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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 computationFri, 25 May 2012 13:13:58 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/25/t13379660555wf12otc9ytjcif.htm/, Retrieved Fri, 03 May 2024 18:23:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167516, Retrieved Fri, 03 May 2024 18:23:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Werk...] [2012-05-25 17:13:58] [bc909d11ab9ae813672fa3903785080c] [Current]
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Dataseries X:
804,7
984,8
904,7
244,7
804,6
254,6
184,7
354,7
204,5
624,4
964,5
324,4
24,6
414,5
884,4
84,5
504,4
194,6
804,7
824,6
144,7
764,7
864,7
5
715
214,9
435,1
295
205,4
845,6
155,8
646,1
876,1
216,5
906,8
257,3
227,8
168,3
808,7
558,9
29,4
749,5
239,5
249,6
259,8
2710
829,9
259,9
179,7
319,8
469,8
789,9
309,6
689,4
269,5
279,6
379,5
469,5
619,8
419,4
419,1
959
148,9
149
659
729,1
739,1
659,1
619
598,9
498,7
398,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167516&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167516&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean511.17361111111145.213144191054211.3058629355897
Geometric Mean376.56243948802
Harmonic Mean152.432072160343
Quadratic Mean637.525432934945
Winsorized Mean ( 1 / 24 )487.48472222222233.624661406380714.4978328950464
Winsorized Mean ( 2 / 24 )487.05416666666733.483540670650614.5460771743767
Winsorized Mean ( 3 / 24 )489.12083333333333.018291389253514.81363246714
Winsorized Mean ( 4 / 24 )489.56527777777831.916592944160515.3388953086031
Winsorized Mean ( 5 / 24 )489.71111111111131.845608487691315.377665378898
Winsorized Mean ( 6 / 24 )488.02777777777831.539360498436315.4736104367739
Winsorized Mean ( 7 / 24 )487.88194444444431.298004401626215.5882764339791
Winsorized Mean ( 8 / 24 )488.00416666666730.873428849261415.8066073272694
Winsorized Mean ( 9 / 24 )487.04166666666730.263167684013816.0935455188302
Winsorized Mean ( 10 / 24 )485.55555555555629.804748146643616.2912148482703
Winsorized Mean ( 11 / 24 )486.25833333333329.460398457406716.5054907195623
Winsorized Mean ( 12 / 24 )485.25833333333328.808194538608916.8444548887987
Winsorized Mean ( 13 / 24 )484.69861111111128.672025681874916.9049308370812
Winsorized Mean ( 14 / 24 )486.54583333333328.420960873444717.1192605169074
Winsorized Mean ( 15 / 24 )486.85833333333328.372870974156317.1592904284094
Winsorized Mean ( 16 / 24 )486.10277777777827.526816415216817.6592443690314
Winsorized Mean ( 17 / 24 )482.91527777777826.251307267524818.3958563608444
Winsorized Mean ( 18 / 24 )480.41527777777825.512255229601418.830764801238
Winsorized Mean ( 19 / 24 )478.96388888888924.938896164105219.2054967363899
Winsorized Mean ( 20 / 24 )477.57524.353273532099619.6103000021955
Winsorized Mean ( 21 / 24 )474.2523.657740084044320.0462934462558
Winsorized Mean ( 22 / 24 )467.19166666666722.452573625359520.8079338458994
Winsorized Mean ( 23 / 24 )457.54444444444421.122634035067221.6613346462777
Winsorized Mean ( 24 / 24 )460.71111111111120.699083650946322.2575607152566
Trimmed Mean ( 1 / 24 )486.99285714285733.182214755380214.6763216600512
Trimmed Mean ( 2 / 24 )486.47205882352932.648926820040914.9000933937258
Trimmed Mean ( 3 / 24 )486.15454545454532.094873214090215.1474206553686
Trimmed Mean ( 4 / 24 )485.042187531.630848383622215.3344665820328
Trimmed Mean ( 5 / 24 )483.72903225806531.447703004472715.3820147751098
Trimmed Mean ( 6 / 24 )482.29333333333331.221771600048215.4473403851494
Trimmed Mean ( 7 / 24 )481.10689655172431.004227983060415.5174609351532
Trimmed Mean ( 8 / 24 )479.862530.76936530568915.5954630598532
Trimmed Mean ( 9 / 24 )478.50555555555630.547824303021415.6641452042209
Trimmed Mean ( 10 / 24 )477.19230769230830.373482973141415.7108194708614
Trimmed Mean ( 11 / 24 )475.98830.214009136187715.7538841619632
Trimmed Mean ( 12 / 24 )474.587530.039630092731815.798713184382
Trimmed Mean ( 13 / 24 )473.19565217391329.904036041320515.8238055732699
Trimmed Mean ( 14 / 24 )471.74772727272729.704307830437215.8814583381519
Trimmed Mean ( 15 / 24 )469.93571428571429.439524188636215.9627482860987
Trimmed Mean ( 16 / 24 )467.90529.045033325810416.1096389441634
Trimmed Mean ( 17 / 24 )465.7528.655630759995516.2533501321565
Trimmed Mean ( 18 / 24 )463.73055555555628.365851596886316.348197901679
Trimmed Mean ( 19 / 24 )461.76764705882428.070029157606516.4505581546107
