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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 computationTue, 15 Nov 2011 16:32:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321392762148tndag07fgwvc.htm/, Retrieved Thu, 28 Mar 2024 10:11:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143580, Retrieved Thu, 28 Mar 2024 10:11:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D    [Central Tendency] [Central tendency ...] [2010-11-06 16:38:19] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R P         [Central Tendency] [] [2011-11-15 21:32:35] [542c32830549043c4555f1bd78aefedb] [Current]
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Dataseries X:
12117
11597
12291
12461
13469
13448
13896
13846
13159
13682
13083
13507
12545
12076
13181
13395
14108
14017
14464
14139
13393
13979
13538
13752
12729
12308
13663
13660
14367
14737
15155
15616
14738
14872
14551
15020
13884
13224
14771
14645
15960
16223
16073
16233
15210
15173
14696
15202
14492
14176
15634
16043
17448
16975
17055
17286
15987
16682
16243
16580




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143580&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143580&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14440.9184.46987673798978.2832419870431
Geometric Mean14371.8199536823
Harmonic Mean14303.2299224354
Quadratic Mean14510.2485092434
Winsorized Mean ( 1 / 20 )14446.1833333333181.8132096840979.4561812006638
Winsorized Mean ( 2 / 20 )14439.85179.54223780316280.4259219261312
Winsorized Mean ( 3 / 20 )14444.55176.71016268467881.741478704736
Winsorized Mean ( 4 / 20 )14426.15171.92966441440483.9072771364717
Winsorized Mean ( 5 / 20 )14430.4167.45685876673686.1738366900889
Winsorized Mean ( 6 / 20 )14405.1158.8048382974190.7094529010638
Winsorized Mean ( 7 / 20 )14425.4154.44379922367993.4022607091391
Winsorized Mean ( 8 / 20 )14471.2666666667145.96135404216799.1445082270612
Winsorized Mean ( 9 / 20 )14460.1666666667139.649440370726103.546184132779
Winsorized Mean ( 10 / 20 )14458.8333333333138.096912189624104.700627291938
Winsorized Mean ( 11 / 20 )14456.45134.882718306461107.177925990149
Winsorized Mean ( 12 / 20 )14484.85128.789369111139112.469298514074
Winsorized Mean ( 13 / 20 )14414.65115.522313800736124.77805824478
Winsorized Mean ( 14 / 20 )14422.8166666667112.940763663908127.702489329596
Winsorized Mean ( 15 / 20 )14326.566666666794.9741040133836150.847084218323
Winsorized Mean ( 16 / 20 )14334.566666666793.0985941341499153.971891842012
Winsorized Mean ( 17 / 20 )14335.133333333390.4875103491648158.421126606515
Winsorized Mean ( 18 / 20 )14366.333333333384.299830329586170.419481002102
Winsorized Mean ( 19 / 20 )14324.533333333377.5181825460027184.789334100197
Winsorized Mean ( 20 / 20 )14281.533333333369.2708899600465206.169335222494
Trimmed Mean ( 1 / 20 )14438.0862068966176.79360222744481.6663387418398
Trimmed Mean ( 2 / 20 )14429.4107142857170.59672157898484.5819930226803
Trimmed Mean ( 3 / 20 )14423.6111111111164.44558278403787.710541486866
Trimmed Mean ( 4 / 20 )14415.5576923077158.1546783139791.1484746830554
Trimmed Mean ( 5 / 20 )14412.38152.20173479126194.6926131937066
Trimmed Mean ( 6 / 20 )14407.875146.2408954097698.5215179353892
Trimmed Mean ( 7 / 20 )14408.4782608696141.43794576271101.871376759407
Trimmed Mean ( 8 / 20 )14405.1818181818136.514503224459105.52125582215
Trimmed Mean ( 9 / 20 )14393.380952381132.432859207552108.684363069012
Trimmed Mean ( 10 / 20 )14382.25128.730137875464111.72403166315
Trimmed Mean ( 11 / 20 )14370.1578947368124.074987228052115.818330638425
Trimmed Mean ( 12 / 20 )14357.0833333333118.558808493627121.096724197469
Trimmed Mean ( 13 / 20 )14338.2941176471112.498758396094127.452909899359
Trimmed Mean ( 14 / 20 )14327.28125108.264630933837132.335751079739
Trimmed Mean ( 15 / 20 )14313.6333333333102.766004523985139.283738816493
Trimmed Mean ( 16 / 20 )14311.7857142857100.731233329602142.078928662138
Trimmed Mean ( 17 / 20 )14308.597.9051699742782146.146521207809
Trimmed Mean ( 18 / 20 )14304.583333333394.1122309633993151.99494461986
Trimmed Mean ( 19 / 20 )14295.227272727390.0757721392697158.70224515672
Trimmed Mean ( 20 / 20 )14290.686.1923918977344165.798856318496
Median14271.5
Midrange14522.5
Midmean - Weighted Average at Xnp14285.7096774194
Midmean - Weighted Average at X(n+1)p14313.6333333333
Midmean - Empirical Distribution Function14285.7096774194
Midmean - Empirical Distribution Function - Averaging14313.6333333333
Midmean - Empirical Distribution Function - Interpolation14313.6333333333
Midmean - Closest Observation14285.7096774194
Midmean - True Basic - Statistics Graphics Toolkit14313.6333333333
Midmean - MS Excel (old versions)14327.28125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14440.9 & 184.469876737989 & 78.2832419870431 \tabularnewline
