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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 30 Dec 2009 12:00:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/30/t12621996849ogrf5f6xi9zibe.htm/, Retrieved Mon, 29 Apr 2024 01:58:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71353, Retrieved Mon, 29 Apr 2024 01:58:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [CT Werkloosheid] [2009-12-30 19:00:08] [d17577076e7e93abbeb88e2adc301f5b] [Current]
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Dataseries X:
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71353&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71353&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.8450.088439867534339588.7043391031079
Geometric Mean7.81448062969416
Harmonic Mean7.78281507436112
Quadratic Mean7.87435711661593
Winsorized Mean ( 1 / 20 )7.840.084612777013275692.6574008884015
Winsorized Mean ( 2 / 20 )7.843333333333330.083678381694966593.7318955560673
Winsorized Mean ( 3 / 20 )7.848333333333330.08235556322876495.298156258522
Winsorized Mean ( 4 / 20 )7.861666666666670.079122720481678699.3604190908361
Winsorized Mean ( 5 / 20 )7.870.0772880736445385101.826836003127
Winsorized Mean ( 6 / 20 )7.860.0755469697126785104.041234610644
Winsorized Mean ( 7 / 20 )7.871666666666670.0731105372647043107.668018334573
Winsorized Mean ( 8 / 20 )7.871666666666670.0731105372647043107.668018334573
Winsorized Mean ( 9 / 20 )7.856666666666670.0706853722178386111.149823791745
Winsorized Mean ( 10 / 20 )7.873333333333330.0673496092651862116.902435206898
Winsorized Mean ( 11 / 20 )7.891666666666670.0638807003677378123.537572713468
Winsorized Mean ( 12 / 20 )7.891666666666670.0638807003677378123.537572713468
Winsorized Mean ( 13 / 20 )7.913333333333330.0600125536145322131.861299956699
Winsorized Mean ( 14 / 20 )7.890.0562831823031489140.183971075114
Winsorized Mean ( 15 / 20 )7.8650.0526058255458075149.508156528242
Winsorized Mean ( 16 / 20 )7.891666666666670.0478516815534762164.919317576069
Winsorized Mean ( 17 / 20 )7.920.0430346070172593184.037930143608
Winsorized Mean ( 18 / 20 )7.890.0387444182238271203.642237042233
Winsorized Mean ( 19 / 20 )7.953333333333330.0284700920153008279.357486061476
Winsorized Mean ( 20 / 20 )7.953333333333330.0284700920153008279.357486061476
Trimmed Mean ( 1 / 20 )7.850.082543138000526695.1017878669686
Trimmed Mean ( 2 / 20 )7.860714285714290.07996259561562698.3048914957705
Trimmed Mean ( 3 / 20 )7.870370370370370.0773707361669893101.722831658002
Trimmed Mean ( 4 / 20 )7.878846153846150.0747714737822195105.372353322795
Trimmed Mean ( 5 / 20 )7.8840.0728072658405991108.285895768437
Trimmed Mean ( 6 / 20 )7.88750.0709375536991705111.189343143253
Trimmed Mean ( 7 / 20 )7.893478260869570.0690447011902062114.324171512082
Trimmed Mean ( 8 / 20 )7.897727272727270.0673013980958948117.348636078468
Trimmed Mean ( 9 / 20 )7.902380952380950.0649745858686673121.622644403675
Trimmed Mean ( 10 / 20 )7.910.0625115373966463126.536641545219
Trimmed Mean ( 11 / 20 )7.915789473684210.0601712014344846131.554452711120
Trimmed Mean ( 12 / 20 )7.919444444444440.057984596263836136.578418316653
Trimmed Mean ( 13 / 20 )7.92352941176470.0548955942323373144.338166342267
Trimmed Mean ( 14 / 20 )7.9250.0517827346989634153.043288386981
Trimmed Mean ( 15 / 20 )7.930.048459012186269163.643451284527
Trimmed Mean ( 16 / 20 )7.939285714285710.0446441798745841177.834730900848
Trimmed Mean ( 17 / 20 )7.946153846153850.0408489786072361194.525153800204
Trimmed Mean ( 18 / 20 )7.950.0371054119260640214.254460126763
Trimmed Mean ( 19 / 20 )7.959090909090910.0326725131103754243.602041942817
Trimmed Mean ( 20 / 20 )7.960.0311194642086199255.788465593027
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.890625
Midmean - Weighted Average at X(n+1)p7.890625
Midmean - Empirical Distribution Function7.890625
Midmean - Empirical Distribution Function - Averaging7.890625
Midmean - Empirical Distribution Function - Interpolation7.890625
Midmean - Closest Observation7.890625
Midmean - True Basic - Statistics Graphics Toolkit7.890625
Midmean - MS Excel (old versions)7.9060606060606
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.845 & 0.0884398675343395 & 88.7043391031079 \tabularnewline
Geometric Mean & 7.81448062969416 &  &  \tabularnewline
Harmonic Mean & 7.78281507436112 &  &  \tabularnewline
