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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 computationMon, 03 Dec 2007 04:19:15 -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/03/t1196680070z3p39l7opfpg2nm.htm/, Retrieved Sat, 04 May 2024 03:40:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2318, Retrieved Sat, 04 May 2024 03:40:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact242
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-03 11:19:15] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
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Dataseries X:
0.0885982730755429 
2.64186885744555 
5.16552116890264 
-9.2200231605203 
-5.32890047417795 
-9.48023161174946 
1.41767703668243 
13.3497552586741 
7.7149014952624 
-0.692090881099297 
1.46470220746573 
-1.53286990142496 
2.63521154013923 
0.535093304602095 
-5.49615861078164 
5.00058937671211 
5.6447881772696 
-2.39321306599373 
-5.54328200971908 
-6.65223873930159 
-3.03300017318545 
0.78204634520444 
5.55337973656612 
-6.63720273179927 
-0.833111293439068 
-0.712330732891254 
-2.01538193012883 
4.50709926364353 
4.94728522032288 
2.39281155098311 
-1.68593422239783 
9.4304135124804 
-4.25521213213979 
11.0723433036131 
4.07420412597221 
-0.70249990328857 
-2.58051433315543 
4.65487508875862 
11.8177553761963 
11.2182770137312 
-1.42796647589004 
-0.0973716015573705 
0.226964888947301 
2.42853637064706 
-2.0608047727898 
2.35759903953638 
2.87530348066173 
-3.31625115315316 
-1.49575546152890 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2318&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2318&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9552092988037360.7534419938945471.26779407909858
Geometric MeanNaN
Harmonic Mean17.9947455140083
Quadratic Mean5.30667664705351
Winsorized Mean ( 1 / 16 )0.9292543716353960.7417761355168951.25274233982718
Winsorized Mean ( 2 / 16 )1.009593394441670.7075216894141051.42694338498330
Winsorized Mean ( 3 / 16 )1.001579249383560.7046408175975891.42140396123851
Winsorized Mean ( 4 / 16 )0.956843815175190.6468627148202281.47920693719549
Winsorized Mean ( 5 / 16 )0.7866000786159480.6008172745858271.30921681497622
Winsorized Mean ( 6 / 16 )0.5535974033438120.540663469004981.02392233816469
Winsorized Mean ( 7 / 16 )0.693923103534480.5049727013319711.37417943921347
Winsorized Mean ( 8 / 16 )0.7838990074239740.4624987100291311.69492150015856
Winsorized Mean ( 9 / 16 )0.805631103138150.4470879549006461.80195215350228
Winsorized Mean ( 10 / 16 )0.887096752860760.4289064560793342.06827558850426
Winsorized Mean ( 11 / 16 )0.8635008853418180.4090633577200122.11092210789716
Winsorized Mean ( 12 / 16 )0.908716999975820.3888467712342342.33695395513115
Winsorized Mean ( 13 / 16 )0.8059182278302170.3651274609484882.20722436416229
Winsorized Mean ( 14 / 16 )0.5575031028075080.2890018325135531.92906424834301
Winsorized Mean ( 15 / 16 )0.5328999490595560.2696761071184261.9760740198817
Winsorized Mean ( 16 / 16 )0.5428451319460020.2673923430368272.03014463982328
Trimmed Mean ( 1 / 16 )0.9552092988037360.7043430623797761.35617052232523
Trimmed Mean ( 2 / 16 )0.9135262126480510.655575206561951.39347279077084
Trimmed Mean ( 3 / 16 )0.8319060814965770.6168814583432351.34856716836787
Trimmed Mean ( 4 / 16 )0.8319060814965770.566557163800531.46835330069089
Trimmed Mean ( 5 / 16 )0.7038381905071190.5268685203729431.33588962576262
Trimmed Mean ( 6 / 16 )0.6819174741972130.4930266582421721.38312495439599
Trimmed Mean ( 7 / 16 )0.7118588240630070.470101799831061.51426525981995
Trimmed Mean ( 8 / 16 )0.7118588240630070.451084855338741.57810402109031
Trimmed Mean ( 9 / 16 )0.7021813297428840.4384835616294541.60138575579322
Trimmed Mean ( 10 / 16 )0.6827597247759570.4245691152319671.60812386082988
Trimmed Mean ( 11 / 16 )0.6456763381976040.4091161848798811.57822242693033
Trimmed Mean ( 12 / 16 )0.6068639643428170.3919009347088821.54851369464994
Trimmed Mean ( 13 / 16 )0.5532741138137690.3712958310343291.49011668747397
Trimmed Mean ( 14 / 16 )0.5079277343749190.3475058630451061.46163788410382
Trimmed Mean ( 15 / 16 )0.4987954296636530.3432739415800581.45305357979620
Trimmed Mean ( 16 / 16 )0.4987954296636530.3407339386446441.46388537533930
Median0.226964888947301
Midrange1.93476182346232
Midmean - Weighted Average at Xnp0.444354160205287
Midmean - Weighted Average at X(n+1)p0.606863964342817
Midmean - Empirical Distribution Function0.606863964342817
Midmean - Empirical Distribution Function - Averaging0.606863964342817
Midmean - Empirical Distribution Function - Interpolation0.606863964342817
Midmean - Closest Observation0.49147638625295
Midmean - True Basic - Statistics Graphics Toolkit0.606863964342817
Midmean - MS Excel (old versions)0.606863964342817
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.955209298803736 & 0.753441993894547 & 1.26779407909858 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 17.9947455140083 &  &  \tabularnewline
