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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 18 Oct 2008 04:47:17 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/18/t1224326875jr9rcz6pum5wm5h.htm/, Retrieved Sun, 19 May 2024 16:32:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16569, Retrieved Sun, 19 May 2024 16:32:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:23:12] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP     [Central Tendency] [Central Tendency ...] [2008-10-18 10:47:17] [fdd69703d301fae09456f660b2f52997] [Current]
F    D      [Central Tendency] [Central Tendency ...] [2008-10-20 21:11:22] [3754dd41128068acfc463ebbabce5a9c]
-    D        [Central Tendency] [] [2008-10-20 21:17:29] [3754dd41128068acfc463ebbabce5a9c]
-    D          [Central Tendency] [Central Tendency ...] [2008-10-20 21:22:30] [3754dd41128068acfc463ebbabce5a9c]
-    D            [Central Tendency] [Central Tendency ...] [2008-10-20 21:26:01] [3754dd41128068acfc463ebbabce5a9c]
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Dataseries X:
744.8
672.1
666.6
760.8
756
604.4
883.9
527.9
756.2
812.9
655.6
707.6
612.6
659.2
833.4
727.8
797.2
753
762
613.7
759.2
816.4
736.8
680.1
736.5
637.2
801.9
772.3
897.3
792.1
826.8
666.8
906.6
871.4
891
739.2
833.6
715.6
871.6
751.6
1005.5
681.2
837.3
674.7
806.3
860.2
689.8
691.6
682.6
800.1
1023.7
733.5
875.3
770.2
1005.7
982.3
742.9
974.2
822.3
773.2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16569&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16569&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean774.07166666666713.661726837369756.6598700062794
Geometric Mean767.045835036099
Harmonic Mean760.075597568644
Quadratic Mean781.152270153948
Winsorized Mean ( 1 / 20 )775.04666666666713.236055121481958.5557146410472
Winsorized Mean ( 2 / 20 )775.31333333333313.175610164296258.8445866009535
Winsorized Mean ( 3 / 20 )774.20833333333312.832708097983860.3308613756257
Winsorized Mean ( 4 / 20 )775.23512.370342432311962.6688391402208
Winsorized Mean ( 5 / 20 )771.13510.700652555475072.064296640063
Winsorized Mean ( 6 / 20 )770.56510.439660314678673.8113096377812
Winsorized Mean ( 7 / 20 )770.69333333333310.136873415236876.0287025163891
Winsorized Mean ( 8 / 20 )769.7733333333339.9449024124154777.4038096514983
Winsorized Mean ( 9 / 20 )769.2783333333339.5598489727765880.4697161559763
Winsorized Mean ( 10 / 20 )769.0959.3703874302624482.0771825843768
Winsorized Mean ( 11 / 20 )770.0483333333339.1969696838332883.7284844688516
Winsorized Mean ( 12 / 20 )768.0283333333338.7508718182840387.7659219883233
Winsorized Mean ( 13 / 20 )763.377.857964148872997.1460273345093
Winsorized Mean ( 14 / 20 )764.1866666666677.4318282026124102.826201821786
Winsorized Mean ( 15 / 20 )764.5866666666677.3478497053153104.055839099918
Winsorized Mean ( 16 / 20 )767.0933333333336.36997674771881120.423254858511
Winsorized Mean ( 17 / 20 )768.0855.81487272208182132.089735529931
Winsorized Mean ( 18 / 20 )769.9754.99213541086898154.237603075348
Winsorized Mean ( 19 / 20 )770.6716666666674.56383232488247168.86502654028
Winsorized Mean ( 20 / 20 )769.4716666666674.0855623513698188.339229826876
Trimmed Mean ( 1 / 20 )774.01206896551712.754374142054760.6860093913497
Trimmed Mean ( 2 / 20 )772.90357142857112.158104550529163.5710581543682
Trimmed Mean ( 3 / 20 )771.56481481481511.452648590186967.3699894604225
Trimmed Mean ( 4 / 20 )770.54807692307710.741803669837471.7335840987999
Trimmed Mean ( 5 / 20 )769.14210.033615373801676.6565162551754
Trimmed Mean ( 6 / 20 )768.643759.7588729885044878.7635776083394
Trimmed Mean ( 7 / 20 )768.2260869565229.4871672466047280.975286614817
Trimmed Mean ( 8 / 20 )767.7454545454559.2218851370776183.2525501167488
Trimmed Mean ( 9 / 20 )767.3833333333338.9265390873187485.9665012192123
Trimmed Mean ( 10 / 20 )767.06758.6411874388051688.7687607093574
Trimmed Mean ( 11 / 20 )766.7473684210538.3069960890419792.3013999528054
Trimmed Mean ( 12 / 20 )766.2472222222227.8958372457445997.0444549924312
Trimmed Mean ( 13 / 20 )765.9852941176477.4629962159752102.637770668835
Trimmed Mean ( 14 / 20 )766.36257.13124478739455107.465459796675
Trimmed Mean ( 15 / 20 )766.6733333333336.78590651299184112.980238066279
Trimmed Mean ( 16 / 20 )766.9714285714296.29639154478664121.811266519229
Trimmed Mean ( 17 / 20 )766.9538461538465.93125289856583129.307223831123
Trimmed Mean ( 18 / 20 )766.78755.57650451688256137.503250948438
Trimmed Mean ( 19 / 20 )766.3045454545455.34101372283988143.475487092943
Trimmed Mean ( 20 / 20 )765.6155.10995558225623149.828112529689
Median760
Midrange775.8
Midmean - Weighted Average at Xnp764.193548387097
Midmean - Weighted Average at X(n+1)p766.673333333334
Midmean - Empirical Distribution Function764.193548387097
Midmean - Empirical Distribution Function - Averaging766.673333333334
