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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 14:42:25 -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/16/t1197840370wyidt5jhkp19crr.htm/, Retrieved Thu, 02 May 2024 09:29:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4273, Retrieved Thu, 02 May 2024 09:29:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper] [2007-12-16 21:42:25] [3463f71ebce131edf0c83e066f45702c] [Current]
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Dataseries X:
0.00464973808683518 
-0.0157665043685968 
0.0772360935489827 
0.0982022735472924 
-0.0329692184122417 
-0.0506006031990456 
-0.075795707738315 
0.113602703805262 
0.148113162075967 
0.112837826310891 
-0.0734448036257923 
0.0309083978812412 
0.0415428680158676 
0.0990601976481093 
0.0837931021624382 
-0.00670321833103682 
-0.125827016687801 
0.0186219853768928 
-0.00636316975306473 
0.154908900176989 
0.0614460994605559 
-0.0534101143074262 
0.0821269584177297 
0.0138257285089529 
0.0530011126754819 
0.0225633643876339 
-0.0790410269770067 
0.0095545808426968 
0.0195756876718177 
0.0297518373674727 
-0.0715088442938308 
-0.00776262321860514 
0.147123612155334 
0.0343408167672056 
-0.0380715639537345 
0.0107156918468574 
-0.0689013420216793 
-0.0974355202331743 
-0.112062090380169 
0.0496777530762346 
0.0362679511082393 
-0.173851591766331 
0.0648912077902307 
-0.0345220779195117 
0.0744086647308337 
-0.0686910230660089 
0.0912384432864405 
-0.0295753025972146 
-0.0303037105364761 
0.095504559080148 




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=4273&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=4273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4273&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 Mean0.01253768488847140.01068880054188461.17297397770142
Geometric MeanNaN
Harmonic Mean0.282616285816048
Quadratic Mean0.0758647871976718
Winsorized Mean ( 1 / 16 )0.01336226162802160.01034890507136651.29117636463712
Winsorized Mean ( 2 / 16 )0.01387327668350160.01019334226528281.36101352455830
Winsorized Mean ( 3 / 16 )0.01273961639131690.009490313229083791.34238102408205
Winsorized Mean ( 4 / 16 )0.01414998565226060.009149283759334691.54656758107692
Winsorized Mean ( 5 / 16 )0.01309675470985160.00879269489221361.48950405653783
Winsorized Mean ( 6 / 16 )0.01327591231125630.00871443496702011.52343925469628
Winsorized Mean ( 7 / 16 )0.01316926659233070.008585109457114511.53396606742356
Winsorized Mean ( 8 / 16 )0.01290388842888180.008369495653103071.54177610739275
Winsorized Mean ( 9 / 16 )0.01160158443858200.00811210808269711.43015654134686
Winsorized Mean ( 10 / 16 )0.01432453744135690.007457991695234771.92069635187572
Winsorized Mean ( 11 / 16 )0.01386663961407630.007146581475972761.94031785136666
Winsorized Mean ( 12 / 16 )0.01619502611659520.006488725699328642.49587158820272
Winsorized Mean ( 13 / 16 )0.01464335368093630.005888814010466832.48663884695782
Winsorized Mean ( 14 / 16 )0.01411352401066300.005648280540356732.49872928758096
Winsorized Mean ( 15 / 16 )0.01237968033787040.005088277342596512.43298065422534
Winsorized Mean ( 16 / 16 )0.0115492958066750.00487675526834342.36823362485405
Trimmed Mean ( 1 / 16 )0.01345472783360240.00998364637666491.34767672311096
Trimmed Mean ( 2 / 16 )0.01355523457879890.009513020949915461.42491377346534
Trimmed Mean ( 3 / 16 )0.01337452883749050.009013388687612031.48385133505586
Trimmed Mean ( 4 / 16 )0.01362647822089270.008734737283212391.56003297856273
Trimmed Mean ( 5 / 16 )0.01346288214859030.008509039518923341.58218587640239
Trimmed Mean ( 6 / 16 )0.01355923147457410.008334042445742291.62696933245178
Trimmed Mean ( 7 / 16 )0.0136248146142310.008112365875670041.67951184932295
Trimmed Mean ( 8 / 16 )0.01372051798017640.007840253386095741.75000950919635
Trimmed Mean ( 9 / 16 )0.01388001593941370.007522322058753361.84517703855316
Trimmed Mean ( 10 / 16 )0.01430194769882690.0071455708990982.00151225154484
Trimmed Mean ( 11 / 16 )0.01429791381623230.006827071632278672.09429673311632
Trimmed Mean ( 12 / 16 )0.01437331140402180.0064525670458862.22753383293955
Trimmed Mean ( 13 / 16 )0.01405704148864450.006124618403209742.29517017440264
Trimmed Mean ( 14 / 16 )0.01395453935712500.005840923374364612.3890981721093
Trimmed Mean ( 15 / 16 )0.01392614924042180.005454227434677412.55327622604821
