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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 12:19:33 -0600
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/Oct/20/t12560628473auomog1vei7wpt.htm/, Retrieved Thu, 02 May 2024 15:33:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48943, Retrieved Thu, 02 May 2024 15:33:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [SHW_WS3_Yt=c+Xt] [2009-10-16 08:10:06] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D    [Central Tendency] [Berekening pt 2 (1)] [2009-10-20 18:19:33] [5edea6bc5a9a9483633d9320282a2734] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,8
2,3
1,7
1,6
1,7
1,8
1,7
1,6
1,4
1,9
2,6
2,8
2,6
1,9
1,5
1,4
1,3
1,2
1
0,8
1,1
1,7
2,9
3,4
3,1
2,4
2
1,9
1,9
2
2,2
2,2
2
1,9
1,7
1,5
1,3
1,6
1,7
1,5
1,1
0,8
0,7
0,7
0,7
0,8
1
1,4
1,4
1,8
1,7
1,6
1,2
0,7
0,3
0
-0,2
-0,2
0,1
0,4

Tables (Output of Computation)





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=48943&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=48943&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48943&T=0

As an alternative you can also use a QR Code:  
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 Mean1.526666666666670.10106401916541915.1059366060621
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.71269767715535
Winsorized Mean ( 1 / 20 )1.521666666666670.099606334364709915.2768062028572
Winsorized Mean ( 2 / 20 )1.521666666666670.096025292885900515.8465194006203
Winsorized Mean ( 3 / 20 )1.521666666666670.093521551541003316.2707594302423
Winsorized Mean ( 4 / 20 )1.5350.090254661679063717.0074317652234
Winsorized Mean ( 5 / 20 )1.526666666666670.084568251000081618.0524800810317
Winsorized Mean ( 6 / 20 )1.556666666666670.078379298931169419.8606862767896
Winsorized Mean ( 7 / 20 )1.533333333333330.073402638026866620.889349137181
Winsorized Mean ( 8 / 20 )1.520.070822448482381321.4621215810992
Winsorized Mean ( 9 / 20 )1.5050.068123558399716222.0922106148564
Winsorized Mean ( 10 / 20 )1.521666666666670.064881102324133923.4531568077359
Winsorized Mean ( 11 / 20 )1.4850.058889199800195525.2168479965501
Winsorized Mean ( 12 / 20 )1.4850.058889199800195525.2168479965501
Winsorized Mean ( 13 / 20 )1.528333333333330.050762083066131230.1077741695956
Winsorized Mean ( 14 / 20 )1.5050.047265627553462131.8413205938649
Winsorized Mean ( 15 / 20 )1.530.042870189028561935.6891358463722
Winsorized Mean ( 16 / 20 )1.530.042870189028561935.6891358463722
Winsorized Mean ( 17 / 20 )1.558333333333330.038200457496200540.7935777598561
Winsorized Mean ( 18 / 20 )1.558333333333330.038200457496200540.7935777598561
Winsorized Mean ( 19 / 20 )1.558333333333330.028551832801220554.5790998491249
Winsorized Mean ( 20 / 20 )1.558333333333330.028551832801220554.5790998491249
Trimmed Mean ( 1 / 20 )1.524137931034480.094728265646144916.0895791835550
Trimmed Mean ( 2 / 20 )1.526785714285710.088658511337902917.2209716951675
Trimmed Mean ( 3 / 20 )1.529629629629630.083579495110955918.3014940159542
Trimmed Mean ( 4 / 20 )1.532692307692310.078481110592327119.5294421310362
Trimmed Mean ( 5 / 20 )1.5320.073425792054124320.8646029840675
Trimmed Mean ( 6 / 20 )1.533333333333330.069147117633843322.1749421494738
Trimmed Mean ( 7 / 20 )1.528260869565220.065766608525082223.2376414694148
Trimmed Mean ( 8 / 20 )1.527272727272730.062991294103296524.2457747378268
Trimmed Mean ( 9 / 20 )1.528571428571430.060128174581169425.4218831557567
Trimmed Mean ( 10 / 20 )1.53250.057108477524166326.8348950355313
Trimmed Mean ( 11 / 20 )1.534210526315790.054037065908750628.3918177368573
Trimmed Mean ( 12 / 20 )1.541666666666670.051543632310364329.9099345072092
Trimmed Mean ( 13 / 20 )1.550.047999182999582932.292216307379
Trimmed Mean ( 14 / 20 )1.5531250.045787107065058133.9205750167441
Trimmed Mean ( 15 / 20 )1.560.043575802628438735.7996848228311
Trimmed Mean ( 16 / 20 )1.564285714285710.041853323407730837.3754241460493
Trimmed Mean ( 17 / 20 )1.569230769230770.039132607206082840.1003378325083
Trimmed Mean ( 18 / 20 )1.570833333333330.036850248591509442.6274826730821
Trimmed Mean ( 19 / 20 )1.572727272727270.033016995611546947.6338698781318
Trimmed Mean ( 20 / 20 )1.5750.031518582655817249.9705211112757
Median1.6
Midrange1.6
Midmean - Weighted Average at Xnp1.53636363636364
Midmean - Weighted Average at X(n+1)p1.57096774193548
Midmean - Empirical Distribution Function1.53636363636364
Midmean - Empirical Distribution Function - Averaging1.57096774193548
Midmean - Empirical Distribution Function - Interpolation1.57096774193548
