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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 computationSun, 03 Mar 2013 11:34:15 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/03/t1362328528cqeecl9dpl3f94j.htm/, Retrieved Fri, 03 May 2024 15:59:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207266, Retrieved Fri, 03 May 2024 15:59:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robustness of Cen...] [2013-03-03 16:34:15] [38b7061a49f7215900abdc4599fce3db] [Current]
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Dataseries X:
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207266&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207266&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23.23545833333330.9214807621256825.2153482615672
Geometric Mean22.0687603192787
Harmonic Mean21.0588547545439
Quadratic Mean24.4984596740852
Winsorized Mean ( 1 / 24 )23.2350.91941352590218825.2715446808337
Winsorized Mean ( 2 / 24 )23.20872222222220.91184402820717225.4525132635394
Winsorized Mean ( 3 / 24 )23.17972222222220.90397341636197125.6420396912873
Winsorized Mean ( 4 / 24 )23.170.89765838071415225.8116010475684
Winsorized Mean ( 5 / 24 )22.90222222222220.8352129261054227.4208186995079
Winsorized Mean ( 6 / 24 )22.82088888888890.81497648145150528.0018987152169
Winsorized Mean ( 7 / 24 )22.82798611111110.80775552953728928.2610087784701
Winsorized Mean ( 8 / 24 )22.82054166666670.80578226310282128.3209779013896
Winsorized Mean ( 9 / 24 )22.69654166666670.78035120096380829.085034582678
Winsorized Mean ( 10 / 24 )22.70015277777780.77950546340131929.1212234468854
Winsorized Mean ( 11 / 24 )22.68793055555560.77586255607420129.2422032458359
Winsorized Mean ( 12 / 24 )22.66493055555560.76525864103999629.6173467897777
Winsorized Mean ( 13 / 24 )22.64597222222220.75696806782134629.9166810132431
Winsorized Mean ( 14 / 24 )22.64461111111110.75619403492024829.9455034890606
Winsorized Mean ( 15 / 24 )22.46440277777780.72027884822056631.1884804520855
Winsorized Mean ( 16 / 24 )22.42640277777780.7107579328215431.5527998241965
Winsorized Mean ( 17 / 24 )22.36477777777780.69177111865368732.3297362013374
Winsorized Mean ( 18 / 24 )22.29427777777780.66684514577505133.4324661715366
Winsorized Mean ( 19 / 24 )22.29797222222220.66050666015657933.7588908141158
Winsorized Mean ( 20 / 24 )21.73102777777780.52052836215784541.748018662599
Winsorized Mean ( 21 / 24 )21.42215277777780.47045675440984445.5347969329304
Winsorized Mean ( 22 / 24 )21.40290277777780.41404577030322951.6921179078902
Winsorized Mean ( 23 / 24 )21.24765277777780.38714839627126954.8824507150738
Winsorized Mean ( 24 / 24 )21.28331944444440.36223472773313158.7556018652206
Trimmed Mean ( 1 / 24 )23.09740.90168172884018425.6159122018694
Trimmed Mean ( 2 / 24 )22.95170588235290.88020126426270726.0755202409056
Trimmed Mean ( 3 / 24 )22.81151515151520.85903736638729226.5547414397696
Trimmed Mean ( 4 / 24 )22.67343750.83691467607946927.0916954237364
Trimmed Mean ( 5 / 24 )22.52927419354840.81215981583464227.7399518595924
Trimmed Mean ( 6 / 24 )22.43976666666670.80216071074122927.9741532665336
Trimmed Mean ( 7 / 24 )22.36091379310340.7950060664329228.126720961305
Trimmed Mean ( 8 / 24 )22.2751250.78724875318493428.2949003220171
Trimmed Mean ( 9 / 24 )22.18422222222220.77735548433989328.5380661346467
Trimmed Mean ( 10 / 24 )22.10540384615380.77022994463770528.699746095371
Trimmed Mean ( 11 / 24 )22.019760.76053355575985928.9530420232409
Trimmed Mean ( 12 / 24 )21.92864583333330.74818528236399129.3091114597268
Trimmed Mean ( 13 / 24 )21.83260869565220.73391080127642529.7483136338649
Trimmed Mean ( 14 / 24 )21.73022727272730.71648987492542530.3287290347111
Trimmed Mean ( 15 / 24 )21.61826190476190.69301458828896831.1945264502104
Trimmed Mean ( 16 / 24 )21.5167250.67058238177960332.0866243799883
Trimmed Mean ( 17 / 24 )21.4090.64215199961665233.3394585904593
Trimmed Mean ( 18 / 24 )21.29655555555560.60792086922982835.0317888947225
Trimmed Mean ( 19 / 24 )21.17917647058820.56705849744075437.3491916022316
Trimmed Mean ( 20 / 24 )21.04668750.50908028915035741.342570019999
Trimmed Mean ( 21 / 24 )20.96456666666670.47802379992529643.8567424256762
Trimmed Mean ( 22 / 24 )20.90853571428570.45072523711319846.3886509843571
Trimmed Mean ( 23 / 24 )20.84630769230770.42936338839023248.5516656892071