Trimmed Mean ( 20 / 24 )459.7312527.715295953467816.5876363280356
Trimmed Mean ( 21 / 24 )457.5927.27502809295116.7768846448324
Trimmed Mean ( 22 / 24 )455.5526.744037312007217.0337034265007
Trimmed Mean ( 23 / 24 )454.08461538461526.243369678282717.3028319515076
Trimmed Mean ( 24 / 24 )453.63333333333325.817101024592417.571040718368
Median427.25
Midrange1357.5
Midmean - Weighted Average at Xnp457.67027027027
Midmean - Weighted Average at X(n+1)p463.730555555556
Midmean - Empirical Distribution Function457.67027027027
Midmean - Empirical Distribution Function - Averaging463.730555555556
Midmean - Empirical Distribution Function - Interpolation463.730555555556
Midmean - Closest Observation457.67027027027
Midmean - True Basic - Statistics Graphics Toolkit463.730555555556
Midmean - MS Excel (old versions)465.75
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 511.173611111111 & 45.2131441910542 & 11.3058629355897 \tabularnewline
Geometric Mean & 376.56243948802 &  &  \tabularnewline
Harmonic Mean & 152.432072160343 &  &  \tabularnewline
Quadratic Mean & 637.525432934945 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 487.484722222222 & 33.6246614063807 & 14.4978328950464 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 487.054166666667 & 33.4835406706506 & 14.5460771743767 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 489.120833333333 & 33.0182913892535 & 14.81363246714 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 489.565277777778 & 31.9165929441605 & 15.3388953086031 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 489.711111111111 & 31.8456084876913 & 15.377665378898 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 488.027777777778 & 31.5393604984363 & 15.4736104367739 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 487.881944444444 & 31.2980044016262 & 15.5882764339791 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 488.004166666667 & 30.8734288492614 & 15.8066073272694 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 487.041666666667 & 30.2631676840138 & 16.0935455188302 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 485.555555555556 & 29.8047481466436 & 16.2912148482703 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 486.258333333333 & 29.4603984574067 & 16.5054907195623 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 485.258333333333 & 28.8081945386089 & 16.8444548887987 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 484.698611111111 & 28.6720256818749 & 16.9049308370812 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 486.545833333333 & 28.4209608734447 & 17.1192605169074 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 486.858333333333 & 28.3728709741563 & 17.1592904284094 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 486.102777777778 & 27.5268164152168 & 17.6592443690314 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 482.915277777778 & 26.2513072675248 & 18.3958563608444 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 480.415277777778 & 25.5122552296014 & 18.830764801238 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 478.963888888889 & 24.9388961641052 & 19.2054967363899 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 477.575 & 24.3532735320996 & 19.6103000021955 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 474.25 & 23.6577400840443 & 20.0462934462558 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 467.191666666667 & 22.4525736253595 & 20.8079338458994 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 457.544444444444 & 21.1226340350672 & 21.6613346462777 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 460.711111111111 & 20.6990836509463 & 22.2575607152566 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 486.992857142857 & 33.1822147553802 & 14.6763216600512 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 486.472058823529 & 32.6489268200409 & 14.9000933937258 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 486.154545454545 & 32.0948732140902 & 15.1474206553686 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 485.0421875 & 31.6308483836222 & 15.3344665820328 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 483.729032258065 & 31.4477030044727 & 15.3820147751098 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 482.293333333333 & 31.2217716000482 & 15.4473403851494 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 481.106896551724 & 