Midmean - Closest Observation1.53636363636364
Midmean - True Basic - Statistics Graphics Toolkit1.57096774193548
Midmean - MS Excel (old versions)1.53636363636364
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.52666666666667 & 0.101064019165419 & 15.1059366060621 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.71269767715535 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.52166666666667 & 0.0996063343647099 & 15.2768062028572 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.52166666666667 & 0.0960252928859005 & 15.8465194006203 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.52166666666667 & 0.0935215515410033 & 16.2707594302423 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.535 & 0.0902546616790637 & 17.0074317652234 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.52666666666667 & 0.0845682510000816 & 18.0524800810317 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.55666666666667 & 0.0783792989311694 & 19.8606862767896 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.53333333333333 & 0.0734026380268666 & 20.889349137181 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.52 & 0.0708224484823813 & 21.4621215810992 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.505 & 0.0681235583997162 & 22.0922106148564 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.52166666666667 & 0.0648811023241339 & 23.4531568077359 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.485 & 0.0588891998001955 & 25.2168479965501 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.485 & 0.0588891998001955 & 25.2168479965501 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.52833333333333 & 0.0507620830661312 & 30.1077741695956 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.505 & 0.0472656275534621 & 31.8413205938649 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.53 & 0.0428701890285619 & 35.6891358463722 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.53 & 0.0428701890285619 & 35.6891358463722 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.55833333333333 & 0.0382004574962005 & 40.7935777598561 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.55833333333333 & 0.0382004574962005 & 40.7935777598561 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.55833333333333 & 0.0285518328012205 & 54.5790998491249 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.55833333333333 & 0.0285518328012205 & 54.5790998491249 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.52413793103448 & 0.0947282656461449 & 16.0895791835550 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.52678571428571 & 0.0886585113379029 & 17.2209716951675 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.52962962962963 & 0.0835794951109559 & 18.3014940159542 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.53269230769231 & 0.0784811105923271 & 19.5294421310362 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.532 & 0.0734257920541243 & 20.8646029840675 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.53333333333333 & 0.0691471176338433 & 22.1749421494738 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.52826086956522 & 0.0657666085250822 & 23.2376414694148 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.52727272727273 & 0.0629912941032965 & 24.2457747378268 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.52857142857143 & 0.0601281745811694 & 25.4218831557567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.5325 & 0.0571084775241663 & 26.8348950355313 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.53421052631579 & 0.0540370659087506 & 28.3918177368573 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.54166666666667 & 0.0515436323103643 & 29.9099345072092 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.55 & 0.0479991829995829 & 32.292216307379 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.553125 & 0.0457871070650581 & 33.9205750167441 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.56 & 0.0435758026284387 & 35.7996848228311 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.56428571428571 & 0.0418533234077308 & 37.3754241460493 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.56923076923077 & 0.0391326072060828 & 40.1003378325083 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.57083333333333 & 0.0368502485915094 & 42.6274826730821 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.57272727272727 & 0.0330169956115469 & 47.6338698781318 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.575 & 0.0315185826558172 & 49.9705211112757 \tabularnewline