Trimmed Mean ( 24 / 24 )20.79395833333330.40637143660662851.1698324738855
Median20.489
Midrange28.0675
Midmean - Weighted Average at Xnp21.158027027027
Midmean - Weighted Average at X(n+1)p21.2965555555556
Midmean - Empirical Distribution Function21.158027027027
Midmean - Empirical Distribution Function - Averaging21.2965555555556
Midmean - Empirical Distribution Function - Interpolation21.2965555555556
Midmean - Closest Observation21.158027027027
Midmean - True Basic - Statistics Graphics Toolkit21.2965555555556
Midmean - MS Excel (old versions)21.409
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23.2354583333333 & 0.92148076212568 & 25.2153482615672 \tabularnewline
Geometric Mean & 22.0687603192787 &  &  \tabularnewline
Harmonic Mean & 21.0588547545439 &  &  \tabularnewline
Quadratic Mean & 24.4984596740852 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 23.235 & 0.919413525902188 & 25.2715446808337 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 23.2087222222222 & 0.911844028207172 & 25.4525132635394 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 23.1797222222222 & 0.903973416361971 & 25.6420396912873 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 23.17 & 0.897658380714152 & 25.8116010475684 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 22.9022222222222 & 0.83521292610542 & 27.4208186995079 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 22.8208888888889 & 0.814976481451505 & 28.0018987152169 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 22.8279861111111 & 0.807755529537289 & 28.2610087784701 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 22.8205416666667 & 0.805782263102821 & 28.3209779013896 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 22.6965416666667 & 0.780351200963808 & 29.085034582678 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 22.7001527777778 & 0.779505463401319 & 29.1212234468854 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 22.6879305555556 & 0.775862556074201 & 29.2422032458359 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 22.6649305555556 & 0.765258641039996 & 29.6173467897777 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 22.6459722222222 & 0.756968067821346 & 29.9166810132431 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 22.6446111111111 & 0.756194034920248 & 29.9455034890606 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 22.4644027777778 & 0.720278848220566 & 31.1884804520855 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 22.4264027777778 & 0.71075793282154 & 31.5527998241965 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 22.3647777777778 & 0.691771118653687 & 32.3297362013374 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 22.2942777777778 & 0.666845145775051 & 33.4324661715366 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 22.2979722222222 & 0.660506660156579 & 33.7588908141158 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 21.7310277777778 & 0.520528362157845 & 41.748018662599 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 21.4221527777778 & 0.470456754409844 & 45.5347969329304 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 21.4029027777778 & 0.414045770303229 & 51.6921179078902 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 21.2476527777778 & 0.387148396271269 & 54.8824507150738 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 21.2833194444444 & 0.362234727733131 & 58.7556018652206 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 23.0974 & 0.901681728840184 & 25.6159122018694 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 22.9517058823529 & 0.880201264262707 & 26.0755202409056 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 22.8115151515152 & 0.859037366387292 & 26.5547414397696 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 22.6734375 & 0.836914676079469 & 27.0916954237364 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 22.5292741935484 & 0.812159815834642 & 27.7399518595924 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 22.4397666666667 & 0.802160710741229 & 27.9741532665336 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 22.3609137931034 & 0.79500606643292 & 28.126720961305 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 22.275125 & 0.787248753184934 & 28.2949003220171 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 22.1842222222222 & 0.777355484339893 & 