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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 03:13:11 -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/t1331108387zc3n7mc4355iezs.htm/, Retrieved Mon, 29 Apr 2024 01:51:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163561, Retrieved Mon, 29 Apr 2024 01:51:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 08:13:11] [426bb746e0076029d53908613853082a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,07
2,08
2,08
2,08
2,09
2,09
2,09
2,1
2,1
2,1
2,11
2,11
2,11
2,13
2,18
2,2
2,21
2,21
2,22
2,22
2,23
2,23
2,23
2,23
2,24
2,25
2,26
2,27
2,28
2,29
2,3
2,3
2,3
2,32
2,32
2,32
2,33
2,34
2,34
2,34
2,35
2,35
2,36
2,37
2,37
2,37
2,38
2,38
2,38
2,39
2,4
2,41
2,42
2,43
2,43
2,43
2,43
2,44
2,44
2,45

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163561&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163561&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.271333333333330.0154379872423241147.126260546864
Geometric Mean2.26820126705323
Harmonic Mean2.26503550908813
Quadratic Mean2.2744266676828
Winsorized Mean ( 1 / 20 )2.271333333333330.0153701351527544147.775755434805
Winsorized Mean ( 2 / 20 )2.271333333333330.0153701351527544147.775755434805
Winsorized Mean ( 3 / 20 )2.270833333333330.0152794897174731148.619710168494
Winsorized Mean ( 4 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 5 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 6 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 7 / 20 )2.27150.0147039043202779154.482778894815
Winsorized Mean ( 8 / 20 )2.270166666666670.0144806351631042156.772589123087
Winsorized Mean ( 9 / 20 )2.268666666666670.0142406013542378159.309751760697
Winsorized Mean ( 10 / 20 )2.268666666666670.0136532247523931166.163430823844
Winsorized Mean ( 11 / 20 )2.266833333333330.0133837148421325169.37250681681
Winsorized Mean ( 12 / 20 )2.266833333333330.0133837148421325169.37250681681
Winsorized Mean ( 13 / 20 )2.271166666666670.0125394105653256181.122282808649
Winsorized Mean ( 14 / 20 )2.28050.0100799767957764226.24060017237
Winsorized Mean ( 15 / 20 )2.28550.00926516164667314246.676753969064
Winsorized Mean ( 16 / 20 )2.288166666666670.00885696657292004258.346539735476
Winsorized Mean ( 17 / 20 )2.285333333333330.00842201401985648271.352354430334
Winsorized Mean ( 18 / 20 )2.285333333333330.00752947753931611303.518181892459
Winsorized Mean ( 19 / 20 )2.285333333333330.00752947753931611303.518181892459
Winsorized Mean ( 20 / 20 )2.285333333333330.00656762590143253347.96947445421
Trimmed Mean ( 1 / 20 )2.271724137931030.0152735451533292148.735877304547
Trimmed Mean ( 2 / 20 )2.272142857142860.0151415706388082150.059918574055
Trimmed Mean ( 3 / 20 )2.272592592592590.0149660346529889151.850015403962
Trimmed Mean ( 4 / 20 )2.273269230769230.0147776918872601153.831142786853
Trimmed Mean ( 5 / 20 )2.27380.0145823208589255155.928539907848
Trimmed Mean ( 6 / 20 )2.2743750.0143224834718501158.79753008409
Trimmed Mean ( 7 / 20 )2.2750.0139797990904267162.734813661085
Trimmed Mean ( 8 / 20 )2.275681818181820.013656917209274166.632174985762
Trimmed Mean ( 9 / 20 )2.276666666666670.0132853375408141171.366866643206
Trimmed Mean ( 10 / 20 )2.2780.0128462306154623177.328281593987
Trimmed Mean ( 11 / 20 )2.279473684210530.0124115497558913183.657458499777
Trimmed Mean ( 12 / 20 )2.281388888888890.0118733580504126192.143526641952
Trimmed Mean ( 13 / 20 )2.283529411764710.0111054125402908205.62310526331
Trimmed Mean ( 14 / 20 )2.28531250.010307611255688221.711165013028
Trimmed Mean ( 15 / 20 )2.2860.0100068941752415228.442507731908
Trimmed Mean ( 16 / 20 )2.286071428571430.00980415749349317233.173674544564
Trimmed Mean ( 17 / 20 )2.285769230769230.00959443872448356238.238973264407
Trimmed Mean ( 18 / 20 )2.285833333333330.00938153958709094243.652261136184
Trimmed Mean ( 19 / 20 )2.285909090909090.00932016133551091245.264970060068
Trimmed Mean ( 20 / 20 )2.2860.00913063092303217250.366050196326
Median2.295
Midrange2.26
Midmean - Weighted Average at Xnp2.2853125
Midmean - Weighted Average at X(n+1)p2.28870967741936
Midmean - Empirical Distribution Function2.2853125
Midmean - Empirical Distribution Function - Averaging2.28870967741936
Midmean - Empirical Distribution Function - Interpolation2.28870967741936
Midmean - Closest Observation2.2853125
Midmean - True Basic - Statistics Graphics Toolkit2.28870967741936
Midmean - MS Excel (old versions)2.2853125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.27133333333333 & 0.0154379872423241 & 147.126260546864 \tabularnewline
Geometric Mean & 2.26820126705323 &  &  \tabularnewline
Harmonic Mean & 2.26503550908813 &  &  \tabularnewline