31.0042279830604 & 15.5174609351532 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 479.8625 & 30.769365305689 & 15.5954630598532 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 478.505555555556 & 30.5478243030214 & 15.6641452042209 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 477.192307692308 & 30.3734829731414 & 15.7108194708614 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 475.988 & 30.2140091361877 & 15.7538841619632 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 474.5875 & 30.0396300927318 & 15.798713184382 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 473.195652173913 & 29.9040360413205 & 15.8238055732699 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 471.747727272727 & 29.7043078304372 & 15.8814583381519 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 469.935714285714 & 29.4395241886362 & 15.9627482860987 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 467.905 & 29.0450333258104 & 16.1096389441634 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 465.75 & 28.6556307599955 & 16.2533501321565 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 463.730555555556 & 28.3658515968863 & 16.348197901679 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 461.767647058824 & 28.0700291576065 & 16.4505581546107 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 459.73125 & 27.7152959534678 & 16.5876363280356 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 457.59 & 27.275028092951 & 16.7768846448324 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 455.55 & 26.7440373120072 & 17.0337034265007 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 454.084615384615 & 26.2433696782827 & 17.3028319515076 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 453.633333333333 & 25.8171010245924 & 17.571040718368 \tabularnewline
Median & 427.25 &  &  \tabularnewline
Midrange & 1357.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 457.67027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 463.730555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 457.67027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 463.730555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 463.730555555556 &  &  \tabularnewline
Midmean - Closest Observation & 457.67027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 463.730555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 465.75 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167516&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]511.173611111111[/C][C]45.2131441910542[/C][C]11.3058629355897[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]376.56243948802[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]152.432072160343[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]637.525432934945[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]487.484722222222[/C][C]33.6246614063807[/C][C]14.4978328950464[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]487.054166666667[/C][C]33.4835406706506[/C][C]14.5460771743767[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]489.120833333333[/C][C]33.0182913892535[/C][C]14.81363246714[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]489.565277777778[/C][C]31.9165929441605[/C][C]15.3388953086031[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]489.711111111111[/C][C]31.8456084876913[/C][C]15.377665378898[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]488.027777777778[/C][C]31.5393604984363[/C][C]15.4736104367739[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]487.881944444444[/C][C]31.2980044016262[/C][C]15.5882764339791[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]488.004166666667[/C][C]30.8734288492614[/C][C]15.8066073272694[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]487.041666666667[/C][C]30.2631676840138[/C][C]16.0935455188302[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]485.555555555556[/C][C]29.8047481466436[/C][C]16.2912148482703[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]486.258333333333[/C][C]29.4603984574067[/C][C]16.5054907195623[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]485.258333333333[/C][C]28.8081945386089[/C][C]16.8444548887987[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]484.698611111111[/C][C]28.6720256818749[/C][C]16.9049308370812[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]486.545833333333[/C][C]28.4209608734447[/C][C]