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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 22 May 2013 05:27:07 -0400
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/May/22/t1369214894gollrcxzk02b0o8.htm/, Retrieved Sun, 28 Apr 2024 04:39:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209369, Retrieved Sun, 28 Apr 2024 04:39:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opdracht 5] [2013-05-22 09:27:07] [0756924702977927793c865c7c536cb0] [Current]
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Dataseries X:
19
14
15
7
12
12
14
9
8
4
7
3
5
0
-2
6
11
9
17
21
21
41
57
65
68
73
71
71
70
69
65
57
57
57
55
65
65
64
60
43
47
40
31
27
24
23
17
16
15
8
5
6
5
12
8
17
22
24
36
31
34
47
33
35
31
35
39
46
40
50
62
57
62
57




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209369&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209369&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32.79729729729732.664157291239712.3105709280535
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean39.9223909266128
Winsorized Mean ( 1 / 24 )32.79729729729732.6539932212444712.3577170562321
Winsorized Mean ( 2 / 24 )32.87837837837842.6408457284896212.4499428435687
Winsorized Mean ( 3 / 24 )32.87837837837842.6267183478716912.5169028514299
Winsorized Mean ( 4 / 24 )32.87837837837842.6083306222256312.6051421925661
Winsorized Mean ( 5 / 24 )32.81081081081082.5956472318610512.6407049494495
Winsorized Mean ( 6 / 24 )32.56756756756762.5518743306514212.7622144932403
Winsorized Mean ( 7 / 24 )32.66216216216222.5380683261531412.8689057838199
Winsorized Mean ( 8 / 24 )32.66216216216222.5380683261531412.8689057838199
Winsorized Mean ( 9 / 24 )32.78378378378382.5207961600190213.0053291510633
Winsorized Mean ( 10 / 24 )32.64864864864862.4973464208358813.0733359121723
Winsorized Mean ( 11 / 24 )32.52.4262731059685713.39502957027
Winsorized Mean ( 12 / 24 )32.52.4262731059685713.39502957027
Winsorized Mean ( 13 / 24 )32.14864864864862.3687058245777413.5722419876177
Winsorized Mean ( 14 / 24 )31.77027027027032.253102455843114.1006771298298
Winsorized Mean ( 15 / 24 )31.77027027027032.253102455843114.1006771298298
Winsorized Mean ( 16 / 24 )32.20270270270272.1945356163753814.6740396749133
Winsorized Mean ( 17 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 18 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 19 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 20 / 24 )32.43243243243242.0120040608842816.1194666864531
Winsorized Mean ( 21 / 24 )31.01351351351351.8001288821401517.2284961489212
Winsorized Mean ( 22 / 24 )30.41891891891891.6351840908646818.6027488212863
Winsorized Mean ( 23 / 24 )30.41891891891891.6351840908646818.6027488212863
Winsorized Mean ( 24 / 24 )30.41891891891891.5486682909162419.6419847280027
Trimmed Mean ( 1 / 24 )32.72222222222222.6357674480107412.414684856556
Trimmed Mean ( 2 / 24 )32.64285714285712.6129979065712312.4924926502107
Trimmed Mean ( 3 / 24 )32.51470588235292.5927477574456812.5406360063293
Trimmed Mean ( 4 / 24 )32.37878787878792.5732862132763812.5826609227282
Trimmed Mean ( 5 / 24 )32.2343752.5547324382606512.6175150545105
Trimmed Mean ( 6 / 24 )32.09677419354842.5344490280826112.6642018986788
Trimmed Mean ( 7 / 24 )322.5197524764097112.6996601053431
Trimmed Mean ( 8 / 24 )31.87931034482762.5028812901726412.7370444894846
Trimmed Mean ( 9 / 24 )31.752.4799520837432212.8026667160749
Trimmed Mean ( 10 / 24 )31.59259259259262.4531271160423512.8784979734606
Trimmed Mean ( 11 / 24 )31.44230769230772.4227761430786212.9778014292125
Trimmed Mean ( 12 / 24 )31.32.3974901842705213.0553193524434
Trimmed Mean ( 13 / 24 )31.14583333333332.3629058590430113.1811570969432
Trimmed Mean ( 14 / 24 )31.02173913043482.328875478764213.3204799540834
Trimmed Mean ( 15 / 24 )30.93181818181822.3066678160514413.4097410847685
Trimmed Mean ( 16 / 24 )30.83333333333332.2741583851659813.5581292554005
Trimmed Mean ( 17 / 24 )30.6752.2399025562596413.6947921748987
Trimmed Mean ( 18 / 24 )30.47368421052632.1965111486908713.873676092511
Trimmed Mean ( 19 / 24 )30.252.1337704165341214.1767829217236
Trimmed Mean ( 20 / 24 )302.0436415018870814.6796783938368
Trimmed Mean ( 21 / 24 )29.718751.9578390691179215.1793630379383
Trimmed Mean ( 22 / 24 )29.56666666666671.9008064430918815.5548013708187
Trimmed Mean ( 23 / 24 )29.46428571428571.8640870376001915.8062821745801
Trimmed Mean ( 24 / 24 )29.34615384615381.8016593272205916.288403363929
Median31
Midrange35.5
Midmean - Weighted Average at Xnp32.5116279069767
Midmean - Weighted Average at X(n+1)p32.5116279069767
Midmean - Empirical Distribution Function32.5116279069767
Midmean - Empirical Distribution Function - Averaging32.5116279069767
Midmean - Empirical Distribution Function - Interpolation32.5116279069767
Midmean - Closest Observation32.5116279069767
Midmean - True Basic - Statistics Graphics Toolkit32.5116279069767
Midmean - MS Excel (old versions)32.5116279069767
