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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 computationThu, 22 Oct 2009 09:47:11 -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/22/t1256226603inxn7wyofxj290e.htm/, Retrieved Thu, 02 May 2024 15:38:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49772, Retrieved Thu, 02 May 2024 15:38:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-22 15:47:11] [60d430b39377ac0bf942b21543df0c0d] [Current]
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Dataseries X:
1.393500739
1.334282761
1.279766646
1.244127634
1.204537003
1.171350399
1.147395261
1.126922617
1.100189587
1.095505063
1.278179022
1.323249646
1.360276339
1.308400567
1.267712757
1.229331621
1.177842357
1.166916899
1.127851357
1.112110211
1.085416517
1.081940491
1.229521098
1.271428902
1.305603577
1.252585041
1.198820914
1.151024105
1.148267327
1.120827871
1.094378356
1.084500306
1.042554938
1.046355857
1.213359948
1.24959477
1.282080112
1.22725858
1.171015422
1.157328016
1.140328698
1.129607372
1.097681229
1.095317826
1.038953636
1.040241512
1.191368409
1.224256823
1.26363344
1.197251179
1.163151829
1.149067644
1.151753947
1.136928391
1.127848005
1.109570941
1.067250186
1.076552598
1.200976789
1.241707386




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49772&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49772&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49772&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.178445974566670.0110568774534306106.580359557212
Geometric Mean1.17542980060799
Harmonic Mean1.17245904449370
Quadratic Mean1.18150240489581
Winsorized Mean ( 1 / 20 )1.177913699166670.0108822687869024108.241555344081
Winsorized Mean ( 2 / 20 )1.177124360766670.0106339957580855110.694454610032
Winsorized Mean ( 3 / 20 )1.176762750966670.0104589307651489112.512720218769
Winsorized Mean ( 4 / 20 )1.177165767633330.0099526666632115118.276418518521
Winsorized Mean ( 5 / 20 )1.177707886133330.00976005150464607120.666154842801
Winsorized Mean ( 6 / 20 )1.175894328933330.00917300227329654128.190781371162
Winsorized Mean ( 7 / 20 )1.175923069650.00906889321053916129.665554809206
Winsorized Mean ( 8 / 20 )1.175833547916670.00900713845507289130.544628994176
Winsorized Mean ( 9 / 20 )1.176165305766670.00859149328254502136.898821553668
Winsorized Mean ( 10 / 20 )1.17570252660.008450884656138139.121828594131
Winsorized Mean ( 11 / 20 )1.17498897860.00830869951782355141.416713419405
Winsorized Mean ( 12 / 20 )1.1732145320.00784846616416718149.483288512653
Winsorized Mean ( 13 / 20 )1.173110117516670.00764980136930127153.351709525997
Winsorized Mean ( 14 / 20 )1.174023435050.00708895388157884165.613072769564
Winsorized Mean ( 15 / 20 )1.174053190550.00689061303609561170.384432328426
Winsorized Mean ( 16 / 20 )1.173128223083330.00601221483594772195.124135629530
Winsorized Mean ( 17 / 20 )1.174801382633330.00575445031070945204.155274474600
Winsorized Mean ( 18 / 20 )1.174457086733330.00561584607962792209.132705932558
Winsorized Mean ( 19 / 20 )1.173507591816670.00546513939148224214.726012962387
Winsorized Mean ( 20 / 20 )1.170460638483330.00482121200080028242.773111468454
Trimmed Mean ( 1 / 20 )1.177143174120690.0105357967449325111.727969191023
Trimmed Mean ( 2 / 20 )1.176317611571430.0101075060988456116.380598741937
Trimmed Mean ( 3 / 20 )1.175869417574070.0097452112323471120.661255004000
Trimmed Mean ( 4 / 20 )1.175525827807690.00937932105326861125.331654725481
Trimmed Mean ( 5 / 20 )1.175033845860.00912295687284911128.799671229075
Trimmed Mean ( 6 / 20 )1.174365335791670.00886114756033996132.529712183984
Trimmed Mean ( 7 / 20 )1.174032945978260.00870867934669239134.811823841484
Trimmed Mean ( 8 / 20 )1.173664740068180.0085338956791924137.529773527680
Trimmed Mean ( 9 / 20 )1.173277452952380.0083155016211939141.095210655966
Trimmed Mean ( 10 / 20 )1.172796144150.00813366185086668144.19042316408
Trimmed Mean ( 11 / 20 )1.172337241657890.00791958222256593148.030187541643
Trimmed Mean ( 12 / 20 )1.171935463333330.00766045418422352152.985114870460
Trimmed Mean ( 13 / 20 )1.1717473650.00742885296306518157.729244450752
Trimmed Mean ( 14 / 20 )1.171550814156250.00715178218625604163.812429356096
Trimmed Mean ( 15 / 20 )1.17119758260.00691709209890056169.319356436812
Trimmed Mean ( 16 / 20 )1.170789638607140.00662272745594452176.783605605912
Trimmed Mean ( 17 / 20 )1.170452342769230.00647005312130627180.903049916988
Trimmed Mean ( 18 / 20 )1.169812778083330.00628988841502049185.983073291058
Trimmed Mean ( 19 / 20 )1.169109094954550.00602423896620381194.067516496820
Trimmed Mean ( 20 / 20 )1.168414595450.00562268263970361207.803760290407
Median1.165034364
Midrange1.2162271875
Midmean - Weighted Average at Xnp1.16920962641935
Midmean - Weighted Average at X(n+1)p1.1711975826
Midmean - Empirical Distribution Function1.16920962641935
Midmean - Empirical Distribution Function - Averaging1.1711975826
Midmean - Empirical Distribution Function - Interpolation1.1711975826
