Geometric Mean41.4484324758706
Harmonic Mean41.4416662321328
Quadratic Mean41.461784831202
Winsorized Mean ( 1 / 24 )41.45930555555560.0868347337502729477.450713153425
Winsorized Mean ( 2 / 24 )41.45930555555560.0862161744219706480.876190964353
Winsorized Mean ( 3 / 24 )41.45930555555560.086065613138021481.717425158738
Winsorized Mean ( 4 / 24 )41.45986111111110.0859387299156389482.435115713368
Winsorized Mean ( 5 / 24 )41.46055555555560.0857809309222856483.330678622704
Winsorized Mean ( 6 / 24 )41.46138888888890.0852957447187065486.089769491113
Winsorized Mean ( 7 / 24 )41.46041666666670.0851697737229884486.797309119491
Winsorized Mean ( 8 / 24 )41.46152777777780.0845286710723869490.502538981972
Winsorized Mean ( 9 / 24 )41.47652777777780.0812430711436404510.523878454151
Winsorized Mean ( 10 / 24 )41.523750.0717658003901148578.600806711264
Winsorized Mean ( 11 / 24 )41.53902777777780.0685283372735442606.158407316475
Winsorized Mean ( 12 / 24 )41.54402777777780.0676632263175877613.982365883419
Winsorized Mean ( 13 / 24 )41.54402777777780.0676632263175877613.98236588342
Winsorized Mean ( 14 / 24 )41.571250.0625757561225081664.334761191117
Winsorized Mean ( 15 / 24 )41.5650.060447923758372687.616669286235
Winsorized Mean ( 16 / 24 )41.55833333333330.0588847180145193705.757533271812
Winsorized Mean ( 17 / 24 )41.54416666666670.0570299560248302728.462190091446
Winsorized Mean ( 18 / 24 )41.53916666666670.0563987556605871736.526297080971
Winsorized Mean ( 19 / 24 )41.54444444444440.055559780746998747.74313155815
Winsorized Mean ( 20 / 24 )41.5750.0500535706758489830.6100731403
Winsorized Mean ( 21 / 24 )41.57791666666670.0496154766211543838.002967988003
Winsorized Mean ( 22 / 24 )41.63902777777780.0392636446595221060.49828381583
Winsorized Mean ( 23 / 24 )41.63902777777780.03757733794670011108.08881238045
Winsorized Mean ( 24 / 24 )41.63236111111110.03670692042201811134.18289065019
Trimmed Mean ( 1 / 24 )41.46785714285710.0858808681474129482.853259839879
Trimmed Mean ( 2 / 24 )41.47691176470590.0847073818122819489.64931836309
Trimmed Mean ( 3 / 24 )41.48651515151510.0836516509963604495.943769876343
Trimmed Mean ( 4 / 24 )41.496718750.0824052650785956503.56877937862
Trimmed Mean ( 5 / 24 )41.50741935483870.0809034573233298513.048771067406
Trimmed Mean ( 6 / 24 )41.51866666666670.0790892604031111524.959602037617
Trimmed Mean ( 7 / 24 )41.53051724137930.0769729104435661539.54718617309
Trimmed Mean ( 8 / 24 )41.54339285714290.0743553580571006558.714179349926
Trimmed Mean ( 9 / 24 )41.5570370370370.0712299009274731583.421238776546
Trimmed Mean ( 10 / 24 )41.56942307692310.0681734399022815609.759799953
Trimmed Mean ( 11 / 24 )41.5760.0667251444206694623.093443423422
Trimmed Mean ( 12 / 24 )41.58104166666670.0655954988288645633.900837847877
Trimmed Mean ( 13 / 24 )41.58586956521740.0642921893566111646.826153866872
Trimmed Mean ( 14 / 24 )41.59113636363640.062553331080693664.890832272134
Trimmed Mean ( 15 / 24 )41.59357142857140.0614382605869142676.99786796097
Trimmed Mean ( 16 / 24 )41.5970.0603602433258762689.145664563078
Trimmed Mean ( 17 / 24 )41.60157894736840.0591758551880656703.016100319215
Trimmed Mean ( 18 / 24 )41.60833333333330.057868899452206719.010275419143
Trimmed Mean ( 19 / 24 )41.61647058823530.0560841650958568742.036018849636
Trimmed Mean ( 20 / 24 )41.6250.0537167001124208774.898679793905
Trimmed Mean ( 21 / 24 )41.6310.052028617236039800.155802933067
Trimmed Mean ( 22 / 24 )41.63750.0495632378912491840.088375407603
Trimmed Mean ( 23 / 24 )41.63730769230770.0493544719891263843.637992955961
Trimmed Mean ( 24 / 24 )41.63708333333330.049238693863972845.617136968761
Median41.75
Midrange41.01
Midmean - Weighted Average at Xnp41.5710526315789
Midmean - Weighted Average at X(n+1)p41.5710526315789
Midmean - Empirical Distribution Function41.5710526315789
Midmean - Empirical Distribution Function - Averaging41.5710526315789
Midmean - Empirical Distribution Function - Interpolation41.5710526315789
Midmean - Closest Observation41.5710526315789
Midmean - True Basic - Statistics Graphics Toolkit41.5710526315789
Midmean - MS Excel (old versions)41.5835897435897
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')