Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Dec 2007 14:44:26 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t11968039363f2810b3zj4a3fo.htm/, Retrieved Thu, 02 May 2024 02:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2457, Retrieved Thu, 02 May 2024 02:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Variance reductio...] [2007-11-30 14:45:44] [6c50c82828af94f83a614a64264ea782]
- RMPD    [Central Tendency] [Residuals - totaa...] [2007-12-04 21:44:26] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
Feedback Forum

Post a new message
Dataseries X:
0.102198199816261 
7.65958537941723 
0.514973279074895 
1.81052007100356 
6.87959574610314 
-14.1296213500912 
-0.89411601543205 
-3.49670825604328 
3.8519113222486 
3.72615523515038 
8.02782696403119 
-0.575486569081918 
3.744615937432 
-3.65014405909330 
-4.15751150058808 
3.86783913045688 
3.51493397782816 
4.59218212526637 
-2.67235971955228 
-3.00118307378568 
0.121624186809227 
6.36107402158039 
-1.95651199658131 
-8.28092934494062 
-0.0670671664132464 
5.09770693112434 
-1.16482135150668 
3.6564160533102 
-5.17441109638801 
-2.69601592064686 
3.39963069069633 
11.4641328336354 
-4.01600766148448 
8.80862536125446 
-0.356300617181422 
-0.310813095324366 
0.90348328510493 
-5.49095052522661 
4.48318326104891 
2.91068976048952 
-0.318643353998573 
-0.470342599089727 
-5.77679194286295 
-1.0953216305939 
-2.66524307913310 
4.15608649881874 
-1.15764641576872 
1.95357586876721 
-0.406863162738059 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2457&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2457&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5638113187126920.6707022005766120.840628401439529
Geometric MeanNaN
Harmonic Mean-4.11868316035247
Quadratic Mean4.68084099412781
Winsorized Mean ( 1 / 16 )0.6289783499937050.6079516336440941.03458616637573
Winsorized Mean ( 2 / 16 )0.6993187175387820.571442154069541.22377866693692
Winsorized Mean ( 3 / 16 )0.6942738093564790.5614411319334891.23659235112601
Winsorized Mean ( 4 / 16 )0.6564411396033780.5396784507012611.21635603339432
Winsorized Mean ( 5 / 16 )0.707296024427580.505014126477231.40054700917257
Winsorized Mean ( 6 / 16 )0.5699250140578920.4677754271255341.21837313592991
Winsorized Mean ( 7 / 16 )0.5499734135626370.4431173890068681.24114608725976
Winsorized Mean ( 8 / 16 )0.5572284239842790.4348461288785241.28143816163520
Winsorized Mean ( 9 / 16 )0.5881642562342150.4064710595626771.44700155742213
Winsorized Mean ( 10 / 16 )0.5916172735356350.3845883499309261.53831303949247
Winsorized Mean ( 11 / 16 )0.5933522188774580.3830096155775081.54918360987568
Winsorized Mean ( 12 / 16 )0.5688186488209470.3780714647739051.50452679405761
Winsorized Mean ( 13 / 16 )0.7519516068518090.3450098820870332.17950744570881
Winsorized Mean ( 14 / 16 )0.9582234534902230.3064456106810963.12689567117801
Winsorized Mean ( 15 / 16 )0.917109022956320.2982250527046753.07522461523215
Winsorized Mean ( 16 / 16 )0.899809920276480.2884686594685643.11926405431415
Trimmed Mean ( 1 / 16 )0.5638113187126920.5782869601171510.97496806533295
Trimmed Mean ( 2 / 16 )0.6445158113484620.5396771578557981.19426179516139
Trimmed Mean ( 3 / 16 )0.63984911850920.5160455889805981.23990812473209
Trimmed Mean ( 4 / 16 )0.63984911850920.4901845305304951.30532295218850
Trimmed Mean ( 5 / 16 )0.6061459638971760.4656163812420751.30181408626609
Trimmed Mean ( 6 / 16 )0.5793548667837180.4464216754894991.29777494819995
Trimmed Mean ( 7 / 16 )0.5815551657530770.4337876261319891.34064489330575
Trimmed Mean ( 8 / 16 )0.5815551657530770.4240971253199441.37127825451386
Trimmed Mean ( 9 / 16 )0.5943844429090.4122739000890251.44172222102988
Trimmed Mean ( 10 / 16 )0.5955522174188260.4038881503288941.47454738876062
Trimmed Mean ( 11 / 16 )0.5962663368642930.3974916398245041.50007264838966
Trimmed Mean ( 12 / 16 )0.5967855797055840.3865069523110171.54404875808122
Trimmed Mean ( 13 / 16 )0.6017507232322040.3694947425315691.62857722713278
Trimmed Mean ( 14 / 16 )0.574791590274840.3544293407257371.62173816958236
Trimmed Mean ( 15 / 16 )0.504159404945690.3426036124208411.47155309129199
Trimmed Mean ( 16 / 16 )0.504159404945690.3220431681217401.56550256254809
Median-0.0670671664132464
Midrange-1.3327442582279
