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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 13 Nov 2007 13:14:19 -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/2007/Nov/13/t1194984571uetn304znqonqtu.htm/, Retrieved Tue, 30 Apr 2024 01:50:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5384, Retrieved Tue, 30 Apr 2024 01:50:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact241
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:14:19] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
99,80
103,50
103,10
105,60
105,70
106,60
107,00
105,20
105,70
105,00
105,10
105,90
105,30
104,90
103,20
103,40
104,40
104,50
105,90
110,60
112,40
111,80
111,00
111,00
109,10
107,80
107,20
108,40
107,50
106,40
106,20
104,90
106,20
107,60
107,00
104,50
105,10
104,70
103,70
104,90
105,90
106,10
106,10
106,80
106,40
107,80
107,60
107,60
108,40
109,50
109,20
109,10
110,00
109,00
109,00
111,90
109,30
112,10
112,10
112,50
113,60
112,90
114,00
116,10
116,50
117,10
117,10
117,10
116,50
116,50
116,30
116,50
119,20
118,60
117,50
117,10
117,60
118,30
118,60
116,70




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5384&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5384&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.4750.544786858797996200.950148176377
Geometric Mean109.369419332514
Harmonic Mean109.265386645048
Quadratic Mean109.582034339576
Winsorized Mean ( 1 / 26 )109.508750.535358018590943204.552367195743
Winsorized Mean ( 2 / 26 )109.511250.534981940278408204.700835215128
Winsorized Mean ( 3 / 26 )109.50750.531488758707944206.039164903909
Winsorized Mean ( 4 / 26 )109.47750.523661569979522209.061550963691
Winsorized Mean ( 5 / 26 )109.483750.520656972250602210.280003601495
Winsorized Mean ( 6 / 26 )109.506250.507857075696936215.624149471037
Winsorized Mean ( 7 / 26 )109.5150.506752192703817216.111546386556
Winsorized Mean ( 8 / 26 )109.5150.506752192703817216.111546386556
Winsorized Mean ( 9 / 26 )109.53750.503975885373471217.346708799028
Winsorized Mean ( 10 / 26 )109.51250.491595101349562222.769713732620
Winsorized Mean ( 11 / 26 )109.4850.486540682207601225.027431423060
Winsorized Mean ( 12 / 26 )109.4850.486540682207601225.027431423060
Winsorized Mean ( 13 / 26 )109.501250.484616165973428225.954596004963
Winsorized Mean ( 14 / 26 )109.518750.482573185077348226.947442142783
Winsorized Mean ( 15 / 26 )109.481250.475737581072069230.129496503693
Winsorized Mean ( 16 / 26 )109.461250.466180595166858234.804389403684
Winsorized Mean ( 17 / 26 )109.036250.386825132008204281.874782628362
Winsorized Mean ( 18 / 26 )109.013750.364204281554366299.320341690512
Winsorized Mean ( 19 / 26 )108.871250.335462998346306324.540263864242
Winsorized Mean ( 20 / 26 )108.771250.320493062337282339.387221697582
Winsorized Mean ( 21 / 26 )108.79750.310343699831842350.570996153462
Winsorized Mean ( 22 / 26 )108.7150.298355726005897364.380471108676
Winsorized Mean ( 23 / 26 )108.7150.298355726005897364.380471108676
Winsorized Mean ( 24 / 26 )108.7150.282669798864105384.600691113327
Winsorized Mean ( 25 / 26 )108.683750.27822586529698390.631366655973
Winsorized Mean ( 26 / 26 )108.456250.238307878129282455.109796836688
Trimmed Mean ( 1 / 26 )109.4743589743590.530072770962256206.527037364374
Trimmed Mean ( 2 / 26 )109.4381578947370.523741489417981208.954532161186
Trimmed Mean ( 3 / 26 )109.3986486486490.516404327306069211.846885984379
Trimmed Mean ( 4 / 26 )109.3583333333330.509156187700963214.783471113507
Trimmed Mean ( 5 / 26 )109.3242857142860.503180096980238217.266712992782
Trimmed Mean ( 6 / 26 )109.2867647058820.496771421813025219.994065494000
Trimmed Mean ( 7 / 26 )109.2424242424240.492195787062575221.949124949613
Trimmed Mean ( 8 / 26 )109.193750.486651556149957224.377685882408
Trimmed Mean ( 9 / 26 )109.1419354838710.47967438049307227.533384984374
Trimmed Mean ( 10 / 26 )109.0833333333330.471481417375404231.362953688753
Trimmed Mean ( 11 / 26 )109.0241379310340.463816660333661235.058692916733
Trimmed Mean ( 12 / 26 )108.9642857142860.455168219020923239.393439965273
Trimmed Mean ( 13 / 26 )108.90.444148224136373245.188417023959
Trimmed Mean ( 14 / 26 )108.8288461538460.430434700285789252.834741440662
Trimmed Mean ( 15 / 26 )108.750.413193140587512263.194107833858
Trimmed Mean ( 16 / 26 )108.668750.392552072820774276.826330884296
Trimmed Mean ( 17 / 26 )108.5826086956520.367815123007871295.209745068934
Trimmed Mean ( 18 / 26 )108.5340909090910.356025499446326304.849206244715
Trimmed Mean ( 19 / 26 )108.4833333333330.345401459206067314.078966495078