Quadratic Mean & 7.87435711661593 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.84 & 0.0846127770132756 & 92.6574008884015 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.84333333333333 & 0.0836783816949665 & 93.7318955560673 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.84833333333333 & 0.082355563228764 & 95.298156258522 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.86166666666667 & 0.0791227204816786 & 99.3604190908361 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.87 & 0.0772880736445385 & 101.826836003127 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.86 & 0.0755469697126785 & 104.041234610644 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.87166666666667 & 0.0731105372647043 & 107.668018334573 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.87166666666667 & 0.0731105372647043 & 107.668018334573 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.85666666666667 & 0.0706853722178386 & 111.149823791745 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.87333333333333 & 0.0673496092651862 & 116.902435206898 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.89166666666667 & 0.0638807003677378 & 123.537572713468 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.89166666666667 & 0.0638807003677378 & 123.537572713468 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.91333333333333 & 0.0600125536145322 & 131.861299956699 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.89 & 0.0562831823031489 & 140.183971075114 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.865 & 0.0526058255458075 & 149.508156528242 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.89166666666667 & 0.0478516815534762 & 164.919317576069 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.92 & 0.0430346070172593 & 184.037930143608 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.89 & 0.0387444182238271 & 203.642237042233 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.95333333333333 & 0.0284700920153008 & 279.357486061476 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.95333333333333 & 0.0284700920153008 & 279.357486061476 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.85 & 0.0825431380005266 & 95.1017878669686 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.86071428571429 & 0.079962595615626 & 98.3048914957705 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.87037037037037 & 0.0773707361669893 & 101.722831658002 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.87884615384615 & 0.0747714737822195 & 105.372353322795 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.884 & 0.0728072658405991 & 108.285895768437 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.8875 & 0.0709375536991705 & 111.189343143253 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.89347826086957 & 0.0690447011902062 & 114.324171512082 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.89772727272727 & 0.0673013980958948 & 117.348636078468 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.90238095238095 & 0.0649745858686673 & 121.622644403675 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.91 & 0.0625115373966463 & 126.536641545219 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.91578947368421 & 0.0601712014344846 & 131.554452711120 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.91944444444444 & 0.057984596263836 & 136.578418316653 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.9235294117647 & 0.0548955942323373 & 144.338166342267 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.925 & 0.0517827346989634 & 153.043288386981 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.93 & 0.048459012186269 & 163.643451284527 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.93928571428571 & 0.0446441798745841 & 177.834730900848 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.94615384615385 & 0.0408489786072361 & 194.525153800204 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.95 & 0.0371054119260640 & 214.254460126763 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.95909090909091 & 0.0326725131103754 & 243.602041942817 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.96 & 0.0311194642086199 & 255.788465593027 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.890625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.890625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.890625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.890625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.890625 &  &  \tabularnewline
