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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Dec 2010 16:21:36 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/12/t1292170781zb583kdd63wnfct.htm/, Retrieved Tue, 07 May 2024 09:25:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108540, Retrieved Tue, 07 May 2024 09:25:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2009-12-20 16:30:59] [ebd107afac1bd6180acb277edd05815b]
- R  D  [Central Tendency] [CLT van resiudu's...] [2010-12-11 20:08:12] [04d4386fa51dbd2ef12d0f1f80644886]
-    D      [Central Tendency] [CLT van resiudu's...] [2010-12-12 16:21:36] [de8ccb310fbbdc3d90ae577a3e011cf9] [Current]
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Dataseries X:
0.119999771107115
2.44692884067448
-10.4874552327714
-8.24515636153588
-7.68872526868891
4.90480187773926
-11.3376070399016
18.8025296767249
-10.2648924101129
3.22904291750184
-15.2411002334852
-22.0063529958090
-6.66268278087993
0.104314699720359
11.1364502056182
-3.54121156148036
4.27349354024696
12.0468903684148
-19.4976679485769
-2.54269612338287
-0.395001151797313
2.78723169128158
13.4899577819542
15.6919085522552
-17.5310325273936
5.7093684737216
-14.4253340531639
10.9750168392126
4.6280737537926
-19.1759128690608
4.67542718308338
4.82273703391406
-2.51534348323854
1.95199787861741
-7.73755204679873
-5.57992291487482
17.2709396846659
22.2688778111519
28.9016258570466
-15.5834920643433
16.569204789179
3.59506948866402
5.2674989345929
16.8084939330501
-8.7536201191921
-0.409279859250539
-7.09725500325083
-3.96832121300299
56.8411641643913




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108540&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108540&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.400641438496532.030836806990730.689686849123038
Geometric MeanNaN
Harmonic Mean3.49847337522174
Quadratic Mean14.1395935937845
Winsorized Mean ( 1 / 16 )0.8816444331881071.756747827659080.501861689712705
Winsorized Mean ( 2 / 16 )0.6240528835400011.671842025468890.373272638223684
Winsorized Mean ( 3 / 16 )0.5125344472485851.593452660129040.321650250473761
Winsorized Mean ( 4 / 16 )0.546489587737671.527972506567920.357656689101808
Winsorized Mean ( 5 / 16 )0.5342391876603541.509647714529750.353883348094074
Winsorized Mean ( 6 / 16 )0.6048282125318081.481637399255020.408216080962806
Winsorized Mean ( 7 / 16 )0.9206040377230211.36536717519760.674253823034665
Winsorized Mean ( 8 / 16 )0.6999021661849321.26095450458540.555057429621586
Winsorized Mean ( 9 / 16 )0.4757278535741541.198670187900110.396879690824344
Winsorized Mean ( 10 / 16 )0.5983466552321541.105496528934260.541246977780186
Winsorized Mean ( 11 / 16 )0.6762514369414771.078395215212380.62709053916592
Winsorized Mean ( 12 / 16 )-0.488983840794160.823319353530656-0.593917583374229
Winsorized Mean ( 13 / 16 )-0.593260491676720.802827258266248-0.738964061780738
Winsorized Mean ( 14 / 16 )-0.5278967177954510.756333847776955-0.697967860815783
Winsorized Mean ( 15 / 16 )-0.4199862957916650.728659708820535-0.576381938932081
Winsorized Mean ( 16 / 16 )-0.114533229612260.659281983255598-0.173724191652688
Trimmed Mean ( 1 / 16 )1.400641438496531.673786767774070.836809960183406
Trimmed Mean ( 2 / 16 )0.7190770067605861.56550479634230.459325968493143
Trimmed Mean ( 3 / 16 )0.4953417783066691.48667904035390.333186763828158
Trimmed Mean ( 4 / 16 )0.4953417783066691.4252818054650.347539536677845
Trimmed Mean ( 5 / 16 )0.4702756845521241.372461495616090.34265127732492
Trimmed Mean ( 6 / 16 )0.453333999945081.307685412774590.346669004270082
Trimmed Mean ( 7 / 16 )0.417985350341511.228729961609840.340176738096206
Trimmed Mean ( 8 / 16 )0.417985350341511.161558031528560.359848874525415
Trimmed Mean ( 9 / 16 )0.2346026838844021.104390419036020.212427308169856
Trimmed Mean ( 10 / 16 )0.1893339738660191.043671851340860.181411402082725
Trimmed Mean ( 11 / 16 )0.115105746506980.9874621495284540.11656724924793
Trimmed Mean ( 12 / 16 )0.01511978712046930.909602137806180.0166224181892711
Trimmed Mean ( 13 / 16 )0.1046164456995160.8932255122903460.117122097678632
Trimmed Mean ( 14 / 16 )0.2298764088183270.8673879739675650.265021438753454
Trimmed Mean ( 15 / 16 )0.3694661952998130.8378474110021860.440970742939789
Trimmed Mean ( 16 / 16 )0.3694661952998130.7915129785265990.466784759471126
Median0.119999771107115
Midrange17.4174055842912
Midmean - Weighted Average at Xnp-0.222140574821244
Midmean - Weighted Average at X(n+1)p0.0151197871204699
Midmean - Empirical Distribution Function0.0151197871204699
Midmean - Empirical Distribution Function - Averaging0.0151197871204699
Midmean - Empirical Distribution Function - Interpolation0.0151197871204699
Midmean - Closest Observation-0.302583141674005
Midmean - True Basic - Statistics Graphics Toolkit0.0151197871204699
Midmean - MS Excel (old versions)0.0151197871204699
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.40064143849653 & 2.03083680699073 & 0.689686849123038 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.49847337522174 &  &  \tabularnewline
