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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 computationWed, 07 Mar 2012 05:31:05 -0500
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/Mar/07/t1331116301sc21vlh8gqcyfse.htm/, Retrieved Mon, 29 Apr 2024 04:19:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163584, Retrieved Mon, 29 Apr 2024 04:19:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid Gem. ...] [2012-03-07 10:31:05] [f106610dfea1594537338d6093b30ca7] [Current]
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Dataseries X:
6,81
6,8
6,8
6,85
6,85
6,85
6,85
6,85
6,85
6,86
6,86
6,88
6,88
6,88
6,91
6,91
6,91
6,91
6,99
6,99
6,99
7,02
7,02
7,05
7,05
7,05
7,05
7,1
7,1
7,1
7,1
7,12
7,13
7,18
7,24
7,24
7,24
7,27
7,27
7,27
7,27
7,3
7,3
7,57
7,76
7,94
7,94
7,96
7,96
7,98
7,99
8
8
8,04
8,04
8,04
8,04
8,04
8,07
8,07




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=163584&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=163584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163584&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 Mean7.289833333333330.0587922184725072123.99316648924
Geometric Mean7.27623539806722
Harmonic Mean7.26304176899202
Quadratic Mean7.30380756865897
Winsorized Mean ( 1 / 20 )7.289833333333330.0587922184725072123.99316648924
Winsorized Mean ( 2 / 20 )7.289166666666670.0585243643631049124.549266719792
Winsorized Mean ( 3 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 4 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 5 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 6 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 7 / 20 )7.28650.0572559053772183127.261982008571
Winsorized Mean ( 8 / 20 )7.28650.0572559053772183127.261982008571
Winsorized Mean ( 9 / 20 )7.28650.0567474457475405128.402255009263
Winsorized Mean ( 10 / 20 )7.284833333333330.0563982467906106129.167726797957
Winsorized Mean ( 11 / 20 )7.284833333333330.0551728110323627132.036653507835
Winsorized Mean ( 12 / 20 )7.284833333333330.0551728110323627132.036653507835
Winsorized Mean ( 13 / 20 )7.28050.0542771840819364134.135551118669
Winsorized Mean ( 14 / 20 )7.28750.0534201050833733136.418675864196
Winsorized Mean ( 15 / 20 )7.24250.0442869590936509163.535725825852
Winsorized Mean ( 16 / 20 )7.191833333333330.034527882507231208.290599107176
Winsorized Mean ( 17 / 20 )7.115333333333330.0215034705734756330.892323126205
Winsorized Mean ( 18 / 20 )7.139333333333330.0178361447702034400.273345238828
Winsorized Mean ( 19 / 20 )7.129833333333330.0164222043199727434.158118752793
Winsorized Mean ( 20 / 20 )7.129833333333330.0164222043199727434.158118752793
Trimmed Mean ( 1 / 20 )7.28482758620690.0586860779046035124.132125476994
Trimmed Mean ( 2 / 20 )7.279464285714290.0584787782813256124.480444011582
Trimmed Mean ( 3 / 20 )7.274074074074070.0583146232459146124.738421843164
Trimmed Mean ( 4 / 20 )7.26750.0581378160589869125.004695611998
Trimmed Mean ( 5 / 20 )7.26040.0578181244092549125.573080659078
Trimmed Mean ( 6 / 20 )7.252708333333330.0573156461744505126.539763876314
Trimmed Mean ( 7 / 20 )7.244347826086960.0565767847901387128.044530154171
Trimmed Mean ( 8 / 20 )7.236136363636360.0558257405649854129.620069351574
Trimmed Mean ( 9 / 20 )7.227142857142860.0547428639320687132.019816612283
Trimmed Mean ( 10 / 20 )7.217250.053348139971901135.285878829166
Trimmed Mean ( 11 / 20 )7.206578947368420.051479223274915139.990048196397
Trimmed Mean ( 12 / 20 )7.194722222222220.0491733023950023146.313586271429
Trimmed Mean ( 13 / 20 )7.18147058823530.0458240694308701156.718307156662
Trimmed Mean ( 14 / 20 )7.16718750.0411924925996544173.992566307098
Trimmed Mean ( 15 / 20 )7.150.0340891326600904209.744262821061
Trimmed Mean ( 16 / 20 )7.136785714285710.0276124615847531258.462494999956
Trimmed Mean ( 17 / 20 )7.128846153846150.0227246184571638313.70586781398
Trimmed Mean ( 18 / 20 )7.130833333333330.0216352894316732329.592694188508
Trimmed Mean ( 19 / 20 )7.129545454545450.021314764030662334.488594116706
Trimmed Mean ( 20 / 20 )7.12950.0211942767845721336.387982117406
Median7.1
Midrange7.435
Midmean - Weighted Average at Xnp7.14225806451613
Midmean - Weighted Average at X(n+1)p7.14225806451613
Midmean - Empirical Distribution Function7.14225806451613
Midmean - Empirical Distribution Function - Averaging7.14225806451613
Midmean - Empirical Distribution Function - Interpolation7.14225806451613
Midmean - Closest Observation7.14225806451613
Midmean - True Basic - Statistics Graphics Toolkit7.14225806451613
Midmean - MS Excel (old versions)7.19060606060606
