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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 02:02:19 -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/Oct/22/h95yd5gfbkjcioj1193043473.htm/, Retrieved Mon, 06 May 2024 02:54:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1476, Retrieved Mon, 06 May 2024 02:54:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws1, deel 1, vraag 8
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vraag 8, deel 1, ...] [2007-10-22 09:02:19] [234bcf6fb77cd83fa17f2489a043102b] [Current]
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Dataseries X:
5,8
7,3
7,0
7,0
7,8
7,8
7,8
7,0
7,0
7,0
8,0
7,9
7,9
7,3
7,3
7,4
7,7
7,7
7,7
7,0
7,0
7,1
7,3
7,3
7,4
7,9
7,7
7,8
8,6
8,6
8,6
7,0
7,0
7,1
8,7
8,9
8,9
7,9
7,8
7,9
8,2
8,2
8,2
7,9
7,9
7,9
8,5
8,5
8,5
8,0
7,8
7,9
8,3
8,2
8,1
7,9
8,0
8,0
7,7
7,7
7,6
7,8
7,6
7,6
8,1
8,0
7,8
7,4
7,3
7,2
7,4
7,5
7,2




Summary of compuational 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 compuational 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=1476&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]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=1476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1476&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.723287671232880.0638539211153131120.952441703392
Geometric Mean7.70384133866927
Harmonic Mean7.68384694855733
Quadratic Mean7.74226967536183
Winsorized Mean ( 1 / 24 )7.739726027397260.0589010122721129131.402258277685
Winsorized Mean ( 2 / 24 )7.734246575342470.0575111390865649134.482583690457
Winsorized Mean ( 3 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 4 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 5 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 6 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 7 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 8 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 9 / 24 )7.69726027397260.0504157978618574152.675562034416
Winsorized Mean ( 10 / 24 )7.69726027397260.0456632419948634168.565785908028
Winsorized Mean ( 11 / 24 )7.69726027397260.0456632419948634168.565785908028
Winsorized Mean ( 12 / 24 )7.713698630136990.0427958886351049180.243917725534
Winsorized Mean ( 13 / 24 )7.713698630136990.0427958886351049180.243917725534
Winsorized Mean ( 14 / 24 )7.713698630136990.0367700425519714209.782151305219
Winsorized Mean ( 15 / 24 )7.713698630136990.0367700425519714209.782151305219
Winsorized Mean ( 16 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 17 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 18 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 19 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 20 / 24 )7.719178082191780.0294971514146287261.692323224254
Winsorized Mean ( 21 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 22 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 23 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 24 / 24 )7.723287671232880.0209660655685123368.370863192951
Trimmed Mean ( 1 / 24 )7.733802816901410.0573367216167954134.883938230538
Trimmed Mean ( 2 / 24 )7.727536231884060.0554714759681294139.306483143226
Trimmed Mean ( 3 / 24 )7.723880597014920.0541406092800902142.663348265187
Trimmed Mean ( 4 / 24 )7.721538461538460.0529646247913637145.786711261618
Trimmed Mean ( 5 / 24 )7.719047619047620.0515433662212613149.758313919815
Trimmed Mean ( 6 / 24 )7.716393442622950.0498182668820418154.890844775745
Trimmed Mean ( 7 / 24 )7.715254237288140.0482186210288295160.005700550317
Trimmed Mean ( 8 / 24 )7.71403508771930.0462529953301698166.779146575349
Trimmed Mean ( 9 / 24 )7.712727272727270.043812774719825176.038320376849
Trimmed Mean ( 10 / 24 )7.715094339622640.0419409553188269183.951325881206
Trimmed Mean ( 11 / 24 )7.717647058823530.0407484759587919189.397195287211
Trimmed Mean ( 12 / 24 )7.72040816326530.0392293526260022196.801824309179
Trimmed Mean ( 13 / 24 )7.721276595744680.0379804918780725203.295855686441
Trimmed Mean ( 14 / 24 )7.722222222222220.036360830419239212.377498896073
Trimmed Mean ( 15 / 24 )7.723255813953490.035661322081578216.572335604551
Trimmed Mean ( 16 / 24 )7.724390243902440.0347079255384334222.554074438961
Trimmed Mean ( 17 / 24 )7.728205128205130.0340573299996248226.917527835866
Trimmed Mean ( 18 / 24 )7.732432432432430.0331195971975708233.470002255932
Trimmed Mean ( 19 / 24 )7.737142857142860.0317780417517353243.474500964817
Trimmed Mean ( 20 / 24 )7.742424242424240.0298450236418064259.420945191640
Trimmed Mean ( 21 / 24 )7.745161290322580.028526052863786271.511846637398
Trimmed Mean ( 22 / 24 )7.751724137931030.0274627780586529282.262927711664
Trimmed Mean ( 23 / 24 )7.759259259259260.0257421242121402301.422648547392
Trimmed Mean ( 24 / 24 )7.7680.0228910462845192339.346655607147
Median7.8
Midrange7.35
Midmean - Weighted Average at Xnp7.7046511627907
Midmean - Weighted Average at X(n+1)p7.7046511627907
Midmean - Empirical Distribution Function7.7046511627907
Midmean - Empirical Distribution Function - Averaging7.7046511627907
Midmean - Empirical Distribution Function - Interpolation7.7046511627907
Midmean - Closest Observation7.7046511627907
Midmean - True Basic - Statistics Graphics Toolkit7.7046511627907
Midmean - MS Excel (old versions)7.7046511627907
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.72328767123288 & 0.0638539211153131 & 120.952441703392 \tabularnewline
Geometric Mean & 7.70384133866927 &  &  \tabularnewline