Midmean - Empirical Distribution Function - Interpolation766.673333333334
Midmean - Closest Observation764.193548387097
Midmean - True Basic - Statistics Graphics Toolkit766.673333333334
Midmean - MS Excel (old versions)766.3625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 774.071666666667 & 13.6617268373697 & 56.6598700062794 \tabularnewline
Geometric Mean & 767.045835036099 &  &  \tabularnewline
Harmonic Mean & 760.075597568644 &  &  \tabularnewline
Quadratic Mean & 781.152270153948 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 775.046666666667 & 13.2360551214819 & 58.5557146410472 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 775.313333333333 & 13.1756101642962 & 58.8445866009535 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 774.208333333333 & 12.8327080979838 & 60.3308613756257 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 775.235 & 12.3703424323119 & 62.6688391402208 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 771.135 & 10.7006525554750 & 72.064296640063 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 770.565 & 10.4396603146786 & 73.8113096377812 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 770.693333333333 & 10.1368734152368 & 76.0287025163891 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 769.773333333333 & 9.94490241241547 & 77.4038096514983 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 769.278333333333 & 9.55984897277658 & 80.4697161559763 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 769.095 & 9.37038743026244 & 82.0771825843768 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 770.048333333333 & 9.19696968383328 & 83.7284844688516 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 768.028333333333 & 8.75087181828403 & 87.7659219883233 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 763.37 & 7.8579641488729 & 97.1460273345093 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 764.186666666667 & 7.4318282026124 & 102.826201821786 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 764.586666666667 & 7.3478497053153 & 104.055839099918 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 767.093333333333 & 6.36997674771881 & 120.423254858511 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 768.085 & 5.81487272208182 & 132.089735529931 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 769.975 & 4.99213541086898 & 154.237603075348 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 770.671666666667 & 4.56383232488247 & 168.86502654028 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 769.471666666667 & 4.0855623513698 & 188.339229826876 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 774.012068965517 & 12.7543741420547 & 60.6860093913497 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 772.903571428571 & 12.1581045505291 & 63.5710581543682 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 771.564814814815 & 11.4526485901869 & 67.3699894604225 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 770.548076923077 & 10.7418036698374 & 71.7335840987999 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 769.142 & 10.0336153738016 & 76.6565162551754 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 768.64375 & 9.75887298850448 & 78.7635776083394 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 768.226086956522 & 9.48716724660472 & 80.975286614817 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 767.745454545455 & 9.22188513707761 & 83.2525501167488 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 767.383333333333 & 8.92653908731874 & 85.9665012192123 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 767.0675 & 8.64118743880516 & 88.7687607093574 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 766.747368421053 & 8.30699608904197 & 92.3013999528054 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 766.247222222222 & 7.89583724574459 & 97.0444549924312 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 765.985294117647 & 7.4629962159752 & 102.637770668835 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 766.3625 & 7.13124478739455 & 107.465459796675 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 766.673333333333 & 6.78590651299184 & 112.980238066279 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 766.971428571429 & 6.29639154478664 & 121.811266519229 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 766.953846153846 & 5.93125289856583 & 129.307223831123 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 766.7875 & 5.57650451688256 & 137.503250948438 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 766.304545454545 & 5.34101372283988 & 143.475487092943 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 765.615 & 5.10995558225623 & 149.828112529689 \tabularnewline
Median & 760 &  &  \tabularnewline