Trimmed Mean ( 16 / 16 )0.01421253237052390.005055204167248792.81146555120419
Median0.0162238569429228
Midrange-0.009471345794671
Midmean - Weighted Average at Xnp0.0119718972709494
Midmean - Weighted Average at X(n+1)p0.0143733114040218
Midmean - Empirical Distribution Function0.0143733114040218
Midmean - Empirical Distribution Function - Averaging0.0143733114040218
Midmean - Empirical Distribution Function - Interpolation0.0140570414886445
Midmean - Closest Observation0.0143733114040218
Midmean - True Basic - Statistics Graphics Toolkit0.0143733114040218
Midmean - MS Excel (old versions)0.0143733114040218
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0125376848884714 & 0.0106888005418846 & 1.17297397770142 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.282616285816048 &  &  \tabularnewline
Quadratic Mean & 0.0758647871976718 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.0133622616280216 & 0.0103489050713665 & 1.29117636463712 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.0138732766835016 & 0.0101933422652828 & 1.36101352455830 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.0127396163913169 & 0.00949031322908379 & 1.34238102408205 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.0141499856522606 & 0.00914928375933469 & 1.54656758107692 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.0130967547098516 & 0.0087926948922136 & 1.48950405653783 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.0132759123112563 & 0.0087144349670201 & 1.52343925469628 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.0131692665923307 & 0.00858510945711451 & 1.53396606742356 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.0129038884288818 & 0.00836949565310307 & 1.54177610739275 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.0116015844385820 & 0.0081121080826971 & 1.43015654134686 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.0143245374413569 & 0.00745799169523477 & 1.92069635187572 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.0138666396140763 & 0.00714658147597276 & 1.94031785136666 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.0161950261165952 & 0.00648872569932864 & 2.49587158820272 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.0146433536809363 & 0.00588881401046683 & 2.48663884695782 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.0141135240106630 & 0.00564828054035673 & 2.49872928758096 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.0123796803378704 & 0.00508827734259651 & 2.43298065422534 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.011549295806675 & 0.0048767552683434 & 2.36823362485405 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.0134547278336024 & 0.0099836463766649 & 1.34767672311096 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.0135552345787989 & 0.00951302094991546 & 1.42491377346534 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.0133745288374905 & 0.00901338868761203 & 1.48385133505586 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.0136264782208927 & 0.00873473728321239 & 1.56003297856273 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.0134628821485903 & 0.00850903951892334 & 1.58218587640239 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.0135592314745741 & 0.00833404244574229 & 1.62696933245178 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.013624814614231 & 0.00811236587567004 & 1.67951184932295 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.0137205179801764 & 0.00784025338609574 & 1.75000950919635 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.0138800159394137 & 0.00752232205875336 & 1.84517703855316 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.0143019476988269 & 0.007145570899098 & 2.00151225154484 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.0142979138162323 & 0.00682707163227867 & 2.09429673311632 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.0143733114040218 & 0.006452567045886 & 2.22753383293955 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.0140570414886445 & 0.00612461840320974 & 2.29517017440264 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.0139545393571250 & 0.00584092337436461 & 2.3890981721093 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.0139261492404218 & 0.00545422743467741 & 2.55327622604821 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.0142125323705239 & 0.00505520416724879 & 2.81146555120419 \tabularnewline