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.28983333333333 & 0.0587922184725072 & 123.99316648924 \tabularnewline
Geometric Mean & 7.27623539806722 &  &  \tabularnewline
Harmonic Mean & 7.26304176899202 &  &  \tabularnewline
Quadratic Mean & 7.30380756865897 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.28983333333333 & 0.0587922184725072 & 123.99316648924 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.28916666666667 & 0.0585243643631049 & 124.549266719792 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.29116666666667 & 0.0582572182994731 & 125.154734117001 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.29116666666667 & 0.0582572182994731 & 125.154734117001 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.29116666666667 & 0.0582572182994731 & 125.154734117001 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.29116666666667 & 0.0582572182994731 & 125.154734117001 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.2865 & 0.0572559053772183 & 127.261982008571 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.2865 & 0.0572559053772183 & 127.261982008571 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.2865 & 0.0567474457475405 & 128.402255009263 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.28483333333333 & 0.0563982467906106 & 129.167726797957 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.28483333333333 & 0.0551728110323627 & 132.036653507835 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.28483333333333 & 0.0551728110323627 & 132.036653507835 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.2805 & 0.0542771840819364 & 134.135551118669 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.2875 & 0.0534201050833733 & 136.418675864196 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.2425 & 0.0442869590936509 & 163.535725825852 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.19183333333333 & 0.034527882507231 & 208.290599107176 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.11533333333333 & 0.0215034705734756 & 330.892323126205 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.13933333333333 & 0.0178361447702034 & 400.273345238828 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.12983333333333 & 0.0164222043199727 & 434.158118752793 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.12983333333333 & 0.0164222043199727 & 434.158118752793 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.2848275862069 & 0.0586860779046035 & 124.132125476994 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.27946428571429 & 0.0584787782813256 & 124.480444011582 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.27407407407407 & 0.0583146232459146 & 124.738421843164 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.2675 & 0.0581378160589869 & 125.004695611998 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.2604 & 0.0578181244092549 & 125.573080659078 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.25270833333333 & 0.0573156461744505 & 126.539763876314 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.24434782608696 & 0.0565767847901387 & 128.044530154171 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.23613636363636 & 0.0558257405649854 & 129.620069351574 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.22714285714286 & 0.0547428639320687 & 132.019816612283 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.21725 & 0.053348139971901 & 135.285878829166 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.20657894736842 & 0.051479223274915 & 139.990048196397 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.19472222222222 & 0.0491733023950023 & 146.313586271429 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.1814705882353 & 0.0458240694308701 & 156.718307156662 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.1671875 & 0.0411924925996544 & 173.992566307098 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.15 & 0.0340891326600904 & 209.744262821061 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.13678571428571 & 0.0276124615847531 & 258.462494999956 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.12884615384615 & 0.0227246184571638 & 313.70586781398 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.13083333333333 & 0.0216352894316732 & 329.592694188508 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.12954545454545 & 0.021314764030662 & 334.488594116706 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.1295 & 0.0211942767845721 & 336.387982117406 \tabularnewline
Median & 7.1 &  &  \tabularnewline
