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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 computationSun, 20 Dec 2009 09:30:59 -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/2009/Dec/20/t1261326697c9znyrsly5xide1.htm/, Retrieved Sat, 27 Apr 2024 07:52:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69945, Retrieved Sat, 27 Apr 2024 07:52:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsshwpaper38
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-20 16:30:59] [4407d6264e55b051ec65750e6dca2820] [Current]
- R  D    [Central Tendency] [CLT van resiudu's...] [2010-12-11 20:08:12] [04d4386fa51dbd2ef12d0f1f80644886]
-    D      [Central Tendency] [CLT van resiudu's...] [2010-12-12 16:21:36] [04d4386fa51dbd2ef12d0f1f80644886]
-   PD    [Central Tendency] [] [2010-12-24 16:08:45] [6e5489189f7de5cfbcc25dd35ae15009]
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Dataseries X:
-59.1433865589441 
681.68750949207 
474.161569921804 
-1055.97981245126 
615.033589537522 
521.894684611647 
578.638216086207 
-912.883184774072 
681.367861336272 
-2155.19911815391 
1589.25493477463 
155.005835713477 
596.726200916196 
-1323.31873224774 
-480.716708999609 
1426.59931262549 
-228.453106978404 
-1813.49420168258 
512.831395924056 
913.75016668727 
-138.554344125264 
-17.0742883176414 
-240.743733678917 
459.599291625499 
697.15584045454 
499.00988464324 
-1578.59103615075 
514.864873876547 
-143.737151824765 
-295.240275749885 
816.253042312365 
1646.01316940914 
-1946.8676497758 
1684.79476995203 
-282.486109641853 
1135.33441263909 
-1021.32992432674 
-1699.19872059425 
513.510287213627 
-945.670566772853 
-3630.81243882240 
-1826.87797093381 
-1439.56288911933 
-57.6014592557804 
577.722101602711 
-748.884702981257 
-365.487695347081 
-210.993720096267 
1648.85512327106 




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69945&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69945&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-115.894670504789162.591754528685-0.712795497168599
Geometric MeanNaN
Harmonic Mean-468.9016587789
Quadratic Mean1132.4148309722
Winsorized Mean ( 1 / 16 )-86.5135751172889151.257952030303-0.571960508231373
Winsorized Mean ( 2 / 16 )-78.126247994179148.906286816611-0.52466722301925
Winsorized Mean ( 3 / 16 )-74.254935083517146.197086790319-0.507909813483601
Winsorized Mean ( 4 / 16 )-86.4403924629382142.883420285561-0.604971467579526
Winsorized Mean ( 5 / 16 )-104.498496432129133.805938849392-0.780970540849828
Winsorized Mean ( 6 / 16 )-116.862973351515125.220781147756-0.933255425180754
Winsorized Mean ( 7 / 16 )-110.929970114870118.142163437827-0.938953265175713
Winsorized Mean ( 8 / 16 )-111.395773377929110.679409202203-1.00647242500561
Winsorized Mean ( 9 / 16 )-65.133828490049699.5212501097928-0.654471566808026
Winsorized Mean ( 10 / 16 )-58.127657067861498.0540004112222-0.592812703449973
Winsorized Mean ( 11 / 16 )-56.034270469769492.3111757389915-0.60701502305859
Winsorized Mean ( 12 / 16 )-52.488149642637590.029342022632-0.583011587815923
Winsorized Mean ( 13 / 16 )-13.777201468826680.8387230832196-0.170428242101791
Winsorized Mean ( 14 / 16 )62.580478387788366.99418894436050.934118008947941
Winsorized Mean ( 15 / 16 )80.764640631093658.48546148619071.38093533980515
Winsorized Mean ( 16 / 16 )101.40712515749254.56080744544711.85860748594831
Trimmed Mean ( 1 / 16 )-115.894670504789146.683982958047-0.790097651888388
Trimmed Mean ( 2 / 16 )-79.421727358815140.740337778571-0.564313889055535
Trimmed Mean ( 3 / 16 )-68.037737456158134.666972712031-0.505229575492488
Trimmed Mean ( 4 / 16 )-68.037737456158128.100022976371-0.531129783393623
Trimmed Mean ( 5 / 16 )-59.0026868050903120.805550057536-0.48841039817284
Trimmed Mean ( 6 / 16 )-46.9524453363071114.642095124973-0.409556762593388
Trimmed Mean ( 7 / 16 )-30.6399887994252109.345044944908-0.280213783942957
Trimmed Mean ( 8 / 16 )-30.6399887994252104.429273420530-0.293404213165785
Trimmed Mean ( 9 / 16 )5.71203647162299.91437746352940.0571693145334064
Trimmed Mean ( 10 / 16 )19.012601157912897.34668606957310.195308149928439
Trimmed Mean ( 11 / 16 )33.012129502590493.73919427940590.35216997283113
Trimmed Mean ( 12 / 16 )48.878578952210890.05218161905950.542780619785293
Trimmed Mean ( 13 / 16 )66.874845985354284.73471310507650.789226086154621
Trimmed Mean ( 14 / 16 )81.350854502771380.19766639741281.01437932245614