Quadratic Mean & 5.30667664705351 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.929254371635396 & 0.741776135516895 & 1.25274233982718 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 1.00959339444167 & 0.707521689414105 & 1.42694338498330 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 1.00157924938356 & 0.704640817597589 & 1.42140396123851 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.95684381517519 & 0.646862714820228 & 1.47920693719549 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.786600078615948 & 0.600817274585827 & 1.30921681497622 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.553597403343812 & 0.54066346900498 & 1.02392233816469 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.69392310353448 & 0.504972701331971 & 1.37417943921347 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.783899007423974 & 0.462498710029131 & 1.69492150015856 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.80563110313815 & 0.447087954900646 & 1.80195215350228 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.88709675286076 & 0.428906456079334 & 2.06827558850426 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.863500885341818 & 0.409063357720012 & 2.11092210789716 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.90871699997582 & 0.388846771234234 & 2.33695395513115 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.805918227830217 & 0.365127460948488 & 2.20722436416229 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.557503102807508 & 0.289001832513553 & 1.92906424834301 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.532899949059556 & 0.269676107118426 & 1.9760740198817 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.542845131946002 & 0.267392343036827 & 2.03014463982328 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.955209298803736 & 0.704343062379776 & 1.35617052232523 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.913526212648051 & 0.65557520656195 & 1.39347279077084 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.831906081496577 & 0.616881458343235 & 1.34856716836787 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.831906081496577 & 0.56655716380053 & 1.46835330069089 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.703838190507119 & 0.526868520372943 & 1.33588962576262 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.681917474197213 & 0.493026658242172 & 1.38312495439599 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.711858824063007 & 0.47010179983106 & 1.51426525981995 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.711858824063007 & 0.45108485533874 & 1.57810402109031 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.702181329742884 & 0.438483561629454 & 1.60138575579322 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.682759724775957 & 0.424569115231967 & 1.60812386082988 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.645676338197604 & 0.409116184879881 & 1.57822242693033 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.606863964342817 & 0.391900934708882 & 1.54851369464994 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.553274113813769 & 0.371295831034329 & 1.49011668747397 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.507927734374919 & 0.347505863045106 & 1.46163788410382 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.498795429663653 & 0.343273941580058 & 1.45305357979620 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.498795429663653 & 0.340733938644644 & 1.46388537533930 \tabularnewline
Median & 0.226964888947301 &  &  \tabularnewline
Midrange & 1.93476182346232 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.444354160205287 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.606863964342817 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.606863964342817 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.606863964342817 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.606863964342817 &  &  \tabularnewline
Midmean - Closest Observation & 0.49147638625295 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.606863964342817 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.606863964342817 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2318&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]0.955209298803736[/C][C]0.753441993894547[/C][C]1.26779407909858[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.9947455140083[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.30667664705351[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.929254371635396[/C][C]0.741776135516895[/C][C]1.25274233982718[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]1.00959339444167[/C][C]0.707521689414105[/C][C]1.42694338498330[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]1.00157924938356[/C][C]0.704640817597589[/C][C]1.42140396123851[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.95684381517519[/C][C]0.646862714820228[/C][C]1.47920693719549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.786600078615948[/C][C]0.600817274585827[/C][C]1.30921681497622[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.553597403343812[/C][C]0.54066346900498[/C][C]1.02392233816469[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.69392310353448[/C][C]0.504972701331971[/C][C]1.37417943921347[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.783899007423974[/C][C]0.462498710029131[/C][C]1.69492150015856[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.80563110313815[/C][C]0.447087954900646[/C][C]1.80195215350228[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.88709675286076[/C][C]0.428906456079334[/C][C]2.06827558850426[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.863500885341818[/C][C]0.409063357720012[/C][C]2.11092210789716[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.90871699997582[/C][C]0.388846771234234[/C][C]2.33695395513115[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.805918227830217[/C][C]0.365127460948488[/C][C]2.20722436416229[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.557503102807508[/C][C]0.289001832513553[/C][C]1.92906424834301[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.532899949059556[/C][C]0.269676107118426[/C][C]1.9760740198817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.542845131946002[/C][C]0.267392343036827[/C][C]2.03014463982328[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.955209298803736[/C][C]0.704343062379776[/C][C]1.35617052232523[