Quadratic Mean & 2.2744266676828 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.27133333333333 & 0.0153701351527544 & 147.775755434805 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.27133333333333 & 0.0153701351527544 & 147.775755434805 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.27083333333333 & 0.0152794897174731 & 148.619710168494 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.2715 & 0.0151411904986865 & 150.021228528698 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.2715 & 0.0151411904986865 & 150.021228528698 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.2715 & 0.0151411904986865 & 150.021228528698 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.2715 & 0.0147039043202779 & 154.482778894815 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.27016666666667 & 0.0144806351631042 & 156.772589123087 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.26866666666667 & 0.0142406013542378 & 159.309751760697 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.26866666666667 & 0.0136532247523931 & 166.163430823844 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.26683333333333 & 0.0133837148421325 & 169.37250681681 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.26683333333333 & 0.0133837148421325 & 169.37250681681 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.27116666666667 & 0.0125394105653256 & 181.122282808649 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.2805 & 0.0100799767957764 & 226.24060017237 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.2855 & 0.00926516164667314 & 246.676753969064 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.28816666666667 & 0.00885696657292004 & 258.346539735476 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.28533333333333 & 0.00842201401985648 & 271.352354430334 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.28533333333333 & 0.00752947753931611 & 303.518181892459 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.28533333333333 & 0.00752947753931611 & 303.518181892459 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.28533333333333 & 0.00656762590143253 & 347.96947445421 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.27172413793103 & 0.0152735451533292 & 148.735877304547 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.27214285714286 & 0.0151415706388082 & 150.059918574055 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.27259259259259 & 0.0149660346529889 & 151.850015403962 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.27326923076923 & 0.0147776918872601 & 153.831142786853 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.2738 & 0.0145823208589255 & 155.928539907848 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.274375 & 0.0143224834718501 & 158.79753008409 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.275 & 0.0139797990904267 & 162.734813661085 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.27568181818182 & 0.013656917209274 & 166.632174985762 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.27666666666667 & 0.0132853375408141 & 171.366866643206 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.278 & 0.0128462306154623 & 177.328281593987 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.27947368421053 & 0.0124115497558913 & 183.657458499777 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.28138888888889 & 0.0118733580504126 & 192.143526641952 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.28352941176471 & 0.0111054125402908 & 205.62310526331 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.2853125 & 0.010307611255688 & 221.711165013028 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.286 & 0.0100068941752415 & 228.442507731908 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.28607142857143 & 0.00980415749349317 & 233.173674544564 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.28576923076923 & 0.00959443872448356 & 238.238973264407 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.28583333333333 & 0.00938153958709094 & 243.652261136184 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.28590909090909 & 0.00932016133551091 & 245.264970060068 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.286 & 0.00913063092303217 & 250.366050196326 \tabularnewline
Median & 2.295 &  &  \tabularnewline
Midrange & 2.26 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.2853125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.28870967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.2853125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.28870967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.28870967741936 &  &  \tabularnewline