Trimmed Mean ( 15 / 16 )84.808555366057679.08038831425311.07243473601877
Trimmed Mean ( 16 / 16 )84.808555366057680.0952284812951.05884653772932
Median-57.6014592557804
Midrange-973.008834435185
Midmean - Weighted Average at Xnp26.0515947037115
Midmean - Weighted Average at X(n+1)p48.8785789522109
Midmean - Empirical Distribution Function48.8785789522109
Midmean - Empirical Distribution Function - Averaging48.8785789522109
Midmean - Empirical Distribution Function - Interpolation48.8785789522109
Midmean - Closest Observation10.6266887320161
Midmean - True Basic - Statistics Graphics Toolkit48.8785789522109
Midmean - MS Excel (old versions)48.8785789522109
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -115.894670504789 & 162.591754528685 & -0.712795497168599 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -468.9016587789 &  &  \tabularnewline
Quadratic Mean & 1132.4148309722 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -86.5135751172889 & 151.257952030303 & -0.571960508231373 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -78.126247994179 & 148.906286816611 & -0.52466722301925 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -74.254935083517 & 146.197086790319 & -0.507909813483601 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -86.4403924629382 & 142.883420285561 & -0.604971467579526 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -104.498496432129 & 133.805938849392 & -0.780970540849828 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -116.862973351515 & 125.220781147756 & -0.933255425180754 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -110.929970114870 & 118.142163437827 & -0.938953265175713 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -111.395773377929 & 110.679409202203 & -1.00647242500561 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -65.1338284900496 & 99.5212501097928 & -0.654471566808026 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -58.1276570678614 & 98.0540004112222 & -0.592812703449973 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -56.0342704697694 & 92.3111757389915 & -0.60701502305859 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -52.4881496426375 & 90.029342022632 & -0.583011587815923 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -13.7772014688266 & 80.8387230832196 & -0.170428242101791 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 62.5804783877883 & 66.9941889443605 & 0.934118008947941 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 80.7646406310936 & 58.4854614861907 & 1.38093533980515 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 101.407125157492 & 54.5608074454471 & 1.85860748594831 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -115.894670504789 & 146.683982958047 & -0.790097651888388 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -79.421727358815 & 140.740337778571 & -0.564313889055535 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -68.037737456158 & 134.666972712031 & -0.505229575492488 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -68.037737456158 & 128.100022976371 & -0.531129783393623 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -59.0026868050903 & 120.805550057536 & -0.48841039817284 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -46.9524453363071 & 114.642095124973 & -0.409556762593388 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -30.6399887994252 & 109.345044944908 & -0.280213783942957 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -30.6399887994252 & 104.429273420530 & -0.293404213165785 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 5.712036471622 & 99.9143774635294 & 0.0571693145334064 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 19.0126011579128 & 97.3466860695731 & 0.195308149928439 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 33.0121295025904 & 93.7391942794059 & 0.35216997283113 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 48.8785789522108 & 90.0521816190595 & 0.542780619785293 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 66.8748459853542 & 84.7347131050765 & 0.789226086154621 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 81.3508545027713 & 80.1976663974128 & 1.01437932245614 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 84.8085553660576 & 79.0803883142531 & 1.07243473601877 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 84.8085553660576 & 80.095228481295 & 1.05884653772932 \tabularnewline
