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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 24 Dec 2009 02:15:55 -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/2009/Dec/24/t12616461905d827pm0or73p06.htm/, Retrieved Sun, 05 May 2024 23:40:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70618, Retrieved Sun, 05 May 2024 23:40:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [aandelenmarkt BEL 20] [2009-12-24 09:08:37] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [maandelijkse prij...] [2009-12-24 09:15:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48
43,8
45,29
44,01
47,48
51,07
57,84
69,04
65,61
72,87
68,41
73,25
77,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70618&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70618&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean70.34052.7794501287775625.3073438057825
Geometric Mean67.5726019710902
Harmonic Mean65.1846498953502
Quadratic Mean73.5090550771355
Winsorized Mean ( 1 / 20 )70.34816666666672.7487063777241925.5931907593971
Winsorized Mean ( 2 / 20 )70.06716666666672.6422193963621326.5183000182108
Winsorized Mean ( 3 / 20 )69.67916666666672.5085697670914727.7764515784049
Winsorized Mean ( 4 / 20 )69.32183333333332.367398718941229.2818580912035
Winsorized Mean ( 5 / 20 )68.79683333333332.2016583053041031.2477341136871
Winsorized Mean ( 6 / 20 )68.82283333333332.1378294353021832.1928551440332
Winsorized Mean ( 7 / 20 )68.38651.8576455060832236.8135361542636
Winsorized Mean ( 8 / 20 )68.28516666666671.7962907087283138.0145409286281
Winsorized Mean ( 9 / 20 )68.44866666666671.7503851951642239.1049163668485
Winsorized Mean ( 10 / 20 )68.1971.6855326288558940.460207552488
Winsorized Mean ( 11 / 20 )66.87151.2941375599260351.6726367201816
Winsorized Mean ( 12 / 20 )66.06751.1290428330787858.5163804811913
Winsorized Mean ( 13 / 20 )65.87466666666671.0839283928510360.7740023244505
Winsorized Mean ( 14 / 20 )65.8771.0359642551039663.5900318716972
Winsorized Mean ( 15 / 20 )66.08450.96636009433383868.3849637288215
Winsorized Mean ( 16 / 20 )65.96183333333330.91460523705158472.1205506607143
Winsorized Mean ( 17 / 20 )65.94766666666670.90977706857281372.4877213822505
Winsorized Mean ( 18 / 20 )65.77366666666670.83731366817204278.553198361444
Winsorized Mean ( 19 / 20 )65.90983333333330.78098950316183284.3927262357532
Winsorized Mean ( 20 / 20 )65.72650.72499864893698490.6574103225851
Trimmed Mean ( 1 / 20 )69.73103448275862.5874113746906826.9501151478453
Trimmed Mean ( 2 / 20 )69.06982142857142.3817444972266828.9996771311939
Trimmed Mean ( 3 / 20 )68.51574074074072.1962219100029631.1970937129246
Trimmed Mean ( 4 / 20 )68.06826923076922.0313277337933433.5092501807463
Trimmed Mean ( 5 / 20 )67.69221.8831114133534535.9469968266261
Trimmed Mean ( 6 / 20 )67.41604166666671.7583851982094938.3397458846415
Trimmed Mean ( 7 / 20 )67.11021739130431.6177384610679241.4839722281207
Trimmed Mean ( 8 / 20 )66.86159090909091.5300778954311043.6981614522655
Trimmed Mean ( 9 / 20 )66.6073809523811.4332622430385346.4725707217213
Trimmed Mean ( 10 / 20 )66.30051.3153346532346850.4058034485393
Trimmed Mean ( 11 / 20 )66.0010526315791.1740895682579556.2146657426723
Trimmed Mean ( 12 / 20 )65.86916666666671.1164747080921858.9974552842518
Trimmed Mean ( 13 / 20 )65.841.0867951544172860.58179384808
Trimmed Mean ( 14 / 20 )65.8351.0564796228741962.3154470513058
Trimmed Mean ( 15 / 20 )65.8291.0254949295704664.192418803644
Trimmed Mean ( 16 / 20 )65.79250.99949347290562765.825842572773
Trimmed Mean ( 17 / 20 )65.76807692307690.9744720099750767.4909861441372
Trimmed Mean ( 18 / 20 )65.74166666666670.93353342834402570.4224023164167
Trimmed Mean ( 19 / 20 )65.73681818181820.8947892412767473.466259035503
Trimmed Mean ( 20 / 20 )65.70950.85164839390566977.1556671394113
Median64.925
Midrange88.015
Midmean - Weighted Average at Xnp65.5158064516129
Midmean - Weighted Average at X(n+1)p65.829
Midmean - Empirical Distribution Function65.5158064516129
Midmean - Empirical Distribution Function - Averaging65.829
Midmean - Empirical Distribution Function - Interpolation65.829
Midmean - Closest Observation65.5158064516129
Midmean - True Basic - Statistics Graphics Toolkit65.829
Midmean - MS Excel (old versions)65.835
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 70.3405 & 2.77945012877756 & 25.3073438057825 \tabularnewline
Geometric Mean & 67.5726019710902 &  &  \tabularnewline
Harmonic Mean & 65.1846498953502 &  &  \tabularnewline