17.1192605169074[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]486.858333333333[/C][C]28.3728709741563[/C][C]17.1592904284094[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]486.102777777778[/C][C]27.5268164152168[/C][C]17.6592443690314[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]482.915277777778[/C][C]26.2513072675248[/C][C]18.3958563608444[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]480.415277777778[/C][C]25.5122552296014[/C][C]18.830764801238[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]478.963888888889[/C][C]24.9388961641052[/C][C]19.2054967363899[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]477.575[/C][C]24.3532735320996[/C][C]19.6103000021955[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]474.25[/C][C]23.6577400840443[/C][C]20.0462934462558[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]467.191666666667[/C][C]22.4525736253595[/C][C]20.8079338458994[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]457.544444444444[/C][C]21.1226340350672[/C][C]21.6613346462777[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]460.711111111111[/C][C]20.6990836509463[/C][C]22.2575607152566[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]486.992857142857[/C][C]33.1822147553802[/C][C]14.6763216600512[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]486.472058823529[/C][C]32.6489268200409[/C][C]14.9000933937258[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]486.154545454545[/C][C]32.0948732140902[/C][C]15.1474206553686[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]485.0421875[/C][C]31.6308483836222[/C][C]15.3344665820328[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]483.729032258065[/C][C]31.4477030044727[/C][C]15.3820147751098[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]482.293333333333[/C][C]31.2217716000482[/C][C]15.4473403851494[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]481.106896551724[/C][C]31.0042279830604[/C][C]15.5174609351532[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]479.8625[/C][C]30.769365305689[/C][C]15.5954630598532[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]478.505555555556[/C][C]30.5478243030214[/C][C]15.6641452042209[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]477.192307692308[/C][C]30.3734829731414[/C][C]15.7108194708614[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]475.988[/C][C]30.2140091361877[/C][C]15.7538841619632[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]474.5875[/C][C]30.0396300927318[/C][C]15.798713184382[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]473.195652173913[/C][C]29.9040360413205[/C][C]15.8238055732699[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]471.747727272727[/C][C]29.7043078304372[/C][C]15.8814583381519[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]469.935714285714[/C][C]29.4395241886362[/C][C]15.9627482860987[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]467.905[/C][C]29.0450333258104[/C][C]16.1096389441634[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]465.75[/C][C]28.6556307599955[/C][C]16.2533501321565[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]463.730555555556[/C][C]28.3658515968863[/C][C]16.348197901679[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]461.767647058824[/C][C]28.0700291576065[/C][C]16.4505581546107[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]459.73125[/C][C]27.7152959534678[/C][C]16.5876363280356[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]457.59[/C][C]27.275028092951[/C][C]16.7768846448324[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]455.55[/C][C]26.7440373120072[/C][C]17.0337034265007[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]454.084615384615[/C][C]26.2433696782827[/C][C]17.3028319515076[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]453.633333333333[/C][C]25.8171010245924[/C][C]17.571040718368[/C][/ROW]
[ROW][C]Median[/C][C]427.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1357.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]457.67027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]463.730555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]457.67027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]463.730555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]463.730555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]457.67027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]463.730555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]465.75[/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=167516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167516&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 Mean511.17361111111145.213144191054211.3058629355897