Quadratic Mean & 14.1395935937845 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.881644433188107 & 1.75674782765908 & 0.501861689712705 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.624052883540001 & 1.67184202546889 & 0.373272638223684 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.512534447248585 & 1.59345266012904 & 0.321650250473761 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.54648958773767 & 1.52797250656792 & 0.357656689101808 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.534239187660354 & 1.50964771452975 & 0.353883348094074 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.604828212531808 & 1.48163739925502 & 0.408216080962806 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.920604037723021 & 1.3653671751976 & 0.674253823034665 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.699902166184932 & 1.2609545045854 & 0.555057429621586 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.475727853574154 & 1.19867018790011 & 0.396879690824344 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.598346655232154 & 1.10549652893426 & 0.541246977780186 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.676251436941477 & 1.07839521521238 & 0.62709053916592 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.48898384079416 & 0.823319353530656 & -0.593917583374229 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.59326049167672 & 0.802827258266248 & -0.738964061780738 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.527896717795451 & 0.756333847776955 & -0.697967860815783 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.419986295791665 & 0.728659708820535 & -0.576381938932081 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.11453322961226 & 0.659281983255598 & -0.173724191652688 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 1.40064143849653 & 1.67378676777407 & 0.836809960183406 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.719077006760586 & 1.5655047963423 & 0.459325968493143 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.495341778306669 & 1.4866790403539 & 0.333186763828158 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.495341778306669 & 1.425281805465 & 0.347539536677845 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.470275684552124 & 1.37246149561609 & 0.34265127732492 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.45333399994508 & 1.30768541277459 & 0.346669004270082 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.41798535034151 & 1.22872996160984 & 0.340176738096206 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.41798535034151 & 1.16155803152856 & 0.359848874525415 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.234602683884402 & 1.10439041903602 & 0.212427308169856 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.189333973866019 & 1.04367185134086 & 0.181411402082725 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.11510574650698 & 0.987462149528454 & 0.11656724924793 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.0151197871204693 & 0.90960213780618 & 0.0166224181892711 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.104616445699516 & 0.893225512290346 & 0.117122097678632 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.229876408818327 & 0.867387973967565 & 0.265021438753454 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.369466195299813 & 0.837847411002186 & 0.440970742939789 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.369466195299813 & 0.791512978526599 & 0.466784759471126 \tabularnewline
Median & 0.119999771107115 &  &  \tabularnewline
Midrange & 17.4174055842912 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.222140574821244 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0151197871204699 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0151197871204699 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0151197871204699 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0151197871204699 &  &  \tabularnewline
Midmean - Closest Observation & -0.302583141674005 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0151197871204699 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0151197871204699 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108540&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]1.40064143849653[/C][C]2.03083680699073[/C][C]0.689686849123038[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.49847337522174[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.1395935937845[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.881644433188107[/C][C]1.75674782765908[/C][C]0.501861689712705[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.624052883540001[/C][C]1.67184202546889[/C][C]0.373272638223684[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.512534447248585[/C][C]1.59345266012904[/C][C]0.321650250473761[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.54648958773767[/C][C]1.52797250656792[/C][C]0.357656689101808[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.534239187660354[/C][C]1.50964771452975[/C][C]0.353883348094074[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.604828212531808[/C][C]1.48163739925502[/C][C]0.408216080962806[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.920604037723021[/C][C]1.3653671751976[/C][C]0.674253823034665[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.699902166184932[/C][C]1.2609545045854[/C][C]0.555057429621586[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.475727853574154[/C][C]1.19867018790011[/C][C]0.396879690824344[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.598346655232154[/C][C]1.10549652893426[/C][C]0.541246977780186[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.676251436941477[/C][C]1.07839521521238[/C][C]0.62709053916592[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.48898384079416[/C][C]0.823319353530656[/C][C]-0.593917583374229[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.59326049167672[/C][C]0.802827258266248[/C][C]-0.738964061780738[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.527896717795451[/C][C]0.756333847776955[/C][C]-0.697967860815783[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.419986295791665[/C][C]0.728659708