Harmonic Mean & 7.68384694855733 &  &  \tabularnewline
Quadratic Mean & 7.74226967536183 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.73972602739726 & 0.0589010122721129 & 131.402258277685 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.73424657534247 & 0.0575111390865649 & 134.482583690457 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.73013698630137 & 0.0565929190912976 & 136.591946667936 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.73013698630137 & 0.0565929190912976 & 136.591946667936 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.73013698630137 & 0.0565929190912976 & 136.591946667936 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.72191780821918 & 0.0549057091063865 & 140.639615331386 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.72191780821918 & 0.0549057091063865 & 140.639615331386 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.72191780821918 & 0.0549057091063865 & 140.639615331386 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.6972602739726 & 0.0504157978618574 & 152.675562034416 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.6972602739726 & 0.0456632419948634 & 168.565785908028 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.6972602739726 & 0.0456632419948634 & 168.565785908028 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.71369863013699 & 0.0427958886351049 & 180.243917725534 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.71369863013699 & 0.0427958886351049 & 180.243917725534 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.71369863013699 & 0.0367700425519714 & 209.782151305219 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.71369863013699 & 0.0367700425519714 & 209.782151305219 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.69178082191781 & 0.0337729810510914 & 227.749537723122 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.69178082191781 & 0.0337729810510914 & 227.749537723122 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.69178082191781 & 0.0337729810510914 & 227.749537723122 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.69178082191781 & 0.0337729810510914 & 227.749537723122 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.71917808219178 & 0.0294971514146287 & 261.692323224254 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.69041095890411 & 0.0259642348233217 & 296.192474426259 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7.69041095890411 & 0.0259642348233217 & 296.192474426259 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7.69041095890411 & 0.0259642348233217 & 296.192474426259 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7.72328767123288 & 0.0209660655685123 & 368.370863192951 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.73380281690141 & 0.0573367216167954 & 134.883938230538 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.72753623188406 & 0.0554714759681294 & 139.306483143226 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.72388059701492 & 0.0541406092800902 & 142.663348265187 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.72153846153846 & 0.0529646247913637 & 145.786711261618 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.71904761904762 & 0.0515433662212613 & 149.758313919815 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.71639344262295 & 0.0498182668820418 & 154.890844775745 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.71525423728814 & 0.0482186210288295 & 160.005700550317 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.7140350877193 & 0.0462529953301698 & 166.779146575349 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.71272727272727 & 0.043812774719825 & 176.038320376849 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.71509433962264 & 0.0419409553188269 & 183.951325881206 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.71764705882353 & 0.0407484759587919 & 189.397195287211 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.7204081632653 & 0.0392293526260022 & 196.801824309179 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.72127659574468 & 0.0379804918780725 & 203.295855686441 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.72222222222222 & 0.036360830419239 & 212.377498896073 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.72325581395349 & 0.035661322081578 & 216.572335604551 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7.72439024390244 & 0.0347079255384334 & 222.554074438961 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7.72820512820513 & 0.0340573299996248 & 226.917527835866 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7.73243243243243 & 0.0331195971975708 & 233.470002255932 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7.73714285714286 & 0.0317780417517353 & 243.474500964817 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7.74242424242424 & 0.0298450236418064 & 259.420945191640 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7.74516129032258 & 0.028526052863786 & 271.511846637398 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7.75172413793103 & 0.0274627780586529 & 282.262927711664 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7.75925925925926 & 0.0257421242121402 & 301.422648547392 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7.768 & 0.0228910462845192 & 339.346655607147 \tabularnewline
Median & 7.8 &  &  \tabularnewline