28.5380661346467 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 22.1054038461538 & 0.770229944637705 & 28.699746095371 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 22.01976 & 0.760533555759859 & 28.9530420232409 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 21.9286458333333 & 0.748185282363991 & 29.3091114597268 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 21.8326086956522 & 0.733910801276425 & 29.7483136338649 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 21.7302272727273 & 0.716489874925425 & 30.3287290347111 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 21.6182619047619 & 0.693014588288968 & 31.1945264502104 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 21.516725 & 0.670582381779603 & 32.0866243799883 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 21.409 & 0.642151999616652 & 33.3394585904593 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 21.2965555555556 & 0.607920869229828 & 35.0317888947225 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 21.1791764705882 & 0.567058497440754 & 37.3491916022316 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 21.0466875 & 0.509080289150357 & 41.342570019999 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 20.9645666666667 & 0.478023799925296 & 43.8567424256762 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 20.9085357142857 & 0.450725237113198 & 46.3886509843571 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 20.8463076923077 & 0.429363388390232 & 48.5516656892071 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 20.7939583333333 & 0.406371436606628 & 51.1698324738855 \tabularnewline
Median & 20.489 &  &  \tabularnewline
Midrange & 28.0675 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.158027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.2965555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.158027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.2965555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.2965555555556 &  &  \tabularnewline
Midmean - Closest Observation & 21.158027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.2965555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.409 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207266&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]23.2354583333333[/C][C]0.92148076212568[/C][C]25.2153482615672[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22.0687603192787[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.0588547545439[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24.4984596740852[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]23.235[/C][C]0.919413525902188[/C][C]25.2715446808337[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]23.2087222222222[/C][C]0.911844028207172[/C][C]25.4525132635394[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]23.1797222222222[/C][C]0.903973416361971[/C][C]25.6420396912873[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]23.17[/C][C]0.897658380714152[/C][C]25.8116010475684[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]22.9022222222222[/C][C]0.83521292610542[/C][C]27.4208186995079[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]22.8208888888889[/C][C]0.814976481451505[/C][C]28.0018987152169[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]22.8279861111111[/C][C]0.807755529537289[/C][C]28.2610087784701[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]22.8205416666667[/C][C]0.805782263102821[/C][C]28.3209779013896[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]22.6965416666667[/C][C]0.780351200963808[/C][C]29.085034582678[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]22.7001527777778[/C][C]0.779505463401319[/C][C]29.1212234468854[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]22.6879305555556[/C][C]0.775862556074201[/C][C]29.2422032458359[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]22.6649305555556[/C][C]0.765258641039996[/C][C]29.6173467897777[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]22.6459722222222[/C][C]0.756968067821346[/C][C]29.9166810132431[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]22.6446111111111[/C][C]0.756194034920248[/C][C]29.9455034890606[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]22.4644027777778[/C][C]0.720278848220566[/C][C]31.1884804520855[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