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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 computationMon, 27 Oct 2008 15:47:23 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/27/t1225144099as1fafycyjbznoe.htm/, Retrieved Tue, 28 May 2024 23:18:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19661, Retrieved Tue, 28 May 2024 23:18:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmedian
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q6 Distributions] [2007-10-22 19:20:42] [b731da8b544846036771bbf9bf2f34ce]
-   PD  [Central Tendency] [Q6 1] [2008-10-27 18:16:38] [fe7291e888d31b8c4db0b24d6c0f75c6]
-   PD      [Central Tendency] [median] [2008-10-27 21:47:23] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
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Dataseries X:
7,6
7,9
7,9
8,1
8,2
8
7,5
6,8
6,5
6,6
7,6
8
8
7,7
7,5
7,6
7,7
7,9
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,1
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,7
6,4
6,3
6,2
6,5
6,8
6,8
6,5
6,3
5,9
5,9
6,4
6,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19661&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19661&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.218333333333330.083783810669604686.1542734287691
Geometric Mean7.18917406813762
Harmonic Mean7.15961140233399
Quadratic Mean7.24696488193506
Winsorized Mean ( 1 / 20 )7.218333333333330.083783810669604686.154273428769
Winsorized Mean ( 2 / 20 )7.228333333333330.0813755910413388.8267997913786
Winsorized Mean ( 3 / 20 )7.228333333333330.079372242749091591.0687802558794
Winsorized Mean ( 4 / 20 )7.228333333333330.079372242749091591.0687802558794
Winsorized Mean ( 5 / 20 )7.236666666666670.077785982887085693.0330426906276
Winsorized Mean ( 6 / 20 )7.226666666666670.075981958409654695.1102974696217
Winsorized Mean ( 7 / 20 )7.226666666666670.075981958409654695.1102974696217
Winsorized Mean ( 8 / 20 )7.226666666666670.075981958409654695.1102974696216
Winsorized Mean ( 9 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 10 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 11 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 12 / 20 )7.246666666666670.0674166849985659107.490700066620
Winsorized Mean ( 13 / 20 )7.246666666666670.0674166849985659107.490700066620
Winsorized Mean ( 14 / 20 )7.246666666666670.0599654640090692120.847337486969
Winsorized Mean ( 15 / 20 )7.221666666666670.0562024019163559128.493915214058
Winsorized Mean ( 16 / 20 )7.221666666666670.0562024019163559128.493915214058
Winsorized Mean ( 17 / 20 )7.250.0518853581994018139.731135171841
Winsorized Mean ( 18 / 20 )7.250.0518853581994018139.731135171841
Winsorized Mean ( 19 / 20 )7.218333333333330.0473889821676423152.320919402698
Winsorized Mean ( 20 / 20 )7.218333333333330.0473889821676423152.320919402698
Trimmed Mean ( 1 / 20 )7.224137931034480.081846149357903188.2648479825754
Trimmed Mean ( 2 / 20 )7.230357142857140.079442850603810691.0133144506062
Trimmed Mean ( 3 / 20 )7.231481481481480.078053900729598692.6472785329901
Trimmed Mean ( 4 / 20 )7.23269230769230.07722179930843793.6612766403396
Trimmed Mean ( 5 / 20 )7.2340.076110017040318495.0466217366352
Trimmed Mean ( 6 / 20 )7.233333333333330.075167268164472396.2298286204334
Trimmed Mean ( 7 / 20 )7.234782608695650.074419972340318797.2156046445619
Trimmed Mean ( 8 / 20 )7.236363636363640.073358780435084598.6434560859027
Trimmed Mean ( 9 / 20 )7.238095238095240.0718877998007329100.686003162687
Trimmed Mean ( 10 / 20 )7.240.0712345349838053101.636095492811
Trimmed Mean ( 11 / 20 )7.24210526315790.0702192845480333103.135560405831
Trimmed Mean ( 12 / 20 )7.244444444444440.0687120105076766105.431996399452
Trimmed Mean ( 13 / 20 )7.244117647058820.0674452542858201107.407373932636
Trimmed Mean ( 14 / 20 )7.243750.0655217121118223110.554956006606
Trimmed Mean ( 15 / 20 )7.243333333333330.0648044509137879111.772158103298
Trimmed Mean ( 16 / 20 )7.246428571428570.064546063051746112.267553260672
Trimmed Mean ( 17 / 20 )7.250.0637905225659013113.653246726582
Trimmed Mean ( 18 / 20 )7.250.0637022057270606113.810815767722
Trimmed Mean ( 19 / 20 )7.250.0630227060023724115.037903953649
Trimmed Mean ( 20 / 20 )7.2550.0630267278307595115.109894638371
Median7.25
Midrange7.05
Midmean - Weighted Average at Xnp7.2258064516129
Midmean - Weighted Average at X(n+1)p7.2258064516129
Midmean - Empirical Distribution Function7.2258064516129
Midmean - Empirical Distribution Function - Averaging7.2258064516129
Midmean - Empirical Distribution Function - Interpolation7.2258064516129
Midmean - Closest Observation7.2258064516129
Midmean - True Basic - Statistics Graphics Toolkit7.2258064516129
