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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 26 May 2012 06:27:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/26/t1338028101col9ietpoyciay8.htm/, Retrieved Thu, 02 May 2024 23:46:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167571, Retrieved Thu, 02 May 2024 23:46:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid prijs...] [2012-05-26 10:27:01] [a2709f7ab86902c8a6d752383a828f6c] [Current]
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Dataseries X:
67,66
68
68,02
68,11
68,41
68,4
68,4
68,55
68,54
68,99
68,97
68,98
68,98
68,94
69,21
69,21
69,67
69,66
69,66
69,66
69,77
70,32
70,34
70,38
70,38
70,29
70,42
70,29
70,59
70,64
70,64
70,68
70,78
70,9
71,04
71,15
71,15
71,15
71,07
71,17
71,24
71,23
71,23
71,23
71,24
71,28
71,52
71,52
71,52
71,6
71,61
71,78
71,66
71,86
71,86
71,82
71,8
72,22
72,51
72,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167571&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167571&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167571&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean70.37433333333330.165925476203879424.132176344407
Geometric Mean70.3627300448637
Harmonic Mean70.351064988874
Quadratic Mean70.3858731328004
Winsorized Mean ( 1 / 20 )70.37916666666670.164259215646095428.464037100372
Winsorized Mean ( 2 / 20 )70.37016666666670.162097043485041434.123690066936
Winsorized Mean ( 3 / 20 )70.35666666666670.157803186198467445.850735727098
Winsorized Mean ( 4 / 20 )70.3760.15335627438307458.905253685332
Winsorized Mean ( 5 / 20 )70.37266666666670.152815361923874460.507803539563
Winsorized Mean ( 6 / 20 )70.37166666666670.152277283263515462.128461701598
Winsorized Mean ( 7 / 20 )70.38450.148654877480929473.475887187285
Winsorized Mean ( 8 / 20 )70.36983333333330.145901152914724482.311701638596
Winsorized Mean ( 9 / 20 )70.42083333333330.133038648576517529.326132569897
Winsorized Mean ( 10 / 20 )70.42416666666670.131847431874504534.13377617926
Winsorized Mean ( 11 / 20 )70.41133333333330.129329751246334544.432604677487
Winsorized Mean ( 12 / 20 )70.41133333333330.129329751246334544.432604677487
Winsorized Mean ( 13 / 20 )70.41350.128923799374661546.163705549616
Winsorized Mean ( 14 / 20 )70.40883333333330.111636286870083630.698452155363
Winsorized Mean ( 15 / 20 )70.39883333333330.110328756711199638.082358868708
Winsorized Mean ( 16 / 20 )70.51883333333330.0894856904467242788.045920876223
Winsorized Mean ( 17 / 20 )70.5160.0890997663385376791.427440247958
Winsorized Mean ( 18 / 20 )70.5160.0890997663385376791.427440247958
Winsorized Mean ( 19 / 20 )70.51916666666670.088584694596532796.06490701191
Winsorized Mean ( 20 / 20 )70.53250.080496210038166876.221376963688
Trimmed Mean ( 1 / 20 )70.3834482758620.160639140805188438.146319278551
Trimmed Mean ( 2 / 20 )70.38803571428570.156158099133093450.748543335522
Trimmed Mean ( 3 / 20 )70.3979629629630.152016352156027463.094673464521
Trimmed Mean ( 4 / 20 )70.41384615384620.148842227159106473.077079655473
Trimmed Mean ( 5 / 20 )70.42520.146523032945928480.642521411561
Trimmed Mean ( 6 / 20 )70.43833333333330.143635464186614490.396530774729
Trimmed Mean ( 7 / 20 )70.45282608695650.139989531369634503.272104689958
Trimmed Mean ( 8 / 20 )70.46613636363640.136278386847993517.074922835969
Trimmed Mean ( 9 / 20 )70.48333333333330.132053673434104533.747615650428
Trimmed Mean ( 10 / 20 )70.493750.130022033389217542.167724673087
Trimmed Mean ( 11 / 20 )70.50473684210530.127406416631491553.384505319167
Trimmed Mean ( 12 / 20 )70.51888888888890.124275537299486567.43982300353
Trimmed Mean ( 13 / 20 )70.5347058823530.119718352852212589.172037552384
Trimmed Mean ( 14 / 20 )70.55218750.113211668702672623.188301245617
Trimmed Mean ( 15 / 20 )70.57266666666670.109179735113193646.389795629195
Trimmed Mean ( 16 / 20 )70.59750.10319707478115684.103693343207
Trimmed Mean ( 17 / 20 )70.60884615384620.101950707430416692.5782854625
Trimmed Mean ( 18 / 20 )70.62250.0995046608769256709.740622977962
Trimmed Mean ( 19 / 20 )70.63863636363640.0949397062130519744.036812217619
Trimmed Mean ( 20 / 20 )70.65750.0868933859756648813.15164792621
Median70.64
Midrange70.11
Midmean - Weighted Average at Xnp70.5287096774194
Midmean - Weighted Average at X(n+1)p70.5287096774194
Midmean - Empirical Distribution Function70.5287096774194
Midmean - Empirical Distribution Function - Averaging70.5287096774194
Midmean - Empirical Distribution Function - Interpolation70.5287096774194
Midmean - Closest Observation70.5287096774194
Midmean - True Basic - Statistics Graphics Toolkit70.5287096774194
Midmean - MS Excel (old versions)70.5521875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 70.3743333333333 & 0.165925476203879 & 424.132176344407 \tabularnewline
