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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 computationSun, 19 Dec 2010 21:01:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292792369tkv2s6ar3ambd78.htm/, Retrieved Sun, 05 May 2024 01:58:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112741, Retrieved Sun, 05 May 2024 01:58:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
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]
-  M D  [Central Tendency] [Robustness of Cen...] [2010-12-18 14:20:59] [1afa3497b02a8d7c9f6727c1b17b89b2]
-         [Central Tendency] [Central tendency ...] [2010-12-19 18:22:32] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendencey...] [2010-12-19 21:01:37] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
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Dataseries X:
0,762253
0,768403
0,757518
0,772917
0,787774
0,82203
0,830772
0,813537
0,815927
0,832293
0,848464
0,843455
0,826241
0,837661
0,831947
0,81493
0,783085
0,790514
0,788395
0,780579
0,785731
0,792959
0,776337
0,75683
0,76929
0,764877
0,755173
0,739864
0,740138
0,745212
0,729076
0,734107
0,719632
0,702889
0,681013
0,686342
0,67944
0,678058
0,644039
0,63488
0,642797
0,642963
0,634115
0,66778
0,695894
0,750638
0,785423
0,74355
0,755344
0,782167
0,766284
0,75815
0,732601
0,71347
0,709824
0,700869
0,686719
0,674946
0,670511
0,684275




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112741&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112741&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.7470483666666670.0075824665387511398.5231339760991
Geometric Mean0.744740599486322
Harmonic Mean0.742397843609237
Quadratic Mean0.74931528495634
Winsorized Mean ( 1 / 20 )0.7469776333333330.0075607642620286698.796577627049
Winsorized Mean ( 2 / 20 )0.74704840.00745553644643146100.20048930987
Winsorized Mean ( 3 / 20 )0.74678830.00739963292563001100.922344054846
Winsorized Mean ( 4 / 20 )0.7468369666666670.00737811949511269101.223213741845
Winsorized Mean ( 5 / 20 )0.7487174666666670.00692806714680647108.070180441567
Winsorized Mean ( 6 / 20 )0.7485374666666670.00678494010171641110.323371385004
Winsorized Mean ( 7 / 20 )0.74856360.00659141568421738113.566437903829
Winsorized Mean ( 8 / 20 )0.74816480.0063630293643368117.57996972217
Winsorized Mean ( 9 / 20 )0.748222550.00629756304815107118.811442502298
Winsorized Mean ( 10 / 20 )0.748252550.00620769634443888120.536267961998
Winsorized Mean ( 11 / 20 )0.745077950.00547736253463593136.02859867108
Winsorized Mean ( 12 / 20 )0.745002350.00532826387805056139.820843533855
Winsorized Mean ( 13 / 20 )0.7446249166666670.00524730941268772141.906043288814
Winsorized Mean ( 14 / 20 )0.746620850.00483569195405139154.397934586067
Winsorized Mean ( 15 / 20 )0.747353850.00454380548938055164.477518183087
Winsorized Mean ( 16 / 20 )0.7478103833333330.00443912716137464168.458878547143
Winsorized Mean ( 17 / 20 )0.7491128666666670.00401218250562655186.709569072727
Winsorized Mean ( 18 / 20 )0.7499312666666670.0037926551602929197.73252114193
Winsorized Mean ( 19 / 20 )0.75137970.00340657382837831220.567566667913
Winsorized Mean ( 20 / 20 )0.75311370.00271512391340456277.377285169889
Trimmed Mean ( 1 / 20 )0.7472469482758620.00738875317627765101.133023454481
Trimmed Mean ( 2 / 20 )0.74753550.0071758908590348104.173198099692
Trimmed Mean ( 3 / 20 )0.7478061111111110.00698163178710167107.110505668984
Trimmed Mean ( 4 / 20 )0.7481975769230770.00676487542937205110.60034803812
Trimmed Mean ( 5 / 20 )0.748605760.00649940660616751115.180631919477
Trimmed Mean ( 6 / 20 )0.7485778333333330.00632348534546437118.380575337344
Trimmed Mean ( 7 / 20 )0.7485866086956520.00614178166934417121.884275442762
Trimmed Mean ( 8 / 20 )0.7485910909090910.0059626478305339125.546755767741
Trimmed Mean ( 9 / 20 )0.7486672142857140.0057914446436979129.27123720338
Trimmed Mean ( 10 / 20 )0.7487413250.00558006567733009134.181453820854
Trimmed Mean ( 11 / 20 )0.74881850.00531966049285536140.764340319408
Trimmed Mean ( 12 / 20 )0.749385250.00516876186831904144.983512317179
Trimmed Mean ( 13 / 20 )0.7500297941176470.00499394774054129150.187753874323
Trimmed Mean ( 14 / 20 )0.750809343750.0047606568431091157.711292473595
Trimmed Mean ( 15 / 20 )0.75140770.00455991039591083164.785628391698
Trimmed Mean ( 16 / 20 )0.7519868214285710.00435648292171927172.613283453847
Trimmed Mean ( 17 / 20 )0.7525891923076920.00407809778847527184.544175089306
Trimmed Mean ( 18 / 20 )0.7531004166666670.00381761379627696197.269932700136
Trimmed Mean ( 19 / 20 )0.7535805909090910.00348914084778289215.978839429179
Trimmed Mean ( 20 / 20 )0.75392810.00313746453609649240.298524915921
Median0.756087
Midrange0.7412895
Midmean - Weighted Average at Xnp0.749616935483871
Midmean - Weighted Average at X(n+1)p0.7514077
Midmean - Empirical Distribution Function0.749616935483871
Midmean - Empirical Distribution Function - Averaging0.7514077
