Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Dec 2007 06:32:02 -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/15/t11977246460ppd8eo8qfuuwee.htm/, Retrieved Thu, 02 May 2024 19:19:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4039, Retrieved Thu, 02 May 2024 19:19:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [voorspelling prijs] [2007-12-15 13:32:02] [d02236afd58a58d13a748bbf41a37c2e] [Current]
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Dataseries X:
0,77632
0,80364
0,83065
0,76103
0,72187
0,72929
0,73339
0,75884
0,75423
0,77581
0,77753
0,77016
0,76800
0,76352
0,80984
0,83697
0,86371
0,85027
0,86945
0,92155
0,93647
0,98323
0,95760
0,93332
0,90135
0,92446
0,98061
1,01953
1,00784
1,07107
1,09458
1,10923
1,12907
1,12374
1,07400
1,04497
1,06290
1,06646
1,08848
1,11763
1,10842
1,10560
1,11306
1,11039
1,05590
1,03703
1,04327
1,03839
0,99784
1,01526
1,05461
1,08300
1,08503
1,09953
1,11442
1,10371
1,13018
1,15868
1,24067
1,21680




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4039&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4039&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9735733333333330.018701705793474852.0579964247445
Geometric Mean0.962470259615614
Harmonic Mean0.950953001282003
Quadratic Mean0.984114073445418
Winsorized Mean ( 1 / 20 )0.9732991666666670.018581491774616852.3800337708214
Winsorized Mean ( 2 / 20 )0.97149850.018166263061123353.4781697661891
Winsorized Mean ( 3 / 20 )0.97111550.017709170948232754.8368697122388
Winsorized Mean ( 4 / 20 )0.9713488333333330.017634644289415655.0818501009596
Winsorized Mean ( 5 / 20 )0.9710871666666670.017531030113525555.3924761054091
Winsorized Mean ( 6 / 20 )0.9707251666666670.017391774764606655.8151873402913
Winsorized Mean ( 7 / 20 )0.9708733333333330.017233612942906556.3360298591918
Winsorized Mean ( 8 / 20 )0.970980.017150772168876356.6143605920001
Winsorized Mean ( 9 / 20 )0.9714270.016927688727840757.3868657215032
Winsorized Mean ( 10 / 20 )0.9713186666666670.016884212224908357.5282194826795
Winsorized Mean ( 11 / 20 )0.9713920.016820301482616257.7511646270986
Winsorized Mean ( 12 / 20 )0.976050.015746620622119261.9847282425125
Winsorized Mean ( 13 / 20 )0.9769838333333330.015441704770519063.2691692952564
Winsorized Mean ( 14 / 20 )0.9808641666666670.014431606596045867.966387535496
Winsorized Mean ( 15 / 20 )0.9812066666666670.013982812744260570.1723383279533
Winsorized Mean ( 16 / 20 )0.9831266666666670.013146547536447074.7821178101007
Winsorized Mean ( 17 / 20 )0.9859571666666670.012368500889051579.7151712653739
Winsorized Mean ( 18 / 20 )0.9870701666666670.011998588100770882.26552644167
Winsorized Mean ( 19 / 20 )0.9943218333333330.009971304490793499.718330159449
Winsorized Mean ( 20 / 20 )1.00007850.00879547739082341113.703720169119
Trimmed Mean ( 1 / 20 )0.9733079310344830.018269253637711853.2757358530159
Trimmed Mean ( 2 / 20 )0.9733173214285710.017879430469900154.4378258058692
Trimmed Mean ( 3 / 20 )0.9743277777777780.017660281737839455.1705681846601
Trimmed Mean ( 4 / 20 )0.975563269230770.017582000571511155.4864769377562
Trimmed Mean ( 5 / 20 )0.97682760.017486915305532255.8604867086517
Trimmed Mean ( 6 / 20 )0.9782627083333330.017373404714609756.3080596119821
Trimmed Mean ( 7 / 20 )0.9799013043478260.017240540487197556.8370408732536
Trimmed Mean ( 8 / 20 )0.981660.017083080696665857.4638741940496
Trimmed Mean ( 9 / 20 )0.9835671428571430.016868599612259258.3075753450415
Trimmed Mean ( 10 / 20 )0.98559050.016613704487213659.3239455269317
Trimmed Mean ( 11 / 20 )0.9878439473684210.016250830872902160.7872886681522
Trimmed Mean ( 12 / 20 )0.9903366666666670.015743872841950062.9029894110859
Trimmed Mean ( 13 / 20 )0.9924376470588240.015340004235886364.6960477844668
Trimmed Mean ( 14 / 20 )0.99466656250.014829060727448067.0754932346396
Trimmed Mean ( 15 / 20 )0.9966383333333330.014388989405483369.2639562965789
Trimmed Mean ( 16 / 20 )0.9988428571428570.013844602379323672.1467348628656
Trimmed Mean ( 17 / 20 )1.001109615384620.013281710680837375.3750506573679
Trimmed Mean ( 18 / 20 )1.003337916666670.012670721271051879.1855408388588
Trimmed Mean ( 19 / 20 )1.005802727272730.011789675929399785.3121606815818
Trimmed Mean ( 20 / 20 )1.00761550.011307822245428689.1078297951973
Median1.017395
Midrange0.98127
Midmean - Weighted Average at Xnp0.991283870967742
Midmean - Weighted Average at X(n+1)p0.996638333333333
Midmean - Empirical Distribution Function0.991283870967742
Midmean - Empirical Distribution Function - Averaging0.996638333333333
Midmean - Empirical Distribution Function - Interpolation0.996638333333333
Midmean - Closest Observation0.991283870967742
Midmean - True Basic - Statistics Graphics Toolkit0.996638333333333
Midmean - MS Excel (old versions)0.9946665625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.973573333333333 & 0.0187017057934748 & 52.0579964247445 \tabularnewline
