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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 computationWed, 28 Oct 2009 12:10:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256753501xdi3yu612sx4gqi.htm/, Retrieved Mon, 06 May 2024 10:29:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51684, Retrieved Mon, 06 May 2024 10:29:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS4V11
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-28 18:10:45] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataseries X:
1256410816
1140526431
1007864447
166138299,5
135283722,2
6140422,585
79137278,97
134356679,6
98369429,33
105460430,1
21774856,02
42065638,96
25567751,16
114535044,4
75328964,67
23324138,06
13590509,17
13199757,27
28729097,11
68325841,3
84946195,58
14449144,92
82236443,17
4782383,081
2711841,26
23608944,35
88513200,67
8043882,726
76501958,05
2337175,834
9558662,783
5485818,713
7703782,549
302780682,3
14730722,75
100991446,5
42456529,69
190835,8522
59383154,1
3990166,948
53614285,25
6962179,933
17689126,36
82008466,25
118106084,3
143116032,4
99834021,54
18746418,18
6880514,095
19905458,8
503980558,4
210299426,3
124446371,8
310605344,2
421057686,9
623098330,3
1062371447
1108824997
817661302,1
986453750,4




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=51684&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=51684&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51684&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 Mean203786572.12898743470166.87378194.68796387924372
Geometric Mean54282762.2891618
Harmonic Mean7107819.7842302
Quadratic Mean391175965.588525
Winsorized Mean ( 1 / 20 )201890938.0453542710955.13874244.72691227319845
Winsorized Mean ( 2 / 20 )200846712.42621742321010.02390974.74579203834563
Winsorized Mean ( 3 / 20 )198587951.21061741483644.3658534.78713850353233
Winsorized Mean ( 4 / 20 )195006965.61948340215472.63029874.84905318438464
Winsorized Mean ( 5 / 20 )193281360.53881739602279.61675064.88056148305827
Winsorized Mean ( 6 / 20 )176467576.09601734023330.18204445.18666383190045
Winsorized Mean ( 7 / 20 )153854906.7288527016758.14022595.6947952796665
Winsorized Mean ( 8 / 20 )137983425.92058322472499.86703796.14010131213635
Winsorized Mean ( 9 / 20 )125656235.58798319107778.77275636.57618224924934
Winsorized Mean ( 10 / 20 )107304195.16748314467107.40202217.41711471309638
Winsorized Mean ( 11 / 20 )106147383.49626714094373.75620777.53118835446773
Winsorized Mean ( 12 / 20 )88379351.19366679831894.455153628.98904596634889
Winsorized Mean ( 13 / 20 )78895769.96533337908470.08180199.97611031580933
Winsorized Mean ( 14 / 20 )73724255.98366676918058.7135272110.6567837939146
Winsorized Mean ( 15 / 20 )71836572.89116676581189.3631811410.9154392810911
Winsorized Mean ( 16 / 20 )72378269.16056425859.5765459811.2635933447218
Winsorized Mean ( 17 / 20 )69869914.63283335933578.576412511.7753415974947
Winsorized Mean ( 18 / 20 )68315540.56883335590715.4467707612.2194630042015
Winsorized Mean ( 19 / 20 )67776687.05355334632.5473446912.7050338429093
Winsorized Mean ( 20 / 20 )65268242.96683334819817.9444467913.5416407256695
Trimmed Mean ( 1 / 20 )189148149.58425940889544.32100264.62583168203966
Trimmed Mean ( 2 / 20 )175495161.94737538549281.50288854.55248853170519
Trimmed Mean ( 3 / 20 )161410967.23690735786826.82133124.51034588908275
Trimmed Mean ( 4 / 20 )147112127.24701932598683.51156654.51282418183611
Trimmed Mean ( 5 / 20 )132743675.7352828903336.14017244.59267660630986
Trimmed Mean ( 6 / 20 )117609254.53439623919255.70854234.91692784957325
Trimmed Mean ( 7 / 20 )104813967.23839119420316.68544635.3971296625116
Trimmed Mean ( 8 / 20 )95260537.467522716231549.52230925.8688504961645
Trimmed Mean ( 9 / 20 )87631450.243761913657057.19914866.41656902844524
Trimmed Mean ( 10 / 20 )81293986.01972511379557.93335487.14386151868369
Trimmed Mean ( 11 / 20 )77187110.891131610099820.70155237.64242387780886
Trimmed Mean ( 12 / 20 )72799190.79944448321980.979886548.74781989713667
Trimmed Mean ( 13 / 20 )70507990.74147067589329.536658949.29041101732293
Trimmed Mean ( 14 / 20 )69298214.8918757253564.188866169.5536777627534
Trimmed Mean ( 15 / 20 )68665923.30733337089233.820166759.68594421473295
Trimmed Mean ( 16 / 20 )68212973.36678576936132.856469379.83443869636423
Trimmed Mean ( 17 / 20 )67612209.55038466729279.4275452810.0474664900412
Trimmed Mean ( 18 / 20 )67280194.09708336568127.8990087110.2434354402930
Trimmed Mean ( 19 / 20 )67123323.41954556410433.4965550110.4709491886341
Trimmed Mean ( 20 / 20 )67020160.74056215579.3617776710.7826088027508
Median75915461.36
Midrange628300825.9261
Midmean - Weighted Average at Xnp66916994.9722581
Midmean - Weighted Average at X(n+1)p68665923.3073333
Midmean - Empirical Distribution Function66916994.9722581
Midmean - Empirical Distribution Function - Averaging68665923.3073333
Midmean - Empirical Distribution Function - Interpolation68665923.3073333
Midmean - Closest Observation66916994.9722581