Geometric Mean & 70.3627300448637 &  &  \tabularnewline
Harmonic Mean & 70.351064988874 &  &  \tabularnewline
Quadratic Mean & 70.3858731328004 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 70.3791666666667 & 0.164259215646095 & 428.464037100372 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 70.3701666666667 & 0.162097043485041 & 434.123690066936 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 70.3566666666667 & 0.157803186198467 & 445.850735727098 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 70.376 & 0.15335627438307 & 458.905253685332 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 70.3726666666667 & 0.152815361923874 & 460.507803539563 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 70.3716666666667 & 0.152277283263515 & 462.128461701598 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 70.3845 & 0.148654877480929 & 473.475887187285 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 70.3698333333333 & 0.145901152914724 & 482.311701638596 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 70.4208333333333 & 0.133038648576517 & 529.326132569897 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 70.4241666666667 & 0.131847431874504 & 534.13377617926 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 70.4113333333333 & 0.129329751246334 & 544.432604677487 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 70.4113333333333 & 0.129329751246334 & 544.432604677487 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 70.4135 & 0.128923799374661 & 546.163705549616 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 70.4088333333333 & 0.111636286870083 & 630.698452155363 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 70.3988333333333 & 0.110328756711199 & 638.082358868708 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 70.5188333333333 & 0.0894856904467242 & 788.045920876223 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 70.516 & 0.0890997663385376 & 791.427440247958 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 70.516 & 0.0890997663385376 & 791.427440247958 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 70.5191666666667 & 0.088584694596532 & 796.06490701191 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 70.5325 & 0.080496210038166 & 876.221376963688 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 70.383448275862 & 0.160639140805188 & 438.146319278551 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 70.3880357142857 & 0.156158099133093 & 450.748543335522 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 70.397962962963 & 0.152016352156027 & 463.094673464521 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 70.4138461538462 & 0.148842227159106 & 473.077079655473 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 70.4252 & 0.146523032945928 & 480.642521411561 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 70.4383333333333 & 0.143635464186614 & 490.396530774729 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 70.4528260869565 & 0.139989531369634 & 503.272104689958 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 70.4661363636364 & 0.136278386847993 & 517.074922835969 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 70.4833333333333 & 0.132053673434104 & 533.747615650428 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 70.49375 & 0.130022033389217 & 542.167724673087 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 70.5047368421053 & 0.127406416631491 & 553.384505319167 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 70.5188888888889 & 0.124275537299486 & 567.43982300353 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 70.534705882353 & 0.119718352852212 & 589.172037552384 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 70.5521875 & 0.113211668702672 & 623.188301245617 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 70.5726666666667 & 0.109179735113193 & 646.389795629195 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 70.5975 & 0.10319707478115 & 684.103693343207 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 70.6088461538462 & 0.101950707430416 & 692.5782854625 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 70.6225 & 0.0995046608769256 & 709.740622977962 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 70.6386363636364 & 0.0949397062130519 & 744.036812217619 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 70.6575 & 0.0868933859756648 & 813.15164792621 \tabularnewline
Median & 70.64 &  &  \tabularnewline