Geometric Mean & 0.962470259615614 &  &  \tabularnewline
Harmonic Mean & 0.950953001282003 &  &  \tabularnewline
Quadratic Mean & 0.984114073445418 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.973299166666667 & 0.0185814917746168 & 52.3800337708214 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.9714985 & 0.0181662630611233 & 53.4781697661891 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.9711155 & 0.0177091709482327 & 54.8368697122388 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.971348833333333 & 0.0176346442894156 & 55.0818501009596 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.971087166666667 & 0.0175310301135255 & 55.3924761054091 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.970725166666667 & 0.0173917747646066 & 55.8151873402913 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.970873333333333 & 0.0172336129429065 & 56.3360298591918 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.97098 & 0.0171507721688763 & 56.6143605920001 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.971427 & 0.0169276887278407 & 57.3868657215032 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.971318666666667 & 0.0168842122249083 & 57.5282194826795 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.971392 & 0.0168203014826162 & 57.7511646270986 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.97605 & 0.0157466206221192 & 61.9847282425125 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.976983833333333 & 0.0154417047705190 & 63.2691692952564 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.980864166666667 & 0.0144316065960458 & 67.966387535496 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.981206666666667 & 0.0139828127442605 & 70.1723383279533 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.983126666666667 & 0.0131465475364470 & 74.7821178101007 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.985957166666667 & 0.0123685008890515 & 79.7151712653739 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.987070166666667 & 0.0119985881007708 & 82.26552644167 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.994321833333333 & 0.0099713044907934 & 99.718330159449 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.0000785 & 0.00879547739082341 & 113.703720169119 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.973307931034483 & 0.0182692536377118 & 53.2757358530159 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.973317321428571 & 0.0178794304699001 & 54.4378258058692 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.974327777777778 & 0.0176602817378394 & 55.1705681846601 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.97556326923077 & 0.0175820005715111 & 55.4864769377562 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.9768276 & 0.0174869153055322 & 55.8604867086517 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.978262708333333 & 0.0173734047146097 & 56.3080596119821 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.979901304347826 & 0.0172405404871975 & 56.8370408732536 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.98166 & 0.0170830806966658 & 57.4638741940496 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.983567142857143 & 0.0168685996122592 & 58.3075753450415 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.9855905 & 0.0166137044872136 & 59.3239455269317 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.987843947368421 & 0.0162508308729021 & 60.7872886681522 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.990336666666667 & 0.0157438728419500 & 62.9029894110859 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.992437647058824 & 0.0153400042358863 & 64.6960477844668 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.9946665625 & 0.0148290607274480 & 67.0754932346396 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.996638333333333 & 0.0143889894054833 & 69.2639562965789 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.998842857142857 & 0.0138446023793236 & 72.1467348628656 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.00110961538462 & 0.0132817106808373 & 75.3750506573679 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.00333791666667 & 0.0126707212710518 & 79.1855408388588 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.00580272727273 & 0.0117896759293997 & 85.3121606815818 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.0076155 & 0.0113078222454286 & 89.1078297951973 \tabularnewline
Median & 1.017395 &  &  \tabularnewline