Median & -57.6014592557804 &  &  \tabularnewline
Midrange & -973.008834435185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.0515947037115 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.8785789522109 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.8785789522109 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.8785789522109 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.8785789522109 &  &  \tabularnewline
Midmean - Closest Observation & 10.6266887320161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.8785789522109 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 48.8785789522109 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69945&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]-115.894670504789[/C][C]162.591754528685[/C][C]-0.712795497168599[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-468.9016587789[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1132.4148309722[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-86.5135751172889[/C][C]151.257952030303[/C][C]-0.571960508231373[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-78.126247994179[/C][C]148.906286816611[/C][C]-0.52466722301925[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-74.254935083517[/C][C]146.197086790319[/C][C]-0.507909813483601[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-86.4403924629382[/C][C]142.883420285561[/C][C]-0.604971467579526[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-104.498496432129[/C][C]133.805938849392[/C][C]-0.780970540849828[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-116.862973351515[/C][C]125.220781147756[/C][C]-0.933255425180754[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-110.929970114870[/C][C]118.142163437827[/C][C]-0.938953265175713[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-111.395773377929[/C][C]110.679409202203[/C][C]-1.00647242500561[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-65.1338284900496[/C][C]99.5212501097928[/C][C]-0.654471566808026[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-58.1276570678614[/C][C]98.0540004112222[/C][C]-0.592812703449973[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-56.0342704697694[/C][C]92.3111757389915[/C][C]-0.60701502305859[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-52.4881496426375[/C][C]90.029342022632[/C][C]-0.583011587815923[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-13.7772014688266[/C][C]80.8387230832196[/C][C]-0.170428242101791[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]62.5804783877883[/C][C]66.9941889443605[/C][C]0.934118008947941[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]80.7646406310936[/C][C]58.4854614861907[/C][C]1.38093533980515[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]101.407125157492[/C][C]54.5608074454471[/C][C]1.85860748594831[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-115.894670504789[/C][C]146.683982958047[/C][C]-0.790097651888388[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-79.421727358815[/C][C]140.740337778571[/C][C]-0.564313889055535[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-68.037737456158[/C][C]134.666972712031[/C][C]-0.505229575492488[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-68.037737456158[/C][C]128.100022976371[/C][C]-0.531129783393623[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-59.0026868050903[/C][C]120.805550057536[/C][C]-0.48841039817284[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-46.9524453363071[/C][C]114.642095124973[/C][C]-0.409556762593388[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-30.6399887994252[/C][C]109.345044944908[/C][C]-0.280213783942957[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-30.6399887994252[/C][C]104.429273420530[/C][C]-0.293404213165785[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]5.712036471622[/C][C]99.9143774635294[/C][C]0.0571693145334064[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]19.0126011579128[/C][C]97.3466860695731[/C][C]0.195308149928439[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]33.0121295025904[/C][C]93.7391942794059[/C][C]0.35216997283113[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]48.8785789522108[/C][C]90.0521816190595[/C][C]0.542780619785293[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]66.8748459853542[/C][C]84.7347131050765[/C][C]0.789226086154621[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]81.3508545027713[/C][C]80.1976663974128[/C][C]1.01437932245614[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]84.8085553660576[/C][C]79.0803883142531[/C][C]1.07243473601877[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]84.8085553660576[/C][C]80.095228481295[/C][C]1.05884653772932[/C][/ROW]