Midmean - Empirical Distribution Function - Interpolation0.7514077
Midmean - Closest Observation0.749616935483871
Midmean - True Basic - Statistics Graphics Toolkit0.7514077
Midmean - MS Excel (old versions)0.75080934375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.747048366666667 & 0.00758246653875113 & 98.5231339760991 \tabularnewline
Geometric Mean & 0.744740599486322 &  &  \tabularnewline
Harmonic Mean & 0.742397843609237 &  &  \tabularnewline
Quadratic Mean & 0.74931528495634 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.746977633333333 & 0.00756076426202866 & 98.796577627049 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.7470484 & 0.00745553644643146 & 100.20048930987 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.7467883 & 0.00739963292563001 & 100.922344054846 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.746836966666667 & 0.00737811949511269 & 101.223213741845 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.748717466666667 & 0.00692806714680647 & 108.070180441567 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.748537466666667 & 0.00678494010171641 & 110.323371385004 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.7485636 & 0.00659141568421738 & 113.566437903829 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.7481648 & 0.0063630293643368 & 117.57996972217 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.74822255 & 0.00629756304815107 & 118.811442502298 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.74825255 & 0.00620769634443888 & 120.536267961998 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.74507795 & 0.00547736253463593 & 136.02859867108 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.74500235 & 0.00532826387805056 & 139.820843533855 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.744624916666667 & 0.00524730941268772 & 141.906043288814 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.74662085 & 0.00483569195405139 & 154.397934586067 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.74735385 & 0.00454380548938055 & 164.477518183087 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.747810383333333 & 0.00443912716137464 & 168.458878547143 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.749112866666667 & 0.00401218250562655 & 186.709569072727 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.749931266666667 & 0.0037926551602929 & 197.73252114193 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.7513797 & 0.00340657382837831 & 220.567566667913 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.7531137 & 0.00271512391340456 & 277.377285169889 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.747246948275862 & 0.00738875317627765 & 101.133023454481 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.7475355 & 0.0071758908590348 & 104.173198099692 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.747806111111111 & 0.00698163178710167 & 107.110505668984 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.748197576923077 & 0.00676487542937205 & 110.60034803812 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.74860576 & 0.00649940660616751 & 115.180631919477 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.748577833333333 & 0.00632348534546437 & 118.380575337344 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.748586608695652 & 0.00614178166934417 & 121.884275442762 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.748591090909091 & 0.0059626478305339 & 125.546755767741 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.748667214285714 & 0.0057914446436979 & 129.27123720338 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.748741325 & 0.00558006567733009 & 134.181453820854 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.7488185 & 0.00531966049285536 & 140.764340319408 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.74938525 & 0.00516876186831904 & 144.983512317179 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.750029794117647 & 0.00499394774054129 & 150.187753874323 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.75080934375 & 0.0047606568431091 & 157.711292473595 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.7514077 & 0.00455991039591083 & 164.785628391698 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.751986821428571 & 0.00435648292171927 & 172.613283453847 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.752589192307692 & 0.00407809778847527 & 184.544175089306 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.753100416666667 & 0.00381761379627696 & 197.269932700136 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.753580590909091 & 0.00348914084778289 & 215.978839429179 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.7539281 & 0.00313746453609649 & 240.298524915921 \tabularnewline
Median & 0.756087 &  &  \tabularnewline
