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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 computationFri, 16 Oct 2009 09:06:22 -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/16/t1255705652p71hgiegvred6u1.htm/, Retrieved Tue, 30 Apr 2024 00:59:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47043, Retrieved Tue, 30 Apr 2024 00:59:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Workshop 3:Deel 2] [2009-10-16 15:06:22] [a5c6be3c0aa55fdb2a703a08e16947ef] [Current]
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Dataseries X:
3,7783
3,2483
2,8659
2,6968
3,2067
4,0351
3,4679
3,0128
3,4400
3,9097
3,9762
3,8906
2,8702
2,9916
3,5755
3,1318
2,7186
1,7651
2,1511
2,5871
2,0968
1,5620
1,6362
0,9663
0,8950
1,3953
1,6232
1,6819
1,8656
1,9041
1,8307
0,9810
0,9394
1,0845
0,7589
1,3183
2,4041
3,7839
4,0625
4,6745
4,7314
6,4473
5,8224
7,3531
8,4097
8,6623
8,0980
8,7066
7,9323
5,0630
4,2419
3,5399
2,7028
0,0899
-0,0058
-1,7598
-3,0174
-3,9706
-2,4319




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47043&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47043&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.905061016949150.3427347366775168.47612076065278
Geometric MeanNaN
Harmonic Mean-0.420641704389302
Quadratic Mean3.9054412421993
Winsorized Mean ( 1 / 19 )2.920466101694910.3372661385540188.6592330739635
Winsorized Mean ( 2 / 19 )2.931750847457630.3289752073317998.91176837074143
Winsorized Mean ( 3 / 19 )2.950076271186440.3152547477624819.35775366469369
Winsorized Mean ( 4 / 19 )3.057757627118640.28549385566089710.7104148355143
Winsorized Mean ( 5 / 19 )3.016783050847460.26995193814448411.1752598317439
Winsorized Mean ( 6 / 19 )2.992701694915250.23333900142906012.8255528505169
Winsorized Mean ( 7 / 19 )2.934708474576270.21248542359039113.8113402086043
Winsorized Mean ( 8 / 19 )2.83775932203390.18884945069285715.0265691090053
Winsorized Mean ( 9 / 19 )2.791279661016950.17823578398255015.6606019209377
Winsorized Mean ( 10 / 19 )2.784127118644070.17599777798047615.8191038011453
Winsorized Mean ( 11 / 19 )2.722769491525420.15839520909207217.1897212493513
Winsorized Mean ( 12 / 19 )2.733833898305080.14420038424344318.9585756837496
Winsorized Mean ( 13 / 19 )2.744762711864410.14040057566678519.5495118081182
Winsorized Mean ( 14 / 19 )2.770342372881360.13178161100637421.0222226889255
Winsorized Mean ( 15 / 19 )2.768994915254240.12669194209053121.8561249402553
Winsorized Mean ( 16 / 19 )2.76734067796610.12534060245009222.0785653161991
Winsorized Mean ( 17 / 19 )2.749764406779660.11860629721526523.1839663773414
Winsorized Mean ( 18 / 19 )2.773438983050850.11444983593075224.2327912530074
Winsorized Mean ( 19 / 19 )2.729255932203390.10158668409287926.8662763882328
Trimmed Mean ( 1 / 19 )2.923905263157890.3171278161397329.2199583712
Trimmed Mean ( 2 / 19 )2.927594545454550.29174418840969110.0347998752365
Trimmed Mean ( 3 / 19 )2.925281132075470.26532330185443911.0253457258734
Trimmed Mean ( 4 / 19 )2.915719607843140.23870644894677912.2146662593653
Trimmed Mean ( 5 / 19 )2.872963265306120.21774004227358313.1944645335209
Trimmed Mean ( 6 / 19 )2.836855319148940.19667881121472514.4237973660101
Trimmed Mean ( 7 / 19 )2.80280.18288690124354115.3253184396605
Trimmed Mean ( 8 / 19 )2.776944186046510.17201794542166616.1433400407116
Trimmed Mean ( 9 / 19 )2.766004878048780.16533839504922616.7293560411377
Trimmed Mean ( 10 / 19 )2.761756410256410.15955806805753217.3087857222024
Trimmed Mean ( 11 / 19 )2.758189189189190.15230894440676518.1091740864739
Trimmed Mean ( 12 / 19 )2.763617142857140.14751752754345218.7341612137792
Trimmed Mean ( 13 / 19 )2.768054545454550.14472872613406219.1258129563753
Trimmed Mean ( 14 / 19 )2.771464516129030.14153225670924919.5818577373672
Trimmed Mean ( 15 / 19 )2.771627586206900.13911662868529519.9230502665269
Trimmed Mean ( 16 / 19 )2.772011111111110.13660980486197020.2914506313214
Trimmed Mean ( 17 / 19 )2.77270.13266230172886320.9004364002885
Trimmed Mean ( 18 / 19 )2.776160869565220.12843637183540521.6150676782038
Trimmed Mean ( 19 / 19 )2.776585714285710.12267257528841222.6341193845304
Median2.8659
Midrange2.368
Midmean - Weighted Average at Xnp2.73130666666667
Midmean - Weighted Average at X(n+1)p2.77146451612903
Midmean - Empirical Distribution Function2.77146451612903
Midmean - Empirical Distribution Function - Averaging2.77146451612903
Midmean - Empirical Distribution Function - Interpolation2.77162758620690
Midmean - Closest Observation2.73130666666667
Midmean - True Basic - Statistics Graphics Toolkit2.77146451612903
Midmean - MS Excel (old versions)2.77146451612903
