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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 computationSat, 11 Dec 2010 20:36:04 +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/11/t1292099650mog60jagei6zmcp.htm/, Retrieved Tue, 07 May 2024 00:52:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108300, Retrieved Tue, 07 May 2024 00:52:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [paper] [2007-12-11 21:01:08] [b3bb3ec527e23fa7d74d4348b38c8499]
- RMPD  [Univariate Explorative Data Analysis] [PAPER] [2009-12-30 15:50:30] [23722951c28e05bb35cc9a97084fe0d9]
- RM D      [Central Tendency] [] [2010-12-11 20:36:04] [297722d8c88c4886be8e106c47d8f3cc] [Current]
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Dataseries X:
548604
563668
586111
604378
600991
544686
537034
551531
563250
574761
580112
575093
557560
564478
580523
596594
586570
536214
523597
536535
536322
532638
528222
516141
501866
506174
517945
533590
528379
477580
469357
490243
492622
507561
516922
514258
509846
527070
541657
564591
555362
498662
511038
525919
531673
548854
560576
557274
565742
587625
619916
625809
619567
572942
572775
574205
579799
590072
593408
597141
595404




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108300&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108300&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean550967.8196721314713.15055995712116.900110162647
Geometric Mean549750.715646028
Harmonic Mean548526.440519696
Quadratic Mean552176.027736003
Winsorized Mean ( 1 / 20 )551006.0163934434651.23731417004118.464395423299
Winsorized Mean ( 2 / 20 )551409.7540983614547.14532052057121.265038882732
Winsorized Mean ( 3 / 20 )550779.7540983614350.63120730747126.597665454441
Winsorized Mean ( 4 / 20 )550953.7213114754220.81548035416130.532529525609
Winsorized Mean ( 5 / 20 )550900.7704918034106.74989215532134.145196313058
Winsorized Mean ( 6 / 20 )551270.7049180334014.7856053616137.310122907144
Winsorized Mean ( 7 / 20 )551293.311475413959.71160873356139.225621951729
Winsorized Mean ( 8 / 20 )551331.2131147543857.15851033286142.937141846207
Winsorized Mean ( 9 / 20 )551014.8852459023738.09180442443147.405391326590
Winsorized Mean ( 10 / 20 )551141.6065573773576.60143987489154.096456041425
Winsorized Mean ( 11 / 20 )551290.9180327873486.67138322318158.113816141502
Winsorized Mean ( 12 / 20 )551354.2622950823445.76597541436160.009201503819
Winsorized Mean ( 13 / 20 )550381.3934426233215.93233141831171.142094025309
Winsorized Mean ( 14 / 20 )551584.2459016392990.5928441322184.439766511143
Winsorized Mean ( 15 / 20 )552078.2622950822890.71120249505190.983541288582
Winsorized Mean ( 16 / 20 )551145.8032786892653.39330325517207.713572881391
Winsorized Mean ( 17 / 20 )551374.3278688522591.29202553405212.779695393543
Winsorized Mean ( 18 / 20 )551256.5901639342559.79557087806215.351802478056
Winsorized Mean ( 19 / 20 )551889.1967213112350.9898193107234.747591073416
Winsorized Mean ( 20 / 20 )552150.8360655742297.74236158187240.301456463312
Trimmed Mean ( 1 / 20 )551082.5593220344491.7015473359122.689041895246
Trimmed Mean ( 2 / 20 )551164.4736842114295.59096166822128.309347561846
Trimmed Mean ( 3 / 20 )551028.4545454554123.83069967818133.620532624789
Trimmed Mean ( 4 / 20 )551123.8679245284006.96912394638137.541331334677
Trimmed Mean ( 5 / 20 )551174.7450980393911.30481411211140.918381791514
Trimmed Mean ( 6 / 20 )551242.9591836733828.05398632833144.000832055244
Trimmed Mean ( 7 / 20 )551236.9574468083748.4669714976147.056639857914
Trimmed Mean ( 8 / 20 )551226.0444444443659.76966749918150.617687593742
Trimmed Mean ( 9 / 20 )551207.3953488373570.85449928761154.362883018282
Trimmed Mean ( 10 / 20 )551239.2195121953483.78036266048158.230187362107
Trimmed Mean ( 11 / 20 )551254.4871794873408.00491537216161.752843927248
Trimmed Mean ( 12 / 20 )551249.0270270273325.72800955268165.752889425606
Trimmed Mean ( 13 / 20 )551233.7428571433220.05684597843171.187581220992
Trimmed Mean ( 14 / 20 )551354.939393943134.05444935979175.923854643485
Trimmed Mean ( 15 / 20 )551322.7096774193071.69562020913179.484811597278
Trimmed Mean ( 16 / 20 )551216.758620693002.10699517534183.609964437159
Trimmed Mean ( 17 / 20 )551226.7777777782963.48271490142186.006408947830
Trimmed Mean ( 18 / 20 )551205.62910.33637574766189.395839117874
Trimmed Mean ( 19 / 20 )551198.0869565222822.83437781204195.264054911982
Trimmed Mean ( 20 / 20 )551092.4285714292750.64759177719200.350066732965
Median551531
Midrange547583
Midmean - Weighted Average at Xnp550373.5
Midmean - Weighted Average at X(n+1)p551322.709677419
Midmean - Empirical Distribution Function551322.709677419
Midmean - Empirical Distribution Function - Averaging551322.709677419
Midmean - Empirical Distribution Function - Interpolation551322.709677419
Midmean - Closest Observation550456.28125
Midmean - True Basic - Statistics Graphics Toolkit551322.709677419
Midmean - MS Excel (old versions)551322.709677419
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 550967.819672131 & 4713.15055995712 & 116.900110162647 \tabularnewline
Geometric Mean & 549750.715646028 &  &  \tabularnewline
Harmonic Mean & 548526.440519696 &  &  \tabularnewline