Midrange & 0.7412895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.749616935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.7514077 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.749616935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.7514077 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.7514077 &  &  \tabularnewline
Midmean - Closest Observation & 0.749616935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.7514077 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.75080934375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112741&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]0.747048366666667[/C][C]0.00758246653875113[/C][C]98.5231339760991[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.744740599486322[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.742397843609237[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.74931528495634[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.746977633333333[/C][C]0.00756076426202866[/C][C]98.796577627049[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.7470484[/C][C]0.00745553644643146[/C][C]100.20048930987[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.7467883[/C][C]0.00739963292563001[/C][C]100.922344054846[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.746836966666667[/C][C]0.00737811949511269[/C][C]101.223213741845[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.748717466666667[/C][C]0.00692806714680647[/C][C]108.070180441567[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.748537466666667[/C][C]0.00678494010171641[/C][C]110.323371385004[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.7485636[/C][C]0.00659141568421738[/C][C]113.566437903829[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.7481648[/C][C]0.0063630293643368[/C][C]117.57996972217[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.74822255[/C][C]0.00629756304815107[/C][C]118.811442502298[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.74825255[/C][C]0.00620769634443888[/C][C]120.536267961998[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.74507795[/C][C]0.00547736253463593[/C][C]136.02859867108[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.74500235[/C][C]0.00532826387805056[/C][C]139.820843533855[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.744624916666667[/C][C]0.00524730941268772[/C][C]141.906043288814[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.74662085[/C][C]0.00483569195405139[/C][C]154.397934586067[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.74735385[/C][C]0.00454380548938055[/C][C]164.477518183087[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.747810383333333[/C][C]0.00443912716137464[/C][C]168.458878547143[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.749112866666667[/C][C]0.00401218250562655[/C][C]186.709569072727[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.749931266666667[/C][C]0.0037926551602929[/C][C]197.73252114193[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.7513797[/C][C]0.00340657382837831[/C][C]220.567566667913[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.7531137[/C][C]0.00271512391340456[/C][C]277.377285169889[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.747246948275862[/C][C]0.00738875317627765[/C][C]101.133023454481[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.7475355[/C][C]0.0071758908590348[/C][C]104.173198099692[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.747806111111111[/C][C]0.00698163178710167[/C][C]107.110505668984[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.748197576923077[/C][C]0.00676487542937205[/C][C]110.60034803812[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.74860576[/C][C]0.00649940660616751[/C][C]115.180631919477[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.748577833333333[/C][C]0.00632348534546437[/C][C]118.380575337344[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.748586608695652[/C][C]0.00614178166934417[/C][C]121.884275442762[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.748591090909091[/C][C]0.0059626478305339[/C][C]125.546755767741[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.748667214285714[/C][C]0.0057914446436979[/C][C]129.27123720338[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.748741325[/C][C]0.00558006567733009[/C][C]134.181453820854[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.7488185[/C][C]0.00531966049285536[/C][C]140.764340319408[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.74938525[/C][C]0.00516876186831904[/C][C]144.983512317179[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.750029794117647[/C][C]0.00499394774054129[/C][C]150.187753874323[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.75080934375[/C][C]0.0047606568431091[/C][C]157.711292473595[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.7514077[/C][C]0.00455991039591083[/C][C]164.785628391698[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.751986821428571[/C][C]0.00435648292171927[/C][C]172.613283453847[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.752589192307692[/C][C]0.00407809778847527[/C][C]184.544175089306[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.753100416666667[/C][C]0.00381761379627696[/C][C]197.269932700136[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.753580590909091[/C][C]0.00348914084778289[/C][C]215.978839429179[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.7539281[/C][C]0.00313746453609649[/C][C]240.298524915921[/C][/ROW]