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.90506101694915 & 0.342734736677516 & 8.47612076065278 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.420641704389302 &  &  \tabularnewline
Quadratic Mean & 3.9054412421993 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 2.92046610169491 & 0.337266138554018 & 8.6592330739635 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 2.93175084745763 & 0.328975207331799 & 8.91176837074143 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 2.95007627118644 & 0.315254747762481 & 9.35775366469369 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 3.05775762711864 & 0.285493855660897 & 10.7104148355143 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 3.01678305084746 & 0.269951938144484 & 11.1752598317439 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 2.99270169491525 & 0.233339001429060 & 12.8255528505169 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 2.93470847457627 & 0.212485423590391 & 13.8113402086043 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 2.8377593220339 & 0.188849450692857 & 15.0265691090053 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 2.79127966101695 & 0.178235783982550 & 15.6606019209377 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 2.78412711864407 & 0.175997777980476 & 15.8191038011453 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 2.72276949152542 & 0.158395209092072 & 17.1897212493513 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 2.73383389830508 & 0.144200384243443 & 18.9585756837496 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 2.74476271186441 & 0.140400575666785 & 19.5495118081182 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 2.77034237288136 & 0.131781611006374 & 21.0222226889255 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 2.76899491525424 & 0.126691942090531 & 21.8561249402553 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 2.7673406779661 & 0.125340602450092 & 22.0785653161991 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 2.74976440677966 & 0.118606297215265 & 23.1839663773414 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 2.77343898305085 & 0.114449835930752 & 24.2327912530074 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 2.72925593220339 & 0.101586684092879 & 26.8662763882328 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 2.92390526315789 & 0.317127816139732 & 9.2199583712 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 2.92759454545455 & 0.291744188409691 & 10.0347998752365 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 2.92528113207547 & 0.265323301854439 & 11.0253457258734 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 2.91571960784314 & 0.238706448946779 & 12.2146662593653 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 2.87296326530612 & 0.217740042273583 & 13.1944645335209 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 2.83685531914894 & 0.196678811214725 & 14.4237973660101 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 2.8028 & 0.182886901243541 & 15.3253184396605 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 2.77694418604651 & 0.172017945421666 & 16.1433400407116 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 2.76600487804878 & 0.165338395049226 & 16.7293560411377 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 2.76175641025641 & 0.159558068057532 & 17.3087857222024 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 2.75818918918919 & 0.152308944406765 & 18.1091740864739 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 2.76361714285714 & 0.147517527543452 & 18.7341612137792 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 2.76805454545455 & 0.144728726134062 & 19.1258129563753 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 2.77146451612903 & 0.141532256709249 & 19.5818577373672 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 2.77162758620690 & 0.139116628685295 & 19.9230502665269 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 2.77201111111111 & 0.136609804861970 & 20.2914506313214 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 2.7727 & 0.132662301728863 & 20.9004364002885 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 2.77616086956522 & 0.128436371835405 & 21.6150676782038 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 2.77658571428571 & 0.122672575288412 & 22.6341193845304 \tabularnewline
Median & 2.8659 &  &  \tabularnewline
Midrange & 2.368 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.73130666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.77146451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.77146451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.77146451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.77162758620690 &  &  \tabularnewline