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32.7972972972973 & 2.6641572912397 & 12.3105709280535 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 39.9223909266128 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 32.7972972972973 & 2.65399322124447 & 12.3577170562321 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 32.8783783783784 & 2.64084572848962 & 12.4499428435687 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 32.8783783783784 & 2.62671834787169 & 12.5169028514299 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 32.8783783783784 & 2.60833062222563 & 12.6051421925661 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 32.8108108108108 & 2.59564723186105 & 12.6407049494495 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 32.5675675675676 & 2.55187433065142 & 12.7622144932403 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 32.6621621621622 & 2.53806832615314 & 12.8689057838199 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 32.6621621621622 & 2.53806832615314 & 12.8689057838199 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 32.7837837837838 & 2.52079616001902 & 13.0053291510633 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 32.6486486486486 & 2.49734642083588 & 13.0733359121723 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 32.5 & 2.42627310596857 & 13.39502957027 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 32.5 & 2.42627310596857 & 13.39502957027 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 32.1486486486486 & 2.36870582457774 & 13.5722419876177 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 31.7702702702703 & 2.2531024558431 & 14.1006771298298 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 31.7702702702703 & 2.2531024558431 & 14.1006771298298 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 32.2027027027027 & 2.19453561637538 & 14.6740396749133 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 32.4324324324324 & 2.1644771945579 & 14.9839566404195 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 32.4324324324324 & 2.1644771945579 & 14.9839566404195 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 32.4324324324324 & 2.1644771945579 & 14.9839566404195 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 32.4324324324324 & 2.01200406088428 & 16.1194666864531 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 31.0135135135135 & 1.80012888214015 & 17.2284961489212 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 30.4189189189189 & 1.63518409086468 & 18.6027488212863 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 30.4189189189189 & 1.63518409086468 & 18.6027488212863 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 30.4189189189189 & 1.54866829091624 & 19.6419847280027 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 32.7222222222222 & 2.63576744801074 & 12.414684856556 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 32.6428571428571 & 2.61299790657123 & 12.4924926502107 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 32.5147058823529 & 2.59274775744568 & 12.5406360063293 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 32.3787878787879 & 2.57328621327638 & 12.5826609227282 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 32.234375 & 2.55473243826065 & 12.6175150545105 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 32.0967741935484 & 2.53444902808261 & 12.6642018986788 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 32 & 2.51975247640971 & 12.6996601053431 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 31.8793103448276 & 2.50288129017264 & 12.7370444894846 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 31.75 & 2.47995208374322 & 12.8026667160749 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 31.5925925925926 & 2.45312711604235 & 12.8784979734606 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 31.4423076923077 & 2.42277614307862 & 12.9778014292125 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 31.3 & 2.39749018427052 & 13.0553193524434 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 31.1458333333333 & 2.36290585904301 & 13.1811570969432 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 31.0217391304348 & 2.3288754787642 & 13.3204799540834 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 30.9318181818182 & 2.30666781605144 & 13.4097410847685 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 30.8333333333333 & 2.27415838516598 & 13.5581292554005 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 30.675 & 2.23990255625964 & 13.6947921748987 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 30.4736842105263 & 2.19651114869087 & 13.873676092511 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 30.25 & 2.13377041653412 & 14.1767829217236 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 30 & 2.04364150188708 & 14.6796783938368 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 29.71875 & 1.95783906911792 & 15.1793630379383 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 29.5666666666667 & 1.90080644309188 & 15.5548013708187 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 29.4642857142857 & 1.86408703760019 & 15.8062821745801 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 29.3461538461538 & 1.80165932722059 & 16.288403363929 \tabularnewline
Median & 31 &  &  \tabularnewline
Midrange & 35.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32.5116279069767 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32.5116279069767 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32.5116279069767 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32.5116279069767 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32.5116279069767 &  &  \tabularnewline