Median & 1.6 &  &  \tabularnewline
Midrange & 1.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.53636363636364 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.57096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.53636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.57096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.57096774193548 &  &  \tabularnewline
Midmean - Closest Observation & 1.53636363636364 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.57096774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.53636363636364 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48943&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]1.52666666666667[/C][C]0.101064019165419[/C][C]15.1059366060621[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.71269767715535[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.52166666666667[/C][C]0.0996063343647099[/C][C]15.2768062028572[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.52166666666667[/C][C]0.0960252928859005[/C][C]15.8465194006203[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.52166666666667[/C][C]0.0935215515410033[/C][C]16.2707594302423[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.535[/C][C]0.0902546616790637[/C][C]17.0074317652234[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.52666666666667[/C][C]0.0845682510000816[/C][C]18.0524800810317[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.55666666666667[/C][C]0.0783792989311694[/C][C]19.8606862767896[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.53333333333333[/C][C]0.0734026380268666[/C][C]20.889349137181[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.52[/C][C]0.0708224484823813[/C][C]21.4621215810992[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.505[/C][C]0.0681235583997162[/C][C]22.0922106148564[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.52166666666667[/C][C]0.0648811023241339[/C][C]23.4531568077359[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.485[/C][C]0.0588891998001955[/C][C]25.2168479965501[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.485[/C][C]0.0588891998001955[/C][C]25.2168479965501[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.52833333333333[/C][C]0.0507620830661312[/C][C]30.1077741695956[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.505[/C][C]0.0472656275534621[/C][C]31.8413205938649[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.53[/C][C]0.0428701890285619[/C][C]35.6891358463722[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.53[/C][C]0.0428701890285619[/C][C]35.6891358463722[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.55833333333333[/C][C]0.0382004574962005[/C][C]40.7935777598561[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.55833333333333[/C][C]0.0382004574962005[/C][C]40.7935777598561[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.55833333333333[/C][C]0.0285518328012205[/C][C]54.5790998491249[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.55833333333333[/C][C]0.0285518328012205[/C][C]54.5790998491249[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.52413793103448[/C][C]0.0947282656461449[/C][C]16.0895791835550[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.52678571428571[/C][C]0.0886585113379029[/C][C]17.2209716951675[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.52962962962963[/C][C]0.0835794951109559[/C][C]18.3014940159542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.53269230769231[/C][C]0.0784811105923271[/C][C]19.5294421310362[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.532[/C][C]0.0734257920541243[/C][C]20.8646029840675[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.53333333333333[/C][C]0.0691471176338433[/C][C]22.1749421494738[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.52826086956522[/C][C]0.0657666085250822[/C][C]23.2376414694148[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.52727272727273[/C][C]0.0629912941032965[/C][C]24.2457747378268[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.52857142857143[/C][C]0.0601281745811694[/C][C]25.4218831557567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.5325[/C][C]0.0571084775241663[/C][C]26.8348950355313[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.53421052631579[/C][C]0.0540370659087506[/C][C]28.3918177368573[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.54166666666667[/C][C]0.0515436323103643[/C][C]29.9099345072092[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.55[/C][C]0.0479991829995829[/C][C]32.292216