Midmean - True Basic - Statistics Graphics Toolkit68665923.3073333
Midmean - MS Excel (old versions)69298214.891875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 203786572.128987 & 43470166.8737819 & 4.68796387924372 \tabularnewline
Geometric Mean & 54282762.2891618 &  &  \tabularnewline
Harmonic Mean & 7107819.7842302 &  &  \tabularnewline
Quadratic Mean & 391175965.588525 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 201890938.04535 & 42710955.1387424 & 4.72691227319845 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 200846712.426217 & 42321010.0239097 & 4.74579203834563 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 198587951.210617 & 41483644.365853 & 4.78713850353233 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 195006965.619483 & 40215472.6302987 & 4.84905318438464 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 193281360.538817 & 39602279.6167506 & 4.88056148305827 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 176467576.096017 & 34023330.1820444 & 5.18666383190045 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 153854906.72885 & 27016758.1402259 & 5.6947952796665 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 137983425.920583 & 22472499.8670379 & 6.14010131213635 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 125656235.587983 & 19107778.7727563 & 6.57618224924934 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 107304195.167483 & 14467107.4020221 & 7.41711471309638 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106147383.496267 & 14094373.7562077 & 7.53118835446773 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 88379351.1936667 & 9831894.45515362 & 8.98904596634889 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 78895769.9653333 & 7908470.0818019 & 9.97611031580933 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 73724255.9836667 & 6918058.71352721 & 10.6567837939146 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 71836572.8911667 & 6581189.36318114 & 10.9154392810911 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 72378269.1605 & 6425859.57654598 & 11.2635933447218 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 69869914.6328333 & 5933578.5764125 & 11.7753415974947 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 68315540.5688333 & 5590715.44677076 & 12.2194630042015 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 67776687.0535 & 5334632.54734469 & 12.7050338429093 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 65268242.9668333 & 4819817.94444679 & 13.5416407256695 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 189148149.584259 & 40889544.3210026 & 4.62583168203966 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 175495161.947375 & 38549281.5028885 & 4.55248853170519 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 161410967.236907 & 35786826.8213312 & 4.51034588908275 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 147112127.247019 & 32598683.5115665 & 4.51282418183611 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 132743675.73528 & 28903336.1401724 & 4.59267660630986 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 117609254.534396 & 23919255.7085423 & 4.91692784957325 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104813967.238391 & 19420316.6854463 & 5.3971296625116 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 95260537.4675227 & 16231549.5223092 & 5.8688504961645 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 87631450.2437619 & 13657057.1991486 & 6.41656902844524 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 81293986.019725 & 11379557.9333548 & 7.14386151868369 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 77187110.8911316 & 10099820.7015523 & 7.64242387780886 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 72799190.7994444 & 8321980.97988654 & 8.74781989713667 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 70507990.7414706 & 7589329.53665894 & 9.29041101732293 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 69298214.891875 & 7253564.18886616 & 9.5536777627534 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 68665923.3073333 & 7089233.82016675 & 9.68594421473295 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 68212973.3667857 & 6936132.85646937 & 9.83443869636423 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 67612209.5503846 & 6729279.42754528 & 10.0474664900412 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 67280194.0970833 & 6568127.89900871 & 10.2434354402930 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 67123323.4195455 & 6410433.49655501 & 10.4709491886341 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 67020160.7405 & 6215579.36177767 & 10.7826088027508 \tabularnewline
Median & 75915461.36 &  &  \tabularnewline
