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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, 13 Dec 2008 04:00:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/13/t1229166051bvzrn54al672pk8.htm/, Retrieved Sat, 18 May 2024 09:56:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32964, Retrieved Sat, 18 May 2024 09:56:21 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - central t...] [2008-12-13 11:00:08] [73ec5abea95a9c3c8c3a1ac44cab1f72] [Current]
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Dataseries X:
535
681
830
720
582
806
728
803
830
699
622
655
571
512
674
522
627
769
633
715
702
678
531
562
504
552
511
695
559
677
636
694
694
624
524
557
490
475
492
491
489
606
618
607
637
597
539
600
448
520
607
566
595
625
667
587
629
562
511
664




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=32964&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=32964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32964&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 Mean613.93333333333311.909566649453651.5495946581314
Geometric Mean607.286931037237
Harmonic Mean600.814164497156
Quadratic Mean620.711339244472
Winsorized Mean ( 1 / 20 )614.38333333333311.811396671736152.0161459654903
Winsorized Mean ( 2 / 20 )614.0511.484389429350253.4682321404649
Winsorized Mean ( 3 / 20 )613.9511.432914744194653.7002167633368
Winsorized Mean ( 4 / 20 )611.7510.822701214665456.5247056040908
Winsorized Mean ( 5 / 20 )608.41666666666710.038155784958160.6104029166752
Winsorized Mean ( 6 / 20 )608.8166666666679.6506927729628263.0852811284507
Winsorized Mean ( 7 / 20 )609.059.3904755509743164.8582701370015
Winsorized Mean ( 8 / 20 )607.3166666666679.0712027017228566.9499609518507
Winsorized Mean ( 9 / 20 )607.0166666666678.9652969256025567.7073689476124
Winsorized Mean ( 10 / 20 )607.6833333333338.615204391326570.5361481551301
Winsorized Mean ( 11 / 20 )607.8666666666678.5208109036490171.3390630939069
Winsorized Mean ( 12 / 20 )608.2666666666678.4528558563399371.9599005359172
Winsorized Mean ( 13 / 20 )606.9666666666677.726868766946978.5527339694286
Winsorized Mean ( 14 / 20 )607.27.4593739607962881.4009329993669
Winsorized Mean ( 15 / 20 )607.957.2565351415043183.7796535322737
Winsorized Mean ( 16 / 20 )610.6166666666676.5852982836005692.7242230146647
Winsorized Mean ( 17 / 20 )610.056.05308087965073100.783388183506
Winsorized Mean ( 18 / 20 )609.755.8213335009097104.744041877126
Winsorized Mean ( 19 / 20 )607.855.23778239398886116.051022031308
Winsorized Mean ( 20 / 20 )601.854.36633403226963137.838744253645
Trimmed Mean ( 1 / 20 )613.06896551724111.376041254376453.8912396508225
Trimmed Mean ( 2 / 20 )611.66071428571410.835406032393456.4501886184145
Trimmed Mean ( 3 / 20 )610.33333333333310.385679276395258.7668189138587
Trimmed Mean ( 4 / 20 )608.9423076923089.8442016323281661.8579678104676
Trimmed Mean ( 5 / 20 )608.19.4207001776266464.5493422499726
Trimmed Mean ( 6 / 20 )608.0208333333339.167012707040466.3270416180796
Trimmed Mean ( 7 / 20 )607.8478260869578.9609980137385667.8326035956078
Trimmed Mean ( 8 / 20 )607.6136363636368.7650936510406269.3219788121144
Trimmed Mean ( 9 / 20 )607.6666666666678.5916975472892470.7271948671413
Trimmed Mean ( 10 / 20 )607.7758.3826352490102272.5040493765684
Trimmed Mean ( 11 / 20 )607.789473684218.189883595441474.2122237271496
Trimmed Mean ( 12 / 20 )607.7777777777787.9439615792872776.5081466862164
Trimmed Mean ( 13 / 20 )607.7058823529417.6148987809051679.8048535952707
Trimmed Mean ( 14 / 20 )607.81257.3646985873325582.5305330275772
Trimmed Mean ( 15 / 20 )607.97.0772989847497885.8943505580177
Trimmed Mean ( 16 / 20 )607.8928571428576.7116220935201890.5731652754637
Trimmed Mean ( 17 / 20 )607.56.3918818704786795.0424323086726
Trimmed Mean ( 18 / 20 )607.1256.0885115443831699.7164899128905
Trimmed Mean ( 19 / 20 )606.7272727272735.68059727142265106.806950702091
Trimmed Mean ( 20 / 20 )606.555.27580126117052114.968318549859
Median607
Midrange639
Midmean - Weighted Average at Xnp605.548387096774
Midmean - Weighted Average at X(n+1)p607.9
Midmean - Empirical Distribution Function605.548387096774
Midmean - Empirical Distribution Function - Averaging607.9
Midmean - Empirical Distribution Function - Interpolation607.9
Midmean - Closest Observation605.548387096774
Midmean - True Basic - Statistics Graphics Toolkit607.9
Midmean - MS Excel (old versions)607.8125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 613.933333333333 & 11.9095666494536 & 51.5495946581314 \tabularnewline
Geometric Mean & 607.286931037237 &  &  \tabularnewline
Harmonic Mean & 600.814164497156 &  &  \tabularnewline
