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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Dec 2011 18:25:55 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324596418np68ed0c1jxbrq2.htm/, Retrieved Fri, 03 May 2024 09:11:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160084, Retrieved Fri, 03 May 2024 09:11:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [autocorrelatie ] [2011-12-07 13:35:25] [141ef847e2c5f8e947fe4eabcb0cf143]
-   PD      [(Partial) Autocorrelation Function] [autocorrelatie D=1] [2011-12-07 13:50:51] [141ef847e2c5f8e947fe4eabcb0cf143]
- RMP         [Standard Deviation-Mean Plot] [ST-MP] [2011-12-07 14:22:28] [141ef847e2c5f8e947fe4eabcb0cf143]
- RMP           [ARIMA Backward Selection] [ARIMA backward ] [2011-12-08 13:48:01] [141ef847e2c5f8e947fe4eabcb0cf143]
- R P             [ARIMA Backward Selection] [ARIMA backward nieuw] [2011-12-19 19:26:36] [141ef847e2c5f8e947fe4eabcb0cf143]
- RMPD                [Central Tendency] [gemiddelde] [2011-12-22 23:25:55] [1a4698f17d8e7f554418314cf0e4bd67] [Current]
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Dataseries X:
-0.352491067189297
-0.693726212281901
-2.62057482256158
4.31439985409331
6.12699035221105
-11.007722453913
9.85737357338869
-5.68308331784826
-2.73868553233788
-6.96089757829408
-2.30558059708951
11.4091362466934
-3.36204181750916
-14.3226417503077
-6.08251008012596
-14.6033454556627
-3.62530423371471
11.273178154969
-0.371222853324218
-3.03711645114068
0.399790646086001
12.6798995234074
4.91702961212093
-1.21903073075922
-3.38013895067434
9.99540956510879
6.92576282552566
10.4736153969682
2.9399140408402
4.36433098901772
-4.23099068714022
-0.0544639004525236
4.9839331308856
-11.0615861073884
-1.41631588881505
-0.599850377760058
0.647026043791595
1.9090371435873
2.89203604596708
-0.00249842894119334
-4.63822948933668
2.83423527757095
-6.86863363017918
9.10508456804962
-12.8257487320615
-3.28367221464237
6.38917992951302
6.82425066542711




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160084&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160084&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.08153146299523450.9891147488634550.0824287203167463
Geometric MeanNaN
Harmonic Mean-0.11288978869094
Quadratic Mean6.78151920598632
Winsorized Mean ( 1 / 16 )0.06090522192525530.9804297310876840.0621209455344519
Winsorized Mean ( 2 / 16 )0.1176108438636640.9603470039379340.122467028460959
Winsorized Mean ( 3 / 16 )0.1778983355306820.9180012624593360.193788770022048
Winsorized Mean ( 4 / 16 )0.1425364873320150.9074714271679780.157069945195785
Winsorized Mean ( 5 / 16 )0.5497019960714750.8063949716431220.681678352918539
Winsorized Mean ( 6 / 16 )0.4671988639184540.7814888883004870.597831742604142
Winsorized Mean ( 7 / 16 )0.2640241275164710.6883991513575610.383533487796725
Winsorized Mean ( 8 / 16 )0.3136765612129960.672062941658750.46673688098141
Winsorized Mean ( 9 / 16 )0.4280108910750260.6196031453690750.69078230844047
Winsorized Mean ( 10 / 16 )0.4582294795947110.5939545069722460.771489186824409
Winsorized Mean ( 11 / 16 )0.3350820119509750.5193583312326480.645184628415778
Winsorized Mean ( 12 / 16 )0.37964745301990.5063559250166950.749764018279005
Winsorized Mean ( 13 / 16 )0.2348595494950170.4775209768148760.491830853298966
Winsorized Mean ( 14 / 16 )0.2431541026448770.4711907390526280.516041769271104
Winsorized Mean ( 15 / 16 )-0.1093240379024410.382578455598185-0.285755866026241
Winsorized Mean ( 16 / 16 )-0.02580639659254790.363870077422804-0.0709220081390804
Trimmed Mean ( 1 / 16 )0.1268903512179690.9409353778983130.134855542897529
Trimmed Mean ( 2 / 16 )0.1988741286282010.8893270979587210.223623151801714
Trimmed Mean ( 3 / 16 )0.2453102913507940.8361796831544460.293370308191863
Trimmed Mean ( 4 / 16 )0.2722750736788390.7891585477238020.345019482414746
Trimmed Mean ( 5 / 16 )0.3132451535778360.7302066289197270.428981525463899
Trimmed Mean ( 6 / 16 )0.2501899955795320.6932411485919990.360898939838869
Trimmed Mean ( 7 / 16 )0.1991290853821390.6515848582532640.305607294061366
Trimmed Mean ( 8 / 16 )0.1852230049247820.6283352238083680.294783736302633
Trimmed Mean ( 9 / 16 )0.1595322936671390.5999168567837110.265924005740441
Trimmed Mean ( 10 / 16 )0.1083935132084940.5764479718888020.188036940876605
Trimmed Mean ( 11 / 16 )0.04380841172180750.5491962470310310.0797682284950724
Trimmed Mean ( 12 / 16 )-0.009150424683495610.535203139974273-0.0170971057530333
