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Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 26 Nov 2012 12:57:58 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/26/t1353952725cwairr1bb1i5vm1.htm/, Retrieved Tue, 30 Apr 2024 04:05:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=193414, Retrieved Tue, 30 Apr 2024 04:05:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-11-26 17:57:58] [cd7f3d5ccbf34a37bb8df43fbba84031] [Current]
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Dataseries X:
-0.201495772702999
-11.3400019538982
10.9272190204048
-3.89041163700983
4.16303048580663
0.308512324249218
11.9002003733679
7.56898181074824
3.37192241904051
-10.2039781851694
1.12804873835857
-2.7819503761412
9.1174596776653
12.032432344505
3.48743145216592
-5.6181992475455
-4.06707647204309
5.49743401016974
-7.87173065032561
0.357281462351981
-2.22959857105356
3.49027700807077
-5.65501619479299
-9.40912850395061
15.1777470152335
-5.56507754122207
-7.09288463341003
6.86764100614091
-9.62591150434642
6.42928395856747
-10.2784590823146
1.45285281491172
-6.70989216699535
0.221097549992618
4.0753079174218
18.3862275184539
9.2109718020317
4.67608518705448
-7.2280732259349
0.593820317341087
1.12499451500879
-4.99617437748183
-0.0475904079090846
-4.64707725343993
2.46003681709183
9.41472617930485
14.6408474195279
2.08078749515246
-11.7958440510021
-1.79328633431859
-5.17578265609024
-1.33587506040935
-5.60037039128776
4.81246722113017
2.17250906904651
11.2708346785196
14.6714044287092
5.11558606821106
3.109869072465
6.0646574440848




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=193414&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=193414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193414&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 Mean1.203651672858510.9509298533510351.26576284109379
Geometric MeanNaN
Harmonic Mean-5.4609515060834
Quadratic Mean7.40274036578578
Winsorized Mean ( 1 / 20 )1.15777436608990.9341862158401151.23934002285477
Winsorized Mean ( 2 / 20 )1.176281042258550.9222078610500081.2755053301316
Winsorized Mean ( 3 / 20 )1.178477236656740.9210471126580631.27949723793798
Winsorized Mean ( 4 / 20 )1.043120677043410.8728437339916251.19508296436189
Winsorized Mean ( 5 / 20 )1.050166596148310.8667802427522311.2115719121767
Winsorized Mean ( 6 / 20 )1.140969812025980.8235222831227841.38547533613716
Winsorized Mean ( 7 / 20 )1.175974684758170.8015690346153751.4670909603219
Winsorized Mean ( 8 / 20 )0.9923341182814880.7585226649149351.30824583652062
Winsorized Mean ( 9 / 20 )1.019219831652720.7425305476991481.37263016964209
Winsorized Mean ( 10 / 20 )1.179447139625380.7097134322959541.66186391007116
Winsorized Mean ( 11 / 20 )0.9023093043526230.657185370347021.37299055192931
Winsorized Mean ( 12 / 20 )0.7656069146827050.6330538145686961.2093867804972
Winsorized Mean ( 13 / 20 )0.6782763385560260.616475484393651.10024868097255
Winsorized Mean ( 14 / 20 )0.6840322917074970.5876700375268371.16397340008382
Winsorized Mean ( 15 / 20 )0.5871285028808340.5584918307659241.05127500625325
Winsorized Mean ( 16 / 20 )0.578394951436360.527781668068091.09589814582522
Winsorized Mean ( 17 / 20 )0.6568448328258790.4880446267009431.34587043251758
Winsorized Mean ( 18 / 20 )0.668929673113150.4734847590786961.41277973638423
Winsorized Mean ( 19 / 20 )0.857475083659730.3940475132718892.1760702828445
Winsorized Mean ( 20 / 20 )1.0123514958940.3614455984496922.80084056974595
Trimmed Mean ( 1 / 20 )1.131529601794120.9098136996186311.24369373891427
Trimmed Mean ( 2 / 20 )1.103410211477210.8797317621875441.25425755770539
Trimmed Mean ( 3 / 20 )1.062926416598690.8504473767678661.2498438417652
Trimmed Mean ( 4 / 20 )1.018483793499430.8143153705056951.25072401969638
Trimmed Mean ( 5 / 20 )1.011092728436240.7886836122875991.28200042790738
Trimmed Mean ( 6 / 20 )1.001324261508220.758169236174351.32071338921744
Trimmed Mean ( 7 / 20 )0.9709665331347960.7331221407640251.32442669392429
Trimmed Mean ( 8 / 20 )0.9310298802211530.707158174594331.31657939294168
Trimmed Mean ( 9 / 20 )0.9200826948532360.6857501710496171.34171704754364
Trimmed Mean ( 10 / 20 )0.9035598387199890.6615879783471941.3657440405391
Trimmed Mean ( 11 / 20 )0.8599986859454540.6379726072129931.34801820050298
Trimmed Mean ( 12 / 20 )0.8535879861867920.6205960641728321.37543248413041
Trimmed Mean ( 13 / 20 )0.866526379055040.6026143534639341.43794513700859
Trimmed Mean ( 14 / 20 )0.8936778272039360.5812200763080691.53758939794477
Trimmed Mean ( 15 / 20 )0.9236271894177130.5586415720106811.65334489177625
Trimmed Mean ( 16 / 20 )0.9716984303515530.5338805354283351.82006716085267
Trimmed Mean ( 17 / 20 )1.028424893656630.5063525375983722.03104520525254
Trimmed Mean ( 18 / 20 )1.083069020249390.4783361220030632.26424259099222
Trimmed Mean ( 19 / 20 )1.145817406179120.4378437648488812.616954946417
Trimmed Mean ( 20 / 20 )1.191345141313760.4103795387829062.90303250704707
Median1.12652162668368
Midrange3.2951917337259
Midmean - Weighted Average at Xnp0.726872033111005