Quadratic Mean & 620.711339244472 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 614.383333333333 & 11.8113966717361 & 52.0161459654903 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 614.05 & 11.4843894293502 & 53.4682321404649 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 613.95 & 11.4329147441946 & 53.7002167633368 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 611.75 & 10.8227012146654 & 56.5247056040908 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 608.416666666667 & 10.0381557849581 & 60.6104029166752 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 608.816666666667 & 9.65069277296282 & 63.0852811284507 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 609.05 & 9.39047555097431 & 64.8582701370015 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 607.316666666667 & 9.07120270172285 & 66.9499609518507 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 607.016666666667 & 8.96529692560255 & 67.7073689476124 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 607.683333333333 & 8.6152043913265 & 70.5361481551301 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 607.866666666667 & 8.52081090364901 & 71.3390630939069 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 608.266666666667 & 8.45285585633993 & 71.9599005359172 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 606.966666666667 & 7.7268687669469 & 78.5527339694286 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 607.2 & 7.45937396079628 & 81.4009329993669 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 607.95 & 7.25653514150431 & 83.7796535322737 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 610.616666666667 & 6.58529828360056 & 92.7242230146647 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 610.05 & 6.05308087965073 & 100.783388183506 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 609.75 & 5.8213335009097 & 104.744041877126 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 607.85 & 5.23778239398886 & 116.051022031308 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 601.85 & 4.36633403226963 & 137.838744253645 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 613.068965517241 & 11.3760412543764 & 53.8912396508225 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 611.660714285714 & 10.8354060323934 & 56.4501886184145 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 610.333333333333 & 10.3856792763952 & 58.7668189138587 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 608.942307692308 & 9.84420163232816 & 61.8579678104676 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 608.1 & 9.42070017762664 & 64.5493422499726 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 608.020833333333 & 9.1670127070404 & 66.3270416180796 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 607.847826086957 & 8.96099801373856 & 67.8326035956078 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 607.613636363636 & 8.76509365104062 & 69.3219788121144 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 607.666666666667 & 8.59169754728924 & 70.7271948671413 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 607.775 & 8.38263524901022 & 72.5040493765684 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 607.78947368421 & 8.1898835954414 & 74.2122237271496 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 607.777777777778 & 7.94396157928727 & 76.5081466862164 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 607.705882352941 & 7.61489878090516 & 79.8048535952707 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 607.8125 & 7.36469858733255 & 82.5305330275772 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 607.9 & 7.07729898474978 & 85.8943505580177 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 607.892857142857 & 6.71162209352018 & 90.5731652754637 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 607.5 & 6.39188187047867 & 95.0424323086726 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 607.125 & 6.08851154438316 & 99.7164899128905 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 606.727272727273 & 5.68059727142265 & 106.806950702091 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 606.55 & 5.27580126117052 & 114.968318549859 \tabularnewline
Median & 607 &  &  \tabularnewline
Midrange & 639 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 605.548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 607.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 605.548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 607.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 607.9 &  &  \tabularnewline