Trimmed Mean ( 13 / 16 )-0.07984094790229480.514666820889194-0.155131328971922
Trimmed Mean ( 14 / 16 )-0.1379395012679520.491465153989784-0.280669952178989
Trimmed Mean ( 15 / 16 )-0.210528759156110.450020455007037-0.467820421969082
Trimmed Mean ( 16 / 16 )-0.2307697034068440.428413694572084-0.538660893268937
Median-0.361856960256758
Midrange-0.96172296612765
Midmean - Weighted Average at Xnp-0.153796577044744
Midmean - Weighted Average at X(n+1)p-0.00915042468349581
Midmean - Empirical Distribution Function-0.153796577044744
Midmean - Empirical Distribution Function - Averaging-0.00915042468349581
Midmean - Empirical Distribution Function - Interpolation-0.00915042468349581
Midmean - Closest Observation-0.153796577044744
Midmean - True Basic - Statistics Graphics Toolkit-0.00915042468349581
Midmean - MS Excel (old versions)0.0438084117218074
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0815314629952345 & 0.989114748863455 & 0.0824287203167463 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.11288978869094 &  &  \tabularnewline
Quadratic Mean & 6.78151920598632 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.0609052219252553 & 0.980429731087684 & 0.0621209455344519 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.117610843863664 & 0.960347003937934 & 0.122467028460959 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.177898335530682 & 0.918001262459336 & 0.193788770022048 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.142536487332015 & 0.907471427167978 & 0.157069945195785 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.549701996071475 & 0.806394971643122 & 0.681678352918539 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.467198863918454 & 0.781488888300487 & 0.597831742604142 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.264024127516471 & 0.688399151357561 & 0.383533487796725 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.313676561212996 & 0.67206294165875 & 0.46673688098141 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.428010891075026 & 0.619603145369075 & 0.69078230844047 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.458229479594711 & 0.593954506972246 & 0.771489186824409 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.335082011950975 & 0.519358331232648 & 0.645184628415778 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.3796474530199 & 0.506355925016695 & 0.749764018279005 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.234859549495017 & 0.477520976814876 & 0.491830853298966 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.243154102644877 & 0.471190739052628 & 0.516041769271104 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.109324037902441 & 0.382578455598185 & -0.285755866026241 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.0258063965925479 & 0.363870077422804 & -0.0709220081390804 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.126890351217969 & 0.940935377898313 & 0.134855542897529 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.198874128628201 & 0.889327097958721 & 0.223623151801714 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.245310291350794 & 0.836179683154446 & 0.293370308191863 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.272275073678839 & 0.789158547723802 & 0.345019482414746 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.313245153577836 & 0.730206628919727 & 0.428981525463899 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.250189995579532 & 0.693241148591999 & 0.360898939838869 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.199129085382139 & 0.651584858253264 & 0.305607294061366 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.185223004924782 & 0.628335223808368 & 0.294783736302633 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.159532293667139 & 0.599916856783711 & 0.265924005740441 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.108393513208494 & 0.576447971888802 & 0.188036940876605 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.0438084117218075 & 0.549196247031031 & 0.0797682284950724 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -0.00915042468349561 & 0.535203139974273 & -0.0170971057530333 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -0.0798409479022948 & 0.514666820889194 & -0.155131328971922 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -0.137939501267952 & 0.491465153989784 & -0.280669952178989 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -0.21052875915611 & 0.450020455007037 & -0.467820421969082 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.230769703406844 & 0.428413694572084 & -0.538660893268937 \tabularnewline