Geometric Mean & 14371.8199536823 &  &  \tabularnewline
Harmonic Mean & 14303.2299224354 &  &  \tabularnewline
Quadratic Mean & 14510.2485092434 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14446.1833333333 & 181.81320968409 & 79.4561812006638 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14439.85 & 179.542237803162 & 80.4259219261312 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14444.55 & 176.710162684678 & 81.741478704736 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14426.15 & 171.929664414404 & 83.9072771364717 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14430.4 & 167.456858766736 & 86.1738366900889 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14405.1 & 158.80483829741 & 90.7094529010638 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14425.4 & 154.443799223679 & 93.4022607091391 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14471.2666666667 & 145.961354042167 & 99.1445082270612 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 14460.1666666667 & 139.649440370726 & 103.546184132779 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 14458.8333333333 & 138.096912189624 & 104.700627291938 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 14456.45 & 134.882718306461 & 107.177925990149 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 14484.85 & 128.789369111139 & 112.469298514074 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 14414.65 & 115.522313800736 & 124.77805824478 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 14422.8166666667 & 112.940763663908 & 127.702489329596 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 14326.5666666667 & 94.9741040133836 & 150.847084218323 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 14334.5666666667 & 93.0985941341499 & 153.971891842012 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 14335.1333333333 & 90.4875103491648 & 158.421126606515 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 14366.3333333333 & 84.299830329586 & 170.419481002102 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 14324.5333333333 & 77.5181825460027 & 184.789334100197 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 14281.5333333333 & 69.2708899600465 & 206.169335222494 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14438.0862068966 & 176.793602227444 & 81.6663387418398 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14429.4107142857 & 170.596721578984 & 84.5819930226803 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14423.6111111111 & 164.445582784037 & 87.710541486866 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 14415.5576923077 & 158.15467831397 & 91.1484746830554 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 14412.38 & 152.201734791261 & 94.6926131937066 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 14407.875 & 146.24089540976 & 98.5215179353892 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 14408.4782608696 & 141.43794576271 & 101.871376759407 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 14405.1818181818 & 136.514503224459 & 105.52125582215 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 14393.380952381 & 132.432859207552 & 108.684363069012 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 14382.25 & 128.730137875464 & 111.72403166315 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 14370.1578947368 & 124.074987228052 & 115.818330638425 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 14357.0833333333 & 118.558808493627 & 121.096724197469 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 14338.2941176471 & 112.498758396094 & 127.452909899359 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 14327.28125 & 108.264630933837 & 132.335751079739 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 14313.6333333333 & 102.766004523985 & 139.283738816493 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 14311.7857142857 & 100.731233329602 & 142.078928662138 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 14308.5 & 97.9051699742782 & 146.146521207809 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 14304.5833333333 & 94.1122309633993 & 151.99494461986 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 14295.2272727273 & 90.0757721392697 & 158.70224515672 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 14290.6 & 86.1923918977344 & 165.798856318496 \tabularnewline
Median & 14271.5 &  &  \tabularnewline
Midrange & 14522.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14285.7096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14313.6333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14285.7096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14313.6333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14313.6333333333 &  &  \tabularnewline