Midmean - Closest Observation1.16920962641935
Midmean - True Basic - Statistics Graphics Toolkit1.1711975826
Midmean - MS Excel (old versions)1.17155081415625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.17844597456667 & 0.0110568774534306 & 106.580359557212 \tabularnewline
Geometric Mean & 1.17542980060799 &  &  \tabularnewline
Harmonic Mean & 1.17245904449370 &  &  \tabularnewline
Quadratic Mean & 1.18150240489581 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.17791369916667 & 0.0108822687869024 & 108.241555344081 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.17712436076667 & 0.0106339957580855 & 110.694454610032 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.17676275096667 & 0.0104589307651489 & 112.512720218769 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.17716576763333 & 0.0099526666632115 & 118.276418518521 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.17770788613333 & 0.00976005150464607 & 120.666154842801 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.17589432893333 & 0.00917300227329654 & 128.190781371162 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.17592306965 & 0.00906889321053916 & 129.665554809206 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.17583354791667 & 0.00900713845507289 & 130.544628994176 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.17616530576667 & 0.00859149328254502 & 136.898821553668 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.1757025266 & 0.008450884656138 & 139.121828594131 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.1749889786 & 0.00830869951782355 & 141.416713419405 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.173214532 & 0.00784846616416718 & 149.483288512653 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.17311011751667 & 0.00764980136930127 & 153.351709525997 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.17402343505 & 0.00708895388157884 & 165.613072769564 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.17405319055 & 0.00689061303609561 & 170.384432328426 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.17312822308333 & 0.00601221483594772 & 195.124135629530 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.17480138263333 & 0.00575445031070945 & 204.155274474600 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.17445708673333 & 0.00561584607962792 & 209.132705932558 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.17350759181667 & 0.00546513939148224 & 214.726012962387 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.17046063848333 & 0.00482121200080028 & 242.773111468454 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.17714317412069 & 0.0105357967449325 & 111.727969191023 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.17631761157143 & 0.0101075060988456 & 116.380598741937 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.17586941757407 & 0.0097452112323471 & 120.661255004000 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.17552582780769 & 0.00937932105326861 & 125.331654725481 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.17503384586 & 0.00912295687284911 & 128.799671229075 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.17436533579167 & 0.00886114756033996 & 132.529712183984 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.17403294597826 & 0.00870867934669239 & 134.811823841484 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.17366474006818 & 0.0085338956791924 & 137.529773527680 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.17327745295238 & 0.0083155016211939 & 141.095210655966 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.17279614415 & 0.00813366185086668 & 144.19042316408 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.17233724165789 & 0.00791958222256593 & 148.030187541643 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.17193546333333 & 0.00766045418422352 & 152.985114870460 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.171747365 & 0.00742885296306518 & 157.729244450752 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.17155081415625 & 0.00715178218625604 & 163.812429356096 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.1711975826 & 0.00691709209890056 & 169.319356436812 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.17078963860714 & 0.00662272745594452 & 176.783605605912 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.17045234276923 & 0.00647005312130627 & 180.903049916988 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.16981277808333 & 0.00628988841502049 & 185.983073291058 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.16910909495455 & 0.00602423896620381 & 194.067516496820 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.16841459545 & 0.00562268263970361 & 207.803760290407 \tabularnewline
Median & 1.165034364 &  &  \tabularnewline