Midmean - Closest Observation & 32.5116279069767 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32.5116279069767 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32.5116279069767 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209369&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]32.7972972972973[/C][C]2.6641572912397[/C][C]12.3105709280535[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]39.9223909266128[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]32.7972972972973[/C][C]2.65399322124447[/C][C]12.3577170562321[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]32.8783783783784[/C][C]2.64084572848962[/C][C]12.4499428435687[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]32.8783783783784[/C][C]2.62671834787169[/C][C]12.5169028514299[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]32.8783783783784[/C][C]2.60833062222563[/C][C]12.6051421925661[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]32.8108108108108[/C][C]2.59564723186105[/C][C]12.6407049494495[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]32.5675675675676[/C][C]2.55187433065142[/C][C]12.7622144932403[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]32.6621621621622[/C][C]2.53806832615314[/C][C]12.8689057838199[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]32.6621621621622[/C][C]2.53806832615314[/C][C]12.8689057838199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]32.7837837837838[/C][C]2.52079616001902[/C][C]13.0053291510633[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]32.6486486486486[/C][C]2.49734642083588[/C][C]13.0733359121723[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]32.5[/C][C]2.42627310596857[/C][C]13.39502957027[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]32.5[/C][C]2.42627310596857[/C][C]13.39502957027[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]32.1486486486486[/C][C]2.36870582457774[/C][C]13.5722419876177[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]31.7702702702703[/C][C]2.2531024558431[/C][C]14.1006771298298[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]31.7702702702703[/C][C]2.2531024558431[/C][C]14.1006771298298[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]32.2027027027027[/C][C]2.19453561637538[/C][C]14.6740396749133[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]32.4324324324324[/C][C]2.1644771945579[/C][C]14.9839566404195[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]32.4324324324324[/C][C]2.1644771945579[/C][C]14.9839566404195[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]32.4324324324324[/C][C]2.1644771945579[/C][C]14.9839566404195[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]32.4324324324324[/C][C]2.01200406088428[/C][C]16.1194666864531[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]31.0135135135135[/C][C]1.80012888214015[/C][C]17.2284961489212[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]30.4189189189189[/C][C]1.63518409086468[/C][C]18.6027488212863[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]30.4189189189189[/C][C]1.63518409086468[/C][C]18.6027488212863[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]30.4189189189189[/C][C]1.54866829091624[/C][C]19.6419847280027[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]32.7222222222222[/C][C]2.63576744801074[/C][C]12.414684856556[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]32.6428571428571[/C][C]2.61299790657123[/C][C]12.4924926502107[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]32.5147058823529[/C][C]2.59274775744568[/C][C]12.5406360063293[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]32.3787878787879[/C][C]2.57328621327638[/C][C]12.5826609227282[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]32.234375[/C][C]2.55473243826065[/C][C]12.6175150545105[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]32.0967741935484[/C][C]2.53444902808261[/C][C]12.6642018986788[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]32[/C][C]2.51975247640971[/C][C]12.6996601053431[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]31.8793103448276[/C][C]2.50288129017264[/C][C]12.7370444894846[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]31.75[/C][C]2.47995208374322[/C][C]12.8026667160749[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]31.5925925925926[/C][C]2.45312711604235[/C][C]12.8784979734606[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]31.4423076923077[/C][C]2.42277614307862[/C][C]12.9778014292125[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]31.3[/C][C]2.39749018427052[/C][C]13.0553193524434[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]31.1458333333333[/C][C]2.36290585904301[/C][C]13.1811570969432[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]31.0217391304348[/C][C]2.3288754787642[/C][C]13.3204799540834[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]30.9318181818182[/C][C]2.30666781605144[/C][C]13.4097410847685[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]30.8333333333333[/C][C]2.27415838516598[/C][C]13.5581292554005[