[ROW][C]Median[/C][C]-57.6014592557804[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-973.008834435185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.0515947037115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.8785789522109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.8785789522109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.8785789522109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.8785789522109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.6266887320161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.8785789522109[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]48.8785789522109[/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=69945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69945&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 Mean-115.894670504789162.591754528685-0.712795497168599
Geometric MeanNaN
Harmonic Mean-468.9016587789
Quadratic Mean1132.4148309722
Winsorized Mean ( 1 / 16 )-86.5135751172889151.257952030303-0.571960508231373
Winsorized Mean ( 2 / 16 )-78.126247994179148.906286816611-0.52466722301925
Winsorized Mean ( 3 / 16 )-74.254935083517146.197086790319-0.507909813483601
Winsorized Mean ( 4 / 16 )-86.4403924629382142.883420285561-0.604971467579526
Winsorized Mean ( 5 / 16 )-104.498496432129133.805938849392-0.780970540849828
Winsorized Mean ( 6 / 16 )-116.862973351515125.220781147756-0.933255425180754
Winsorized Mean ( 7 / 16 )-110.929970114870118.142163437827-0.938953265175713
Winsorized Mean ( 8 / 16 )-111.395773377929110.679409202203-1.00647242500561
Winsorized Mean ( 9 / 16 )-65.133828490049699.5212501097928-0.654471566808026
Winsorized Mean ( 10 / 16 )-58.127657067861498.0540004112222-0.592812703449973
Winsorized Mean ( 11 / 16 )-56.034270469769492.3111757389915-0.60701502305859
Winsorized Mean ( 12 / 16 )-52.488149642637590.029342022632-0.583011587815923
Winsorized Mean ( 13 / 16 )-13.777201468826680.8387230832196-0.170428242101791
Winsorized Mean ( 14 / 16 )62.580478387788366.99418894436050.934118008947941
Winsorized Mean ( 15 / 16 )80.764640631093658.48546148619071.38093533980515
Winsorized Mean ( 16 / 16 )101.40712515749254.56080744544711.85860748594831
Trimmed Mean ( 1 / 16 )-115.894670504789146.683982958047-0.790097651888388
Trimmed Mean ( 2 / 16 )-79.421727358815140.740337778571-0.564313889055535
Trimmed Mean ( 3 / 16 )-68.037737456158134.666972712031-0.505229575492488
Trimmed Mean ( 4 / 16 )-68.037737456158128.100022976371-0.531129783393623
Trimmed Mean ( 5 / 16 )-59.0026868050903120.805550057536-0.48841039817284
Trimmed Mean ( 6 / 16 )-46.9524453363071114.642095124973-0.409556762593388
Trimmed Mean ( 7 / 16 )-30.6399887994252109.345044944908-0.280213783942957
Trimmed Mean ( 8 / 16 )-30.6399887994252104.429273420530-0.293404213165785
Trimmed Mean ( 9 / 16 )5.71203647162299.91437746352940.0571693145334064
Trimmed Mean ( 10 / 16 )19.012601157912897.34668606957310.195308149928439
Trimmed Mean ( 11 / 16 )33.012129502590493.73919427940590.35216997283113
Trimmed Mean ( 12 / 16 )48.878578952210890.05218161905950.542780619785293
Trimmed Mean ( 13 / 16 )66.874845985354284.73471310507650.789226086154621
Trimmed Mean ( 14 / 16 )81.350854502771380.19766639741281.01437932245614
Trimmed Mean ( 15 / 16 )84.808555366057679.08038831425311.07243473601877
Trimmed Mean ( 16 / 16 )84.808555366057680.0952284812951.05884653772932
Median-57.6014592557804
Midrange-973.008834435185
Midmean - Weighted Average at Xnp26.0515947037115
Midmean - Weighted Average at X(n+1)p48.8785789522109
Midmean - Empirical Distribution Function48.8785789522109
Midmean - Empirical Distribution Function - Averaging48.8785789522109
Midmean - Empirical Distribution Function - Interpolation48.8785789522109
Midmean - Closest Observation10.6266887320161
Midmean - True Basic - Statistics Graphics Toolkit48.8785789522109
Midmean - MS Excel (old versions)48.8785789522109
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')