Midrange & 1.2162271875 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.16920962641935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.1711975826 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.16920962641935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.1711975826 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.1711975826 &  &  \tabularnewline
Midmean - Closest Observation & 1.16920962641935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.1711975826 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.17155081415625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49772&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]1.17844597456667[/C][C]0.0110568774534306[/C][C]106.580359557212[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.17542980060799[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.17245904449370[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.18150240489581[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.17791369916667[/C][C]0.0108822687869024[/C][C]108.241555344081[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.17712436076667[/C][C]0.0106339957580855[/C][C]110.694454610032[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.17676275096667[/C][C]0.0104589307651489[/C][C]112.512720218769[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.17716576763333[/C][C]0.0099526666632115[/C][C]118.276418518521[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.17770788613333[/C][C]0.00976005150464607[/C][C]120.666154842801[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.17589432893333[/C][C]0.00917300227329654[/C][C]128.190781371162[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.17592306965[/C][C]0.00906889321053916[/C][C]129.665554809206[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.17583354791667[/C][C]0.00900713845507289[/C][C]130.544628994176[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.17616530576667[/C][C]0.00859149328254502[/C][C]136.898821553668[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.1757025266[/C][C]0.008450884656138[/C][C]139.121828594131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.1749889786[/C][C]0.00830869951782355[/C][C]141.416713419405[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.173214532[/C][C]0.00784846616416718[/C][C]149.483288512653[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.17311011751667[/C][C]0.00764980136930127[/C][C]153.351709525997[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.17402343505[/C][C]0.00708895388157884[/C][C]165.613072769564[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.17405319055[/C][C]0.00689061303609561[/C][C]170.384432328426[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.17312822308333[/C][C]0.00601221483594772[/C][C]195.124135629530[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.17480138263333[/C][C]0.00575445031070945[/C][C]204.155274474600[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.17445708673333[/C][C]0.00561584607962792[/C][C]209.132705932558[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.17350759181667[/C][C]0.00546513939148224[/C][C]214.726012962387[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.17046063848333[/C][C]0.00482121200080028[/C][C]242.773111468454[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.17714317412069[/C][C]0.0105357967449325[/C][C]111.727969191023[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.17631761157143[/C][C]0.0101075060988456[/C][C]116.380598741937[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.17586941757407[/C][C]0.0097452112323471[/C][C]120.661255004000[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.17552582780769[/C][C]0.00937932105326861[/C][C]125.331654725481[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.17503384586[/C][C]0.00912295687284911[/C][C]128.799671229075[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.17436533579167[/C][C]0.00886114756033996[/C][C]132.529712183984[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.17403294597826[/C][C]0.00870867934669239[/C][C]134.811823841484[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.17366474006818[/C][C]0.0085338956791924[/C][C]137.529773527680[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.17327745295238[/C][C]0.0083155016211939[/C][C]141.095210655966[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.17279614415[/C][C]0.00813366185086668[/C][C]144.19042316408[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.17233724165789[/C][C]0.00791958222256593[/C][C]148.030187541643[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.17193546333333[/C][C]0.00766045418422352[/C][C]152.985114870460[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.171747365[/C][C]0.00742885296306518[/C][C]157.729244450752[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.17155081415625[/C][C]0.00715178218625604[/C][C]163.812429356096[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.1711975826[/C][C]0.00691709209890056[/C][C]169.319356436812[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.17078963860714[/C][C]0.00662272745594452[/C][C]176.783605605912[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.17045234276923[/C][C]0.00647005312130627[/C][C]180.903049916988[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.16981277808333[/C][C]0.00628988841502049[/C][C]185.983073291058[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.16910909495455[/C][C]0.00602423896620381[/C][C]194.067516496820[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.16841459545[/C][C]0.00562268263970361[/C][C]207.803760290407[/C][/ROW]