Midmean - Weighted Average at X(n+1)p0.923627189417713
Midmean - Empirical Distribution Function0.726872033111005
Midmean - Empirical Distribution Function - Averaging0.923627189417713
Midmean - Empirical Distribution Function - Interpolation0.923627189417713
Midmean - Closest Observation0.726872033111005
Midmean - True Basic - Statistics Graphics Toolkit0.923627189417713
Midmean - MS Excel (old versions)0.893677827203936
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.20365167285851 & 0.950929853351035 & 1.26576284109379 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -5.4609515060834 &  &  \tabularnewline
Quadratic Mean & 7.40274036578578 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.1577743660899 & 0.934186215840115 & 1.23934002285477 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.17628104225855 & 0.922207861050008 & 1.2755053301316 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.17847723665674 & 0.921047112658063 & 1.27949723793798 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.04312067704341 & 0.872843733991625 & 1.19508296436189 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.05016659614831 & 0.866780242752231 & 1.2115719121767 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.14096981202598 & 0.823522283122784 & 1.38547533613716 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.17597468475817 & 0.801569034615375 & 1.4670909603219 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.992334118281488 & 0.758522664914935 & 1.30824583652062 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.01921983165272 & 0.742530547699148 & 1.37263016964209 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.17944713962538 & 0.709713432295954 & 1.66186391007116 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.902309304352623 & 0.65718537034702 & 1.37299055192931 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.765606914682705 & 0.633053814568696 & 1.2093867804972 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.678276338556026 & 0.61647548439365 & 1.10024868097255 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.684032291707497 & 0.587670037526837 & 1.16397340008382 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.587128502880834 & 0.558491830765924 & 1.05127500625325 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.57839495143636 & 0.52778166806809 & 1.09589814582522 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.656844832825879 & 0.488044626700943 & 1.34587043251758 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.66892967311315 & 0.473484759078696 & 1.41277973638423 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.85747508365973 & 0.394047513271889 & 2.1760702828445 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.012351495894 & 0.361445598449692 & 2.80084056974595 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.13152960179412 & 0.909813699618631 & 1.24369373891427 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.10341021147721 & 0.879731762187544 & 1.25425755770539 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.06292641659869 & 0.850447376767866 & 1.2498438417652 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.01848379349943 & 0.814315370505695 & 1.25072401969638 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.01109272843624 & 0.788683612287599 & 1.28200042790738 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.00132426150822 & 0.75816923617435 & 1.32071338921744 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.970966533134796 & 0.733122140764025 & 1.32442669392429 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.931029880221153 & 0.70715817459433 & 1.31657939294168 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.920082694853236 & 0.685750171049617 & 1.34171704754364 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.903559838719989 & 0.661587978347194 & 1.3657440405391 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.859998685945454 & 0.637972607212993 & 1.34801820050298 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.853587986186792 & 0.620596064172832 & 1.37543248413041 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.86652637905504 & 0.602614353463934 & 1.43794513700859 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.893677827203936 & 0.581220076308069 & 1.53758939794477 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.923627189417713 & 0.558641572010681 & 1.65334489177625 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.971698430351553 & 0.533880535428335 & 1.82006716085267 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.02842489365663 & 0.506352537598372 & 2.03104520525254 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.08306902024939 & 0.478336122003063 & 2.26424259099222 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.14581740617912 & 0.437843764848881 & 2.616954946417 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.19134514131376 & 0.410379538782906 & 2.90303250704707 \tabularnewline
Median & 1.12652162668368 &  &  \tabularnewline
