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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 08:11:40 -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/13/t1197557855x3n48lsogq6i9gn.htm/, Retrieved Sun, 05 May 2024 15:51:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3598, Retrieved Sun, 05 May 2024 15:51:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [CT voorspellingsf...] [2007-12-13 15:11:40] [919a0fafa615dc0e3c6b6d22cd1007a0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,46
9,36
-1,84
-7,74
-12,24
-8,74
-2,04
-5,74
-6,14
0,16
-20,34
-30,54
-0,44
1,66
-7,14
-1,74
-15,34
-10,54
12,36
2,46
-5,84
14,36
-14,34
-12,44
8,96
8,76
-0,24
4,36
-7,64
-3,34
12,56
1,46
-5,34
25,06
-21,34
-15,44
11,56
-0,14
9,06
7,86
-3,54
2,96
22,26
-1,44
13,56
24,46
-16,84
-10,54
18,36
21,86
20,26
12,36
10,86
6,76
25,56
8,96
14,16
29,16
-2,24
-1,94

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3598&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]2 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=3598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3598&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.846666666666671.666106911652011.10837225015508
Geometric MeanNaN
Harmonic Mean-6.93747320451683
Quadratic Mean12.930158545045
Winsorized Mean ( 1 / 20 )1.941.606065128735481.20792112678982
Winsorized Mean ( 2 / 20 )1.956666666666671.593893656056551.22760176579638
Winsorized Mean ( 3 / 20 )2.101666666666671.547599365057681.35801727121304
Winsorized Mean ( 4 / 20 )2.048333333333331.493857652985151.37117035832710
Winsorized Mean ( 5 / 20 )2.023333333333331.484608351912631.36287346809457
Winsorized Mean ( 6 / 20 )1.963333333333331.429540969086771.37340123563409
Winsorized Mean ( 7 / 20 )1.963333333333331.340848805007771.46424662199102
Winsorized Mean ( 8 / 20 )1.456666666666671.233011028278691.18138981181718
Winsorized Mean ( 9 / 20 )1.681666666666671.181266417197771.42361337136458
Winsorized Mean ( 10 / 20 )1.581666666666671.163588574625121.35930061635079
Winsorized Mean ( 11 / 20 )1.728333333333331.075504064365661.60699842111031
Winsorized Mean ( 12 / 20 )1.888333333333331.036408105346841.82199784389123
Winsorized Mean ( 13 / 20 )1.911.033004777363831.84897499203654
Winsorized Mean ( 14 / 20 )1.840.9831800129442761.87147823976797
Winsorized Mean ( 15 / 20 )1.9150.9160231690998232.09055847559169
Winsorized Mean ( 16 / 20 )1.5950.8395277963855361.89987753457007
Winsorized Mean ( 17 / 20 )1.538333333333330.822020700478441.87140461601268
Winsorized Mean ( 18 / 20 )1.628333333333330.7994931009431812.03670717284783
Winsorized Mean ( 19 / 20 )2.198333333333330.7186305701971253.05905902768695
Winsorized Mean ( 20 / 20 )2.198333333333330.6990230942196073.14486510032628
Trimmed Mean ( 1 / 20 )1.934137931034481.558631413617021.24092066548694
Trimmed Mean ( 2 / 20 )1.927857142857141.500162560764621.28509882413979
Trimmed Mean ( 3 / 20 )1.911851851851851.435855955600101.33150671861984
Trimmed Mean ( 4 / 20 )1.838846153846151.378597273124581.33385303285739
Trimmed Mean ( 5 / 20 )1.7761.328560245728671.33678544553012
Trimmed Mean ( 6 / 20 )1.714166666666671.268116791936191.35174195118845
Trimmed Mean ( 7 / 20 )1.661.209083974739151.37294020488373
Trimmed Mean ( 8 / 20 )1.600909090909091.160540071576991.37945180017241
Trimmed Mean ( 9 / 20 )1.626666666666671.128722601694361.44115716671645
Trimmed Mean ( 10 / 20 )1.61751.100331462298101.47001158780079
Trimmed Mean ( 11 / 20 )1.623157894736841.066197435223281.52238022819566
Trimmed Mean ( 12 / 20 )1.607222222222221.043228247492771.54062375715469
Trimmed Mean ( 13 / 20 )1.565882352941181.020397507182551.53458073144924
Trimmed Mean ( 14 / 20 )1.516250.9872670968712151.53580525959510
Trimmed Mean ( 15 / 20 )1.470.9535336579175431.54163409733264
Trimmed Mean ( 16 / 20 )1.406428571428570.9235525231618121.52284633104961
Trimmed Mean ( 17 / 20 )1.379230769230770.9021686560858061.52879482115325
Trimmed Mean ( 18 / 20 )1.355833333333330.8716027043066061.55556347706832
Trimmed Mean ( 19 / 20 )1.314545454545450.8278885486802031.58782900988432
Trimmed Mean ( 20 / 20 )1.1750.785134081743871.49655966709558
Median0.01
Midrange-0.69
Midmean - Weighted Average at Xnp1.19225806451613
Midmean - Weighted Average at X(n+1)p1.47
Midmean - Empirical Distribution Function1.19225806451613
Midmean - Empirical Distribution Function - Averaging1.47
Midmean - Empirical Distribution Function - Interpolation1.47
Midmean - Closest Observation1.19225806451613
Midmean - True Basic - Statistics Graphics Toolkit1.47