Midmean - Closest Observation & 2.73130666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.77146451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.77146451612903 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47043&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]2.90506101694915[/C][C]0.342734736677516[/C][C]8.47612076065278[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.420641704389302[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.9054412421993[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]2.92046610169491[/C][C]0.337266138554018[/C][C]8.6592330739635[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]2.93175084745763[/C][C]0.328975207331799[/C][C]8.91176837074143[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]2.95007627118644[/C][C]0.315254747762481[/C][C]9.35775366469369[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]3.05775762711864[/C][C]0.285493855660897[/C][C]10.7104148355143[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]3.01678305084746[/C][C]0.269951938144484[/C][C]11.1752598317439[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]2.99270169491525[/C][C]0.233339001429060[/C][C]12.8255528505169[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]2.93470847457627[/C][C]0.212485423590391[/C][C]13.8113402086043[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]2.8377593220339[/C][C]0.188849450692857[/C][C]15.0265691090053[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]2.79127966101695[/C][C]0.178235783982550[/C][C]15.6606019209377[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]2.78412711864407[/C][C]0.175997777980476[/C][C]15.8191038011453[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]2.72276949152542[/C][C]0.158395209092072[/C][C]17.1897212493513[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]2.73383389830508[/C][C]0.144200384243443[/C][C]18.9585756837496[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]2.74476271186441[/C][C]0.140400575666785[/C][C]19.5495118081182[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]2.77034237288136[/C][C]0.131781611006374[/C][C]21.0222226889255[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]2.76899491525424[/C][C]0.126691942090531[/C][C]21.8561249402553[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]2.7673406779661[/C][C]0.125340602450092[/C][C]22.0785653161991[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]2.74976440677966[/C][C]0.118606297215265[/C][C]23.1839663773414[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]2.77343898305085[/C][C]0.114449835930752[/C][C]24.2327912530074[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]2.72925593220339[/C][C]0.101586684092879[/C][C]26.8662763882328[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]2.92390526315789[/C][C]0.317127816139732[/C][C]9.2199583712[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]2.92759454545455[/C][C]0.291744188409691[/C][C]10.0347998752365[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]2.92528113207547[/C][C]0.265323301854439[/C][C]11.0253457258734[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]2.91571960784314[/C][C]0.238706448946779[/C][C]12.2146662593653[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]2.87296326530612[/C][C]0.217740042273583[/C][C]13.1944645335209[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]2.83685531914894[/C][C]0.196678811214725[/C][C]14.4237973660101[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]2.8028[/C][C]0.182886901243541[/C][C]15.3253184396605[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]2.77694418604651[/C][C]0.172017945421666[/C][C]16.1433400407116[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]2.76600487804878[/C][C]0.165338395049226[/C][C]16.7293560411377[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]2.76175641025641[/C][C]0.159558068057532[/C][C]17.3087857222024[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]2.75818918918919[/C][C]0.152308944406765[/C][C]18.1091740864739[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]2.76361714285714[/C][C]0.147517527543452[/C][C]18.7341612137792[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]2.76805454545455[/C][C]0.144728726134062[/C][C]19.1258129563753[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]2.77146451612903[/C][C]0.141532256709249[/C][C]19.5818577373672[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]2.77162758620690[/C][C]0.139116628685295[/C][C]19.9230502665269[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]2.77201111111111[/C][C]0.136609804861970[/C][C]20.2914506313214[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]2.7727[/C][C]0.132662301728863[/C][C]20.9004364002885[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]2.77616086956522[/C][C]0.128436371835405[/C][C]21.6150676782038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]2.77658571428571[/C][C]0.122672575288412[/C][C]22.6341193845304[/C][/ROW]