[ROW][C]Median[/C][C]1.165034364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2162271875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.16920962641935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.1711975826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.16920962641935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.1711975826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.1711975826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.16920962641935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.1711975826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.17155081415625[/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=49772&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49772&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 Mean1.178445974566670.0110568774534306106.580359557212
Geometric Mean1.17542980060799
Harmonic Mean1.17245904449370
Quadratic Mean1.18150240489581
Winsorized Mean ( 1 / 20 )1.177913699166670.0108822687869024108.241555344081
Winsorized Mean ( 2 / 20 )1.177124360766670.0106339957580855110.694454610032
Winsorized Mean ( 3 / 20 )1.176762750966670.0104589307651489112.512720218769
Winsorized Mean ( 4 / 20 )1.177165767633330.0099526666632115118.276418518521
Winsorized Mean ( 5 / 20 )1.177707886133330.00976005150464607120.666154842801
Winsorized Mean ( 6 / 20 )1.175894328933330.00917300227329654128.190781371162
Winsorized Mean ( 7 / 20 )1.175923069650.00906889321053916129.665554809206
Winsorized Mean ( 8 / 20 )1.175833547916670.00900713845507289130.544628994176
Winsorized Mean ( 9 / 20 )1.176165305766670.00859149328254502136.898821553668
Winsorized Mean ( 10 / 20 )1.17570252660.008450884656138139.121828594131
Winsorized Mean ( 11 / 20 )1.17498897860.00830869951782355141.416713419405
Winsorized Mean ( 12 / 20 )1.1732145320.00784846616416718149.483288512653
Winsorized Mean ( 13 / 20 )1.173110117516670.00764980136930127153.351709525997
Winsorized Mean ( 14 / 20 )1.174023435050.00708895388157884165.613072769564
Winsorized Mean ( 15 / 20 )1.174053190550.00689061303609561170.384432328426
Winsorized Mean ( 16 / 20 )1.173128223083330.00601221483594772195.124135629530
Winsorized Mean ( 17 / 20 )1.174801382633330.00575445031070945204.155274474600
Winsorized Mean ( 18 / 20 )1.174457086733330.00561584607962792209.132705932558
Winsorized Mean ( 19 / 20 )1.173507591816670.00546513939148224214.726012962387
Winsorized Mean ( 20 / 20 )1.170460638483330.00482121200080028242.773111468454
Trimmed Mean ( 1 / 20 )1.177143174120690.0105357967449325111.727969191023
Trimmed Mean ( 2 / 20 )1.176317611571430.0101075060988456116.380598741937
Trimmed Mean ( 3 / 20 )1.175869417574070.0097452112323471120.661255004000
Trimmed Mean ( 4 / 20 )1.175525827807690.00937932105326861125.331654725481
Trimmed Mean ( 5 / 20 )1.175033845860.00912295687284911128.799671229075
Trimmed Mean ( 6 / 20 )1.174365335791670.00886114756033996132.529712183984
Trimmed Mean ( 7 / 20 )1.174032945978260.00870867934669239134.811823841484
Trimmed Mean ( 8 / 20 )1.173664740068180.0085338956791924137.529773527680
Trimmed Mean ( 9 / 20 )1.173277452952380.0083155016211939141.095210655966
Trimmed Mean ( 10 / 20 )1.172796144150.00813366185086668144.19042316408
Trimmed Mean ( 11 / 20 )1.172337241657890.00791958222256593148.030187541643
Trimmed Mean ( 12 / 20 )1.171935463333330.00766045418422352152.985114870460
Trimmed Mean ( 13 / 20 )1.1717473650.00742885296306518157.729244450752
Trimmed Mean ( 14 / 20 )1.171550814156250.00715178218625604163.812429356096
Trimmed Mean ( 15 / 20 )1.17119758260.00691709209890056169.319356436812
Trimmed Mean ( 16 / 20 )1.170789638607140.00662272745594452176.783605605912
Trimmed Mean ( 17 / 20 )1.170452342769230.00647005312130627180.903049916988
Trimmed Mean ( 18 / 20 )1.169812778083330.00628988841502049185.983073291058
Trimmed Mean ( 19 / 20 )1.169109094954550.00602423896620381194.067516496820
Trimmed Mean ( 20 / 20 )1.168414595450.00562268263970361207.803760290407
Median1.165034364
Midrange1.2162271875
Midmean - Weighted Average at Xnp1.16920962641935
Midmean - Weighted Average at X(n+1)p1.1711975826
Midmean - Empirical Distribution Function1.16920962641935
Midmean - Empirical Distribution Function - Averaging1.1711975826
Midmean - Empirical Distribution Function - Interpolation1.1711975826
Midmean - Closest Observation1.16920962641935
Midmean - True Basic - Statistics Graphics Toolkit1.1711975826
Midmean - MS Excel (old versions)1.17155081415625
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')