Quadratic Mean & 552176.027736003 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 551006.016393443 & 4651.23731417004 & 118.464395423299 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 551409.754098361 & 4547.14532052057 & 121.265038882732 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 550779.754098361 & 4350.63120730747 & 126.597665454441 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 550953.721311475 & 4220.81548035416 & 130.532529525609 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 550900.770491803 & 4106.74989215532 & 134.145196313058 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 551270.704918033 & 4014.7856053616 & 137.310122907144 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 551293.31147541 & 3959.71160873356 & 139.225621951729 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 551331.213114754 & 3857.15851033286 & 142.937141846207 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 551014.885245902 & 3738.09180442443 & 147.405391326590 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 551141.606557377 & 3576.60143987489 & 154.096456041425 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 551290.918032787 & 3486.67138322318 & 158.113816141502 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 551354.262295082 & 3445.76597541436 & 160.009201503819 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 550381.393442623 & 3215.93233141831 & 171.142094025309 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 551584.245901639 & 2990.5928441322 & 184.439766511143 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 552078.262295082 & 2890.71120249505 & 190.983541288582 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 551145.803278689 & 2653.39330325517 & 207.713572881391 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 551374.327868852 & 2591.29202553405 & 212.779695393543 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 551256.590163934 & 2559.79557087806 & 215.351802478056 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 551889.196721311 & 2350.9898193107 & 234.747591073416 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 552150.836065574 & 2297.74236158187 & 240.301456463312 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 551082.559322034 & 4491.7015473359 & 122.689041895246 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 551164.473684211 & 4295.59096166822 & 128.309347561846 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 551028.454545455 & 4123.83069967818 & 133.620532624789 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 551123.867924528 & 4006.96912394638 & 137.541331334677 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 551174.745098039 & 3911.30481411211 & 140.918381791514 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 551242.959183673 & 3828.05398632833 & 144.000832055244 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 551236.957446808 & 3748.4669714976 & 147.056639857914 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 551226.044444444 & 3659.76966749918 & 150.617687593742 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 551207.395348837 & 3570.85449928761 & 154.362883018282 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 551239.219512195 & 3483.78036266048 & 158.230187362107 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 551254.487179487 & 3408.00491537216 & 161.752843927248 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 551249.027027027 & 3325.72800955268 & 165.752889425606 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 551233.742857143 & 3220.05684597843 & 171.187581220992 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 551354.93939394 & 3134.05444935979 & 175.923854643485 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 551322.709677419 & 3071.69562020913 & 179.484811597278 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 551216.75862069 & 3002.10699517534 & 183.609964437159 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 551226.777777778 & 2963.48271490142 & 186.006408947830 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 551205.6 & 2910.33637574766 & 189.395839117874 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 551198.086956522 & 2822.83437781204 & 195.264054911982 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 551092.428571429 & 2750.64759177719 & 200.350066732965 \tabularnewline
Median & 551531 &  &  \tabularnewline
Midrange & 547583 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 550373.5 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 551322.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 551322.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 551322.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 551322.709677419 &  &  \tabularnewline