Midrange & 775.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 764.193548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 766.673333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 764.193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 766.673333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 766.673333333334 &  &  \tabularnewline
Midmean - Closest Observation & 764.193548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 766.673333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 766.3625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16569&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]774.071666666667[/C][C]13.6617268373697[/C][C]56.6598700062794[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]767.045835036099[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]760.075597568644[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]781.152270153948[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]775.046666666667[/C][C]13.2360551214819[/C][C]58.5557146410472[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]775.313333333333[/C][C]13.1756101642962[/C][C]58.8445866009535[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]774.208333333333[/C][C]12.8327080979838[/C][C]60.3308613756257[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]775.235[/C][C]12.3703424323119[/C][C]62.6688391402208[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]771.135[/C][C]10.7006525554750[/C][C]72.064296640063[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]770.565[/C][C]10.4396603146786[/C][C]73.8113096377812[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]770.693333333333[/C][C]10.1368734152368[/C][C]76.0287025163891[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]769.773333333333[/C][C]9.94490241241547[/C][C]77.4038096514983[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]769.278333333333[/C][C]9.55984897277658[/C][C]80.4697161559763[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]769.095[/C][C]9.37038743026244[/C][C]82.0771825843768[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]770.048333333333[/C][C]9.19696968383328[/C][C]83.7284844688516[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]768.028333333333[/C][C]8.75087181828403[/C][C]87.7659219883233[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]763.37[/C][C]7.8579641488729[/C][C]97.1460273345093[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]764.186666666667[/C][C]7.4318282026124[/C][C]102.826201821786[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]764.586666666667[/C][C]7.3478497053153[/C][C]104.055839099918[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]767.093333333333[/C][C]6.36997674771881[/C][C]120.423254858511[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]768.085[/C][C]5.81487272208182[/C][C]132.089735529931[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]769.975[/C][C]4.99213541086898[/C][C]154.237603075348[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]770.671666666667[/C][C]4.56383232488247[/C][C]168.86502654028[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]769.471666666667[/C][C]4.0855623513698[/C][C]188.339229826876[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]774.012068965517[/C][C]12.7543741420547[/C][C]60.6860093913497[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]772.903571428571[/C][C]12.1581045505291[/C][C]63.5710581543682[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]771.564814814815[/C][C]11.4526485901869[/C][C]67.3699894604225[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]770.548076923077[/C][C]10.7418036698374[/C][C]71.7335840987999[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]769.142[/C][C]10.0336153738016[/C][C]76.6565162551754[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]768.64375[/C][C]9.75887298850448[/C][C]78.7635776083394[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]768.226086956522[/C][C]9.48716724660472[/C][C]80.975286614817[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]767.745454545455[/C][C]9.22188513707761[/C][C]83.2525501167488[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]767.383333333333[/C][C]8.92653908731874[/C][C]85.9665012192123[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]767.0675[/C][C]8.64118743880516[/C][C]88.7687607093574[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]766.747368421053[/C][C]8.30699608904197[/C][C]92.3013999528054[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]766.247222222222[/C][C]7.89583724574459[/C][C]97.0444549924312[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]765.985294117647[/C][C]7.4629962159752[/C][C]102.637770668835[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]766.3625[/C][C]7.13124478739455[/C][C]107.465459796675[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]766.673333333333[/C][C]6.78590651299184[/C][C]112.980238066279[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]766.971428571429[/C][C]6.29639154478664[/C][C]121.811266519229[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]766.953846153846[/C][C]5.93125289856583[/C][C]129.307223831123[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]766.7875[/C][C]5.57650451688256[/C][C]137.503250948438[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]766.304545454545[/C][C]5.34101372283988[/C][C]143.475487092943[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]765.615[/C][C]5.10995558225623[/C][C]149.828112529689[/C][/ROW]