Midmean - MS Excel (old versions)7.24375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.21833333333333 & 0.0837838106696046 & 86.1542734287691 \tabularnewline
Geometric Mean & 7.18917406813762 &  &  \tabularnewline
Harmonic Mean & 7.15961140233399 &  &  \tabularnewline
Quadratic Mean & 7.24696488193506 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.21833333333333 & 0.0837838106696046 & 86.154273428769 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.22833333333333 & 0.08137559104133 & 88.8267997913786 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.22833333333333 & 0.0793722427490915 & 91.0687802558794 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.22833333333333 & 0.0793722427490915 & 91.0687802558794 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.23666666666667 & 0.0777859828870856 & 93.0330426906276 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.22666666666667 & 0.0759819584096546 & 95.1102974696217 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.22666666666667 & 0.0759819584096546 & 95.1102974696217 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.22666666666667 & 0.0759819584096546 & 95.1102974696216 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.22666666666667 & 0.0707852113040549 & 102.092888239393 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.22666666666667 & 0.0707852113040549 & 102.092888239393 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.22666666666667 & 0.0707852113040549 & 102.092888239393 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.24666666666667 & 0.0674166849985659 & 107.490700066620 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.24666666666667 & 0.0674166849985659 & 107.490700066620 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.24666666666667 & 0.0599654640090692 & 120.847337486969 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.22166666666667 & 0.0562024019163559 & 128.493915214058 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.22166666666667 & 0.0562024019163559 & 128.493915214058 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.25 & 0.0518853581994018 & 139.731135171841 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.25 & 0.0518853581994018 & 139.731135171841 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.21833333333333 & 0.0473889821676423 & 152.320919402698 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.21833333333333 & 0.0473889821676423 & 152.320919402698 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.22413793103448 & 0.0818461493579031 & 88.2648479825754 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.23035714285714 & 0.0794428506038106 & 91.0133144506062 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.23148148148148 & 0.0780539007295986 & 92.6472785329901 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.2326923076923 & 0.077221799308437 & 93.6612766403396 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.234 & 0.0761100170403184 & 95.0466217366352 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.23333333333333 & 0.0751672681644723 & 96.2298286204334 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.23478260869565 & 0.0744199723403187 & 97.2156046445619 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.23636363636364 & 0.0733587804350845 & 98.6434560859027 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.23809523809524 & 0.0718877998007329 & 100.686003162687 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.24 & 0.0712345349838053 & 101.636095492811 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.2421052631579 & 0.0702192845480333 & 103.135560405831 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.24444444444444 & 0.0687120105076766 & 105.431996399452 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.24411764705882 & 0.0674452542858201 & 107.407373932636 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.24375 & 0.0655217121118223 & 110.554956006606 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.24333333333333 & 0.0648044509137879 & 111.772158103298 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.24642857142857 & 0.064546063051746 & 112.267553260672 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.25 & 0.0637905225659013 & 113.653246726582 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.25 & 0.0637022057270606 & 113.810815767722 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.25 & 0.0630227060023724 & 115.037903953649 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.255 & 0.0630267278307595 & 115.109894638371 \tabularnewline
Median & 7.25 &  &  \tabularnewline