Quadratic Mean & 73.5090550771355 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 70.3481666666667 & 2.74870637772419 & 25.5931907593971 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 70.0671666666667 & 2.64221939636213 & 26.5183000182108 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 69.6791666666667 & 2.50856976709147 & 27.7764515784049 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 69.3218333333333 & 2.3673987189412 & 29.2818580912035 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 68.7968333333333 & 2.20165830530410 & 31.2477341136871 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 68.8228333333333 & 2.13782943530218 & 32.1928551440332 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 68.3865 & 1.85764550608322 & 36.8135361542636 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 68.2851666666667 & 1.79629070872831 & 38.0145409286281 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 68.4486666666667 & 1.75038519516422 & 39.1049163668485 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 68.197 & 1.68553262885589 & 40.460207552488 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 66.8715 & 1.29413755992603 & 51.6726367201816 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 66.0675 & 1.12904283307878 & 58.5163804811913 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 65.8746666666667 & 1.08392839285103 & 60.7740023244505 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 65.877 & 1.03596425510396 & 63.5900318716972 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 66.0845 & 0.966360094333838 & 68.3849637288215 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 65.9618333333333 & 0.914605237051584 & 72.1205506607143 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 65.9476666666667 & 0.909777068572813 & 72.4877213822505 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 65.7736666666667 & 0.837313668172042 & 78.553198361444 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 65.9098333333333 & 0.780989503161832 & 84.3927262357532 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 65.7265 & 0.724998648936984 & 90.6574103225851 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 69.7310344827586 & 2.58741137469068 & 26.9501151478453 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 69.0698214285714 & 2.38174449722668 & 28.9996771311939 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 68.5157407407407 & 2.19622191000296 & 31.1970937129246 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 68.0682692307692 & 2.03132773379334 & 33.5092501807463 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 67.6922 & 1.88311141335345 & 35.9469968266261 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 67.4160416666667 & 1.75838519820949 & 38.3397458846415 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 67.1102173913043 & 1.61773846106792 & 41.4839722281207 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 66.8615909090909 & 1.53007789543110 & 43.6981614522655 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 66.607380952381 & 1.43326224303853 & 46.4725707217213 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 66.3005 & 1.31533465323468 & 50.4058034485393 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 66.001052631579 & 1.17408956825795 & 56.2146657426723 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 65.8691666666667 & 1.11647470809218 & 58.9974552842518 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 65.84 & 1.08679515441728 & 60.58179384808 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 65.835 & 1.05647962287419 & 62.3154470513058 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 65.829 & 1.02549492957046 & 64.192418803644 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 65.7925 & 0.999493472905627 & 65.825842572773 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 65.7680769230769 & 0.97447200997507 & 67.4909861441372 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 65.7416666666667 & 0.933533428344025 & 70.4224023164167 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 65.7368181818182 & 0.89478924127674 & 73.466259035503 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 65.7095 & 0.851648393905669 & 77.1556671394113 \tabularnewline
Median & 64.925 &  &  \tabularnewline
Midrange & 88.015 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65.5158064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 65.829 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65.5158064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 65.829 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 65.829 &  &  \tabularnewline