Median & 0.0162238569429228 &  &  \tabularnewline
Midrange & -0.009471345794671 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.0119718972709494 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0143733114040218 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0143733114040218 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0143733114040218 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0140570414886445 &  &  \tabularnewline
Midmean - Closest Observation & 0.0143733114040218 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0143733114040218 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0143733114040218 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4273&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]0.0125376848884714[/C][C]0.0106888005418846[/C][C]1.17297397770142[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.282616285816048[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.0758647871976718[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.0133622616280216[/C][C]0.0103489050713665[/C][C]1.29117636463712[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.0138732766835016[/C][C]0.0101933422652828[/C][C]1.36101352455830[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.0127396163913169[/C][C]0.00949031322908379[/C][C]1.34238102408205[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.0141499856522606[/C][C]0.00914928375933469[/C][C]1.54656758107692[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.0130967547098516[/C][C]0.0087926948922136[/C][C]1.48950405653783[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.0132759123112563[/C][C]0.0087144349670201[/C][C]1.52343925469628[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.0131692665923307[/C][C]0.00858510945711451[/C][C]1.53396606742356[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.0129038884288818[/C][C]0.00836949565310307[/C][C]1.54177610739275[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.0116015844385820[/C][C]0.0081121080826971[/C][C]1.43015654134686[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.0143245374413569[/C][C]0.00745799169523477[/C][C]1.92069635187572[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.0138666396140763[/C][C]0.00714658147597276[/C][C]1.94031785136666[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.0161950261165952[/C][C]0.00648872569932864[/C][C]2.49587158820272[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.0146433536809363[/C][C]0.00588881401046683[/C][C]2.48663884695782[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.0141135240106630[/C][C]0.00564828054035673[/C][C]2.49872928758096[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.0123796803378704[/C][C]0.00508827734259651[/C][C]2.43298065422534[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.011549295806675[/C][C]0.0048767552683434[/C][C]2.36823362485405[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.0134547278336024[/C][C]0.0099836463766649[/C][C]1.34767672311096[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.0135552345787989[/C][C]0.00951302094991546[/C][C]1.42491377346534[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.0133745288374905[/C][C]0.00901338868761203[/C][C]1.48385133505586[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.0136264782208927[/C][C]0.00873473728321239[/C][C]1.56003297856273[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.0134628821485903[/C][C]0.00850903951892334[/C][C]1.58218587640239[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.0135592314745741[/C][C]0.00833404244574229[/C][C]1.62696933245178[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.013624814614231[/C][C]0.00811236587567004[/C][C]1.67951184932295[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.0137205179801764[/C][C]0.00784025338609574[/C][C]1.75000950919635[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.0138800159394137[/C][C]0.00752232205875336[/C][C]1.84517703855316[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.0143019476988269[/C][C]0.007145570899098[/C][C]2.00151225154484[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.0142979138162323[/C][C]0.00682707163227867[/C][C]2.09429673311632[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.0143733114040218[/C][C]0.006452567045886[/C][C]2.22753383293955[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.0140570414886445[/C][C]0.00612461840320974[/C][C]2.29517017440264[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.0139545393571250[/C][C]0.00584092337436461[/C][C]2.3890981721093[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.0139261492404218[/C][C]0.00545422743467741[/C][C]2.55327622604821[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.0142125323705239[/C][C]0.00505520416724879[/C][C]2.81146555120419[/C][/ROW]