[ROW][C]Median[/C][C]2.8659[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.73130666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.77146451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.77146451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.77146451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.77162758620690[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.73130666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.77146451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.77146451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47043&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 Mean2.905061016949150.3427347366775168.47612076065278
Geometric MeanNaN
Harmonic Mean-0.420641704389302
Quadratic Mean3.9054412421993
Winsorized Mean ( 1 / 19 )2.920466101694910.3372661385540188.6592330739635
Winsorized Mean ( 2 / 19 )2.931750847457630.3289752073317998.91176837074143
Winsorized Mean ( 3 / 19 )2.950076271186440.3152547477624819.35775366469369
Winsorized Mean ( 4 / 19 )3.057757627118640.28549385566089710.7104148355143
Winsorized Mean ( 5 / 19 )3.016783050847460.26995193814448411.1752598317439
Winsorized Mean ( 6 / 19 )2.992701694915250.23333900142906012.8255528505169
Winsorized Mean ( 7 / 19 )2.934708474576270.21248542359039113.8113402086043
Winsorized Mean ( 8 / 19 )2.83775932203390.18884945069285715.0265691090053
Winsorized Mean ( 9 / 19 )2.791279661016950.17823578398255015.6606019209377
Winsorized Mean ( 10 / 19 )2.784127118644070.17599777798047615.8191038011453
Winsorized Mean ( 11 / 19 )2.722769491525420.15839520909207217.1897212493513
Winsorized Mean ( 12 / 19 )2.733833898305080.14420038424344318.9585756837496
Winsorized Mean ( 13 / 19 )2.744762711864410.14040057566678519.5495118081182
Winsorized Mean ( 14 / 19 )2.770342372881360.13178161100637421.0222226889255
Winsorized Mean ( 15 / 19 )2.768994915254240.12669194209053121.8561249402553
Winsorized Mean ( 16 / 19 )2.76734067796610.12534060245009222.0785653161991
Winsorized Mean ( 17 / 19 )2.749764406779660.11860629721526523.1839663773414
Winsorized Mean ( 18 / 19 )2.773438983050850.11444983593075224.2327912530074
Winsorized Mean ( 19 / 19 )2.729255932203390.10158668409287926.8662763882328
Trimmed Mean ( 1 / 19 )2.923905263157890.3171278161397329.2199583712
Trimmed Mean ( 2 / 19 )2.927594545454550.29174418840969110.0347998752365
Trimmed Mean ( 3 / 19 )2.925281132075470.26532330185443911.0253457258734
Trimmed Mean ( 4 / 19 )2.915719607843140.23870644894677912.2146662593653
Trimmed Mean ( 5 / 19 )2.872963265306120.21774004227358313.1944645335209
Trimmed Mean ( 6 / 19 )2.836855319148940.19667881121472514.4237973660101
Trimmed Mean ( 7 / 19 )2.80280.18288690124354115.3253184396605
Trimmed Mean ( 8 / 19 )2.776944186046510.17201794542166616.1433400407116
Trimmed Mean ( 9 / 19 )2.766004878048780.16533839504922616.7293560411377
Trimmed Mean ( 10 / 19 )2.761756410256410.15955806805753217.3087857222024
Trimmed Mean ( 11 / 19 )2.758189189189190.15230894440676518.1091740864739
Trimmed Mean ( 12 / 19 )2.763617142857140.14751752754345218.7341612137792
Trimmed Mean ( 13 / 19 )2.768054545454550.14472872613406219.1258129563753
Trimmed Mean ( 14 / 19 )2.771464516129030.14153225670924919.5818577373672
Trimmed Mean ( 15 / 19 )2.771627586206900.13911662868529519.9230502665269
Trimmed Mean ( 16 / 19 )2.772011111111110.13660980486197020.2914506313214
Trimmed Mean ( 17 / 19 )2.77270.13266230172886320.9004364002885
Trimmed Mean ( 18 / 19 )2.776160869565220.12843637183540521.6150676782038
Trimmed Mean ( 19 / 19 )2.776585714285710.12267257528841222.6341193845304
Median2.8659
Midrange2.368
Midmean - Weighted Average at Xnp2.73130666666667
Midmean - Weighted Average at X(n+1)p2.77146451612903
Midmean - Empirical Distribution Function2.77146451612903
Midmean - Empirical Distribution Function - Averaging2.77146451612903
Midmean - Empirical Distribution Function - Interpolation2.77162758620690
Midmean - Closest Observation2.73130666666667
Midmean - True Basic - Statistics Graphics Toolkit2.77146451612903
Midmean - MS Excel (old versions)2.77146451612903
Number of observations59



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')