Midmean - Closest Observation & 65.5158064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 65.829 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 65.835 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70618&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]70.3405[/C][C]2.77945012877756[/C][C]25.3073438057825[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]67.5726019710902[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]65.1846498953502[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]73.5090550771355[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]70.3481666666667[/C][C]2.74870637772419[/C][C]25.5931907593971[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]70.0671666666667[/C][C]2.64221939636213[/C][C]26.5183000182108[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]69.6791666666667[/C][C]2.50856976709147[/C][C]27.7764515784049[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]69.3218333333333[/C][C]2.3673987189412[/C][C]29.2818580912035[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]68.7968333333333[/C][C]2.20165830530410[/C][C]31.2477341136871[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]68.8228333333333[/C][C]2.13782943530218[/C][C]32.1928551440332[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]68.3865[/C][C]1.85764550608322[/C][C]36.8135361542636[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]68.2851666666667[/C][C]1.79629070872831[/C][C]38.0145409286281[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]68.4486666666667[/C][C]1.75038519516422[/C][C]39.1049163668485[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]68.197[/C][C]1.68553262885589[/C][C]40.460207552488[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]66.8715[/C][C]1.29413755992603[/C][C]51.6726367201816[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]66.0675[/C][C]1.12904283307878[/C][C]58.5163804811913[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]65.8746666666667[/C][C]1.08392839285103[/C][C]60.7740023244505[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]65.877[/C][C]1.03596425510396[/C][C]63.5900318716972[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]66.0845[/C][C]0.966360094333838[/C][C]68.3849637288215[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]65.9618333333333[/C][C]0.914605237051584[/C][C]72.1205506607143[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]65.9476666666667[/C][C]0.909777068572813[/C][C]72.4877213822505[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]65.7736666666667[/C][C]0.837313668172042[/C][C]78.553198361444[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]65.9098333333333[/C][C]0.780989503161832[/C][C]84.3927262357532[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]65.7265[/C][C]0.724998648936984[/C][C]90.6574103225851[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]69.7310344827586[/C][C]2.58741137469068[/C][C]26.9501151478453[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]69.0698214285714[/C][C]2.38174449722668[/C][C]28.9996771311939[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]68.5157407407407[/C][C]2.19622191000296[/C][C]31.1970937129246[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]68.0682692307692[/C][C]2.03132773379334[/C][C]33.5092501807463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]67.6922[/C][C]1.88311141335345[/C][C]35.9469968266261[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]67.4160416666667[/C][C]1.75838519820949[/C][C]38.3397458846415[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]67.1102173913043[/C][C]1.61773846106792[/C][C]41.4839722281207[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]66.8615909090909[/C][C]1.53007789543110[/C][C]43.6981614522655[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]66.607380952381[/C][C]1.43326224303853[/C][C]46.4725707217213[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]66.3005[/C][C]1.31533465323468[/C][C]50.4058034485393[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]66.001052631579[/C][C]1.17408956825795[/C][C]56.2146657426723[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]65.8691666666667[/C][C]1.11647470809218[/C][C]58.9974552842518[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]65.84[/C][C]1.08679515441728[/C][C]60.58179384808[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]65.835[/C][C]1.05647962287419[/C][C]62.3154470513058[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]65.829[/C][C]1.02549492957046[/C][C]64.192418803644[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]65.7925[/C][C]0.999493472905627[/C][C]65.825842572773[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]65.7680769230769[/C][C]0.97447200997507[/C][C]67.4909861441372[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]65.7416666666667[/C][C]0.933533428344025[/C][C]70.4224023164167[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]65.7368181818182[/C][C]0.89478924127674[/C][C]73.466259035503[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]65.7095[/C][C]0.851648393905669[/C][C]77.1556671394113[/C][/ROW]