[ROW][C]Median[/C][C]0.0162238569429228[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.009471345794671[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.0119718972709494[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0140570414886445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0143733114040218[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4273&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 Mean0.01253768488847140.01068880054188461.17297397770142
Geometric MeanNaN
Harmonic Mean0.282616285816048
Quadratic Mean0.0758647871976718
Winsorized Mean ( 1 / 16 )0.01336226162802160.01034890507136651.29117636463712
Winsorized Mean ( 2 / 16 )0.01387327668350160.01019334226528281.36101352455830
Winsorized Mean ( 3 / 16 )0.01273961639131690.009490313229083791.34238102408205
Winsorized Mean ( 4 / 16 )0.01414998565226060.009149283759334691.54656758107692
Winsorized Mean ( 5 / 16 )0.01309675470985160.00879269489221361.48950405653783
Winsorized Mean ( 6 / 16 )0.01327591231125630.00871443496702011.52343925469628
Winsorized Mean ( 7 / 16 )0.01316926659233070.008585109457114511.53396606742356
Winsorized Mean ( 8 / 16 )0.01290388842888180.008369495653103071.54177610739275
Winsorized Mean ( 9 / 16 )0.01160158443858200.00811210808269711.43015654134686
Winsorized Mean ( 10 / 16 )0.01432453744135690.007457991695234771.92069635187572
Winsorized Mean ( 11 / 16 )0.01386663961407630.007146581475972761.94031785136666
Winsorized Mean ( 12 / 16 )0.01619502611659520.006488725699328642.49587158820272
Winsorized Mean ( 13 / 16 )0.01464335368093630.005888814010466832.48663884695782
Winsorized Mean ( 14 / 16 )0.01411352401066300.005648280540356732.49872928758096
Winsorized Mean ( 15 / 16 )0.01237968033787040.005088277342596512.43298065422534
Winsorized Mean ( 16 / 16 )0.0115492958066750.00487675526834342.36823362485405
Trimmed Mean ( 1 / 16 )0.01345472783360240.00998364637666491.34767672311096
Trimmed Mean ( 2 / 16 )0.01355523457879890.009513020949915461.42491377346534
Trimmed Mean ( 3 / 16 )0.01337452883749050.009013388687612031.48385133505586
Trimmed Mean ( 4 / 16 )0.01362647822089270.008734737283212391.56003297856273
Trimmed Mean ( 5 / 16 )0.01346288214859030.008509039518923341.58218587640239
Trimmed Mean ( 6 / 16 )0.01355923147457410.008334042445742291.62696933245178
Trimmed Mean ( 7 / 16 )0.0136248146142310.008112365875670041.67951184932295
Trimmed Mean ( 8 / 16 )0.01372051798017640.007840253386095741.75000950919635
Trimmed Mean ( 9 / 16 )0.01388001593941370.007522322058753361.84517703855316
Trimmed Mean ( 10 / 16 )0.01430194769882690.0071455708990982.00151225154484
Trimmed Mean ( 11 / 16 )0.01429791381623230.006827071632278672.09429673311632
Trimmed Mean ( 12 / 16 )0.01437331140402180.0064525670458862.22753383293955
Trimmed Mean ( 13 / 16 )0.01405704148864450.006124618403209742.29517017440264
Trimmed Mean ( 14 / 16 )0.01395453935712500.005840923374364612.3890981721093
Trimmed Mean ( 15 / 16 )0.01392614924042180.005454227434677412.55327622604821
Trimmed Mean ( 16 / 16 )0.01421253237052390.005055204167248792.81146555120419
Median0.0162238569429228
Midrange-0.009471345794671
Midmean - Weighted Average at Xnp0.0119718972709494
Midmean - Weighted Average at X(n+1)p0.0143733114040218
Midmean - Empirical Distribution Function0.0143733114040218
Midmean - Empirical Distribution Function - Averaging0.0143733114040218
Midmean - Empirical Distribution Function - Interpolation0.0140570414886445
Midmean - Closest Observation0.0143733114040218
Midmean - True Basic - Statistics Graphics Toolkit0.0143733114040218
Midmean - MS Excel (old versions)0.0143733114040218
Number of observations50



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')