Median & -0.361856960256758 &  &  \tabularnewline
Midrange & -0.96172296612765 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.153796577044744 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.00915042468349581 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.153796577044744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.00915042468349581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.00915042468349581 &  &  \tabularnewline
Midmean - Closest Observation & -0.153796577044744 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.00915042468349581 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0438084117218074 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160084&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]0.0815314629952345[/C][C]0.989114748863455[/C][C]0.0824287203167463[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.11288978869094[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.78151920598632[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.0609052219252553[/C][C]0.980429731087684[/C][C]0.0621209455344519[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.117610843863664[/C][C]0.960347003937934[/C][C]0.122467028460959[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.177898335530682[/C][C]0.918001262459336[/C][C]0.193788770022048[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.142536487332015[/C][C]0.907471427167978[/C][C]0.157069945195785[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.549701996071475[/C][C]0.806394971643122[/C][C]0.681678352918539[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.467198863918454[/C][C]0.781488888300487[/C][C]0.597831742604142[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.264024127516471[/C][C]0.688399151357561[/C][C]0.383533487796725[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.313676561212996[/C][C]0.67206294165875[/C][C]0.46673688098141[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.428010891075026[/C][C]0.619603145369075[/C][C]0.69078230844047[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.458229479594711[/C][C]0.593954506972246[/C][C]0.771489186824409[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.335082011950975[/C][C]0.519358331232648[/C][C]0.645184628415778[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.3796474530199[/C][C]0.506355925016695[/C][C]0.749764018279005[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.234859549495017[/C][C]0.477520976814876[/C][C]0.491830853298966[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.243154102644877[/C][C]0.471190739052628[/C][C]0.516041769271104[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.109324037902441[/C][C]0.382578455598185[/C][C]-0.285755866026241[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.0258063965925479[/C][C]0.363870077422804[/C][C]-0.0709220081390804[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.126890351217969[/C][C]0.940935377898313[/C][C]0.134855542897529[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.198874128628201[/C][C]0.889327097958721[/C][C]0.223623151801714[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.245310291350794[/C][C]0.836179683154446[/C][C]0.293370308191863[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.272275073678839[/C][C]0.789158547723802[/C][C]0.345019482414746[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.313245153577836[/C][C]0.730206628919727[/C][C]0.428981525463899[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.250189995579532[/C][C]0.693241148591999[/C][C]0.360898939838869[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.199129085382139[/C][C]0.651584858253264[/C][C]0.305607294061366[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.185223004924782[/C][C]0.628335223808368[/C][C]0.294783736302633[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.159532293667139[/C][C]0.599916856783711[/C][C]0.265924005740441[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.108393513208494[/C][C]0.576447971888802[/C][C]0.188036940876605[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.0438084117218075[/C][C]0.549196247031031[/C][C]0.0797682284950724[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-0.00915042468349561[/C][C]0.535203139974273[/C][C]-0.0170971057530333[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-0.0798409479022948[/C][C]0.514666820889194[/C][C]-0.155131328971922[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-0.137939501267952[/C][C]0.491465153989784[/C][C]-0.280669952178989[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-0.21052875915611[/C][C]0.450020455007037[/C][C]-0.467820421969082[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.230769703406844[/C][C]0.428413694572084[/C][C]-0.538660893268937[/C][/ROW]