[ROW][C]Median[/C][C]760[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]775.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]764.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]766.673333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]764.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]766.673333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]766.673333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]764.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]766.673333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]766.3625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16569&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 Mean774.07166666666713.661726837369756.6598700062794
Geometric Mean767.045835036099
Harmonic Mean760.075597568644
Quadratic Mean781.152270153948
Winsorized Mean ( 1 / 20 )775.04666666666713.236055121481958.5557146410472
Winsorized Mean ( 2 / 20 )775.31333333333313.175610164296258.8445866009535
Winsorized Mean ( 3 / 20 )774.20833333333312.832708097983860.3308613756257
Winsorized Mean ( 4 / 20 )775.23512.370342432311962.6688391402208
Winsorized Mean ( 5 / 20 )771.13510.700652555475072.064296640063
Winsorized Mean ( 6 / 20 )770.56510.439660314678673.8113096377812
Winsorized Mean ( 7 / 20 )770.69333333333310.136873415236876.0287025163891
Winsorized Mean ( 8 / 20 )769.7733333333339.9449024124154777.4038096514983
Winsorized Mean ( 9 / 20 )769.2783333333339.5598489727765880.4697161559763
Winsorized Mean ( 10 / 20 )769.0959.3703874302624482.0771825843768
Winsorized Mean ( 11 / 20 )770.0483333333339.1969696838332883.7284844688516
Winsorized Mean ( 12 / 20 )768.0283333333338.7508718182840387.7659219883233
Winsorized Mean ( 13 / 20 )763.377.857964148872997.1460273345093
Winsorized Mean ( 14 / 20 )764.1866666666677.4318282026124102.826201821786
Winsorized Mean ( 15 / 20 )764.5866666666677.3478497053153104.055839099918
Winsorized Mean ( 16 / 20 )767.0933333333336.36997674771881120.423254858511
Winsorized Mean ( 17 / 20 )768.0855.81487272208182132.089735529931
Winsorized Mean ( 18 / 20 )769.9754.99213541086898154.237603075348
Winsorized Mean ( 19 / 20 )770.6716666666674.56383232488247168.86502654028
Winsorized Mean ( 20 / 20 )769.4716666666674.0855623513698188.339229826876
Trimmed Mean ( 1 / 20 )774.01206896551712.754374142054760.6860093913497
Trimmed Mean ( 2 / 20 )772.90357142857112.158104550529163.5710581543682
Trimmed Mean ( 3 / 20 )771.56481481481511.452648590186967.3699894604225
Trimmed Mean ( 4 / 20 )770.54807692307710.741803669837471.7335840987999
Trimmed Mean ( 5 / 20 )769.14210.033615373801676.6565162551754
Trimmed Mean ( 6 / 20 )768.643759.7588729885044878.7635776083394
Trimmed Mean ( 7 / 20 )768.2260869565229.4871672466047280.975286614817
Trimmed Mean ( 8 / 20 )767.7454545454559.2218851370776183.2525501167488
Trimmed Mean ( 9 / 20 )767.3833333333338.9265390873187485.9665012192123
Trimmed Mean ( 10 / 20 )767.06758.6411874388051688.7687607093574
Trimmed Mean ( 11 / 20 )766.7473684210538.3069960890419792.3013999528054
Trimmed Mean ( 12 / 20 )766.2472222222227.8958372457445997.0444549924312
Trimmed Mean ( 13 / 20 )765.9852941176477.4629962159752102.637770668835
Trimmed Mean ( 14 / 20 )766.36257.13124478739455107.465459796675
Trimmed Mean ( 15 / 20 )766.6733333333336.78590651299184112.980238066279
Trimmed Mean ( 16 / 20 )766.9714285714296.29639154478664121.811266519229
Trimmed Mean ( 17 / 20 )766.9538461538465.93125289856583129.307223831123
Trimmed Mean ( 18 / 20 )766.78755.57650451688256137.503250948438
Trimmed Mean ( 19 / 20 )766.3045454545455.34101372283988143.475487092943
Trimmed Mean ( 20 / 20 )765.6155.10995558225623149.828112529689
Median760
Midrange775.8
Midmean - Weighted Average at Xnp764.193548387097
Midmean - Weighted Average at X(n+1)p766.673333333334
Midmean - Empirical Distribution Function764.193548387097
Midmean - Empirical Distribution Function - Averaging766.673333333334
Midmean - Empirical Distribution Function - Interpolation766.673333333334
Midmean - Closest Observation764.193548387097
Midmean - True Basic - Statistics Graphics Toolkit766.673333333334
Midmean - MS Excel (old versions)766.3625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')