Midmean - Weighted Average at Xnp0.465625981466983
Midmean - Weighted Average at X(n+1)p0.596785579705584
Midmean - Empirical Distribution Function0.596785579705584
Midmean - Empirical Distribution Function - Averaging0.596785579705584
Midmean - Empirical Distribution Function - Interpolation0.596785579705584
Midmean - Closest Observation0.47104922204182
Midmean - True Basic - Statistics Graphics Toolkit0.596785579705584
Midmean - MS Excel (old versions)0.596785579705584
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.563811318712692 & 0.670702200576612 & 0.840628401439529 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -4.11868316035247 &  &  \tabularnewline
Quadratic Mean & 4.68084099412781 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.628978349993705 & 0.607951633644094 & 1.03458616637573 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.699318717538782 & 0.57144215406954 & 1.22377866693692 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.694273809356479 & 0.561441131933489 & 1.23659235112601 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.656441139603378 & 0.539678450701261 & 1.21635603339432 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.70729602442758 & 0.50501412647723 & 1.40054700917257 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.569925014057892 & 0.467775427125534 & 1.21837313592991 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.549973413562637 & 0.443117389006868 & 1.24114608725976 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.557228423984279 & 0.434846128878524 & 1.28143816163520 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.588164256234215 & 0.406471059562677 & 1.44700155742213 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.591617273535635 & 0.384588349930926 & 1.53831303949247 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.593352218877458 & 0.383009615577508 & 1.54918360987568 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.568818648820947 & 0.378071464773905 & 1.50452679405761 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.751951606851809 & 0.345009882087033 & 2.17950744570881 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.958223453490223 & 0.306445610681096 & 3.12689567117801 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.91710902295632 & 0.298225052704675 & 3.07522461523215 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.89980992027648 & 0.288468659468564 & 3.11926405431415 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.563811318712692 & 0.578286960117151 & 0.97496806533295 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.644515811348462 & 0.539677157855798 & 1.19426179516139 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.6398491185092 & 0.516045588980598 & 1.23990812473209 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.6398491185092 & 0.490184530530495 & 1.30532295218850 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.606145963897176 & 0.465616381242075 & 1.30181408626609 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.579354866783718 & 0.446421675489499 & 1.29777494819995 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.581555165753077 & 0.433787626131989 & 1.34064489330575 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.581555165753077 & 0.424097125319944 & 1.37127825451386 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.594384442909 & 0.412273900089025 & 1.44172222102988 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.595552217418826 & 0.403888150328894 & 1.47454738876062 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.596266336864293 & 0.397491639824504 & 1.50007264838966 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.596785579705584 & 0.386506952311017 & 1.54404875808122 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.601750723232204 & 0.369494742531569 & 1.62857722713278 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.57479159027484 & 0.354429340725737 & 1.62173816958236 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.50415940494569 & 0.342603612420841 & 1.47155309129199 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.50415940494569 & 0.322043168121740 & 1.56550256254809 \tabularnewline
Median & -0.0670671664132464 &  &  \tabularnewline