Midrange & 7.435 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.14225806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.14225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.14225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.14225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.14225806451613 &  &  \tabularnewline
Midmean - Closest Observation & 7.14225806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.14225806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.19060606060606 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163584&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]7.28983333333333[/C][C]0.0587922184725072[/C][C]123.99316648924[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.27623539806722[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.26304176899202[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.30380756865897[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.28983333333333[/C][C]0.0587922184725072[/C][C]123.99316648924[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.28916666666667[/C][C]0.0585243643631049[/C][C]124.549266719792[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.29116666666667[/C][C]0.0582572182994731[/C][C]125.154734117001[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.29116666666667[/C][C]0.0582572182994731[/C][C]125.154734117001[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.29116666666667[/C][C]0.0582572182994731[/C][C]125.154734117001[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.29116666666667[/C][C]0.0582572182994731[/C][C]125.154734117001[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.2865[/C][C]0.0572559053772183[/C][C]127.261982008571[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.2865[/C][C]0.0572559053772183[/C][C]127.261982008571[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.2865[/C][C]0.0567474457475405[/C][C]128.402255009263[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.28483333333333[/C][C]0.0563982467906106[/C][C]129.167726797957[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.28483333333333[/C][C]0.0551728110323627[/C][C]132.036653507835[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.28483333333333[/C][C]0.0551728110323627[/C][C]132.036653507835[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.2805[/C][C]0.0542771840819364[/C][C]134.135551118669[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.2875[/C][C]0.0534201050833733[/C][C]136.418675864196[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.2425[/C][C]0.0442869590936509[/C][C]163.535725825852[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.19183333333333[/C][C]0.034527882507231[/C][C]208.290599107176[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.11533333333333[/C][C]0.0215034705734756[/C][C]330.892323126205[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.13933333333333[/C][C]0.0178361447702034[/C][C]400.273345238828[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.12983333333333[/C][C]0.0164222043199727[/C][C]434.158118752793[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.12983333333333[/C][C]0.0164222043199727[/C][C]434.158118752793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.2848275862069[/C][C]0.0586860779046035[/C][C]124.132125476994[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.27946428571429[/C][C]0.0584787782813256[/C][C]124.480444011582[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.27407407407407[/C][C]0.0583146232459146[/C][C]124.738421843164[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.2675[/C][C]0.0581378160589869[/C][C]125.004695611998[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.2604[/C][C]0.0578181244092549[/C][C]125.573080659078[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.25270833333333[/C][C]0.0573156461744505[/C][C]126.539763876314[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.24434782608696[/C][C]0.0565767847901387[/C][C]128.044530154171[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.23613636363636[/C][C]0.0558257405649854[/C][C]129.620069351574[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.22714285714286[/C][C]0.0547428639320687[/C][C]132.019816612283[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.21725[/C][C]0.053348139971901[/C][C]135.285878829166[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.20657894736842[/C][C]0.051479223274915[/C][C]139.990048196397[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.19472222222222[/C][C]0.0491733023950023[/C][C]146.313586271429[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.1814705882353[/C][C]0.0458240694308701[/C][C]156.718307156662[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.1