Midrange & 3.2951917337259 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.726872033111005 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.923627189417713 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.726872033111005 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.923627189417713 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.923627189417713 &  &  \tabularnewline
Midmean - Closest Observation & 0.726872033111005 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.923627189417713 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.893677827203936 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193414&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]1.20365167285851[/C][C]0.950929853351035[/C][C]1.26576284109379[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-5.4609515060834[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.40274036578578[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.1577743660899[/C][C]0.934186215840115[/C][C]1.23934002285477[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.17628104225855[/C][C]0.922207861050008[/C][C]1.2755053301316[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.17847723665674[/C][C]0.921047112658063[/C][C]1.27949723793798[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.04312067704341[/C][C]0.872843733991625[/C][C]1.19508296436189[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.05016659614831[/C][C]0.866780242752231[/C][C]1.2115719121767[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.14096981202598[/C][C]0.823522283122784[/C][C]1.38547533613716[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.17597468475817[/C][C]0.801569034615375[/C][C]1.4670909603219[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.992334118281488[/C][C]0.758522664914935[/C][C]1.30824583652062[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.01921983165272[/C][C]0.742530547699148[/C][C]1.37263016964209[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.17944713962538[/C][C]0.709713432295954[/C][C]1.66186391007116[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.902309304352623[/C][C]0.65718537034702[/C][C]1.37299055192931[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.765606914682705[/C][C]0.633053814568696[/C][C]1.2093867804972[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.678276338556026[/C][C]0.61647548439365[/C][C]1.10024868097255[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.684032291707497[/C][C]0.587670037526837[/C][C]1.16397340008382[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.587128502880834[/C][C]0.558491830765924[/C][C]1.05127500625325[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.57839495143636[/C][C]0.52778166806809[/C][C]1.09589814582522[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.656844832825879[/C][C]0.488044626700943[/C][C]1.34587043251758[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.66892967311315[/C][C]0.473484759078696[/C][C]1.41277973638423[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.85747508365973[/C][C]0.394047513271889[/C][C]2.1760702828445[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.012351495894[/C][C]0.361445598449692[/C][C]2.80084056974595[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.13152960179412[/C][C]0.909813699618631[/C][C]1.24369373891427[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.10341021147721[/C][C]0.879731762187544[/C][C]1.25425755770539[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.06292641659869[/C][C]0.850447376767866[/C][C]1.2498438417652[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.01848379349943[/C][C]0.814315370505695[/C][C]1.25072401969638[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.01109272843624[/C][C]0.788683612287599[/C][C]1.28200042790738[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.00132426150822[/C][C]0.75816923617435[/C][C]1.32071338921744[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.970966533134796[/C][C]0.733122140764025[/C][C]1.32442669392429[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.931029880221153[/C][C]0.70715817459433[/C][C]1.31657939294168[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.920082694853236[/C][C]0.685750171049617[/C][C]1.34171704754364[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.903559838719989[/C][C]0.661587978347194[/C][C]1.3657440405391[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.859998685945454[/C][C]0.637972607212993[/C][C]1.34801820050298[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.853587986186792[/C][C]0.620596064172832[/C][C]1.37543248413041[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.86652637905504[/C][C]0.602614353463934[/C][C]1.43794513700859[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.893677827203936[/C][C]0.581220076308069[/C][C]1.53758939794477[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.923627189417713[/C][C]0.558641572010681[/C][C]1.65334489177625[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.971698430351553[/C][C]0.533880535428335[/C][C]1.82006716085267[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.02842489365663[/C][C]0.506352537598372[/C][C]2.03104520525254[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.08306902024939[/C][C]0.478336122003063[/C][C]2.26424259099222[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.14581740617912[/C][C]0.437843764848881[/C][C]2.616954946417[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.19134514131376[/C][C]0.410379538782906[/C][C]2.90303250704707[/C][/ROW]