Midrange & 70.11 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 70.5287096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 70.5287096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 70.5287096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 70.5287096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 70.5287096774194 &  &  \tabularnewline
Midmean - Closest Observation & 70.5287096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 70.5287096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 70.5521875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167571&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]70.3743333333333[/C][C]0.165925476203879[/C][C]424.132176344407[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]70.3627300448637[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]70.351064988874[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]70.3858731328004[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]70.3791666666667[/C][C]0.164259215646095[/C][C]428.464037100372[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]70.3701666666667[/C][C]0.162097043485041[/C][C]434.123690066936[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]70.3566666666667[/C][C]0.157803186198467[/C][C]445.850735727098[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]70.376[/C][C]0.15335627438307[/C][C]458.905253685332[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]70.3726666666667[/C][C]0.152815361923874[/C][C]460.507803539563[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]70.3716666666667[/C][C]0.152277283263515[/C][C]462.128461701598[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]70.3845[/C][C]0.148654877480929[/C][C]473.475887187285[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]70.3698333333333[/C][C]0.145901152914724[/C][C]482.311701638596[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]70.4208333333333[/C][C]0.133038648576517[/C][C]529.326132569897[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]70.4241666666667[/C][C]0.131847431874504[/C][C]534.13377617926[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]70.4113333333333[/C][C]0.129329751246334[/C][C]544.432604677487[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]70.4113333333333[/C][C]0.129329751246334[/C][C]544.432604677487[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]70.4135[/C][C]0.128923799374661[/C][C]546.163705549616[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]70.4088333333333[/C][C]0.111636286870083[/C][C]630.698452155363[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]70.3988333333333[/C][C]0.110328756711199[/C][C]638.082358868708[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]70.5188333333333[/C][C]0.0894856904467242[/C][C]788.045920876223[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]70.516[/C][C]0.0890997663385376[/C][C]791.427440247958[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]70.516[/C][C]0.0890997663385376[/C][C]791.427440247958[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]70.5191666666667[/C][C]0.088584694596532[/C][C]796.06490701191[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]70.5325[/C][C]0.080496210038166[/C][C]876.221376963688[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]70.383448275862[/C][C]0.160639140805188[/C][C]438.146319278551[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]70.3880357142857[/C][C]0.156158099133093[/C][C]450.748543335522[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]70.397962962963[/C][C]0.152016352156027[/C][C]463.094673464521[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]70.4138461538462[/C][C]0.148842227159106[/C][C]473.077079655473[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]70.4252[/C][C]0.146523032945928[/C][C]480.642521411561[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]70.4383333333333[/C][C]0.143635464186614[/C][C]490.396530774729[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]70.4528260869565[/C][C]0.139989531369634[/C][C]503.272104689958[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]70.4661363636364[/C][C]0.136278386847993[/C][C]517.074922835969[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]70.4833333333333[/C][C]0.132053673434104[/C][C]533.747615650428[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]70.49375[/C][C]0.130022033389217[/C][C]542.167724673087[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]70.5047368421053[/C][C]0.127406416631491[/C][C]553.384505319167[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]70.5188888888889[/C][C]0.124275537299486[/C][C]567.43982300353[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]70.534705882353[/C][C]0.119718352852212[/C][C]589.172037552384[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]70.5521875[/C][C]0.113211668702672[/C][C]623