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.913526212648051[/C][C]0.65557520656195[/C][C]1.39347279077084[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.831906081496577[/C][C]0.616881458343235[/C][C]1.34856716836787[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.831906081496577[/C][C]0.56655716380053[/C][C]1.46835330069089[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.703838190507119[/C][C]0.526868520372943[/C][C]1.33588962576262[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.681917474197213[/C][C]0.493026658242172[/C][C]1.38312495439599[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.711858824063007[/C][C]0.47010179983106[/C][C]1.51426525981995[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.711858824063007[/C][C]0.45108485533874[/C][C]1.57810402109031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.702181329742884[/C][C]0.438483561629454[/C][C]1.60138575579322[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.682759724775957[/C][C]0.424569115231967[/C][C]1.60812386082988[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.645676338197604[/C][C]0.409116184879881[/C][C]1.57822242693033[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.606863964342817[/C][C]0.391900934708882[/C][C]1.54851369464994[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.553274113813769[/C][C]0.371295831034329[/C][C]1.49011668747397[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.507927734374919[/C][C]0.347505863045106[/C][C]1.46163788410382[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.498795429663653[/C][C]0.343273941580058[/C][C]1.45305357979620[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.498795429663653[/C][C]0.340733938644644[/C][C]1.46388537533930[/C][/ROW]
[ROW][C]Median[/C][C]0.226964888947301[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.93476182346232[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.444354160205287[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.606863964342817[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.606863964342817[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.606863964342817[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.606863964342817[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.49147638625295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.606863964342817[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.606863964342817[/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=2318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2318&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 Mean0.9552092988037360.7534419938945471.26779407909858
Geometric MeanNaN
Harmonic Mean17.9947455140083
Quadratic Mean5.30667664705351
Winsorized Mean ( 1 / 16 )0.9292543716353960.7417761355168951.25274233982718
Winsorized Mean ( 2 / 16 )1.009593394441670.7075216894141051.42694338498330
Winsorized Mean ( 3 / 16 )1.001579249383560.7046408175975891.42140396123851
Winsorized Mean ( 4 / 16 )0.956843815175190.6468627148202281.47920693719549
Winsorized Mean ( 5 / 16 )0.7866000786159480.6008172745858271.30921681497622
Winsorized Mean ( 6 / 16 )0.5535974033438120.540663469004981.02392233816469
Winsorized Mean ( 7 / 16 )0.693923103534480.5049727013319711.37417943921347
Winsorized Mean ( 8 / 16 )0.7838990074239740.4624987100291311.69492150015856
Winsorized Mean ( 9 / 16 )0.805631103138150.4470879549006461.80195215350228
Winsorized Mean ( 10 / 16 )0.887096752860760.4289064560793342.06827558850426
Winsorized Mean ( 11 / 16 )0.8635008853418180.4090633577200122.11092210789716
Winsorized Mean ( 12 / 16 )0.908716999975820.3888467712342342.33695395513115
Winsorized Mean ( 13 / 16 )0.8059182278302170.3651274609484882.20722436416229
Winsorized Mean ( 14 / 16 )0.5575031028075080.2890018325135531.92906424834301
Winsorized Mean ( 15 / 16 )0.5328999490595560.2696761071184261.9760740198817
Winsorized Mean ( 16 / 16 )0.5428451319460020.2673923430368272.03014463982328
Trimmed Mean ( 1 / 16 )0.9552092988037360.7043430623797761.35617052232523
Trimmed Mean ( 2 / 16 )0.9135262126480510.655575206561951.39347279077084
Trimmed Mean ( 3 / 16 )0.8319060814965770.6168814583432351.34856716836787
Trimmed Mean ( 4 / 16 )0.8319060814965770.566557163800531.46835330069089
Trimmed Mean ( 5 / 16 )0.7038381905071190.5268685203729431.33588962576262
Trimmed Mean ( 6 / 16 )0.6819174741972130.4930266582421721.38312495439599
Trimmed Mean ( 7 / 16 )0.7118588240630070.470101799831061.51426525981995
Trimmed Mean ( 8 / 16 )0.7118588240630070.451084855338741.57810402109031
Trimmed Mean ( 9 / 16 )0.7021813297428840.4384835616294541.60138575579322
Trimmed Mean ( 10 / 16 )0.6827597247759570.4245691152319671.60812386082988
Trimmed Mean ( 11 / 16 )0.6456763381976040.4091161848798811.57822242693033
Trimmed Mean ( 12 / 16 )0.6068639643428170.3919009347088821.54851369464994
Trimmed Mean ( 13 / 16 )0.5532741138137690.3712958310343291.49011668747397
Trimmed Mean ( 14 / 16 )0.5079277343749190.3475058630451061.46163788410382
Trimmed Mean ( 15 / 16 )0.4987954296636530.3432739415800581.45305357979620
Trimmed Mean ( 16 / 16 )0.4987954296636530.3407339386446441.46388537533930
Median0.226964888947301
Midrange1.93476182346232
Midmean - Weighted Average at Xnp0.444354160205287
Midmean - Weighted Average at X(n+1)p0.606863964342817
Midmean - Empirical Distribution Function0.606863964342817
Midmean - Empirical Distribution Function - Averaging0.606863964342817
Midmean - Empirical Distribution Function - Interpolation0.606863964342817
Midmean - Closest Observation0.49147638625295
Midmean - True Basic - Statistics Graphics Toolkit0.606863964342817
Midmean - MS Excel (old versions)0.606863964342817
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')