307379[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.553125[/C][C]0.0457871070650581[/C][C]33.9205750167441[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.56[/C][C]0.0435758026284387[/C][C]35.7996848228311[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.56428571428571[/C][C]0.0418533234077308[/C][C]37.3754241460493[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.56923076923077[/C][C]0.0391326072060828[/C][C]40.1003378325083[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.57083333333333[/C][C]0.0368502485915094[/C][C]42.6274826730821[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.57272727272727[/C][C]0.0330169956115469[/C][C]47.6338698781318[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.575[/C][C]0.0315185826558172[/C][C]49.9705211112757[/C][/ROW]
[ROW][C]Median[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48943&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48943&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.526666666666670.10106401916541915.1059366060621
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.71269767715535
Winsorized Mean ( 1 / 20 )1.521666666666670.099606334364709915.2768062028572
Winsorized Mean ( 2 / 20 )1.521666666666670.096025292885900515.8465194006203
Winsorized Mean ( 3 / 20 )1.521666666666670.093521551541003316.2707594302423
Winsorized Mean ( 4 / 20 )1.5350.090254661679063717.0074317652234
Winsorized Mean ( 5 / 20 )1.526666666666670.084568251000081618.0524800810317
Winsorized Mean ( 6 / 20 )1.556666666666670.078379298931169419.8606862767896
Winsorized Mean ( 7 / 20 )1.533333333333330.073402638026866620.889349137181
Winsorized Mean ( 8 / 20 )1.520.070822448482381321.4621215810992
Winsorized Mean ( 9 / 20 )1.5050.068123558399716222.0922106148564
Winsorized Mean ( 10 / 20 )1.521666666666670.064881102324133923.4531568077359
Winsorized Mean ( 11 / 20 )1.4850.058889199800195525.2168479965501
Winsorized Mean ( 12 / 20 )1.4850.058889199800195525.2168479965501
Winsorized Mean ( 13 / 20 )1.528333333333330.050762083066131230.1077741695956
Winsorized Mean ( 14 / 20 )1.5050.047265627553462131.8413205938649
Winsorized Mean ( 15 / 20 )1.530.042870189028561935.6891358463722
Winsorized Mean ( 16 / 20 )1.530.042870189028561935.6891358463722
Winsorized Mean ( 17 / 20 )1.558333333333330.038200457496200540.7935777598561
Winsorized Mean ( 18 / 20 )1.558333333333330.038200457496200540.7935777598561
Winsorized Mean ( 19 / 20 )1.558333333333330.028551832801220554.5790998491249
Winsorized Mean ( 20 / 20 )1.558333333333330.028551832801220554.5790998491249
Trimmed Mean ( 1 / 20 )1.524137931034480.094728265646144916.0895791835550
Trimmed Mean ( 2 / 20 )1.526785714285710.088658511337902917.2209716951675
Trimmed Mean ( 3 / 20 )1.529629629629630.083579495110955918.3014940159542
Trimmed Mean ( 4 / 20 )1.532692307692310.078481110592327119.5294421310362
Trimmed Mean ( 5 / 20 )1.5320.073425792054124320.8646029840675
Trimmed Mean ( 6 / 20 )1.533333333333330.069147117633843322.1749421494738
Trimmed Mean ( 7 / 20 )1.528260869565220.065766608525082223.2376414694148
Trimmed Mean ( 8 / 20 )1.527272727272730.062991294103296524.2457747378268
Trimmed Mean ( 9 / 20 )1.528571428571430.060128174581169425.4218831557567
Trimmed Mean ( 10 / 20 )1.53250.057108477524166326.8348950355313
Trimmed Mean ( 11 / 20 )1.534210526315790.054037065908750628.3918177368573
Trimmed Mean ( 12 / 20 )1.541666666666670.051543632310364329.9099345072092
Trimmed Mean ( 13 / 20 )1.550.047999182999582932.292216307379
Trimmed Mean ( 14 / 20 )1.5531250.045787107065058133.9205750167441
Trimmed Mean ( 15 / 20 )1.560.043575802628438735.7996848228311
Trimmed Mean ( 16 / 20 )1.564285714285710.041853323407730837.3754241460493
Trimmed Mean ( 17 / 20 )1.569230769230770.039132607206082840.1003378325083
Trimmed Mean ( 18 / 20 )1.570833333333330.036850248591509442.6274826730821
Trimmed Mean ( 19 / 20 )1.572727272727270.033016995611546947.6338698781318
Trimmed Mean ( 20 / 20 )1.5750.031518582655817249.9705211112757
Median1.6
Midrange1.6
Midmean - Weighted Average at Xnp1.53636363636364
Midmean - Weighted Average at X(n+1)p1.57096774193548
Midmean - Empirical Distribution Function1.53636363636364
Midmean - Empirical Distribution Function - Averaging1.57096774193548
Midmean - Empirical Distribution Function - Interpolation1.57096774193548
Midmean - Closest Observation1.53636363636364
Midmean - True Basic - Statistics Graphics Toolkit1.57096774193548
Midmean - MS Excel (old versions)1.53636363636364
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')