Midrange & 7.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.7046511627907 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.7046511627907 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.7046511627907 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.7046511627907 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.7046511627907 &  &  \tabularnewline
Midmean - Closest Observation & 7.7046511627907 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.7046511627907 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.7046511627907 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1476&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]7.72328767123288[/C][C]0.0638539211153131[/C][C]120.952441703392[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.70384133866927[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.68384694855733[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.74226967536183[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.73972602739726[/C][C]0.0589010122721129[/C][C]131.402258277685[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.73424657534247[/C][C]0.0575111390865649[/C][C]134.482583690457[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.73013698630137[/C][C]0.0565929190912976[/C][C]136.591946667936[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.73013698630137[/C][C]0.0565929190912976[/C][C]136.591946667936[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.73013698630137[/C][C]0.0565929190912976[/C][C]136.591946667936[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.72191780821918[/C][C]0.0549057091063865[/C][C]140.639615331386[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.72191780821918[/C][C]0.0549057091063865[/C][C]140.639615331386[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.72191780821918[/C][C]0.0549057091063865[/C][C]140.639615331386[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.6972602739726[/C][C]0.0504157978618574[/C][C]152.675562034416[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.6972602739726[/C][C]0.0456632419948634[/C][C]168.565785908028[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.6972602739726[/C][C]0.0456632419948634[/C][C]168.565785908028[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.71369863013699[/C][C]0.0427958886351049[/C][C]180.243917725534[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.71369863013699[/C][C]0.0427958886351049[/C][C]180.243917725534[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.71369863013699[/C][C]0.0367700425519714[/C][C]209.782151305219[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.71369863013699[/C][C]0.0367700425519714[/C][C]209.782151305219[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.69178082191781[/C][C]0.0337729810510914[/C][C]227.749537723122[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.69178082191781[/C][C]0.0337729810510914[/C][C]227.749537723122[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.69178082191781[/C][C]0.0337729810510914[/C][C]227.749537723122[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.69178082191781[/C][C]0.0337729810510914[/C][C]227.749537723122[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.71917808219178[/C][C]0.0294971514146287[/C][C]261.692323224254[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.69041095890411[/C][C]0.0259642348233217[/C][C]296.192474426259[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7.69041095890411[/C][C]0.0259642348233217[/C][C]296.192474426259[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7.69041095890411[/C][C]0.0259642348233217[/C][C]296.192474426259[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7.72328767123288[/C][C]0.0209660655685123[/C][C]368.370863192951[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.73380281690141[/C][C]0.0573367216167954[/C][C]134.883938230538[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.72753623188406[/C][C]0.0554714759681294[/C][C]139.306483143226[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.72388059701492[/C][C]0.0541406092800902[/C][C]142.663348265187[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.72153846153846[/C][C]0.0529646247913637[/C][C]145.786711261618[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.71904761904762[/C][C]0.0515433662212613[/C][C]149.758313919815[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.71639344262295[/C][C]0.0498182668820418[/C][C]154.890844775745[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.71525423728814[/C][C]0.0482186210288295[/C][C]160.005700550317[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.7140350877193[/C][C]0.0462529953301698[/C][C]166.779146575349[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.71272727272727[/C][C]0.043812774719825[/C][C]176.038320376849[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.71509433962264[/C][C]0.0419409553188269[/C][C]183.951325881206[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.71764705882353[/C][C]0.0407484759587919[/C][C]189.397195287211[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.7204081632653[/C][C]0.0392293526260022[/C][C]196.801824309179[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.72127659574468[/C][C]0.0379804918780725[/C][C]203.295855686441[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.72222222222222[/C][C]0.036360830419239[/C][C]212.377498896073[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.72325581395349[/C][C]0.035661322081578[/C][