]22.4264027777778[/C][C]0.71075793282154[/C][C]31.5527998241965[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]22.3647777777778[/C][C]0.691771118653687[/C][C]32.3297362013374[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]22.2942777777778[/C][C]0.666845145775051[/C][C]33.4324661715366[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]22.2979722222222[/C][C]0.660506660156579[/C][C]33.7588908141158[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]21.7310277777778[/C][C]0.520528362157845[/C][C]41.748018662599[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]21.4221527777778[/C][C]0.470456754409844[/C][C]45.5347969329304[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]21.4029027777778[/C][C]0.414045770303229[/C][C]51.6921179078902[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]21.2476527777778[/C][C]0.387148396271269[/C][C]54.8824507150738[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]21.2833194444444[/C][C]0.362234727733131[/C][C]58.7556018652206[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]23.0974[/C][C]0.901681728840184[/C][C]25.6159122018694[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]22.9517058823529[/C][C]0.880201264262707[/C][C]26.0755202409056[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]22.8115151515152[/C][C]0.859037366387292[/C][C]26.5547414397696[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]22.6734375[/C][C]0.836914676079469[/C][C]27.0916954237364[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]22.5292741935484[/C][C]0.812159815834642[/C][C]27.7399518595924[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]22.4397666666667[/C][C]0.802160710741229[/C][C]27.9741532665336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]22.3609137931034[/C][C]0.79500606643292[/C][C]28.126720961305[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]22.275125[/C][C]0.787248753184934[/C][C]28.2949003220171[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]22.1842222222222[/C][C]0.777355484339893[/C][C]28.5380661346467[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]22.1054038461538[/C][C]0.770229944637705[/C][C]28.699746095371[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]22.01976[/C][C]0.760533555759859[/C][C]28.9530420232409[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]21.9286458333333[/C][C]0.748185282363991[/C][C]29.3091114597268[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]21.8326086956522[/C][C]0.733910801276425[/C][C]29.7483136338649[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]21.7302272727273[/C][C]0.716489874925425[/C][C]30.3287290347111[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]21.6182619047619[/C][C]0.693014588288968[/C][C]31.1945264502104[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]21.516725[/C][C]0.670582381779603[/C][C]32.0866243799883[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]21.409[/C][C]0.642151999616652[/C][C]33.3394585904593[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]21.2965555555556[/C][C]0.607920869229828[/C][C]35.0317888947225[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]21.1791764705882[/C][C]0.567058497440754[/C][C]37.3491916022316[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]21.0466875[/C][C]0.509080289150357[/C][C]41.342570019999[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]20.9645666666667[/C][C]0.478023799925296[/C][C]43.8567424256762[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]20.9085357142857[/C][C]0.450725237113198[/C][C]46.3886509843571[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]20.8463076923077[/C][C]0.429363388390232[/C][C]48.5516656892071[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]20.7939583333333[/C][C]0.406371436606628[/C][C]51.1698324738855[/C][/ROW]
[ROW][C]Median[/C][C]20.489[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]28.0675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.158027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.2965555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.158027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.2965555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.2965555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.158027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.2965555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.409[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207266&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 Mean23.23545833333330.9214807621256825.2153482615672