Midrange & 628300825.9261 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 66916994.9722581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 68665923.3073333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 66916994.9722581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 68665923.3073333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 68665923.3073333 &  &  \tabularnewline
Midmean - Closest Observation & 66916994.9722581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 68665923.3073333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 69298214.891875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51684&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]203786572.128987[/C][C]43470166.8737819[/C][C]4.68796387924372[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]54282762.2891618[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7107819.7842302[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]391175965.588525[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]201890938.04535[/C][C]42710955.1387424[/C][C]4.72691227319845[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]200846712.426217[/C][C]42321010.0239097[/C][C]4.74579203834563[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]198587951.210617[/C][C]41483644.365853[/C][C]4.78713850353233[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]195006965.619483[/C][C]40215472.6302987[/C][C]4.84905318438464[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]193281360.538817[/C][C]39602279.6167506[/C][C]4.88056148305827[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]176467576.096017[/C][C]34023330.1820444[/C][C]5.18666383190045[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]153854906.72885[/C][C]27016758.1402259[/C][C]5.6947952796665[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]137983425.920583[/C][C]22472499.8670379[/C][C]6.14010131213635[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]125656235.587983[/C][C]19107778.7727563[/C][C]6.57618224924934[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]107304195.167483[/C][C]14467107.4020221[/C][C]7.41711471309638[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106147383.496267[/C][C]14094373.7562077[/C][C]7.53118835446773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]88379351.1936667[/C][C]9831894.45515362[/C][C]8.98904596634889[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]78895769.9653333[/C][C]7908470.0818019[/C][C]9.97611031580933[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]73724255.9836667[/C][C]6918058.71352721[/C][C]10.6567837939146[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]71836572.8911667[/C][C]6581189.36318114[/C][C]10.9154392810911[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]72378269.1605[/C][C]6425859.57654598[/C][C]11.2635933447218[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]69869914.6328333[/C][C]5933578.5764125[/C][C]11.7753415974947[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]68315540.5688333[/C][C]5590715.44677076[/C][C]12.2194630042015[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]67776687.0535[/C][C]5334632.54734469[/C][C]12.7050338429093[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]65268242.9668333[/C][C]4819817.94444679[/C][C]13.5416407256695[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]189148149.584259[/C][C]40889544.3210026[/C][C]4.62583168203966[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]175495161.947375[/C][C]38549281.5028885[/C][C]4.55248853170519[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]161410967.236907[/C][C]35786826.8213312[/C][C]4.51034588908275[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]147112127.247019[/C][C]32598683.5115665[/C][C]4.51282418183611[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]132743675.73528[/C][C]28903336.1401724[/C][C]4.59267660630986[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]117609254.534396[/C][C]23919255.7085423[/C][C]4.91692784957325[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104813967.238391[/C][C]19420316.6854463[/C][C]5.3971296625116[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]95260537.4675227[/C][C]16231549.5223092[/C][C]5.8688504961645[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]87631450.2437619[/C][C]13657057.1991486[/C][C]6.41656902844524[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]81293986.019725[/C][C]11379557.9333548[/C][C]7.14386151868369[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]77187110.8911316[/C][C]10099820.7015523[/C][C]7.64242387780886[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]72799190.7994444[/C][C]8321980.97988654[/C][C]8.74781989713667[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]70507990.7414706[/C][C]7589329.53665894[/C][C]9.29041101732293[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]69298214.891875[/C][C]7253564.18886616[/C][C]9.5536777627534[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]68665923.3073333[/C][C]7089233.82016675[/C][C]9.68594421473295[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]68212973.3667857[/C][C]6936132.85646937[/C][C]9.83443869636423[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]67612209.5503846[/C][C]6729279.42754528[/C][C]10.0474664900412[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]67280194.0970833[/C][C]6568127.89900871[/C][C]10.2434354402930[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]67123323.4195455[/C][C]6410433.49655501[/C][C]10.4709491886341[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]67020160.7405[/C][C]6215579.36177767[/C][C]10.7826088027508[/C][/ROW]