Midrange & 0.98127 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.991283870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.996638333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.991283870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.996638333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.996638333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.991283870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.996638333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.9946665625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4039&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]0.973573333333333[/C][C]0.0187017057934748[/C][C]52.0579964247445[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.962470259615614[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.950953001282003[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.984114073445418[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.973299166666667[/C][C]0.0185814917746168[/C][C]52.3800337708214[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.9714985[/C][C]0.0181662630611233[/C][C]53.4781697661891[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.9711155[/C][C]0.0177091709482327[/C][C]54.8368697122388[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.971348833333333[/C][C]0.0176346442894156[/C][C]55.0818501009596[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.971087166666667[/C][C]0.0175310301135255[/C][C]55.3924761054091[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.970725166666667[/C][C]0.0173917747646066[/C][C]55.8151873402913[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.970873333333333[/C][C]0.0172336129429065[/C][C]56.3360298591918[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.97098[/C][C]0.0171507721688763[/C][C]56.6143605920001[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.971427[/C][C]0.0169276887278407[/C][C]57.3868657215032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.971318666666667[/C][C]0.0168842122249083[/C][C]57.5282194826795[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.971392[/C][C]0.0168203014826162[/C][C]57.7511646270986[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.97605[/C][C]0.0157466206221192[/C][C]61.9847282425125[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.976983833333333[/C][C]0.0154417047705190[/C][C]63.2691692952564[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.980864166666667[/C][C]0.0144316065960458[/C][C]67.966387535496[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.981206666666667[/C][C]0.0139828127442605[/C][C]70.1723383279533[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.983126666666667[/C][C]0.0131465475364470[/C][C]74.7821178101007[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.985957166666667[/C][C]0.0123685008890515[/C][C]79.7151712653739[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.987070166666667[/C][C]0.0119985881007708[/C][C]82.26552644167[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.994321833333333[/C][C]0.0099713044907934[/C][C]99.718330159449[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.0000785[/C][C]0.00879547739082341[/C][C]113.703720169119[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.973307931034483[/C][C]0.0182692536377118[/C][C]53.2757358530159[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.973317321428571[/C][C]0.0178794304699001[/C][C]54.4378258058692[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.974327777777778[/C][C]0.0176602817378394[/C][C]55.1705681846601[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.97556326923077[/C][C]0.0175820005715111[/C][C]55.4864769377562[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.9768276[/C][C]0.0174869153055322[/C][C]55.8604867086517[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.978262708333333[/C][C]0.0173734047146097[/C][C]56.3080596119821[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.979901304347826[/C][C]0.0172405404871975[/C][C]56.8370408732536[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.98166[/C][C]0.0170830806966658[/C][C]57.4638741940496[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.983567142857143[/C][C]0.0168685996122592[/C][C]58.3075753450415[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.9855905[/C][C]0.0166137044872136[/C][C]59.3239455269317[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.987843947368421[/C][C]0.0162508308729021[/C][C]60.7872886681522[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.990336666666667[/C][C]0.0157438728419500[/C][C]62.9029894110859[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.992437647058824[/C][C]0.0153400042358863[/C][C]64.6960477844668[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.9946665625[/C][C]0.0148290607274480[/C][C]67.0754932346396[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.996638333333333[/C][C]0.0143889894054833[/C][C]69.2639562965789[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.998842857142857[/C][C]0.0138446023793236[/C][C]72.1467348628656[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.00110961538462[/C][C]0.0132817106808373[/C][C]75.3750506573679[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.00333791666667[/C][C]0.0126707212710518[/C][C]79.1855408388588[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.00580272727273[/C][C]0.0117896759293997[/C][C]85.3121606815818[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.0076155[/C][C]0.0113078222454286[/C][C]89.1078297951973[/C][/ROW]