820535[/C][C]-0.576381938932081[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.11453322961226[/C][C]0.659281983255598[/C][C]-0.173724191652688[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]1.40064143849653[/C][C]1.67378676777407[/C][C]0.836809960183406[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.719077006760586[/C][C]1.5655047963423[/C][C]0.459325968493143[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.495341778306669[/C][C]1.4866790403539[/C][C]0.333186763828158[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.495341778306669[/C][C]1.425281805465[/C][C]0.347539536677845[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.470275684552124[/C][C]1.37246149561609[/C][C]0.34265127732492[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.45333399994508[/C][C]1.30768541277459[/C][C]0.346669004270082[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.41798535034151[/C][C]1.22872996160984[/C][C]0.340176738096206[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.41798535034151[/C][C]1.16155803152856[/C][C]0.359848874525415[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.234602683884402[/C][C]1.10439041903602[/C][C]0.212427308169856[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.189333973866019[/C][C]1.04367185134086[/C][C]0.181411402082725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.11510574650698[/C][C]0.987462149528454[/C][C]0.11656724924793[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.0151197871204693[/C][C]0.90960213780618[/C][C]0.0166224181892711[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.104616445699516[/C][C]0.893225512290346[/C][C]0.117122097678632[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.229876408818327[/C][C]0.867387973967565[/C][C]0.265021438753454[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.369466195299813[/C][C]0.837847411002186[/C][C]0.440970742939789[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.369466195299813[/C][C]0.791512978526599[/C][C]0.466784759471126[/C][/ROW]
[ROW][C]Median[/C][C]0.119999771107115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17.4174055842912[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.222140574821244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.302583141674005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0151197871204699[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108540&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 Mean1.400641438496532.030836806990730.689686849123038
Geometric MeanNaN
Harmonic Mean3.49847337522174
Quadratic Mean14.1395935937845
Winsorized Mean ( 1 / 16 )0.8816444331881071.756747827659080.501861689712705
Winsorized Mean ( 2 / 16 )0.6240528835400011.671842025468890.373272638223684
Winsorized Mean ( 3 / 16 )0.5125344472485851.593452660129040.321650250473761
Winsorized Mean ( 4 / 16 )0.546489587737671.527972506567920.357656689101808
Winsorized Mean ( 5 / 16 )0.5342391876603541.509647714529750.353883348094074
Winsorized Mean ( 6 / 16 )0.6048282125318081.481637399255020.408216080962806
Winsorized Mean ( 7 / 16 )0.9206040377230211.36536717519760.674253823034665
Winsorized Mean ( 8 / 16 )0.6999021661849321.26095450458540.555057429621586
Winsorized Mean ( 9 / 16 )0.4757278535741541.198670187900110.396879690824344
Winsorized Mean ( 10 / 16 )0.5983466552321541.105496528934260.541246977780186
Winsorized Mean ( 11 / 16 )0.6762514369414771.078395215212380.62709053916592
Winsorized Mean ( 12 / 16 )-0.488983840794160.823319353530656-0.593917583374229
Winsorized Mean ( 13 / 16 )-0.593260491676720.802827258266248-0.738964061780738
Winsorized Mean ( 14 / 16 )-0.5278967177954510.756333847776955-0.697967860815783
Winsorized Mean ( 15 / 16 )-0.4199862957916650.728659708820535-0.576381938932081
Winsorized Mean ( 16 / 16 )-0.114533229612260.659281983255598-0.173724191652688
Trimmed Mean ( 1 / 16 )1.400641438496531.673786767774070.836809960183406
Trimmed Mean ( 2 / 16 )0.7190770067605861.56550479634230.459325968493143
Trimmed Mean ( 3 / 16 )0.4953417783066691.48667904035390.333186763828158
Trimmed Mean ( 4 / 16 )0.4953417783066691.4252818054650.347539536677845
Trimmed Mean ( 5 / 16 )0.4702756845521241.372461495616090.34265127732492
Trimmed Mean ( 6 / 16 )0.453333999945081.307685412774590.346669004270082
Trimmed Mean ( 7 / 16 )0.417985350341511.228729961609840.340176738096206
Trimmed Mean ( 8 / 16 )0.417985350341511.161558031528560.359848874525415
Trimmed Mean ( 9 / 16 )0.2346026838844021.104390419036020.212427308169856
Trimmed Mean ( 10 / 16 )0.1893339738660191.043671851340860.181411402082725
Trimmed Mean ( 11 / 16 )0.115105746506980.9874621495284540.11656724924793
Trimmed Mean ( 12 / 16 )0.01511978712046930.909602137806180.0166224181892711
Trimmed Mean ( 13 / 16 )0.1046164456995160.8932255122903460.117122097678632
Trimmed Mean ( 14 / 16 )0.2298764088183270.8673879739675650.265021438753454
Trimmed Mean ( 15 / 16 )0.3694661952998130.8378474110021860.440970742939789
Trimmed Mean ( 16 / 16 )0.3694661952998130.7915129785265990.466784759471126
Median0.119999771107115
Midrange17.4174055842912
Midmean - Weighted Average at Xnp-0.222140574821244
Midmean - Weighted Average at X(n+1)p0.0151197871204699
Midmean - Empirical Distribution Function0.0151197871204699
Midmean - Empirical Distribution Function - Averaging0.0151197871204699
Midmean - Empirical Distribution Function - Interpolation0.0151197871204699
Midmean - Closest Observation-0.302583141674005
Midmean - True Basic - Statistics Graphics Toolkit0.0151197871204699
Midmean - MS Excel (old versions)0.0151197871204699
Number of observations49



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')