[ROW][C]Median[/C][C]75915461.36[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]628300825.9261[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]66916994.9722581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]68665923.3073333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]66916994.9722581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]68665923.3073333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]68665923.3073333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]66916994.9722581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]68665923.3073333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]69298214.891875[/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=51684&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51684&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 Mean203786572.12898743470166.87378194.68796387924372
Geometric Mean54282762.2891618
Harmonic Mean7107819.7842302
Quadratic Mean391175965.588525
Winsorized Mean ( 1 / 20 )201890938.0453542710955.13874244.72691227319845
Winsorized Mean ( 2 / 20 )200846712.42621742321010.02390974.74579203834563
Winsorized Mean ( 3 / 20 )198587951.21061741483644.3658534.78713850353233
Winsorized Mean ( 4 / 20 )195006965.61948340215472.63029874.84905318438464
Winsorized Mean ( 5 / 20 )193281360.53881739602279.61675064.88056148305827
Winsorized Mean ( 6 / 20 )176467576.09601734023330.18204445.18666383190045
Winsorized Mean ( 7 / 20 )153854906.7288527016758.14022595.6947952796665
Winsorized Mean ( 8 / 20 )137983425.92058322472499.86703796.14010131213635
Winsorized Mean ( 9 / 20 )125656235.58798319107778.77275636.57618224924934
Winsorized Mean ( 10 / 20 )107304195.16748314467107.40202217.41711471309638
Winsorized Mean ( 11 / 20 )106147383.49626714094373.75620777.53118835446773
Winsorized Mean ( 12 / 20 )88379351.19366679831894.455153628.98904596634889
Winsorized Mean ( 13 / 20 )78895769.96533337908470.08180199.97611031580933
Winsorized Mean ( 14 / 20 )73724255.98366676918058.7135272110.6567837939146
Winsorized Mean ( 15 / 20 )71836572.89116676581189.3631811410.9154392810911
Winsorized Mean ( 16 / 20 )72378269.16056425859.5765459811.2635933447218
Winsorized Mean ( 17 / 20 )69869914.63283335933578.576412511.7753415974947
Winsorized Mean ( 18 / 20 )68315540.56883335590715.4467707612.2194630042015
Winsorized Mean ( 19 / 20 )67776687.05355334632.5473446912.7050338429093
Winsorized Mean ( 20 / 20 )65268242.96683334819817.9444467913.5416407256695
Trimmed Mean ( 1 / 20 )189148149.58425940889544.32100264.62583168203966
Trimmed Mean ( 2 / 20 )175495161.94737538549281.50288854.55248853170519
Trimmed Mean ( 3 / 20 )161410967.23690735786826.82133124.51034588908275
Trimmed Mean ( 4 / 20 )147112127.24701932598683.51156654.51282418183611
Trimmed Mean ( 5 / 20 )132743675.7352828903336.14017244.59267660630986
Trimmed Mean ( 6 / 20 )117609254.53439623919255.70854234.91692784957325
Trimmed Mean ( 7 / 20 )104813967.23839119420316.68544635.3971296625116
Trimmed Mean ( 8 / 20 )95260537.467522716231549.52230925.8688504961645
Trimmed Mean ( 9 / 20 )87631450.243761913657057.19914866.41656902844524
Trimmed Mean ( 10 / 20 )81293986.01972511379557.93335487.14386151868369
Trimmed Mean ( 11 / 20 )77187110.891131610099820.70155237.64242387780886
Trimmed Mean ( 12 / 20 )72799190.79944448321980.979886548.74781989713667
Trimmed Mean ( 13 / 20 )70507990.74147067589329.536658949.29041101732293
Trimmed Mean ( 14 / 20 )69298214.8918757253564.188866169.5536777627534
Trimmed Mean ( 15 / 20 )68665923.30733337089233.820166759.68594421473295
Trimmed Mean ( 16 / 20 )68212973.36678576936132.856469379.83443869636423
Trimmed Mean ( 17 / 20 )67612209.55038466729279.4275452810.0474664900412
Trimmed Mean ( 18 / 20 )67280194.09708336568127.8990087110.2434354402930
Trimmed Mean ( 19 / 20 )67123323.41954556410433.4965550110.4709491886341
Trimmed Mean ( 20 / 20 )67020160.74056215579.3617776710.7826088027508
Median75915461.36
Midrange628300825.9261
Midmean - Weighted Average at Xnp66916994.9722581
Midmean - Weighted Average at X(n+1)p68665923.3073333
Midmean - Empirical Distribution Function66916994.9722581
Midmean - Empirical Distribution Function - Averaging68665923.3073333
Midmean - Empirical Distribution Function - Interpolation68665923.3073333
Midmean - Closest Observation66916994.9722581
Midmean - True Basic - Statistics Graphics Toolkit68665923.3073333
Midmean - MS Excel (old versions)69298214.891875
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')