Midmean - Closest Observation & 14285.7096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14313.6333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14327.28125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143580&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]14440.9[/C][C]184.469876737989[/C][C]78.2832419870431[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14371.8199536823[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14303.2299224354[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14510.2485092434[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14446.1833333333[/C][C]181.81320968409[/C][C]79.4561812006638[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14439.85[/C][C]179.542237803162[/C][C]80.4259219261312[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14444.55[/C][C]176.710162684678[/C][C]81.741478704736[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14426.15[/C][C]171.929664414404[/C][C]83.9072771364717[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14430.4[/C][C]167.456858766736[/C][C]86.1738366900889[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14405.1[/C][C]158.80483829741[/C][C]90.7094529010638[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14425.4[/C][C]154.443799223679[/C][C]93.4022607091391[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14471.2666666667[/C][C]145.961354042167[/C][C]99.1445082270612[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]14460.1666666667[/C][C]139.649440370726[/C][C]103.546184132779[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]14458.8333333333[/C][C]138.096912189624[/C][C]104.700627291938[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]14456.45[/C][C]134.882718306461[/C][C]107.177925990149[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]14484.85[/C][C]128.789369111139[/C][C]112.469298514074[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]14414.65[/C][C]115.522313800736[/C][C]124.77805824478[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]14422.8166666667[/C][C]112.940763663908[/C][C]127.702489329596[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]14326.5666666667[/C][C]94.9741040133836[/C][C]150.847084218323[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]14334.5666666667[/C][C]93.0985941341499[/C][C]153.971891842012[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]14335.1333333333[/C][C]90.4875103491648[/C][C]158.421126606515[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]14366.3333333333[/C][C]84.299830329586[/C][C]170.419481002102[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]14324.5333333333[/C][C]77.5181825460027[/C][C]184.789334100197[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]14281.5333333333[/C][C]69.2708899600465[/C][C]206.169335222494[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14438.0862068966[/C][C]176.793602227444[/C][C]81.6663387418398[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14429.4107142857[/C][C]170.596721578984[/C][C]84.5819930226803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14423.6111111111[/C][C]164.445582784037[/C][C]87.710541486866[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]14415.5576923077[/C][C]158.15467831397[/C][C]91.1484746830554[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]14412.38[/C][C]152.201734791261[/C][C]94.6926131937066[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]14407.875[/C][C]146.24089540976[/C][C]98.5215179353892[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]14408.4782608696[/C][C]141.43794576271[/C][C]101.871376759407[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]14405.1818181818[/C][C]136.514503224459[/C][C]105.52125582215[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]14393.380952381[/C][C]132.432859207552[/C][C]108.684363069012[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]14382.25[/C][C]128.730137875464[/C][C]111.72403166315[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]14370.1578947368[/C][C]124.074987228052[/C][C]115.818330638425[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]14357.0833333333[/C][C]118.558808493627[/C][C]121.096724197469[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]14338.2941176471[/C][C]112.498758396094[/C][C]127.452909899359[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]14327.28125[/C][C]108.264630933837[/C][C]132.335751079739[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]14313.6333333333[/C][C]102.766004523985[/C][C]139.283738816493[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]14311.7857142857[/C][C]100.731233329602[/C][C]142.078928662138[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]14308.5[/C][C]97.9051699742782[/C][C]146.146521207809[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]14304.5833333333[/C][C]94.1122309633993[/C][C]151.99494461986[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]14295.2272727273[/C][C]90.0757721392697[/C][C]158.70224515672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]14290.6[/C][C]86.1923918977344[/C][C]165.798856318496[/C][/ROW]