.188301245617[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]70.5726666666667[/C][C]0.109179735113193[/C][C]646.389795629195[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]70.5975[/C][C]0.10319707478115[/C][C]684.103693343207[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]70.6088461538462[/C][C]0.101950707430416[/C][C]692.5782854625[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]70.6225[/C][C]0.0995046608769256[/C][C]709.740622977962[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]70.6386363636364[/C][C]0.0949397062130519[/C][C]744.036812217619[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]70.6575[/C][C]0.0868933859756648[/C][C]813.15164792621[/C][/ROW]
[ROW][C]Median[/C][C]70.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]70.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]70.5287096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]70.5521875[/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=167571&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167571&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 Mean70.37433333333330.165925476203879424.132176344407
Geometric Mean70.3627300448637
Harmonic Mean70.351064988874
Quadratic Mean70.3858731328004
Winsorized Mean ( 1 / 20 )70.37916666666670.164259215646095428.464037100372
Winsorized Mean ( 2 / 20 )70.37016666666670.162097043485041434.123690066936
Winsorized Mean ( 3 / 20 )70.35666666666670.157803186198467445.850735727098
Winsorized Mean ( 4 / 20 )70.3760.15335627438307458.905253685332
Winsorized Mean ( 5 / 20 )70.37266666666670.152815361923874460.507803539563
Winsorized Mean ( 6 / 20 )70.37166666666670.152277283263515462.128461701598
Winsorized Mean ( 7 / 20 )70.38450.148654877480929473.475887187285
Winsorized Mean ( 8 / 20 )70.36983333333330.145901152914724482.311701638596
Winsorized Mean ( 9 / 20 )70.42083333333330.133038648576517529.326132569897
Winsorized Mean ( 10 / 20 )70.42416666666670.131847431874504534.13377617926
Winsorized Mean ( 11 / 20 )70.41133333333330.129329751246334544.432604677487
Winsorized Mean ( 12 / 20 )70.41133333333330.129329751246334544.432604677487
Winsorized Mean ( 13 / 20 )70.41350.128923799374661546.163705549616
Winsorized Mean ( 14 / 20 )70.40883333333330.111636286870083630.698452155363
Winsorized Mean ( 15 / 20 )70.39883333333330.110328756711199638.082358868708
Winsorized Mean ( 16 / 20 )70.51883333333330.0894856904467242788.045920876223
Winsorized Mean ( 17 / 20 )70.5160.0890997663385376791.427440247958
Winsorized Mean ( 18 / 20 )70.5160.0890997663385376791.427440247958
Winsorized Mean ( 19 / 20 )70.51916666666670.088584694596532796.06490701191
Winsorized Mean ( 20 / 20 )70.53250.080496210038166876.221376963688
Trimmed Mean ( 1 / 20 )70.3834482758620.160639140805188438.146319278551
Trimmed Mean ( 2 / 20 )70.38803571428570.156158099133093450.748543335522
Trimmed Mean ( 3 / 20 )70.3979629629630.152016352156027463.094673464521
Trimmed Mean ( 4 / 20 )70.41384615384620.148842227159106473.077079655473
Trimmed Mean ( 5 / 20 )70.42520.146523032945928480.642521411561
Trimmed Mean ( 6 / 20 )70.43833333333330.143635464186614490.396530774729
Trimmed Mean ( 7 / 20 )70.45282608695650.139989531369634503.272104689958
Trimmed Mean ( 8 / 20 )70.46613636363640.136278386847993517.074922835969
Trimmed Mean ( 9 / 20 )70.48333333333330.132053673434104533.747615650428
Trimmed Mean ( 10 / 20 )70.493750.130022033389217542.167724673087
Trimmed Mean ( 11 / 20 )70.50473684210530.127406416631491553.384505319167
Trimmed Mean ( 12 / 20 )70.51888888888890.124275537299486567.43982300353
Trimmed Mean ( 13 / 20 )70.5347058823530.119718352852212589.172037552384
Trimmed Mean ( 14 / 20 )70.55218750.113211668702672623.188301245617
Trimmed Mean ( 15 / 20 )70.57266666666670.109179735113193646.389795629195
Trimmed Mean ( 16 / 20 )70.59750.10319707478115684.103693343207
Trimmed Mean ( 17 / 20 )70.60884615384620.101950707430416692.5782854625
Trimmed Mean ( 18 / 20 )70.62250.0995046608769256709.740622977962
Trimmed Mean ( 19 / 20 )70.63863636363640.0949397062130519744.036812217619
Trimmed Mean ( 20 / 20 )70.65750.0868933859756648813.15164792621
Median70.64
Midrange70.11
Midmean - Weighted Average at Xnp70.5287096774194
Midmean - Weighted Average at X(n+1)p70.5287096774194
Midmean - Empirical Distribution Function70.5287096774194
Midmean - Empirical Distribution Function - Averaging70.5287096774194
Midmean - Empirical Distribution Function - Interpolation70.5287096774194
Midmean - Closest Observation70.5287096774194
Midmean - True Basic - Statistics Graphics Toolkit70.5287096774194
Midmean - MS Excel (old versions)70.5521875
Number of observations60



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')