Geometric Mean22.0687603192787
Harmonic Mean21.0588547545439
Quadratic Mean24.4984596740852
Winsorized Mean ( 1 / 24 )23.2350.91941352590218825.2715446808337
Winsorized Mean ( 2 / 24 )23.20872222222220.91184402820717225.4525132635394
Winsorized Mean ( 3 / 24 )23.17972222222220.90397341636197125.6420396912873
Winsorized Mean ( 4 / 24 )23.170.89765838071415225.8116010475684
Winsorized Mean ( 5 / 24 )22.90222222222220.8352129261054227.4208186995079
Winsorized Mean ( 6 / 24 )22.82088888888890.81497648145150528.0018987152169
Winsorized Mean ( 7 / 24 )22.82798611111110.80775552953728928.2610087784701
Winsorized Mean ( 8 / 24 )22.82054166666670.80578226310282128.3209779013896
Winsorized Mean ( 9 / 24 )22.69654166666670.78035120096380829.085034582678
Winsorized Mean ( 10 / 24 )22.70015277777780.77950546340131929.1212234468854
Winsorized Mean ( 11 / 24 )22.68793055555560.77586255607420129.2422032458359
Winsorized Mean ( 12 / 24 )22.66493055555560.76525864103999629.6173467897777
Winsorized Mean ( 13 / 24 )22.64597222222220.75696806782134629.9166810132431
Winsorized Mean ( 14 / 24 )22.64461111111110.75619403492024829.9455034890606
Winsorized Mean ( 15 / 24 )22.46440277777780.72027884822056631.1884804520855
Winsorized Mean ( 16 / 24 )22.42640277777780.7107579328215431.5527998241965
Winsorized Mean ( 17 / 24 )22.36477777777780.69177111865368732.3297362013374
Winsorized Mean ( 18 / 24 )22.29427777777780.66684514577505133.4324661715366
Winsorized Mean ( 19 / 24 )22.29797222222220.66050666015657933.7588908141158
Winsorized Mean ( 20 / 24 )21.73102777777780.52052836215784541.748018662599
Winsorized Mean ( 21 / 24 )21.42215277777780.47045675440984445.5347969329304
Winsorized Mean ( 22 / 24 )21.40290277777780.41404577030322951.6921179078902
Winsorized Mean ( 23 / 24 )21.24765277777780.38714839627126954.8824507150738
Winsorized Mean ( 24 / 24 )21.28331944444440.36223472773313158.7556018652206
Trimmed Mean ( 1 / 24 )23.09740.90168172884018425.6159122018694
Trimmed Mean ( 2 / 24 )22.95170588235290.88020126426270726.0755202409056
Trimmed Mean ( 3 / 24 )22.81151515151520.85903736638729226.5547414397696
Trimmed Mean ( 4 / 24 )22.67343750.83691467607946927.0916954237364
Trimmed Mean ( 5 / 24 )22.52927419354840.81215981583464227.7399518595924
Trimmed Mean ( 6 / 24 )22.43976666666670.80216071074122927.9741532665336
Trimmed Mean ( 7 / 24 )22.36091379310340.7950060664329228.126720961305
Trimmed Mean ( 8 / 24 )22.2751250.78724875318493428.2949003220171
Trimmed Mean ( 9 / 24 )22.18422222222220.77735548433989328.5380661346467
Trimmed Mean ( 10 / 24 )22.10540384615380.77022994463770528.699746095371
Trimmed Mean ( 11 / 24 )22.019760.76053355575985928.9530420232409
Trimmed Mean ( 12 / 24 )21.92864583333330.74818528236399129.3091114597268
Trimmed Mean ( 13 / 24 )21.83260869565220.73391080127642529.7483136338649
Trimmed Mean ( 14 / 24 )21.73022727272730.71648987492542530.3287290347111
Trimmed Mean ( 15 / 24 )21.61826190476190.69301458828896831.1945264502104
Trimmed Mean ( 16 / 24 )21.5167250.67058238177960332.0866243799883
Trimmed Mean ( 17 / 24 )21.4090.64215199961665233.3394585904593
Trimmed Mean ( 18 / 24 )21.29655555555560.60792086922982835.0317888947225
Trimmed Mean ( 19 / 24 )21.17917647058820.56705849744075437.3491916022316
Trimmed Mean ( 20 / 24 )21.04668750.50908028915035741.342570019999
Trimmed Mean ( 21 / 24 )20.96456666666670.47802379992529643.8567424256762
Trimmed Mean ( 22 / 24 )20.90853571428570.45072523711319846.3886509843571
Trimmed Mean ( 23 / 24 )20.84630769230770.42936338839023248.5516656892071
Trimmed Mean ( 24 / 24 )20.79395833333330.40637143660662851.1698324738855
Median20.489
Midrange28.0675
Midmean - Weighted Average at Xnp21.158027027027
Midmean - Weighted Average at X(n+1)p21.2965555555556
Midmean - Empirical Distribution Function21.158027027027
Midmean - Empirical Distribution Function - Averaging21.2965555555556
Midmean - Empirical Distribution Function - Interpolation21.2965555555556
Midmean - Closest Observation21.158027027027
Midmean - True Basic - Statistics Graphics Toolkit21.2965555555556
Midmean - MS Excel (old versions)21.409
Number of observations72



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')