[ROW][C]Median[/C][C]14271.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14522.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14285.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14313.6333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14285.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14313.6333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14313.6333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14285.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14313.6333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14327.28125[/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=143580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143580&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 Mean14440.9184.46987673798978.2832419870431
Geometric Mean14371.8199536823
Harmonic Mean14303.2299224354
Quadratic Mean14510.2485092434
Winsorized Mean ( 1 / 20 )14446.1833333333181.8132096840979.4561812006638
Winsorized Mean ( 2 / 20 )14439.85179.54223780316280.4259219261312
Winsorized Mean ( 3 / 20 )14444.55176.71016268467881.741478704736
Winsorized Mean ( 4 / 20 )14426.15171.92966441440483.9072771364717
Winsorized Mean ( 5 / 20 )14430.4167.45685876673686.1738366900889
Winsorized Mean ( 6 / 20 )14405.1158.8048382974190.7094529010638
Winsorized Mean ( 7 / 20 )14425.4154.44379922367993.4022607091391
Winsorized Mean ( 8 / 20 )14471.2666666667145.96135404216799.1445082270612
Winsorized Mean ( 9 / 20 )14460.1666666667139.649440370726103.546184132779
Winsorized Mean ( 10 / 20 )14458.8333333333138.096912189624104.700627291938
Winsorized Mean ( 11 / 20 )14456.45134.882718306461107.177925990149
Winsorized Mean ( 12 / 20 )14484.85128.789369111139112.469298514074
Winsorized Mean ( 13 / 20 )14414.65115.522313800736124.77805824478
Winsorized Mean ( 14 / 20 )14422.8166666667112.940763663908127.702489329596
Winsorized Mean ( 15 / 20 )14326.566666666794.9741040133836150.847084218323
Winsorized Mean ( 16 / 20 )14334.566666666793.0985941341499153.971891842012
Winsorized Mean ( 17 / 20 )14335.133333333390.4875103491648158.421126606515
Winsorized Mean ( 18 / 20 )14366.333333333384.299830329586170.419481002102
Winsorized Mean ( 19 / 20 )14324.533333333377.5181825460027184.789334100197
Winsorized Mean ( 20 / 20 )14281.533333333369.2708899600465206.169335222494
Trimmed Mean ( 1 / 20 )14438.0862068966176.79360222744481.6663387418398
Trimmed Mean ( 2 / 20 )14429.4107142857170.59672157898484.5819930226803
Trimmed Mean ( 3 / 20 )14423.6111111111164.44558278403787.710541486866
Trimmed Mean ( 4 / 20 )14415.5576923077158.1546783139791.1484746830554
Trimmed Mean ( 5 / 20 )14412.38152.20173479126194.6926131937066
Trimmed Mean ( 6 / 20 )14407.875146.2408954097698.5215179353892
Trimmed Mean ( 7 / 20 )14408.4782608696141.43794576271101.871376759407
Trimmed Mean ( 8 / 20 )14405.1818181818136.514503224459105.52125582215
Trimmed Mean ( 9 / 20 )14393.380952381132.432859207552108.684363069012
Trimmed Mean ( 10 / 20 )14382.25128.730137875464111.72403166315
Trimmed Mean ( 11 / 20 )14370.1578947368124.074987228052115.818330638425
Trimmed Mean ( 12 / 20 )14357.0833333333118.558808493627121.096724197469
Trimmed Mean ( 13 / 20 )14338.2941176471112.498758396094127.452909899359
Trimmed Mean ( 14 / 20 )14327.28125108.264630933837132.335751079739
Trimmed Mean ( 15 / 20 )14313.6333333333102.766004523985139.283738816493
Trimmed Mean ( 16 / 20 )14311.7857142857100.731233329602142.078928662138
Trimmed Mean ( 17 / 20 )14308.597.9051699742782146.146521207809
Trimmed Mean ( 18 / 20 )14304.583333333394.1122309633993151.99494461986
Trimmed Mean ( 19 / 20 )14295.227272727390.0757721392697158.70224515672
Trimmed Mean ( 20 / 20 )14290.686.1923918977344165.798856318496
Median14271.5
Midrange14522.5
Midmean - Weighted Average at Xnp14285.7096774194
Midmean - Weighted Average at X(n+1)p14313.6333333333
Midmean - Empirical Distribution Function14285.7096774194
Midmean - Empirical Distribution Function - Averaging14313.6333333333
Midmean - Empirical Distribution Function - Interpolation14313.6333333333
Midmean - Closest Observation14285.7096774194
Midmean - True Basic - Statistics Graphics Toolkit14313.6333333333
Midmean - MS Excel (old versions)14327.28125
Number of observations60



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')