[ROW][C]Median[/C][C]0.756087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.7412895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.749616935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.7514077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.749616935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.7514077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.7514077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.749616935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.7514077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.75080934375[/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=112741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112741&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 Mean0.7470483666666670.0075824665387511398.5231339760991
Geometric Mean0.744740599486322
Harmonic Mean0.742397843609237
Quadratic Mean0.74931528495634
Winsorized Mean ( 1 / 20 )0.7469776333333330.0075607642620286698.796577627049
Winsorized Mean ( 2 / 20 )0.74704840.00745553644643146100.20048930987
Winsorized Mean ( 3 / 20 )0.74678830.00739963292563001100.922344054846
Winsorized Mean ( 4 / 20 )0.7468369666666670.00737811949511269101.223213741845
Winsorized Mean ( 5 / 20 )0.7487174666666670.00692806714680647108.070180441567
Winsorized Mean ( 6 / 20 )0.7485374666666670.00678494010171641110.323371385004
Winsorized Mean ( 7 / 20 )0.74856360.00659141568421738113.566437903829
Winsorized Mean ( 8 / 20 )0.74816480.0063630293643368117.57996972217
Winsorized Mean ( 9 / 20 )0.748222550.00629756304815107118.811442502298
Winsorized Mean ( 10 / 20 )0.748252550.00620769634443888120.536267961998
Winsorized Mean ( 11 / 20 )0.745077950.00547736253463593136.02859867108
Winsorized Mean ( 12 / 20 )0.745002350.00532826387805056139.820843533855
Winsorized Mean ( 13 / 20 )0.7446249166666670.00524730941268772141.906043288814
Winsorized Mean ( 14 / 20 )0.746620850.00483569195405139154.397934586067
Winsorized Mean ( 15 / 20 )0.747353850.00454380548938055164.477518183087
Winsorized Mean ( 16 / 20 )0.7478103833333330.00443912716137464168.458878547143
Winsorized Mean ( 17 / 20 )0.7491128666666670.00401218250562655186.709569072727
Winsorized Mean ( 18 / 20 )0.7499312666666670.0037926551602929197.73252114193
Winsorized Mean ( 19 / 20 )0.75137970.00340657382837831220.567566667913
Winsorized Mean ( 20 / 20 )0.75311370.00271512391340456277.377285169889
Trimmed Mean ( 1 / 20 )0.7472469482758620.00738875317627765101.133023454481
Trimmed Mean ( 2 / 20 )0.74753550.0071758908590348104.173198099692
Trimmed Mean ( 3 / 20 )0.7478061111111110.00698163178710167107.110505668984
Trimmed Mean ( 4 / 20 )0.7481975769230770.00676487542937205110.60034803812
Trimmed Mean ( 5 / 20 )0.748605760.00649940660616751115.180631919477
Trimmed Mean ( 6 / 20 )0.7485778333333330.00632348534546437118.380575337344
Trimmed Mean ( 7 / 20 )0.7485866086956520.00614178166934417121.884275442762
Trimmed Mean ( 8 / 20 )0.7485910909090910.0059626478305339125.546755767741
Trimmed Mean ( 9 / 20 )0.7486672142857140.0057914446436979129.27123720338
Trimmed Mean ( 10 / 20 )0.7487413250.00558006567733009134.181453820854
Trimmed Mean ( 11 / 20 )0.74881850.00531966049285536140.764340319408
Trimmed Mean ( 12 / 20 )0.749385250.00516876186831904144.983512317179
Trimmed Mean ( 13 / 20 )0.7500297941176470.00499394774054129150.187753874323
Trimmed Mean ( 14 / 20 )0.750809343750.0047606568431091157.711292473595
Trimmed Mean ( 15 / 20 )0.75140770.00455991039591083164.785628391698
Trimmed Mean ( 16 / 20 )0.7519868214285710.00435648292171927172.613283453847
Trimmed Mean ( 17 / 20 )0.7525891923076920.00407809778847527184.544175089306
Trimmed Mean ( 18 / 20 )0.7531004166666670.00381761379627696197.269932700136
Trimmed Mean ( 19 / 20 )0.7535805909090910.00348914084778289215.978839429179
Trimmed Mean ( 20 / 20 )0.75392810.00313746453609649240.298524915921
Median0.756087
Midrange0.7412895
Midmean - Weighted Average at Xnp0.749616935483871
Midmean - Weighted Average at X(n+1)p0.7514077
Midmean - Empirical Distribution Function0.749616935483871
Midmean - Empirical Distribution Function - Averaging0.7514077
Midmean - Empirical Distribution Function - Interpolation0.7514077
Midmean - Closest Observation0.749616935483871
Midmean - True Basic - Statistics Graphics Toolkit0.7514077
Midmean - MS Excel (old versions)0.75080934375
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')