Trimmed Mean ( 20 / 26 )108.44250.33790241915647320.928451091628
Trimmed Mean ( 21 / 26 )108.4078947368420.331048199035427327.468613491055
Trimmed Mean ( 22 / 26 )108.3666666666670.323424140414989335.060538547371
Trimmed Mean ( 23 / 26 )108.3294117647060.315565570750710343.286536319527
Trimmed Mean ( 24 / 26 )108.28750.303798200742193356.445494856285
Trimmed Mean ( 25 / 26 )108.240.290959569810597372.010448291698
Trimmed Mean ( 26 / 26 )108.1892857142860.272958477263304396.358035108479
Median107.8
Midrange109.5
Midmean - Weighted Average at Xnp108.375609756098
Midmean - Weighted Average at X(n+1)p108.375609756098
Midmean - Empirical Distribution Function108.375609756098
Midmean - Empirical Distribution Function - Averaging108.375609756098
Midmean - Empirical Distribution Function - Interpolation108.375609756098
Midmean - Closest Observation108.375609756098
Midmean - True Basic - Statistics Graphics Toolkit108.375609756098
Midmean - MS Excel (old versions)108.483333333333
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.475 & 0.544786858797996 & 200.950148176377 \tabularnewline
Geometric Mean & 109.369419332514 &  &  \tabularnewline
Harmonic Mean & 109.265386645048 &  &  \tabularnewline
Quadratic Mean & 109.582034339576 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 109.50875 & 0.535358018590943 & 204.552367195743 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 109.51125 & 0.534981940278408 & 204.700835215128 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 109.5075 & 0.531488758707944 & 206.039164903909 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 109.4775 & 0.523661569979522 & 209.061550963691 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 109.48375 & 0.520656972250602 & 210.280003601495 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 109.50625 & 0.507857075696936 & 215.624149471037 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 109.515 & 0.506752192703817 & 216.111546386556 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 109.515 & 0.506752192703817 & 216.111546386556 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 109.5375 & 0.503975885373471 & 217.346708799028 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 109.5125 & 0.491595101349562 & 222.769713732620 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 109.485 & 0.486540682207601 & 225.027431423060 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 109.485 & 0.486540682207601 & 225.027431423060 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 109.50125 & 0.484616165973428 & 225.954596004963 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 109.51875 & 0.482573185077348 & 226.947442142783 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 109.48125 & 0.475737581072069 & 230.129496503693 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 109.46125 & 0.466180595166858 & 234.804389403684 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 109.03625 & 0.386825132008204 & 281.874782628362 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 109.01375 & 0.364204281554366 & 299.320341690512 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 108.87125 & 0.335462998346306 & 324.540263864242 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 108.77125 & 0.320493062337282 & 339.387221697582 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 108.7975 & 0.310343699831842 & 350.570996153462 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 108.715 & 0.298355726005897 & 364.380471108676 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 108.715 & 0.298355726005897 & 364.380471108676 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 108.715 & 0.282669798864105 & 384.600691113327 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 108.68375 & 0.27822586529698 & 390.631366655973 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 108.45625 & 0.238307878129282 & 455.109796836688 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 109.474358974359 & 0.530072770962256 & 206.527037364374 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 109.438157894737 & 0.523741489417981 & 208.954532161186 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 109.398648648649 & 0.516404327306069 & 211.846885984379 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 109.358333333333 & 0.509156187700963 & 214.783471113507 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 109.324285714286 & 0.503180096980238 & 217.266712992782 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 109.286764705882 & 0.496771421813025 & 