Midrange & 7.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.2258064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.2258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.2258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.2258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.2258064516129 &  &  \tabularnewline
Midmean - Closest Observation & 7.2258064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.2258064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.24375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19661&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]7.21833333333333[/C][C]0.0837838106696046[/C][C]86.1542734287691[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.18917406813762[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.15961140233399[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.24696488193506[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.21833333333333[/C][C]0.0837838106696046[/C][C]86.154273428769[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.22833333333333[/C][C]0.08137559104133[/C][C]88.8267997913786[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.22833333333333[/C][C]0.0793722427490915[/C][C]91.0687802558794[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.22833333333333[/C][C]0.0793722427490915[/C][C]91.0687802558794[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.23666666666667[/C][C]0.0777859828870856[/C][C]93.0330426906276[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.22666666666667[/C][C]0.0759819584096546[/C][C]95.1102974696217[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.22666666666667[/C][C]0.0759819584096546[/C][C]95.1102974696217[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.22666666666667[/C][C]0.0759819584096546[/C][C]95.1102974696216[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.22666666666667[/C][C]0.0707852113040549[/C][C]102.092888239393[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.22666666666667[/C][C]0.0707852113040549[/C][C]102.092888239393[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.22666666666667[/C][C]0.0707852113040549[/C][C]102.092888239393[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.24666666666667[/C][C]0.0674166849985659[/C][C]107.490700066620[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.24666666666667[/C][C]0.0674166849985659[/C][C]107.490700066620[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.24666666666667[/C][C]0.0599654640090692[/C][C]120.847337486969[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.22166666666667[/C][C]0.0562024019163559[/C][C]128.493915214058[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.22166666666667[/C][C]0.0562024019163559[/C][C]128.493915214058[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.25[/C][C]0.0518853581994018[/C][C]139.731135171841[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.25[/C][C]0.0518853581994018[/C][C]139.731135171841[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.21833333333333[/C][C]0.0473889821676423[/C][C]152.320919402698[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.21833333333333[/C][C]0.0473889821676423[/C][C]152.320919402698[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.22413793103448[/C][C]0.0818461493579031[/C][C]88.2648479825754[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.23035714285714[/C][C]0.0794428506038106[/C][C]91.0133144506062[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.23148148148148[/C][C]0.0780539007295986[/C][C]92.6472785329901[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.2326923076923[/C][C]0.077221799308437[/C][C]93.6612766403396[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.234[/C][C]0.0761100170403184[/C][C]95.0466217366352[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.23333333333333[/C][C]0.0751672681644723[/C][C]96.2298286204334[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.23478260869565[/C][C]0.0744199723403187[/C][C]97.2156046445619[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.23636363636364[/C][C]0.0733587804350845[/C][C]98.6434560859027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.23809523809524[/C][C]0.0718877998007329[/C][C]100.686003162687[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.24[/C][C]0.0712345349838053[/C][C]101.636095492811[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.2421052631579[/C][C]0.0702192845480333[/C][C]103.135560405831[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.24444444444444[/C][C]0.0687120105076766[/C][C]105.431996399452[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.24411764705882[/C][C]0.0674452542858201[/C][C]107.407373932