Midmean - MS Excel (old versions)1.51625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.84666666666667 & 1.66610691165201 & 1.10837225015508 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -6.93747320451683 &  &  \tabularnewline
Quadratic Mean & 12.930158545045 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.94 & 1.60606512873548 & 1.20792112678982 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.95666666666667 & 1.59389365605655 & 1.22760176579638 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.10166666666667 & 1.54759936505768 & 1.35801727121304 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.04833333333333 & 1.49385765298515 & 1.37117035832710 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.02333333333333 & 1.48460835191263 & 1.36287346809457 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.96333333333333 & 1.42954096908677 & 1.37340123563409 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.96333333333333 & 1.34084880500777 & 1.46424662199102 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.45666666666667 & 1.23301102827869 & 1.18138981181718 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.68166666666667 & 1.18126641719777 & 1.42361337136458 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.58166666666667 & 1.16358857462512 & 1.35930061635079 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.72833333333333 & 1.07550406436566 & 1.60699842111031 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.88833333333333 & 1.03640810534684 & 1.82199784389123 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.91 & 1.03300477736383 & 1.84897499203654 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.84 & 0.983180012944276 & 1.87147823976797 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.915 & 0.916023169099823 & 2.09055847559169 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.595 & 0.839527796385536 & 1.89987753457007 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.53833333333333 & 0.82202070047844 & 1.87140461601268 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.62833333333333 & 0.799493100943181 & 2.03670717284783 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.19833333333333 & 0.718630570197125 & 3.05905902768695 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.19833333333333 & 0.699023094219607 & 3.14486510032628 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.93413793103448 & 1.55863141361702 & 1.24092066548694 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.92785714285714 & 1.50016256076462 & 1.28509882413979 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.91185185185185 & 1.43585595560010 & 1.33150671861984 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.83884615384615 & 1.37859727312458 & 1.33385303285739 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.776 & 1.32856024572867 & 1.33678544553012 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.71416666666667 & 1.26811679193619 & 1.35174195118845 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.66 & 1.20908397473915 & 1.37294020488373 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.60090909090909 & 1.16054007157699 & 1.37945180017241 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.62666666666667 & 1.12872260169436 & 1.44115716671645 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.6175 & 1.10033146229810 & 1.47001158780079 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.62315789473684 & 1.06619743522328 & 1.52238022819566 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.60722222222222 & 1.04322824749277 & 1.54062375715469 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.56588235294118 & 1.02039750718255 & 1.53458073144924 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.51625 & 0.987267096871215 & 1.53580525959510 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.47 & 0.953533657917543 & 1.54163409733264 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.40642857142857 & 0.923552523161812 & 1.52284633104961 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.37923076923077 & 0.902168656085806 & 1.52879482115325 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.35583333333333 & 0.871602704306606 & 1.55556347706832 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.31454545454545 & 0.827888548680203 & 1.58782900988432 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.175 & 0.78513408174387 & 1.49655966709558 \tabularnewline
Median & 0.01 &  &  \tabularnewline