Geometric Mean376.56243948802
Harmonic Mean152.432072160343
Quadratic Mean637.525432934945
Winsorized Mean ( 1 / 24 )487.48472222222233.624661406380714.4978328950464
Winsorized Mean ( 2 / 24 )487.05416666666733.483540670650614.5460771743767
Winsorized Mean ( 3 / 24 )489.12083333333333.018291389253514.81363246714
Winsorized Mean ( 4 / 24 )489.56527777777831.916592944160515.3388953086031
Winsorized Mean ( 5 / 24 )489.71111111111131.845608487691315.377665378898
Winsorized Mean ( 6 / 24 )488.02777777777831.539360498436315.4736104367739
Winsorized Mean ( 7 / 24 )487.88194444444431.298004401626215.5882764339791
Winsorized Mean ( 8 / 24 )488.00416666666730.873428849261415.8066073272694
Winsorized Mean ( 9 / 24 )487.04166666666730.263167684013816.0935455188302
Winsorized Mean ( 10 / 24 )485.55555555555629.804748146643616.2912148482703
Winsorized Mean ( 11 / 24 )486.25833333333329.460398457406716.5054907195623
Winsorized Mean ( 12 / 24 )485.25833333333328.808194538608916.8444548887987
Winsorized Mean ( 13 / 24 )484.69861111111128.672025681874916.9049308370812
Winsorized Mean ( 14 / 24 )486.54583333333328.420960873444717.1192605169074
Winsorized Mean ( 15 / 24 )486.85833333333328.372870974156317.1592904284094
Winsorized Mean ( 16 / 24 )486.10277777777827.526816415216817.6592443690314
Winsorized Mean ( 17 / 24 )482.91527777777826.251307267524818.3958563608444
Winsorized Mean ( 18 / 24 )480.41527777777825.512255229601418.830764801238
Winsorized Mean ( 19 / 24 )478.96388888888924.938896164105219.2054967363899
Winsorized Mean ( 20 / 24 )477.57524.353273532099619.6103000021955
Winsorized Mean ( 21 / 24 )474.2523.657740084044320.0462934462558
Winsorized Mean ( 22 / 24 )467.19166666666722.452573625359520.8079338458994
Winsorized Mean ( 23 / 24 )457.54444444444421.122634035067221.6613346462777
Winsorized Mean ( 24 / 24 )460.71111111111120.699083650946322.2575607152566
Trimmed Mean ( 1 / 24 )486.99285714285733.182214755380214.6763216600512
Trimmed Mean ( 2 / 24 )486.47205882352932.648926820040914.9000933937258
Trimmed Mean ( 3 / 24 )486.15454545454532.094873214090215.1474206553686
Trimmed Mean ( 4 / 24 )485.042187531.630848383622215.3344665820328
Trimmed Mean ( 5 / 24 )483.72903225806531.447703004472715.3820147751098
Trimmed Mean ( 6 / 24 )482.29333333333331.221771600048215.4473403851494
Trimmed Mean ( 7 / 24 )481.10689655172431.004227983060415.5174609351532
Trimmed Mean ( 8 / 24 )479.862530.76936530568915.5954630598532
Trimmed Mean ( 9 / 24 )478.50555555555630.547824303021415.6641452042209
Trimmed Mean ( 10 / 24 )477.19230769230830.373482973141415.7108194708614
Trimmed Mean ( 11 / 24 )475.98830.214009136187715.7538841619632
Trimmed Mean ( 12 / 24 )474.587530.039630092731815.798713184382
Trimmed Mean ( 13 / 24 )473.19565217391329.904036041320515.8238055732699
Trimmed Mean ( 14 / 24 )471.74772727272729.704307830437215.8814583381519
Trimmed Mean ( 15 / 24 )469.93571428571429.439524188636215.9627482860987
Trimmed Mean ( 16 / 24 )467.90529.045033325810416.1096389441634
Trimmed Mean ( 17 / 24 )465.7528.655630759995516.2533501321565
Trimmed Mean ( 18 / 24 )463.73055555555628.365851596886316.348197901679
Trimmed Mean ( 19 / 24 )461.76764705882428.070029157606516.4505581546107
Trimmed Mean ( 20 / 24 )459.7312527.715295953467816.5876363280356
Trimmed Mean ( 21 / 24 )457.5927.27502809295116.7768846448324
Trimmed Mean ( 22 / 24 )455.5526.744037312007217.0337034265007
Trimmed Mean ( 23 / 24 )454.08461538461526.243369678282717.3028319515076
Trimmed Mean ( 24 / 24 )453.63333333333325.817101024592417.571040718368
Median427.25
Midrange1357.5
Midmean - Weighted Average at Xnp457.67027027027
Midmean - Weighted Average at X(n+1)p463.730555555556
Midmean - Empirical Distribution Function457.67027027027
Midmean - Empirical Distribution Function - Averaging463.730555555556
Midmean - Empirical Distribution Function - Interpolation463.730555555556
Midmean - Closest Observation457.67027027027
Midmean - True Basic - Statistics Graphics Toolkit463.730555555556
Midmean - MS Excel (old versions)465.75
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')