[ROW][C]Median[/C][C]1.017395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.98127[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.991283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.996638333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.991283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.996638333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.996638333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.991283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.996638333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.9946665625[/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=4039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4039&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 Mean0.9735733333333330.018701705793474852.0579964247445
Geometric Mean0.962470259615614
Harmonic Mean0.950953001282003
Quadratic Mean0.984114073445418
Winsorized Mean ( 1 / 20 )0.9732991666666670.018581491774616852.3800337708214
Winsorized Mean ( 2 / 20 )0.97149850.018166263061123353.4781697661891
Winsorized Mean ( 3 / 20 )0.97111550.017709170948232754.8368697122388
Winsorized Mean ( 4 / 20 )0.9713488333333330.017634644289415655.0818501009596
Winsorized Mean ( 5 / 20 )0.9710871666666670.017531030113525555.3924761054091
Winsorized Mean ( 6 / 20 )0.9707251666666670.017391774764606655.8151873402913
Winsorized Mean ( 7 / 20 )0.9708733333333330.017233612942906556.3360298591918
Winsorized Mean ( 8 / 20 )0.970980.017150772168876356.6143605920001
Winsorized Mean ( 9 / 20 )0.9714270.016927688727840757.3868657215032
Winsorized Mean ( 10 / 20 )0.9713186666666670.016884212224908357.5282194826795
Winsorized Mean ( 11 / 20 )0.9713920.016820301482616257.7511646270986
Winsorized Mean ( 12 / 20 )0.976050.015746620622119261.9847282425125
Winsorized Mean ( 13 / 20 )0.9769838333333330.015441704770519063.2691692952564
Winsorized Mean ( 14 / 20 )0.9808641666666670.014431606596045867.966387535496
Winsorized Mean ( 15 / 20 )0.9812066666666670.013982812744260570.1723383279533
Winsorized Mean ( 16 / 20 )0.9831266666666670.013146547536447074.7821178101007
Winsorized Mean ( 17 / 20 )0.9859571666666670.012368500889051579.7151712653739
Winsorized Mean ( 18 / 20 )0.9870701666666670.011998588100770882.26552644167
Winsorized Mean ( 19 / 20 )0.9943218333333330.009971304490793499.718330159449
Winsorized Mean ( 20 / 20 )1.00007850.00879547739082341113.703720169119
Trimmed Mean ( 1 / 20 )0.9733079310344830.018269253637711853.2757358530159
Trimmed Mean ( 2 / 20 )0.9733173214285710.017879430469900154.4378258058692
Trimmed Mean ( 3 / 20 )0.9743277777777780.017660281737839455.1705681846601
Trimmed Mean ( 4 / 20 )0.975563269230770.017582000571511155.4864769377562
Trimmed Mean ( 5 / 20 )0.97682760.017486915305532255.8604867086517
Trimmed Mean ( 6 / 20 )0.9782627083333330.017373404714609756.3080596119821
Trimmed Mean ( 7 / 20 )0.9799013043478260.017240540487197556.8370408732536
Trimmed Mean ( 8 / 20 )0.981660.017083080696665857.4638741940496
Trimmed Mean ( 9 / 20 )0.9835671428571430.016868599612259258.3075753450415
Trimmed Mean ( 10 / 20 )0.98559050.016613704487213659.3239455269317
Trimmed Mean ( 11 / 20 )0.9878439473684210.016250830872902160.7872886681522
Trimmed Mean ( 12 / 20 )0.9903366666666670.015743872841950062.9029894110859
Trimmed Mean ( 13 / 20 )0.9924376470588240.015340004235886364.6960477844668
Trimmed Mean ( 14 / 20 )0.99466656250.014829060727448067.0754932346396
Trimmed Mean ( 15 / 20 )0.9966383333333330.014388989405483369.2639562965789
Trimmed Mean ( 16 / 20 )0.9988428571428570.013844602379323672.1467348628656
Trimmed Mean ( 17 / 20 )1.001109615384620.013281710680837375.3750506573679
Trimmed Mean ( 18 / 20 )1.003337916666670.012670721271051879.1855408388588
Trimmed Mean ( 19 / 20 )1.005802727272730.011789675929399785.3121606815818
Trimmed Mean ( 20 / 20 )1.00761550.011307822245428689.1078297951973
Median1.017395
Midrange0.98127
Midmean - Weighted Average at Xnp0.991283870967742
Midmean - Weighted Average at X(n+1)p0.996638333333333
Midmean - Empirical Distribution Function0.991283870967742
Midmean - Empirical Distribution Function - Averaging0.996638333333333
Midmean - Empirical Distribution Function - Interpolation0.996638333333333
Midmean - Closest Observation0.991283870967742
Midmean - True Basic - Statistics Graphics Toolkit0.996638333333333
Midmean - MS Excel (old versions)0.9946665625
Number of observations60



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')