[ROW][C]Median[/C][C]1.12652162668368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.2951917337259[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.726872033111005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.923627189417713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.726872033111005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.923627189417713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.923627189417713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.726872033111005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.923627189417713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.893677827203936[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193414&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 Mean1.203651672858510.9509298533510351.26576284109379
Geometric MeanNaN
Harmonic Mean-5.4609515060834
Quadratic Mean7.40274036578578
Winsorized Mean ( 1 / 20 )1.15777436608990.9341862158401151.23934002285477
Winsorized Mean ( 2 / 20 )1.176281042258550.9222078610500081.2755053301316
Winsorized Mean ( 3 / 20 )1.178477236656740.9210471126580631.27949723793798
Winsorized Mean ( 4 / 20 )1.043120677043410.8728437339916251.19508296436189
Winsorized Mean ( 5 / 20 )1.050166596148310.8667802427522311.2115719121767
Winsorized Mean ( 6 / 20 )1.140969812025980.8235222831227841.38547533613716
Winsorized Mean ( 7 / 20 )1.175974684758170.8015690346153751.4670909603219
Winsorized Mean ( 8 / 20 )0.9923341182814880.7585226649149351.30824583652062
Winsorized Mean ( 9 / 20 )1.019219831652720.7425305476991481.37263016964209
Winsorized Mean ( 10 / 20 )1.179447139625380.7097134322959541.66186391007116
Winsorized Mean ( 11 / 20 )0.9023093043526230.657185370347021.37299055192931
Winsorized Mean ( 12 / 20 )0.7656069146827050.6330538145686961.2093867804972
Winsorized Mean ( 13 / 20 )0.6782763385560260.616475484393651.10024868097255
Winsorized Mean ( 14 / 20 )0.6840322917074970.5876700375268371.16397340008382
Winsorized Mean ( 15 / 20 )0.5871285028808340.5584918307659241.05127500625325
Winsorized Mean ( 16 / 20 )0.578394951436360.527781668068091.09589814582522
Winsorized Mean ( 17 / 20 )0.6568448328258790.4880446267009431.34587043251758
Winsorized Mean ( 18 / 20 )0.668929673113150.4734847590786961.41277973638423
Winsorized Mean ( 19 / 20 )0.857475083659730.3940475132718892.1760702828445
Winsorized Mean ( 20 / 20 )1.0123514958940.3614455984496922.80084056974595
Trimmed Mean ( 1 / 20 )1.131529601794120.9098136996186311.24369373891427
Trimmed Mean ( 2 / 20 )1.103410211477210.8797317621875441.25425755770539
Trimmed Mean ( 3 / 20 )1.062926416598690.8504473767678661.2498438417652
Trimmed Mean ( 4 / 20 )1.018483793499430.8143153705056951.25072401969638
Trimmed Mean ( 5 / 20 )1.011092728436240.7886836122875991.28200042790738
Trimmed Mean ( 6 / 20 )1.001324261508220.758169236174351.32071338921744
Trimmed Mean ( 7 / 20 )0.9709665331347960.7331221407640251.32442669392429
Trimmed Mean ( 8 / 20 )0.9310298802211530.707158174594331.31657939294168
Trimmed Mean ( 9 / 20 )0.9200826948532360.6857501710496171.34171704754364
Trimmed Mean ( 10 / 20 )0.9035598387199890.6615879783471941.3657440405391
Trimmed Mean ( 11 / 20 )0.8599986859454540.6379726072129931.34801820050298
Trimmed Mean ( 12 / 20 )0.8535879861867920.6205960641728321.37543248413041
Trimmed Mean ( 13 / 20 )0.866526379055040.6026143534639341.43794513700859
Trimmed Mean ( 14 / 20 )0.8936778272039360.5812200763080691.53758939794477
Trimmed Mean ( 15 / 20 )0.9236271894177130.5586415720106811.65334489177625
Trimmed Mean ( 16 / 20 )0.9716984303515530.5338805354283351.82006716085267
Trimmed Mean ( 17 / 20 )1.028424893656630.5063525375983722.03104520525254
Trimmed Mean ( 18 / 20 )1.083069020249390.4783361220030632.26424259099222
Trimmed Mean ( 19 / 20 )1.145817406179120.4378437648488812.616954946417
Trimmed Mean ( 20 / 20 )1.191345141313760.4103795387829062.90303250704707
Median1.12652162668368
Midrange3.2951917337259
Midmean - Weighted Average at Xnp0.726872033111005
Midmean - Weighted Average at X(n+1)p0.923627189417713
Midmean - Empirical Distribution Function0.726872033111005
Midmean - Empirical Distribution Function - Averaging0.923627189417713
Midmean - Empirical Distribution Function - Interpolation0.923627189417713
Midmean - Closest Observation0.726872033111005
Midmean - True Basic - Statistics Graphics Toolkit0.923627189417713
Midmean - MS Excel (old versions)0.893677827203936
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')