Midrange & -1.3327442582279 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.465625981466983 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.596785579705584 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.596785579705584 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.596785579705584 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.596785579705584 &  &  \tabularnewline
Midmean - Closest Observation & 0.47104922204182 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.596785579705584 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.596785579705584 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2457&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]0.563811318712692[/C][C]0.670702200576612[/C][C]0.840628401439529[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-4.11868316035247[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.68084099412781[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.628978349993705[/C][C]0.607951633644094[/C][C]1.03458616637573[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.699318717538782[/C][C]0.57144215406954[/C][C]1.22377866693692[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.694273809356479[/C][C]0.561441131933489[/C][C]1.23659235112601[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.656441139603378[/C][C]0.539678450701261[/C][C]1.21635603339432[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.70729602442758[/C][C]0.50501412647723[/C][C]1.40054700917257[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.569925014057892[/C][C]0.467775427125534[/C][C]1.21837313592991[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.549973413562637[/C][C]0.443117389006868[/C][C]1.24114608725976[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.557228423984279[/C][C]0.434846128878524[/C][C]1.28143816163520[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.588164256234215[/C][C]0.406471059562677[/C][C]1.44700155742213[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.591617273535635[/C][C]0.384588349930926[/C][C]1.53831303949247[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.593352218877458[/C][C]0.383009615577508[/C][C]1.54918360987568[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.568818648820947[/C][C]0.378071464773905[/C][C]1.50452679405761[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.751951606851809[/C][C]0.345009882087033[/C][C]2.17950744570881[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.958223453490223[/C][C]0.306445610681096[/C][C]3.12689567117801[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.91710902295632[/C][C]0.298225052704675[/C][C]3.07522461523215[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.89980992027648[/C][C]0.288468659468564[/C][C]3.11926405431415[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.563811318712692[/C][C]0.578286960117151[/C][C]0.97496806533295[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.644515811348462[/C][C]0.539677157855798[/C][C]1.19426179516139[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.6398491185092[/C][C]0.516045588980598[/C][C]1.23990812473209[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.6398491185092[/C][C]0.490184530530495[/C][C]1.30532295218850[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.606145963897176[/C][C]0.465616381242075[/C][C]1.30181408626609[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.579354866783718[/C][C]0.446421675489499[/C][C]1.29777494819995[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.581555165753077[/C][C]0.433787626131989[/C][C]1.34064489330575[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.581555165753077[/C][C]0.424097125319944[/C][C]1.37127825451386[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.594384442909[/C][C]0.412273900089025[/C][C]1.44172222102988[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.595552217418826[/C][C]0.403888150328894[/C][C]1.47454738876062[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.596266336864293[/C][C]0.397491639824504[/C][C]1.50007264838966[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.596785579705584[/C][C]0.386506952311017[/C][C]1.54404875808122[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.601750723232204[/C][C]0.369494742531569[/C][C]1.62857722713278[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.57479159027484[/C][C]0.354429340725737[/C][C]1.62173816958236[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.50415940494569[/C][C]0.342603612420841[/C][C]1.47155309129199[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.50415940494569[/C][C]0.322043168121740[/C][C]1.56550256254809[/C][/ROW]