219.994065494000 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 109.242424242424 & 0.492195787062575 & 221.949124949613 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 109.19375 & 0.486651556149957 & 224.377685882408 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 109.141935483871 & 0.47967438049307 & 227.533384984374 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 109.083333333333 & 0.471481417375404 & 231.362953688753 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 109.024137931034 & 0.463816660333661 & 235.058692916733 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 108.964285714286 & 0.455168219020923 & 239.393439965273 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 108.9 & 0.444148224136373 & 245.188417023959 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 108.828846153846 & 0.430434700285789 & 252.834741440662 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 108.75 & 0.413193140587512 & 263.194107833858 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 108.66875 & 0.392552072820774 & 276.826330884296 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 108.582608695652 & 0.367815123007871 & 295.209745068934 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 108.534090909091 & 0.356025499446326 & 304.849206244715 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 108.483333333333 & 0.345401459206067 & 314.078966495078 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 108.4425 & 0.33790241915647 & 320.928451091628 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 108.407894736842 & 0.331048199035427 & 327.468613491055 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 108.366666666667 & 0.323424140414989 & 335.060538547371 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 108.329411764706 & 0.315565570750710 & 343.286536319527 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 108.2875 & 0.303798200742193 & 356.445494856285 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 108.24 & 0.290959569810597 & 372.010448291698 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 108.189285714286 & 0.272958477263304 & 396.358035108479 \tabularnewline
Median & 107.8 &  &  \tabularnewline
Midrange & 109.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.375609756098 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.375609756098 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.375609756098 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.375609756098 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.375609756098 &  &  \tabularnewline
Midmean - Closest Observation & 108.375609756098 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.375609756098 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.483333333333 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5384&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]109.475[/C][C]0.544786858797996[/C][C]200.950148176377[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.369419332514[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.265386645048[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.582034339576[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]109.50875[/C][C]0.535358018590943[/C][C]204.552367195743[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]109.51125[/C][C]0.534981940278408[/C][C]204.700835215128[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]109.5075[/C][C]0.531488758707944[/C][C]206.039164903909[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]109.4775[/C][C]0.523661569979522[/C][C]209.061550963691[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]109.48375[/C][C]0.520656972250602[/C][C]210.280003601495[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]109.50625[/C][C]0.507857075696936[/C][C]215.624149471037[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]109.515[/C][C]0.506752192703817[/C][C]216.111546386556[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]109.515[/C][C]0.506752192703817[/C][C]216.111546386556[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]109.5375[/C][C]0.503975885373471[/C][C]217.346708799028[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]109.5125[/C][C]0.491595101349562[/C][C]222.769713732620[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]109.485[/C][C]0.486540682207601[/C][C]225.027431423060[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]109.485[/C][C]0.486540682207601[/C][C]225.027431423060[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]109.50125[/C][C]0.484616165973428[/C][C]225