Midmean - Closest Observation & 7.890625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.890625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.9060606060606 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71353&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]7.845[/C][C]0.0884398675343395[/C][C]88.7043391031079[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.81448062969416[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.78281507436112[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.87435711661593[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.84[/C][C]0.0846127770132756[/C][C]92.6574008884015[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.84333333333333[/C][C]0.0836783816949665[/C][C]93.7318955560673[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.84833333333333[/C][C]0.082355563228764[/C][C]95.298156258522[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.86166666666667[/C][C]0.0791227204816786[/C][C]99.3604190908361[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.87[/C][C]0.0772880736445385[/C][C]101.826836003127[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.86[/C][C]0.0755469697126785[/C][C]104.041234610644[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.87166666666667[/C][C]0.0731105372647043[/C][C]107.668018334573[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.87166666666667[/C][C]0.0731105372647043[/C][C]107.668018334573[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.85666666666667[/C][C]0.0706853722178386[/C][C]111.149823791745[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.87333333333333[/C][C]0.0673496092651862[/C][C]116.902435206898[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.89166666666667[/C][C]0.0638807003677378[/C][C]123.537572713468[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.89166666666667[/C][C]0.0638807003677378[/C][C]123.537572713468[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.91333333333333[/C][C]0.0600125536145322[/C][C]131.861299956699[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.89[/C][C]0.0562831823031489[/C][C]140.183971075114[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.865[/C][C]0.0526058255458075[/C][C]149.508156528242[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.89166666666667[/C][C]0.0478516815534762[/C][C]164.919317576069[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.92[/C][C]0.0430346070172593[/C][C]184.037930143608[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.89[/C][C]0.0387444182238271[/C][C]203.642237042233[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.95333333333333[/C][C]0.0284700920153008[/C][C]279.357486061476[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.95333333333333[/C][C]0.0284700920153008[/C][C]279.357486061476[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.85[/C][C]0.0825431380005266[/C][C]95.1017878669686[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.86071428571429[/C][C]0.079962595615626[/C][C]98.3048914957705[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.87037037037037[/C][C]0.0773707361669893[/C][C]101.722831658002[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.87884615384615[/C][C]0.0747714737822195[/C][C]105.372353322795[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.884[/C][C]0.0728072658405991[/C][C]108.285895768437[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.8875[/C][C]0.0709375536991705[/C][C]111.189343143253[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.89347826086957[/C][C]0.0690447011902062[/C][C]114.324171512082[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.89772727272727[/C][C]0.0673013980958948[/C][C]117.348636078468[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.90238095238095[/C][C]0.0649745858686673[/C][C]121.622644403675[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.91[/C][C]0.0625115373966463[/C][C]126.536641545219[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.91578947368421[/C][C]0.0601712014344846[/C][C]131.554452711120[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.91944444444444[/C][C]0.057984596263836[/C][C]136.578418316653[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.9235294117647[/C][C]0.0548955942323373[/C][C]144.338166342267[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.925[/C][C]0.0517827346989634[/C][C]153.043288386981[