C]216.572335604551[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7.72439024390244[/C][C]0.0347079255384334[/C][C]222.554074438961[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7.72820512820513[/C][C]0.0340573299996248[/C][C]226.917527835866[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7.73243243243243[/C][C]0.0331195971975708[/C][C]233.470002255932[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7.73714285714286[/C][C]0.0317780417517353[/C][C]243.474500964817[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7.74242424242424[/C][C]0.0298450236418064[/C][C]259.420945191640[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7.74516129032258[/C][C]0.028526052863786[/C][C]271.511846637398[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7.75172413793103[/C][C]0.0274627780586529[/C][C]282.262927711664[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7.75925925925926[/C][C]0.0257421242121402[/C][C]301.422648547392[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7.768[/C][C]0.0228910462845192[/C][C]339.346655607147[/C][/ROW]
[ROW][C]Median[/C][C]7.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.7046511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1476&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 Mean7.723287671232880.0638539211153131120.952441703392
Geometric Mean7.70384133866927
Harmonic Mean7.68384694855733
Quadratic Mean7.74226967536183
Winsorized Mean ( 1 / 24 )7.739726027397260.0589010122721129131.402258277685
Winsorized Mean ( 2 / 24 )7.734246575342470.0575111390865649134.482583690457
Winsorized Mean ( 3 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 4 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 5 / 24 )7.730136986301370.0565929190912976136.591946667936
Winsorized Mean ( 6 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 7 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 8 / 24 )7.721917808219180.0549057091063865140.639615331386
Winsorized Mean ( 9 / 24 )7.69726027397260.0504157978618574152.675562034416
Winsorized Mean ( 10 / 24 )7.69726027397260.0456632419948634168.565785908028
Winsorized Mean ( 11 / 24 )7.69726027397260.0456632419948634168.565785908028
Winsorized Mean ( 12 / 24 )7.713698630136990.0427958886351049180.243917725534
Winsorized Mean ( 13 / 24 )7.713698630136990.0427958886351049180.243917725534
Winsorized Mean ( 14 / 24 )7.713698630136990.0367700425519714209.782151305219
Winsorized Mean ( 15 / 24 )7.713698630136990.0367700425519714209.782151305219
Winsorized Mean ( 16 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 17 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 18 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 19 / 24 )7.691780821917810.0337729810510914227.749537723122
Winsorized Mean ( 20 / 24 )7.719178082191780.0294971514146287261.692323224254
Winsorized Mean ( 21 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 22 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 23 / 24 )7.690410958904110.0259642348233217296.192474426259
Winsorized Mean ( 24 / 24 )7.723287671232880.0209660655685123368.370863192951
Trimmed Mean ( 1 / 24 )7.733802816901410.0573367216167954134.883938230538
Trimmed Mean ( 2 / 24 )7.727536231884060.0554714759681294139.306483143226
Trimmed Mean ( 3 / 24 )7.723880597014920.0541406092800902142.663348265187
Trimmed Mean ( 4 / 24 )7.721538461538460.0529646247913637145.786711261618
Trimmed Mean ( 5 / 24 )7.719047619047620.0515433662212613149.758313919815
Trimmed Mean ( 6 / 24 )7.716393442622950.0498182668820418154.890844775745
Trimmed Mean ( 7 / 24 )7.715254237288140.0482186210288295160.005700550317
Trimmed Mean ( 8 / 24 )7.71403508771930.0462529953301698166.779146575349
Trimmed Mean ( 9 / 24 )7.712727272727270.043812774719825176.038320376849
Trimmed Mean ( 10 / 24 )7.715094339622640.0419409553188269183.951325881206
Trimmed Mean ( 11 / 24 )7.717647058823530.0407484759587919189.397195287211
Trimmed Mean ( 12 / 24 )7.72040816326530.0392293526260022196.801824309179
Trimmed Mean ( 13 / 24 )7.721276595744680.0379804918780725203.295855686441
Trimmed Mean ( 14 / 24 )7.722222222222220.036360830419239212.377498896073
Trimmed Mean ( 15 / 24 )7.723255813953490.035661322081578216.572335604551
Trimmed Mean ( 16 / 24 )7.724390243902440.0347079255384334222.554074438961
Trimmed Mean ( 17 / 24 )7.728205128205130.0340573299996248226.917527835866
Trimmed Mean ( 18 / 24 )7.732432432432430.0331195971975708233.470002255932
Trimmed Mean ( 19 / 24 )7.737142857142860.0317780417517353243.474500964817
Trimmed Mean ( 20 / 24 )7.742424242424240.0298450236418064259.420945191640
Trimmed Mean ( 21 / 24 )7.745161290322580.028526052863786271.511846637398
Trimmed Mean ( 22 / 24 )7.751724137931030.0274627780586529282.262927711664
Trimmed Mean ( 23 / 24 )7.759259259259260.0257421242121402301.422648547392
Trimmed Mean ( 24 / 24 )7.7680.0228910462845192339.346655607147
Median7.8
Midrange7.35
Midmean - Weighted Average at Xnp7.7046511627907
Midmean - Weighted Average at X(n+1)p7.7046511627907
Midmean - Empirical Distribution Function7.7046511627907
Midmean - Empirical Distribution Function - Averaging7.7046511627907
Midmean - Empirical Distribution Function - Interpolation7.7046511627907
Midmean - Closest Observation7.7046511627907
Midmean - True Basic - Statistics Graphics Toolkit7.7046511627907
Midmean - MS Excel (old versions)7.7046511627907
Number of observations73



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')