.954596004963[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]109.51875[/C][C]0.482573185077348[/C][C]226.947442142783[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]109.48125[/C][C]0.475737581072069[/C][C]230.129496503693[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]109.46125[/C][C]0.466180595166858[/C][C]234.804389403684[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]109.03625[/C][C]0.386825132008204[/C][C]281.874782628362[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]109.01375[/C][C]0.364204281554366[/C][C]299.320341690512[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]108.87125[/C][C]0.335462998346306[/C][C]324.540263864242[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]108.77125[/C][C]0.320493062337282[/C][C]339.387221697582[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]108.7975[/C][C]0.310343699831842[/C][C]350.570996153462[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]108.715[/C][C]0.298355726005897[/C][C]364.380471108676[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]108.715[/C][C]0.298355726005897[/C][C]364.380471108676[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]108.715[/C][C]0.282669798864105[/C][C]384.600691113327[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]108.68375[/C][C]0.27822586529698[/C][C]390.631366655973[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]108.45625[/C][C]0.238307878129282[/C][C]455.109796836688[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]109.474358974359[/C][C]0.530072770962256[/C][C]206.527037364374[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]109.438157894737[/C][C]0.523741489417981[/C][C]208.954532161186[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]109.398648648649[/C][C]0.516404327306069[/C][C]211.846885984379[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]109.358333333333[/C][C]0.509156187700963[/C][C]214.783471113507[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]109.324285714286[/C][C]0.503180096980238[/C][C]217.266712992782[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]109.286764705882[/C][C]0.496771421813025[/C][C]219.994065494000[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]109.242424242424[/C][C]0.492195787062575[/C][C]221.949124949613[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]109.19375[/C][C]0.486651556149957[/C][C]224.377685882408[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]109.141935483871[/C][C]0.47967438049307[/C][C]227.533384984374[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]109.083333333333[/C][C]0.471481417375404[/C][C]231.362953688753[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]109.024137931034[/C][C]0.463816660333661[/C][C]235.058692916733[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]108.964285714286[/C][C]0.455168219020923[/C][C]239.393439965273[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]108.9[/C][C]0.444148224136373[/C][C]245.188417023959[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]108.828846153846[/C][C]0.430434700285789[/C][C]252.834741440662[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]108.75[/C][C]0.413193140587512[/C][C]263.194107833858[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]108.66875[/C][C]0.392552072820774[/C][C]276.826330884296[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]108.582608695652[/C][C]0.367815123007871[/C][C]295.209745068934[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]108.534090909091[/C][C]0.356025499446326[/C][C]304.849206244715[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]108.483333333333[/C][C]0.345401459206067[/C][C]314.078966495078[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]108.4425[/C][C]0.33790241915647[/C][C]320.928451091628[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]108.407894736842[/C][C]0.331048199035427[/C][C]327.468613491055[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]108.366666666667[/C][C]0.323424140414989[/C][C]335.060538547371[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]108.329411764706[/C][C]0.315565570750710[/C][C]343.286536319527[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]108.2875[/C][C]0.303798200742193[/C][C]356.445494856285[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]108.24[/C][C]0.290959569810597[/C][C]372.010448291698[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]108.189285714286[/C][C]0.272958477263304[/C][C]396.358035108479[/C][/ROW]