[ROW][C]Median[/C][C]64.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]88.015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65.5158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]65.829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65.5158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]65.829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]65.829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65.5158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]65.829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]65.835[/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=70618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70618&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 Mean70.34052.7794501287775625.3073438057825
Geometric Mean67.5726019710902
Harmonic Mean65.1846498953502
Quadratic Mean73.5090550771355
Winsorized Mean ( 1 / 20 )70.34816666666672.7487063777241925.5931907593971
Winsorized Mean ( 2 / 20 )70.06716666666672.6422193963621326.5183000182108
Winsorized Mean ( 3 / 20 )69.67916666666672.5085697670914727.7764515784049
Winsorized Mean ( 4 / 20 )69.32183333333332.367398718941229.2818580912035
Winsorized Mean ( 5 / 20 )68.79683333333332.2016583053041031.2477341136871
Winsorized Mean ( 6 / 20 )68.82283333333332.1378294353021832.1928551440332
Winsorized Mean ( 7 / 20 )68.38651.8576455060832236.8135361542636
Winsorized Mean ( 8 / 20 )68.28516666666671.7962907087283138.0145409286281
Winsorized Mean ( 9 / 20 )68.44866666666671.7503851951642239.1049163668485
Winsorized Mean ( 10 / 20 )68.1971.6855326288558940.460207552488
Winsorized Mean ( 11 / 20 )66.87151.2941375599260351.6726367201816
Winsorized Mean ( 12 / 20 )66.06751.1290428330787858.5163804811913
Winsorized Mean ( 13 / 20 )65.87466666666671.0839283928510360.7740023244505
Winsorized Mean ( 14 / 20 )65.8771.0359642551039663.5900318716972
Winsorized Mean ( 15 / 20 )66.08450.96636009433383868.3849637288215
Winsorized Mean ( 16 / 20 )65.96183333333330.91460523705158472.1205506607143
Winsorized Mean ( 17 / 20 )65.94766666666670.90977706857281372.4877213822505
Winsorized Mean ( 18 / 20 )65.77366666666670.83731366817204278.553198361444
Winsorized Mean ( 19 / 20 )65.90983333333330.78098950316183284.3927262357532
Winsorized Mean ( 20 / 20 )65.72650.72499864893698490.6574103225851
Trimmed Mean ( 1 / 20 )69.73103448275862.5874113746906826.9501151478453
Trimmed Mean ( 2 / 20 )69.06982142857142.3817444972266828.9996771311939
Trimmed Mean ( 3 / 20 )68.51574074074072.1962219100029631.1970937129246
Trimmed Mean ( 4 / 20 )68.06826923076922.0313277337933433.5092501807463
Trimmed Mean ( 5 / 20 )67.69221.8831114133534535.9469968266261
Trimmed Mean ( 6 / 20 )67.41604166666671.7583851982094938.3397458846415
Trimmed Mean ( 7 / 20 )67.11021739130431.6177384610679241.4839722281207
Trimmed Mean ( 8 / 20 )66.86159090909091.5300778954311043.6981614522655
Trimmed Mean ( 9 / 20 )66.6073809523811.4332622430385346.4725707217213
Trimmed Mean ( 10 / 20 )66.30051.3153346532346850.4058034485393
Trimmed Mean ( 11 / 20 )66.0010526315791.1740895682579556.2146657426723
Trimmed Mean ( 12 / 20 )65.86916666666671.1164747080921858.9974552842518
Trimmed Mean ( 13 / 20 )65.841.0867951544172860.58179384808
Trimmed Mean ( 14 / 20 )65.8351.0564796228741962.3154470513058
Trimmed Mean ( 15 / 20 )65.8291.0254949295704664.192418803644
Trimmed Mean ( 16 / 20 )65.79250.99949347290562765.825842572773
Trimmed Mean ( 17 / 20 )65.76807692307690.9744720099750767.4909861441372
Trimmed Mean ( 18 / 20 )65.74166666666670.93353342834402570.4224023164167
Trimmed Mean ( 19 / 20 )65.73681818181820.8947892412767473.466259035503
Trimmed Mean ( 20 / 20 )65.70950.85164839390566977.1556671394113
Median64.925
Midrange88.015
Midmean - Weighted Average at Xnp65.5158064516129
Midmean - Weighted Average at X(n+1)p65.829
Midmean - Empirical Distribution Function65.5158064516129
Midmean - Empirical Distribution Function - Averaging65.829
Midmean - Empirical Distribution Function - Interpolation65.829
Midmean - Closest Observation65.5158064516129
Midmean - True Basic - Statistics Graphics Toolkit65.829
Midmean - MS Excel (old versions)65.835
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')