Midmean - Closest Observation & 2.2853125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.28870967741936 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.2853125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163561&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]2.27133333333333[/C][C]0.0154379872423241[/C][C]147.126260546864[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.26820126705323[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.26503550908813[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.2744266676828[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.27133333333333[/C][C]0.0153701351527544[/C][C]147.775755434805[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.27133333333333[/C][C]0.0153701351527544[/C][C]147.775755434805[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.27083333333333[/C][C]0.0152794897174731[/C][C]148.619710168494[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.2715[/C][C]0.0151411904986865[/C][C]150.021228528698[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.2715[/C][C]0.0151411904986865[/C][C]150.021228528698[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.2715[/C][C]0.0151411904986865[/C][C]150.021228528698[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.2715[/C][C]0.0147039043202779[/C][C]154.482778894815[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.27016666666667[/C][C]0.0144806351631042[/C][C]156.772589123087[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.26866666666667[/C][C]0.0142406013542378[/C][C]159.309751760697[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.26866666666667[/C][C]0.0136532247523931[/C][C]166.163430823844[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.26683333333333[/C][C]0.0133837148421325[/C][C]169.37250681681[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.26683333333333[/C][C]0.0133837148421325[/C][C]169.37250681681[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.27116666666667[/C][C]0.0125394105653256[/C][C]181.122282808649[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.2805[/C][C]0.0100799767957764[/C][C]226.24060017237[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.2855[/C][C]0.00926516164667314[/C][C]246.676753969064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.28816666666667[/C][C]0.00885696657292004[/C][C]258.346539735476[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.28533333333333[/C][C]0.00842201401985648[/C][C]271.352354430334[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.28533333333333[/C][C]0.00752947753931611[/C][C]303.518181892459[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.28533333333333[/C][C]0.00752947753931611[/C][C]303.518181892459[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.28533333333333[/C][C]0.00656762590143253[/C][C]347.96947445421[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.27172413793103[/C][C]0.0152735451533292[/C][C]148.735877304547[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.27214285714286[/C][C]0.0151415706388082[/C][C]150.059918574055[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.27259259259259[/C][C]0.0149660346529889[/C][C]151.850015403962[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.27326923076923[/C][C]0.0147776918872601[/C][C]153.831142786853[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.2738[/C][C]0.0145823208589255[/C][C]155.928539907848[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.274375[/C][C]0.0143224834718501[/C][C]158.79753008409[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.275[/C][C]0.0139797990904267[/C][C]162.734813661085[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.27568181818182[/C][C]0.013656917209274[/C][C]166.632174985762[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.27666666666667[/C][C]0.0132853375408141[/C][C]171.366866643206[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.278[/C][C]0.0128462306154623[/C][C]177.328281593987[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.27947368421053[/C][C]0.0124115497558913[/C][C]183.657458499777[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.28138888888889[/C][C]0.0118733580504126[/C][C]192.143526641952[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.28352941176471[/C][C]0.0111054125402908[/C][C]205.62310526331[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.2853125[/C][C]0.010307611255688[/C][C]221.711165013028[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.286[/C][C]0.0100068941752415[/C][C]228.442507731908[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.28607142857143[/C][C]0.00980415749349317[/C][C]233.173674544564[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.28576923076923[/C][C]0.00959443872448356[/C][C]238.238973264407[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.28583333333333[/C][C]0.00938153958709094[/C][C]243.652261136184[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.28590909090909[/C][C]0.00932016133551091[/C][C]245.264970060068[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.286[/C][C]0.00913063092303217[/C][C]250.366050196326[/C][/ROW]