[ROW][C]Median[/C][C]-0.0670671664132464[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.3327442582279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.465625981466983[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.596785579705584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.596785579705584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.596785579705584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.596785579705584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.47104922204182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.596785579705584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.596785579705584[/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=2457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2457&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 Mean0.5638113187126920.6707022005766120.840628401439529
Geometric MeanNaN
Harmonic Mean-4.11868316035247
Quadratic Mean4.68084099412781
Winsorized Mean ( 1 / 16 )0.6289783499937050.6079516336440941.03458616637573
Winsorized Mean ( 2 / 16 )0.6993187175387820.571442154069541.22377866693692
Winsorized Mean ( 3 / 16 )0.6942738093564790.5614411319334891.23659235112601
Winsorized Mean ( 4 / 16 )0.6564411396033780.5396784507012611.21635603339432
Winsorized Mean ( 5 / 16 )0.707296024427580.505014126477231.40054700917257
Winsorized Mean ( 6 / 16 )0.5699250140578920.4677754271255341.21837313592991
Winsorized Mean ( 7 / 16 )0.5499734135626370.4431173890068681.24114608725976
Winsorized Mean ( 8 / 16 )0.5572284239842790.4348461288785241.28143816163520
Winsorized Mean ( 9 / 16 )0.5881642562342150.4064710595626771.44700155742213
Winsorized Mean ( 10 / 16 )0.5916172735356350.3845883499309261.53831303949247
Winsorized Mean ( 11 / 16 )0.5933522188774580.3830096155775081.54918360987568
Winsorized Mean ( 12 / 16 )0.5688186488209470.3780714647739051.50452679405761
Winsorized Mean ( 13 / 16 )0.7519516068518090.3450098820870332.17950744570881
Winsorized Mean ( 14 / 16 )0.9582234534902230.3064456106810963.12689567117801
Winsorized Mean ( 15 / 16 )0.917109022956320.2982250527046753.07522461523215
Winsorized Mean ( 16 / 16 )0.899809920276480.2884686594685643.11926405431415
Trimmed Mean ( 1 / 16 )0.5638113187126920.5782869601171510.97496806533295
Trimmed Mean ( 2 / 16 )0.6445158113484620.5396771578557981.19426179516139
Trimmed Mean ( 3 / 16 )0.63984911850920.5160455889805981.23990812473209
Trimmed Mean ( 4 / 16 )0.63984911850920.4901845305304951.30532295218850
Trimmed Mean ( 5 / 16 )0.6061459638971760.4656163812420751.30181408626609
Trimmed Mean ( 6 / 16 )0.5793548667837180.4464216754894991.29777494819995
Trimmed Mean ( 7 / 16 )0.5815551657530770.4337876261319891.34064489330575
Trimmed Mean ( 8 / 16 )0.5815551657530770.4240971253199441.37127825451386
Trimmed Mean ( 9 / 16 )0.5943844429090.4122739000890251.44172222102988
Trimmed Mean ( 10 / 16 )0.5955522174188260.4038881503288941.47454738876062
Trimmed Mean ( 11 / 16 )0.5962663368642930.3974916398245041.50007264838966
Trimmed Mean ( 12 / 16 )0.5967855797055840.3865069523110171.54404875808122
Trimmed Mean ( 13 / 16 )0.6017507232322040.3694947425315691.62857722713278
Trimmed Mean ( 14 / 16 )0.574791590274840.3544293407257371.62173816958236
Trimmed Mean ( 15 / 16 )0.504159404945690.3426036124208411.47155309129199
Trimmed Mean ( 16 / 16 )0.504159404945690.3220431681217401.56550256254809
Median-0.0670671664132464
Midrange-1.3327442582279
Midmean - Weighted Average at Xnp0.465625981466983
Midmean - Weighted Average at X(n+1)p0.596785579705584
Midmean - Empirical Distribution Function0.596785579705584
Midmean - Empirical Distribution Function - Averaging0.596785579705584
Midmean - Empirical Distribution Function - Interpolation0.596785579705584
Midmean - Closest Observation0.47104922204182
Midmean - True Basic - Statistics Graphics Toolkit0.596785579705584
Midmean - MS Excel (old versions)0.596785579705584
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')