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.93[/C][C]0.048459012186269[/C][C]163.643451284527[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.93928571428571[/C][C]0.0446441798745841[/C][C]177.834730900848[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.94615384615385[/C][C]0.0408489786072361[/C][C]194.525153800204[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.95[/C][C]0.0371054119260640[/C][C]214.254460126763[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.95909090909091[/C][C]0.0326725131103754[/C][C]243.602041942817[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.96[/C][C]0.0311194642086199[/C][C]255.788465593027[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.890625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.9060606060606[/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=71353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71353&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 Mean7.8450.088439867534339588.7043391031079
Geometric Mean7.81448062969416
Harmonic Mean7.78281507436112
Quadratic Mean7.87435711661593
Winsorized Mean ( 1 / 20 )7.840.084612777013275692.6574008884015
Winsorized Mean ( 2 / 20 )7.843333333333330.083678381694966593.7318955560673
Winsorized Mean ( 3 / 20 )7.848333333333330.08235556322876495.298156258522
Winsorized Mean ( 4 / 20 )7.861666666666670.079122720481678699.3604190908361
Winsorized Mean ( 5 / 20 )7.870.0772880736445385101.826836003127
Winsorized Mean ( 6 / 20 )7.860.0755469697126785104.041234610644
Winsorized Mean ( 7 / 20 )7.871666666666670.0731105372647043107.668018334573
Winsorized Mean ( 8 / 20 )7.871666666666670.0731105372647043107.668018334573
Winsorized Mean ( 9 / 20 )7.856666666666670.0706853722178386111.149823791745
Winsorized Mean ( 10 / 20 )7.873333333333330.0673496092651862116.902435206898
Winsorized Mean ( 11 / 20 )7.891666666666670.0638807003677378123.537572713468
Winsorized Mean ( 12 / 20 )7.891666666666670.0638807003677378123.537572713468
Winsorized Mean ( 13 / 20 )7.913333333333330.0600125536145322131.861299956699
Winsorized Mean ( 14 / 20 )7.890.0562831823031489140.183971075114
Winsorized Mean ( 15 / 20 )7.8650.0526058255458075149.508156528242
Winsorized Mean ( 16 / 20 )7.891666666666670.0478516815534762164.919317576069
Winsorized Mean ( 17 / 20 )7.920.0430346070172593184.037930143608
Winsorized Mean ( 18 / 20 )7.890.0387444182238271203.642237042233
Winsorized Mean ( 19 / 20 )7.953333333333330.0284700920153008279.357486061476
Winsorized Mean ( 20 / 20 )7.953333333333330.0284700920153008279.357486061476
Trimmed Mean ( 1 / 20 )7.850.082543138000526695.1017878669686
Trimmed Mean ( 2 / 20 )7.860714285714290.07996259561562698.3048914957705
Trimmed Mean ( 3 / 20 )7.870370370370370.0773707361669893101.722831658002
Trimmed Mean ( 4 / 20 )7.878846153846150.0747714737822195105.372353322795
Trimmed Mean ( 5 / 20 )7.8840.0728072658405991108.285895768437
Trimmed Mean ( 6 / 20 )7.88750.0709375536991705111.189343143253
Trimmed Mean ( 7 / 20 )7.893478260869570.0690447011902062114.324171512082
Trimmed Mean ( 8 / 20 )7.897727272727270.0673013980958948117.348636078468
Trimmed Mean ( 9 / 20 )7.902380952380950.0649745858686673121.622644403675
Trimmed Mean ( 10 / 20 )7.910.0625115373966463126.536641545219
Trimmed Mean ( 11 / 20 )7.915789473684210.0601712014344846131.554452711120
Trimmed Mean ( 12 / 20 )7.919444444444440.057984596263836136.578418316653
Trimmed Mean ( 13 / 20 )7.92352941176470.0548955942323373144.338166342267
Trimmed Mean ( 14 / 20 )7.9250.0517827346989634153.043288386981
Trimmed Mean ( 15 / 20 )7.930.048459012186269163.643451284527
Trimmed Mean ( 16 / 20 )7.939285714285710.0446441798745841177.834730900848
Trimmed Mean ( 17 / 20 )7.946153846153850.0408489786072361194.525153800204
Trimmed Mean ( 18 / 20 )7.950.0371054119260640214.254460126763
Trimmed Mean ( 19 / 20 )7.959090909090910.0326725131103754243.602041942817
Trimmed Mean ( 20 / 20 )7.960.0311194642086199255.788465593027
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.890625
Midmean - Weighted Average at X(n+1)p7.890625
Midmean - Empirical Distribution Function7.890625
Midmean - Empirical Distribution Function - Averaging7.890625
Midmean - Empirical Distribution Function - Interpolation7.890625
Midmean - Closest Observation7.890625
Midmean - True Basic - Statistics Graphics Toolkit7.890625
Midmean - MS Excel (old versions)7.9060606060606
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')