Midrange & -0.69 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.19225806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.47 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.19225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.47 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.47 &  &  \tabularnewline
Midmean - Closest Observation & 1.19225806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.47 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.51625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3598&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]1.84666666666667[/C][C]1.66610691165201[/C][C]1.10837225015508[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-6.93747320451683[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.930158545045[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.94[/C][C]1.60606512873548[/C][C]1.20792112678982[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.95666666666667[/C][C]1.59389365605655[/C][C]1.22760176579638[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.10166666666667[/C][C]1.54759936505768[/C][C]1.35801727121304[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.04833333333333[/C][C]1.49385765298515[/C][C]1.37117035832710[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.02333333333333[/C][C]1.48460835191263[/C][C]1.36287346809457[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.96333333333333[/C][C]1.42954096908677[/C][C]1.37340123563409[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.96333333333333[/C][C]1.34084880500777[/C][C]1.46424662199102[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.45666666666667[/C][C]1.23301102827869[/C][C]1.18138981181718[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.68166666666667[/C][C]1.18126641719777[/C][C]1.42361337136458[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.58166666666667[/C][C]1.16358857462512[/C][C]1.35930061635079[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.72833333333333[/C][C]1.07550406436566[/C][C]1.60699842111031[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.88833333333333[/C][C]1.03640810534684[/C][C]1.82199784389123[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.91[/C][C]1.03300477736383[/C][C]1.84897499203654[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.84[/C][C]0.983180012944276[/C][C]1.87147823976797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.915[/C][C]0.916023169099823[/C][C]2.09055847559169[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.595[/C][C]0.839527796385536[/C][C]1.89987753457007[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.53833333333333[/C][C]0.82202070047844[/C][C]1.87140461601268[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.62833333333333[/C][C]0.799493100943181[/C][C]2.03670717284783[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.19833333333333[/C][C]0.718630570197125[/C][C]3.05905902768695[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.19833333333333[/C][C]0.699023094219607[/C][C]3.14486510032628[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.93413793103448[/C][C]1.55863141361702[/C][C]1.24092066548694[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.92785714285714[/C][C]1.50016256076462[/C][C]1.28509882413979[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.91185185185185[/C][C]1.43585595560010[/C][C]1.33150671861984[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.83884615384615[/C][C]1.37859727312458[/C][C]1.33385303285739[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.776[/C][C]1.32856024572867[/C][C]1.33678544553012[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.71416666666667[/C][C]1.26811679193619[/C][C]1.35174195118845[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.66[/C][C]1.20908397473915[/C][C]1.37294020488373[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.60090909090909[/C][C]1.16054007157699[/C][C]1.37945180017241[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.62666666666667[/C][C]1.12872260169436[/C][C]1.44115716671645[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.6175[/C][C]1.10033146229810[/C][C]1.47001158780079[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.62315789473684[/C][C]1.06619743522328[/C][C]1.52238022819566[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.60722222222222[/C][C]1.04322824749277[/C][C]1.54062375715469[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.56588235294118[/C][C]1.02039750718255[/C][C]1.53458073144924[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.51625[/C][C]0.987267096871215[/C][C]1.53580525959510[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.47[/C][C]0.953533657917543[/C][C]1.54163409733264[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.40642857142857[/C][C]0.923552523161812[/C][C]1.52284633104961[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.37923076923077[/C][C]0.902168656085806[/C][C]1.52879482115325[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.35583333333333[/C][C]0.871602704306606[/C][C]1.55556347706832[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.31454545454545[/C][C]0.827888548680203[/C][C]1.58782900988432[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.175[/C][C]0.78513408174387[/C][C]1.49655966709558[/C][/ROW]