671875[/C][C]0.0411924925996544[/C][C]173.992566307098[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.15[/C][C]0.0340891326600904[/C][C]209.744262821061[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.13678571428571[/C][C]0.0276124615847531[/C][C]258.462494999956[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.12884615384615[/C][C]0.0227246184571638[/C][C]313.70586781398[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.13083333333333[/C][C]0.0216352894316732[/C][C]329.592694188508[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.12954545454545[/C][C]0.021314764030662[/C][C]334.488594116706[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.1295[/C][C]0.0211942767845721[/C][C]336.387982117406[/C][/ROW]
[ROW][C]Median[/C][C]7.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.14225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.19060606060606[/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=163584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163584&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 Mean7.289833333333330.0587922184725072123.99316648924
Geometric Mean7.27623539806722
Harmonic Mean7.26304176899202
Quadratic Mean7.30380756865897
Winsorized Mean ( 1 / 20 )7.289833333333330.0587922184725072123.99316648924
Winsorized Mean ( 2 / 20 )7.289166666666670.0585243643631049124.549266719792
Winsorized Mean ( 3 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 4 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 5 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 6 / 20 )7.291166666666670.0582572182994731125.154734117001
Winsorized Mean ( 7 / 20 )7.28650.0572559053772183127.261982008571
Winsorized Mean ( 8 / 20 )7.28650.0572559053772183127.261982008571
Winsorized Mean ( 9 / 20 )7.28650.0567474457475405128.402255009263
Winsorized Mean ( 10 / 20 )7.284833333333330.0563982467906106129.167726797957
Winsorized Mean ( 11 / 20 )7.284833333333330.0551728110323627132.036653507835
Winsorized Mean ( 12 / 20 )7.284833333333330.0551728110323627132.036653507835
Winsorized Mean ( 13 / 20 )7.28050.0542771840819364134.135551118669
Winsorized Mean ( 14 / 20 )7.28750.0534201050833733136.418675864196
Winsorized Mean ( 15 / 20 )7.24250.0442869590936509163.535725825852
Winsorized Mean ( 16 / 20 )7.191833333333330.034527882507231208.290599107176
Winsorized Mean ( 17 / 20 )7.115333333333330.0215034705734756330.892323126205
Winsorized Mean ( 18 / 20 )7.139333333333330.0178361447702034400.273345238828
Winsorized Mean ( 19 / 20 )7.129833333333330.0164222043199727434.158118752793
Winsorized Mean ( 20 / 20 )7.129833333333330.0164222043199727434.158118752793
Trimmed Mean ( 1 / 20 )7.28482758620690.0586860779046035124.132125476994
Trimmed Mean ( 2 / 20 )7.279464285714290.0584787782813256124.480444011582
Trimmed Mean ( 3 / 20 )7.274074074074070.0583146232459146124.738421843164
Trimmed Mean ( 4 / 20 )7.26750.0581378160589869125.004695611998
Trimmed Mean ( 5 / 20 )7.26040.0578181244092549125.573080659078
Trimmed Mean ( 6 / 20 )7.252708333333330.0573156461744505126.539763876314
Trimmed Mean ( 7 / 20 )7.244347826086960.0565767847901387128.044530154171
Trimmed Mean ( 8 / 20 )7.236136363636360.0558257405649854129.620069351574
Trimmed Mean ( 9 / 20 )7.227142857142860.0547428639320687132.019816612283
Trimmed Mean ( 10 / 20 )7.217250.053348139971901135.285878829166
Trimmed Mean ( 11 / 20 )7.206578947368420.051479223274915139.990048196397
Trimmed Mean ( 12 / 20 )7.194722222222220.0491733023950023146.313586271429
Trimmed Mean ( 13 / 20 )7.18147058823530.0458240694308701156.718307156662
Trimmed Mean ( 14 / 20 )7.16718750.0411924925996544173.992566307098
Trimmed Mean ( 15 / 20 )7.150.0340891326600904209.744262821061
Trimmed Mean ( 16 / 20 )7.136785714285710.0276124615847531258.462494999956
Trimmed Mean ( 17 / 20 )7.128846153846150.0227246184571638313.70586781398
Trimmed Mean ( 18 / 20 )7.130833333333330.0216352894316732329.592694188508
Trimmed Mean ( 19 / 20 )7.129545454545450.021314764030662334.488594116706
Trimmed Mean ( 20 / 20 )7.12950.0211942767845721336.387982117406
Median7.1
Midrange7.435
Midmean - Weighted Average at Xnp7.14225806451613
Midmean - Weighted Average at X(n+1)p7.14225806451613
Midmean - Empirical Distribution Function7.14225806451613
Midmean - Empirical Distribution Function - Averaging7.14225806451613
Midmean - Empirical Distribution Function - Interpolation7.14225806451613
Midmean - Closest Observation7.14225806451613
Midmean - True Basic - Statistics Graphics Toolkit7.14225806451613
Midmean - MS Excel (old versions)7.19060606060606
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')