[ROW][C]Median[/C][C]-0.361856960256758[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.96172296612765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.153796577044744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.00915042468349581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.153796577044744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.00915042468349581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.00915042468349581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.153796577044744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.00915042468349581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0438084117218074[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160084&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 Mean0.08153146299523450.9891147488634550.0824287203167463
Geometric MeanNaN
Harmonic Mean-0.11288978869094
Quadratic Mean6.78151920598632
Winsorized Mean ( 1 / 16 )0.06090522192525530.9804297310876840.0621209455344519
Winsorized Mean ( 2 / 16 )0.1176108438636640.9603470039379340.122467028460959
Winsorized Mean ( 3 / 16 )0.1778983355306820.9180012624593360.193788770022048
Winsorized Mean ( 4 / 16 )0.1425364873320150.9074714271679780.157069945195785
Winsorized Mean ( 5 / 16 )0.5497019960714750.8063949716431220.681678352918539
Winsorized Mean ( 6 / 16 )0.4671988639184540.7814888883004870.597831742604142
Winsorized Mean ( 7 / 16 )0.2640241275164710.6883991513575610.383533487796725
Winsorized Mean ( 8 / 16 )0.3136765612129960.672062941658750.46673688098141
Winsorized Mean ( 9 / 16 )0.4280108910750260.6196031453690750.69078230844047
Winsorized Mean ( 10 / 16 )0.4582294795947110.5939545069722460.771489186824409
Winsorized Mean ( 11 / 16 )0.3350820119509750.5193583312326480.645184628415778
Winsorized Mean ( 12 / 16 )0.37964745301990.5063559250166950.749764018279005
Winsorized Mean ( 13 / 16 )0.2348595494950170.4775209768148760.491830853298966
Winsorized Mean ( 14 / 16 )0.2431541026448770.4711907390526280.516041769271104
Winsorized Mean ( 15 / 16 )-0.1093240379024410.382578455598185-0.285755866026241
Winsorized Mean ( 16 / 16 )-0.02580639659254790.363870077422804-0.0709220081390804
Trimmed Mean ( 1 / 16 )0.1268903512179690.9409353778983130.134855542897529
Trimmed Mean ( 2 / 16 )0.1988741286282010.8893270979587210.223623151801714
Trimmed Mean ( 3 / 16 )0.2453102913507940.8361796831544460.293370308191863
Trimmed Mean ( 4 / 16 )0.2722750736788390.7891585477238020.345019482414746
Trimmed Mean ( 5 / 16 )0.3132451535778360.7302066289197270.428981525463899
Trimmed Mean ( 6 / 16 )0.2501899955795320.6932411485919990.360898939838869
Trimmed Mean ( 7 / 16 )0.1991290853821390.6515848582532640.305607294061366
Trimmed Mean ( 8 / 16 )0.1852230049247820.6283352238083680.294783736302633
Trimmed Mean ( 9 / 16 )0.1595322936671390.5999168567837110.265924005740441
Trimmed Mean ( 10 / 16 )0.1083935132084940.5764479718888020.188036940876605
Trimmed Mean ( 11 / 16 )0.04380841172180750.5491962470310310.0797682284950724
Trimmed Mean ( 12 / 16 )-0.009150424683495610.535203139974273-0.0170971057530333
Trimmed Mean ( 13 / 16 )-0.07984094790229480.514666820889194-0.155131328971922
Trimmed Mean ( 14 / 16 )-0.1379395012679520.491465153989784-0.280669952178989
Trimmed Mean ( 15 / 16 )-0.210528759156110.450020455007037-0.467820421969082
Trimmed Mean ( 16 / 16 )-0.2307697034068440.428413694572084-0.538660893268937
Median-0.361856960256758
Midrange-0.96172296612765
Midmean - Weighted Average at Xnp-0.153796577044744
Midmean - Weighted Average at X(n+1)p-0.00915042468349581
Midmean - Empirical Distribution Function-0.153796577044744
Midmean - Empirical Distribution Function - Averaging-0.00915042468349581
Midmean - Empirical Distribution Function - Interpolation-0.00915042468349581
Midmean - Closest Observation-0.153796577044744
Midmean - True Basic - Statistics Graphics Toolkit-0.00915042468349581
Midmean - MS Excel (old versions)0.0438084117218074
Number of observations48



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')