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]30.675[/C][C]2.23990255625964[/C][C]13.6947921748987[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]30.4736842105263[/C][C]2.19651114869087[/C][C]13.873676092511[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]30.25[/C][C]2.13377041653412[/C][C]14.1767829217236[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]30[/C][C]2.04364150188708[/C][C]14.6796783938368[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]29.71875[/C][C]1.95783906911792[/C][C]15.1793630379383[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]29.5666666666667[/C][C]1.90080644309188[/C][C]15.5548013708187[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]29.4642857142857[/C][C]1.86408703760019[/C][C]15.8062821745801[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]29.3461538461538[/C][C]1.80165932722059[/C][C]16.288403363929[/C][/ROW]
[ROW][C]Median[/C][C]31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]35.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32.5116279069767[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209369&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 Mean32.79729729729732.664157291239712.3105709280535
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean39.9223909266128
Winsorized Mean ( 1 / 24 )32.79729729729732.6539932212444712.3577170562321
Winsorized Mean ( 2 / 24 )32.87837837837842.6408457284896212.4499428435687
Winsorized Mean ( 3 / 24 )32.87837837837842.6267183478716912.5169028514299
Winsorized Mean ( 4 / 24 )32.87837837837842.6083306222256312.6051421925661
Winsorized Mean ( 5 / 24 )32.81081081081082.5956472318610512.6407049494495
Winsorized Mean ( 6 / 24 )32.56756756756762.5518743306514212.7622144932403
Winsorized Mean ( 7 / 24 )32.66216216216222.5380683261531412.8689057838199
Winsorized Mean ( 8 / 24 )32.66216216216222.5380683261531412.8689057838199
Winsorized Mean ( 9 / 24 )32.78378378378382.5207961600190213.0053291510633
Winsorized Mean ( 10 / 24 )32.64864864864862.4973464208358813.0733359121723
Winsorized Mean ( 11 / 24 )32.52.4262731059685713.39502957027
Winsorized Mean ( 12 / 24 )32.52.4262731059685713.39502957027
Winsorized Mean ( 13 / 24 )32.14864864864862.3687058245777413.5722419876177
Winsorized Mean ( 14 / 24 )31.77027027027032.253102455843114.1006771298298
Winsorized Mean ( 15 / 24 )31.77027027027032.253102455843114.1006771298298
Winsorized Mean ( 16 / 24 )32.20270270270272.1945356163753814.6740396749133
Winsorized Mean ( 17 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 18 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 19 / 24 )32.43243243243242.164477194557914.9839566404195
Winsorized Mean ( 20 / 24 )32.43243243243242.0120040608842816.1194666864531
Winsorized Mean ( 21 / 24 )31.01351351351351.8001288821401517.2284961489212
Winsorized Mean ( 22 / 24 )30.41891891891891.6351840908646818.6027488212863
Winsorized Mean ( 23 / 24 )30.41891891891891.6351840908646818.6027488212863
Winsorized Mean ( 24 / 24 )30.41891891891891.5486682909162419.6419847280027
Trimmed Mean ( 1 / 24 )32.72222222222222.6357674480107412.414684856556
Trimmed Mean ( 2 / 24 )32.64285714285712.6129979065712312.4924926502107
Trimmed Mean ( 3 / 24 )32.51470588235292.5927477574456812.5406360063293
Trimmed Mean ( 4 / 24 )32.37878787878792.5732862132763812.5826609227282
Trimmed Mean ( 5 / 24 )32.2343752.5547324382606512.6175150545105
Trimmed Mean ( 6 / 24 )32.09677419354842.5344490280826112.6642018986788
Trimmed Mean ( 7 / 24 )322.5197524764097112.6996601053431
Trimmed Mean ( 8 / 24 )31.87931034482762.5028812901726412.7370444894846
Trimmed Mean ( 9 / 24 )31.752.4799520837432212.8026667160749
Trimmed Mean ( 10 / 24 )31.59259259259262.4531271160423512.8784979734606
Trimmed Mean ( 11 / 24 )31.44230769230772.4227761430786212.9778014292125
Trimmed Mean ( 12 / 24 )31.32.3974901842705213.0553193524434
Trimmed Mean ( 13 / 24 )31.14583333333332.3629058590430113.1811570969432
Trimmed Mean ( 14 / 24 )31.02173913043482.328875478764213.3204799540834
Trimmed Mean ( 15 / 24 )30.93181818181822.3066678160514413.4097410847685
Trimmed Mean ( 16 / 24 )30.83333333333332.2741583851659813.5581292554005
Trimmed Mean ( 17 / 24 )30.6752.2399025562596413.6947921748987
Trimmed Mean ( 18 / 24 )30.47368421052632.1965111486908713.873676092511
Trimmed Mean ( 19 / 24 )30.252.1337704165341214.1767829217236
Trimmed Mean ( 20 / 24 )302.0436415018870814.6796783938368
Trimmed Mean ( 21 / 24 )29.718751.9578390691179215.1793630379383
Trimmed Mean ( 22 / 24 )29.56666666666671.9008064430918815.5548013708187
Trimmed Mean ( 23 / 24 )29.46428571428571.8640870376001915.8062821745801
Trimmed Mean ( 24 / 24 )29.34615384615381.8016593272205916.288403363929
Median31
Midrange35.5
Midmean - Weighted Average at Xnp32.5116279069767
Midmean - Weighted Average at X(n+1)p32.5116279069767
Midmean - Empirical Distribution Function32.5116279069767
Midmean - Empirical Distribution Function - Averaging32.5116279069767
Midmean - Empirical Distribution Function - Interpolation32.5116279069767
Midmean - Closest Observation32.5116279069767
Midmean - True Basic - Statistics Graphics Toolkit32.5116279069767
Midmean - MS Excel (old versions)32.5116279069767
Number of observations74



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')