636[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.24375[/C][C]0.0655217121118223[/C][C]110.554956006606[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.24333333333333[/C][C]0.0648044509137879[/C][C]111.772158103298[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.24642857142857[/C][C]0.064546063051746[/C][C]112.267553260672[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.25[/C][C]0.0637905225659013[/C][C]113.653246726582[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.25[/C][C]0.0637022057270606[/C][C]113.810815767722[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.25[/C][C]0.0630227060023724[/C][C]115.037903953649[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.255[/C][C]0.0630267278307595[/C][C]115.109894638371[/C][/ROW]
[ROW][C]Median[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.2258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.24375[/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=19661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19661&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 Mean7.218333333333330.083783810669604686.1542734287691
Geometric Mean7.18917406813762
Harmonic Mean7.15961140233399
Quadratic Mean7.24696488193506
Winsorized Mean ( 1 / 20 )7.218333333333330.083783810669604686.154273428769
Winsorized Mean ( 2 / 20 )7.228333333333330.0813755910413388.8267997913786
Winsorized Mean ( 3 / 20 )7.228333333333330.079372242749091591.0687802558794
Winsorized Mean ( 4 / 20 )7.228333333333330.079372242749091591.0687802558794
Winsorized Mean ( 5 / 20 )7.236666666666670.077785982887085693.0330426906276
Winsorized Mean ( 6 / 20 )7.226666666666670.075981958409654695.1102974696217
Winsorized Mean ( 7 / 20 )7.226666666666670.075981958409654695.1102974696217
Winsorized Mean ( 8 / 20 )7.226666666666670.075981958409654695.1102974696216
Winsorized Mean ( 9 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 10 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 11 / 20 )7.226666666666670.0707852113040549102.092888239393
Winsorized Mean ( 12 / 20 )7.246666666666670.0674166849985659107.490700066620
Winsorized Mean ( 13 / 20 )7.246666666666670.0674166849985659107.490700066620
Winsorized Mean ( 14 / 20 )7.246666666666670.0599654640090692120.847337486969
Winsorized Mean ( 15 / 20 )7.221666666666670.0562024019163559128.493915214058
Winsorized Mean ( 16 / 20 )7.221666666666670.0562024019163559128.493915214058
Winsorized Mean ( 17 / 20 )7.250.0518853581994018139.731135171841
Winsorized Mean ( 18 / 20 )7.250.0518853581994018139.731135171841
Winsorized Mean ( 19 / 20 )7.218333333333330.0473889821676423152.320919402698
Winsorized Mean ( 20 / 20 )7.218333333333330.0473889821676423152.320919402698
Trimmed Mean ( 1 / 20 )7.224137931034480.081846149357903188.2648479825754
Trimmed Mean ( 2 / 20 )7.230357142857140.079442850603810691.0133144506062
Trimmed Mean ( 3 / 20 )7.231481481481480.078053900729598692.6472785329901
Trimmed Mean ( 4 / 20 )7.23269230769230.07722179930843793.6612766403396
Trimmed Mean ( 5 / 20 )7.2340.076110017040318495.0466217366352
Trimmed Mean ( 6 / 20 )7.233333333333330.075167268164472396.2298286204334
Trimmed Mean ( 7 / 20 )7.234782608695650.074419972340318797.2156046445619
Trimmed Mean ( 8 / 20 )7.236363636363640.073358780435084598.6434560859027
Trimmed Mean ( 9 / 20 )7.238095238095240.0718877998007329100.686003162687
Trimmed Mean ( 10 / 20 )7.240.0712345349838053101.636095492811
Trimmed Mean ( 11 / 20 )7.24210526315790.0702192845480333103.135560405831
Trimmed Mean ( 12 / 20 )7.244444444444440.0687120105076766105.431996399452
Trimmed Mean ( 13 / 20 )7.244117647058820.0674452542858201107.407373932636
Trimmed Mean ( 14 / 20 )7.243750.0655217121118223110.554956006606
Trimmed Mean ( 15 / 20 )7.243333333333330.0648044509137879111.772158103298
Trimmed Mean ( 16 / 20 )7.246428571428570.064546063051746112.267553260672
Trimmed Mean ( 17 / 20 )7.250.0637905225659013113.653246726582
Trimmed Mean ( 18 / 20 )7.250.0637022057270606113.810815767722
Trimmed Mean ( 19 / 20 )7.250.0630227060023724115.037903953649
Trimmed Mean ( 20 / 20 )7.2550.0630267278307595115.109894638371
Median7.25
Midrange7.05
Midmean - Weighted Average at Xnp7.2258064516129
Midmean - Weighted Average at X(n+1)p7.2258064516129
Midmean - Empirical Distribution Function7.2258064516129
Midmean - Empirical Distribution Function - Averaging7.2258064516129
Midmean - Empirical Distribution Function - Interpolation7.2258064516129
Midmean - Closest Observation7.2258064516129
Midmean - True Basic - Statistics Graphics Toolkit7.2258064516129
Midmean - MS Excel (old versions)7.24375
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')