[ROW][C]Median[/C][C]0.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.19225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.19225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.19225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.51625[/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=3598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3598&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 Mean1.846666666666671.666106911652011.10837225015508
Geometric MeanNaN
Harmonic Mean-6.93747320451683
Quadratic Mean12.930158545045
Winsorized Mean ( 1 / 20 )1.941.606065128735481.20792112678982
Winsorized Mean ( 2 / 20 )1.956666666666671.593893656056551.22760176579638
Winsorized Mean ( 3 / 20 )2.101666666666671.547599365057681.35801727121304
Winsorized Mean ( 4 / 20 )2.048333333333331.493857652985151.37117035832710
Winsorized Mean ( 5 / 20 )2.023333333333331.484608351912631.36287346809457
Winsorized Mean ( 6 / 20 )1.963333333333331.429540969086771.37340123563409
Winsorized Mean ( 7 / 20 )1.963333333333331.340848805007771.46424662199102
Winsorized Mean ( 8 / 20 )1.456666666666671.233011028278691.18138981181718
Winsorized Mean ( 9 / 20 )1.681666666666671.181266417197771.42361337136458
Winsorized Mean ( 10 / 20 )1.581666666666671.163588574625121.35930061635079
Winsorized Mean ( 11 / 20 )1.728333333333331.075504064365661.60699842111031
Winsorized Mean ( 12 / 20 )1.888333333333331.036408105346841.82199784389123
Winsorized Mean ( 13 / 20 )1.911.033004777363831.84897499203654
Winsorized Mean ( 14 / 20 )1.840.9831800129442761.87147823976797
Winsorized Mean ( 15 / 20 )1.9150.9160231690998232.09055847559169
Winsorized Mean ( 16 / 20 )1.5950.8395277963855361.89987753457007
Winsorized Mean ( 17 / 20 )1.538333333333330.822020700478441.87140461601268
Winsorized Mean ( 18 / 20 )1.628333333333330.7994931009431812.03670717284783
Winsorized Mean ( 19 / 20 )2.198333333333330.7186305701971253.05905902768695
Winsorized Mean ( 20 / 20 )2.198333333333330.6990230942196073.14486510032628
Trimmed Mean ( 1 / 20 )1.934137931034481.558631413617021.24092066548694
Trimmed Mean ( 2 / 20 )1.927857142857141.500162560764621.28509882413979
Trimmed Mean ( 3 / 20 )1.911851851851851.435855955600101.33150671861984
Trimmed Mean ( 4 / 20 )1.838846153846151.378597273124581.33385303285739
Trimmed Mean ( 5 / 20 )1.7761.328560245728671.33678544553012
Trimmed Mean ( 6 / 20 )1.714166666666671.268116791936191.35174195118845
Trimmed Mean ( 7 / 20 )1.661.209083974739151.37294020488373
Trimmed Mean ( 8 / 20 )1.600909090909091.160540071576991.37945180017241
Trimmed Mean ( 9 / 20 )1.626666666666671.128722601694361.44115716671645
Trimmed Mean ( 10 / 20 )1.61751.100331462298101.47001158780079
Trimmed Mean ( 11 / 20 )1.623157894736841.066197435223281.52238022819566
Trimmed Mean ( 12 / 20 )1.607222222222221.043228247492771.54062375715469
Trimmed Mean ( 13 / 20 )1.565882352941181.020397507182551.53458073144924
Trimmed Mean ( 14 / 20 )1.516250.9872670968712151.53580525959510
Trimmed Mean ( 15 / 20 )1.470.9535336579175431.54163409733264
Trimmed Mean ( 16 / 20 )1.406428571428570.9235525231618121.52284633104961
Trimmed Mean ( 17 / 20 )1.379230769230770.9021686560858061.52879482115325
Trimmed Mean ( 18 / 20 )1.355833333333330.8716027043066061.55556347706832
Trimmed Mean ( 19 / 20 )1.314545454545450.8278885486802031.58782900988432
Trimmed Mean ( 20 / 20 )1.1750.785134081743871.49655966709558
Median0.01
Midrange-0.69
Midmean - Weighted Average at Xnp1.19225806451613
Midmean - Weighted Average at X(n+1)p1.47
Midmean - Empirical Distribution Function1.19225806451613
Midmean - Empirical Distribution Function - Averaging1.47
Midmean - Empirical Distribution Function - Interpolation1.47
Midmean - Closest Observation1.19225806451613
Midmean - True Basic - Statistics Graphics Toolkit1.47
Midmean - MS Excel (old versions)1.51625
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')