[ROW][C]Median[/C][C]2.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.2853125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.28870967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.2853125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.28870967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.28870967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.2853125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.28870967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.2853125[/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=163561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163561&T=1

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.271333333333330.0154379872423241147.126260546864
Geometric Mean2.26820126705323
Harmonic Mean2.26503550908813
Quadratic Mean2.2744266676828
Winsorized Mean ( 1 / 20 )2.271333333333330.0153701351527544147.775755434805
Winsorized Mean ( 2 / 20 )2.271333333333330.0153701351527544147.775755434805
Winsorized Mean ( 3 / 20 )2.270833333333330.0152794897174731148.619710168494
Winsorized Mean ( 4 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 5 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 6 / 20 )2.27150.0151411904986865150.021228528698
Winsorized Mean ( 7 / 20 )2.27150.0147039043202779154.482778894815
Winsorized Mean ( 8 / 20 )2.270166666666670.0144806351631042156.772589123087
Winsorized Mean ( 9 / 20 )2.268666666666670.0142406013542378159.309751760697
Winsorized Mean ( 10 / 20 )2.268666666666670.0136532247523931166.163430823844
Winsorized Mean ( 11 / 20 )2.266833333333330.0133837148421325169.37250681681
Winsorized Mean ( 12 / 20 )2.266833333333330.0133837148421325169.37250681681
Winsorized Mean ( 13 / 20 )2.271166666666670.0125394105653256181.122282808649
Winsorized Mean ( 14 / 20 )2.28050.0100799767957764226.24060017237
Winsorized Mean ( 15 / 20 )2.28550.00926516164667314246.676753969064
Winsorized Mean ( 16 / 20 )2.288166666666670.00885696657292004258.346539735476
Winsorized Mean ( 17 / 20 )2.285333333333330.00842201401985648271.352354430334
Winsorized Mean ( 18 / 20 )2.285333333333330.00752947753931611303.518181892459
Winsorized Mean ( 19 / 20 )2.285333333333330.00752947753931611303.518181892459
Winsorized Mean ( 20 / 20 )2.285333333333330.00656762590143253347.96947445421
Trimmed Mean ( 1 / 20 )2.271724137931030.0152735451533292148.735877304547
Trimmed Mean ( 2 / 20 )2.272142857142860.0151415706388082150.059918574055
Trimmed Mean ( 3 / 20 )2.272592592592590.0149660346529889151.850015403962
Trimmed Mean ( 4 / 20 )2.273269230769230.0147776918872601153.831142786853
Trimmed Mean ( 5 / 20 )2.27380.0145823208589255155.928539907848
Trimmed Mean ( 6 / 20 )2.2743750.0143224834718501158.79753008409
Trimmed Mean ( 7 / 20 )2.2750.0139797990904267162.734813661085
Trimmed Mean ( 8 / 20 )2.275681818181820.013656917209274166.632174985762
Trimmed Mean ( 9 / 20 )2.276666666666670.0132853375408141171.366866643206
Trimmed Mean ( 10 / 20 )2.2780.0128462306154623177.328281593987
Trimmed Mean ( 11 / 20 )2.279473684210530.0124115497558913183.657458499777
Trimmed Mean ( 12 / 20 )2.281388888888890.0118733580504126192.143526641952
Trimmed Mean ( 13 / 20 )2.283529411764710.0111054125402908205.62310526331
Trimmed Mean ( 14 / 20 )2.28531250.010307611255688221.711165013028
Trimmed Mean ( 15 / 20 )2.2860.0100068941752415228.442507731908
Trimmed Mean ( 16 / 20 )2.286071428571430.00980415749349317233.173674544564
Trimmed Mean ( 17 / 20 )2.285769230769230.00959443872448356238.238973264407
Trimmed Mean ( 18 / 20 )2.285833333333330.00938153958709094243.652261136184
Trimmed Mean ( 19 / 20 )2.285909090909090.00932016133551091245.264970060068
Trimmed Mean ( 20 / 20 )2.2860.00913063092303217250.366050196326
Median2.295
Midrange2.26
Midmean - Weighted Average at Xnp2.2853125
Midmean - Weighted Average at X(n+1)p2.28870967741936
Midmean - Empirical Distribution Function2.2853125
Midmean - Empirical Distribution Function - Averaging2.28870967741936
Midmean - Empirical Distribution Function - Interpolation2.28870967741936
Midmean - Closest Observation2.2853125
Midmean - True Basic - Statistics Graphics Toolkit2.28870967741936
Midmean - MS Excel (old versions)2.2853125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')