[ROW][C]Median[/C][C]107.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.375609756098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.483333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5384&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 Mean109.4750.544786858797996200.950148176377
Geometric Mean109.369419332514
Harmonic Mean109.265386645048
Quadratic Mean109.582034339576
Winsorized Mean ( 1 / 26 )109.508750.535358018590943204.552367195743
Winsorized Mean ( 2 / 26 )109.511250.534981940278408204.700835215128
Winsorized Mean ( 3 / 26 )109.50750.531488758707944206.039164903909
Winsorized Mean ( 4 / 26 )109.47750.523661569979522209.061550963691
Winsorized Mean ( 5 / 26 )109.483750.520656972250602210.280003601495
Winsorized Mean ( 6 / 26 )109.506250.507857075696936215.624149471037
Winsorized Mean ( 7 / 26 )109.5150.506752192703817216.111546386556
Winsorized Mean ( 8 / 26 )109.5150.506752192703817216.111546386556
Winsorized Mean ( 9 / 26 )109.53750.503975885373471217.346708799028
Winsorized Mean ( 10 / 26 )109.51250.491595101349562222.769713732620
Winsorized Mean ( 11 / 26 )109.4850.486540682207601225.027431423060
Winsorized Mean ( 12 / 26 )109.4850.486540682207601225.027431423060
Winsorized Mean ( 13 / 26 )109.501250.484616165973428225.954596004963
Winsorized Mean ( 14 / 26 )109.518750.482573185077348226.947442142783
Winsorized Mean ( 15 / 26 )109.481250.475737581072069230.129496503693
Winsorized Mean ( 16 / 26 )109.461250.466180595166858234.804389403684
Winsorized Mean ( 17 / 26 )109.036250.386825132008204281.874782628362
Winsorized Mean ( 18 / 26 )109.013750.364204281554366299.320341690512
Winsorized Mean ( 19 / 26 )108.871250.335462998346306324.540263864242
Winsorized Mean ( 20 / 26 )108.771250.320493062337282339.387221697582
Winsorized Mean ( 21 / 26 )108.79750.310343699831842350.570996153462
Winsorized Mean ( 22 / 26 )108.7150.298355726005897364.380471108676
Winsorized Mean ( 23 / 26 )108.7150.298355726005897364.380471108676
Winsorized Mean ( 24 / 26 )108.7150.282669798864105384.600691113327
Winsorized Mean ( 25 / 26 )108.683750.27822586529698390.631366655973
Winsorized Mean ( 26 / 26 )108.456250.238307878129282455.109796836688
Trimmed Mean ( 1 / 26 )109.4743589743590.530072770962256206.527037364374
Trimmed Mean ( 2 / 26 )109.4381578947370.523741489417981208.954532161186
Trimmed Mean ( 3 / 26 )109.3986486486490.516404327306069211.846885984379
Trimmed Mean ( 4 / 26 )109.3583333333330.509156187700963214.783471113507
Trimmed Mean ( 5 / 26 )109.3242857142860.503180096980238217.266712992782
Trimmed Mean ( 6 / 26 )109.2867647058820.496771421813025219.994065494000
Trimmed Mean ( 7 / 26 )109.2424242424240.492195787062575221.949124949613
Trimmed Mean ( 8 / 26 )109.193750.486651556149957224.377685882408
Trimmed Mean ( 9 / 26 )109.1419354838710.47967438049307227.533384984374
Trimmed Mean ( 10 / 26 )109.0833333333330.471481417375404231.362953688753
Trimmed Mean ( 11 / 26 )109.0241379310340.463816660333661235.058692916733
Trimmed Mean ( 12 / 26 )108.9642857142860.455168219020923239.393439965273
Trimmed Mean ( 13 / 26 )108.90.444148224136373245.188417023959
Trimmed Mean ( 14 / 26 )108.8288461538460.430434700285789252.834741440662
Trimmed Mean ( 15 / 26 )108.750.413193140587512263.194107833858
Trimmed Mean ( 16 / 26 )108.668750.392552072820774276.826330884296
Trimmed Mean ( 17 / 26 )108.5826086956520.367815123007871295.209745068934
Trimmed Mean ( 18 / 26 )108.5340909090910.356025499446326304.849206244715
Trimmed Mean ( 19 / 26 )108.4833333333330.345401459206067314.078966495078
Trimmed Mean ( 20 / 26 )108.44250.33790241915647320.928451091628
Trimmed Mean ( 21 / 26 )108.4078947368420.331048199035427327.468613491055
Trimmed Mean ( 22 / 26 )108.3666666666670.323424140414989335.060538547371
Trimmed Mean ( 23 / 26 )108.3294117647060.315565570750710343.286536319527
Trimmed Mean ( 24 / 26 )108.28750.303798200742193356.445494856285
Trimmed Mean ( 25 / 26 )108.240.290959569810597372.010448291698
Trimmed Mean ( 26 / 26 )108.1892857142860.272958477263304396.358035108479
Median107.8
Midrange109.5
Midmean - Weighted Average at Xnp108.375609756098
Midmean - Weighted Average at X(n+1)p108.375609756098
Midmean - Empirical Distribution Function108.375609756098
Midmean - Empirical Distribution Function - Averaging108.375609756098
Midmean - Empirical Distribution Function - Interpolation108.375609756098
Midmean - Closest Observation108.375609756098
Midmean - True Basic - Statistics Graphics Toolkit108.375609756098
Midmean - MS Excel (old versions)108.483333333333
Number of observations80



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')