Midmean - Closest Observation & 605.548387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 607.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 607.8125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32964&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]613.933333333333[/C][C]11.9095666494536[/C][C]51.5495946581314[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]607.286931037237[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]600.814164497156[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]620.711339244472[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]614.383333333333[/C][C]11.8113966717361[/C][C]52.0161459654903[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]614.05[/C][C]11.4843894293502[/C][C]53.4682321404649[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]613.95[/C][C]11.4329147441946[/C][C]53.7002167633368[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]611.75[/C][C]10.8227012146654[/C][C]56.5247056040908[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]608.416666666667[/C][C]10.0381557849581[/C][C]60.6104029166752[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]608.816666666667[/C][C]9.65069277296282[/C][C]63.0852811284507[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]609.05[/C][C]9.39047555097431[/C][C]64.8582701370015[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]607.316666666667[/C][C]9.07120270172285[/C][C]66.9499609518507[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]607.016666666667[/C][C]8.96529692560255[/C][C]67.7073689476124[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]607.683333333333[/C][C]8.6152043913265[/C][C]70.5361481551301[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]607.866666666667[/C][C]8.52081090364901[/C][C]71.3390630939069[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]608.266666666667[/C][C]8.45285585633993[/C][C]71.9599005359172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]606.966666666667[/C][C]7.7268687669469[/C][C]78.5527339694286[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]607.2[/C][C]7.45937396079628[/C][C]81.4009329993669[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]607.95[/C][C]7.25653514150431[/C][C]83.7796535322737[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]610.616666666667[/C][C]6.58529828360056[/C][C]92.7242230146647[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]610.05[/C][C]6.05308087965073[/C][C]100.783388183506[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]609.75[/C][C]5.8213335009097[/C][C]104.744041877126[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]607.85[/C][C]5.23778239398886[/C][C]116.051022031308[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]601.85[/C][C]4.36633403226963[/C][C]137.838744253645[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]613.068965517241[/C][C]11.3760412543764[/C][C]53.8912396508225[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]611.660714285714[/C][C]10.8354060323934[/C][C]56.4501886184145[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]610.333333333333[/C][C]10.3856792763952[/C][C]58.7668189138587[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]608.942307692308[/C][C]9.84420163232816[/C][C]61.8579678104676[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]608.1[/C][C]9.42070017762664[/C][C]64.5493422499726[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]608.020833333333[/C][C]9.1670127070404[/C][C]66.3270416180796[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]607.847826086957[/C][C]8.96099801373856[/C][C]67.8326035956078[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]607.613636363636[/C][C]8.76509365104062[/C][C]69.3219788121144[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]607.666666666667[/C][C]8.59169754728924[/C][C]70.7271948671413[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]607.775[/C][C]8.38263524901022[/C][C]72.5040493765684[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]607.78947368421[/C][C]8.1898835954414[/C][C]74.2122237271496[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]607.777777777778[/C][C]7.94396157928727[/C][C]76.5081466862164[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]607.705882352941[/C][C]7.61489878090516[/C][C]79.8048535952707[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]607.8125[/C][C]7.36469858733255[/C][C]82.5305330275772[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]607.9[/C][C]7.07729898474978[/C][C]85.8943505580177[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]607.892857142857[/C][C]6.71162209352018[/C][C]90.5731652754637[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]607.5[/C][C]6.39188187047867[/C][C]95.0424323086726[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]607.125[/C][C]6.08851154438316[/C][C]99.7164899128905[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]606.727272727273[/C][C]5.68059727142265[/C][C]106.806950702091[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]606.55[/C][C]5.27580126117052[/C][C]114.968318549859[/C][/ROW]
[ROW][C]Median[/C][C]607[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]639[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]605.548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]607.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]605.548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]607.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]607.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]605.548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]607.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]607.8125[/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=32964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32964&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 Mean613.93333333333311.909566649453651.5495946581314
Geometric Mean607.286931037237
Harmonic Mean600.814164497156
Quadratic Mean620.711339244472
Winsorized Mean ( 1 / 20 )614.38333333333311.811396671736152.0161459654903
Winsorized Mean ( 2 / 20 )614.0511.484389429350253.4682321404649
Winsorized Mean ( 3 / 20 )613.9511.432914744194653.7002167633368
Winsorized Mean ( 4 / 20 )611.7510.822701214665456.5247056040908
Winsorized Mean ( 5 / 20 )608.41666666666710.038155784958160.6104029166752
Winsorized Mean ( 6 / 20 )608.8166666666679.6506927729628263.0852811284507
Winsorized Mean ( 7 / 20 )609.059.3904755509743164.8582701370015
Winsorized Mean ( 8 / 20 )607.3166666666679.0712027017228566.9499609518507
Winsorized Mean ( 9 / 20 )607.0166666666678.9652969256025567.7073689476124
Winsorized Mean ( 10 / 20 )607.6833333333338.615204391326570.5361481551301
Winsorized Mean ( 11 / 20 )607.8666666666678.5208109036490171.3390630939069
Winsorized Mean ( 12 / 20 )608.2666666666678.4528558563399371.9599005359172
Winsorized Mean ( 13 / 20 )606.9666666666677.726868766946978.5527339694286
Winsorized Mean ( 14 / 20 )607.27.4593739607962881.4009329993669
Winsorized Mean ( 15 / 20 )607.957.2565351415043183.7796535322737
Winsorized Mean ( 16 / 20 )610.6166666666676.5852982836005692.7242230146647
Winsorized Mean ( 17 / 20 )610.056.05308087965073100.783388183506
Winsorized Mean ( 18 / 20 )609.755.8213335009097104.744041877126
Winsorized Mean ( 19 / 20 )607.855.23778239398886116.051022031308
Winsorized Mean ( 20 / 20 )601.854.36633403226963137.838744253645
Trimmed Mean ( 1 / 20 )613.06896551724111.376041254376453.8912396508225
Trimmed Mean ( 2 / 20 )611.66071428571410.835406032393456.4501886184145
Trimmed Mean ( 3 / 20 )610.33333333333310.385679276395258.7668189138587
Trimmed Mean ( 4 / 20 )608.9423076923089.8442016323281661.8579678104676
Trimmed Mean ( 5 / 20 )608.19.4207001776266464.5493422499726
Trimmed Mean ( 6 / 20 )608.0208333333339.167012707040466.3270416180796
Trimmed Mean ( 7 / 20 )607.8478260869578.9609980137385667.8326035956078
Trimmed Mean ( 8 / 20 )607.6136363636368.7650936510406269.3219788121144
Trimmed Mean ( 9 / 20 )607.6666666666678.5916975472892470.7271948671413
Trimmed Mean ( 10 / 20 )607.7758.3826352490102272.5040493765684
Trimmed Mean ( 11 / 20 )607.789473684218.189883595441474.2122237271496
Trimmed Mean ( 12 / 20 )607.7777777777787.9439615792872776.5081466862164
Trimmed Mean ( 13 / 20 )607.7058823529417.6148987809051679.8048535952707
Trimmed Mean ( 14 / 20 )607.81257.3646985873325582.5305330275772
Trimmed Mean ( 15 / 20 )607.97.0772989847497885.8943505580177
Trimmed Mean ( 16 / 20 )607.8928571428576.7116220935201890.5731652754637
Trimmed Mean ( 17 / 20 )607.56.3918818704786795.0424323086726
Trimmed Mean ( 18 / 20 )607.1256.0885115443831699.7164899128905
Trimmed Mean ( 19 / 20 )606.7272727272735.68059727142265106.806950702091
Trimmed Mean ( 20 / 20 )606.555.27580126117052114.968318549859
Median607
Midrange639
Midmean - Weighted Average at Xnp605.548387096774
Midmean - Weighted Average at X(n+1)p607.9
Midmean - Empirical Distribution Function605.548387096774
Midmean - Empirical Distribution Function - Averaging607.9
Midmean - Empirical Distribution Function - Interpolation607.9
Midmean - Closest Observation605.548387096774
Midmean - True Basic - Statistics Graphics Toolkit607.9
Midmean - MS Excel (old versions)607.8125
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')