Midmean - Closest Observation & 550456.28125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 551322.709677419 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 551322.709677419 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108300&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]550967.819672131[/C][C]4713.15055995712[/C][C]116.900110162647[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]549750.715646028[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]548526.440519696[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]552176.027736003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]551006.016393443[/C][C]4651.23731417004[/C][C]118.464395423299[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]551409.754098361[/C][C]4547.14532052057[/C][C]121.265038882732[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]550779.754098361[/C][C]4350.63120730747[/C][C]126.597665454441[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]550953.721311475[/C][C]4220.81548035416[/C][C]130.532529525609[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]550900.770491803[/C][C]4106.74989215532[/C][C]134.145196313058[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]551270.704918033[/C][C]4014.7856053616[/C][C]137.310122907144[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]551293.31147541[/C][C]3959.71160873356[/C][C]139.225621951729[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]551331.213114754[/C][C]3857.15851033286[/C][C]142.937141846207[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]551014.885245902[/C][C]3738.09180442443[/C][C]147.405391326590[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]551141.606557377[/C][C]3576.60143987489[/C][C]154.096456041425[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]551290.918032787[/C][C]3486.67138322318[/C][C]158.113816141502[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]551354.262295082[/C][C]3445.76597541436[/C][C]160.009201503819[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]550381.393442623[/C][C]3215.93233141831[/C][C]171.142094025309[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]551584.245901639[/C][C]2990.5928441322[/C][C]184.439766511143[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]552078.262295082[/C][C]2890.71120249505[/C][C]190.983541288582[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]551145.803278689[/C][C]2653.39330325517[/C][C]207.713572881391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]551374.327868852[/C][C]2591.29202553405[/C][C]212.779695393543[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]551256.590163934[/C][C]2559.79557087806[/C][C]215.351802478056[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]551889.196721311[/C][C]2350.9898193107[/C][C]234.747591073416[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]552150.836065574[/C][C]2297.74236158187[/C][C]240.301456463312[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]551082.559322034[/C][C]4491.7015473359[/C][C]122.689041895246[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]551164.473684211[/C][C]4295.59096166822[/C][C]128.309347561846[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]551028.454545455[/C][C]4123.83069967818[/C][C]133.620532624789[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]551123.867924528[/C][C]4006.96912394638[/C][C]137.541331334677[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]551174.745098039[/C][C]3911.30481411211[/C][C]140.918381791514[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]551242.959183673[/C][C]3828.05398632833[/C][C]144.000832055244[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]551236.957446808[/C][C]3748.4669714976[/C][C]147.056639857914[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]551226.044444444[/C][C]3659.76966749918[/C][C]150.617687593742[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]551207.395348837[/C][C]3570.85449928761[/C][C]154.362883018282[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]551239.219512195[/C][C]3483.78036266048[/C][C]158.230187362107[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]551254.487179487[/C][C]3408.00491537216[/C][C]161.752843927248[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]551249.027027027[/C][C]3325.72800955268[/C][C]165.752889425606[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]551233.742857143[/C][C]3220.05684597843[/C][C]171.187581220992[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]551354.93939394[/C][C]3134.05444935979[/C][C]175.923854643485[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]551322.709677419[/C][C]3071.69562020913[/C][C]179.484811597278[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]551216.75862069[/C][C]3002.10699517534[/C][C]183.609964437159[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]551226.777777778[/C][C]2963.48271490142[/C][C]186.006408947830[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]551205.6[/C][C]2910.33637574766[/C][C]189.395839117874[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]551198.086956522[/C][C]2822.83437781204[/C][C]195.264054911982[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]551092.428571429[/C][C]2750.64759177719[/C][C]200.350066732965[/C][/ROW]
[ROW][C]Median[/C][C]551531[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]547583[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]550373.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]550456.28125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]551322.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108300&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 Mean550967.8196721314713.15055995712116.900110162647
Geometric Mean549750.715646028
Harmonic Mean548526.440519696
Quadratic Mean552176.027736003
Winsorized Mean ( 1 / 20 )551006.0163934434651.23731417004118.464395423299
Winsorized Mean ( 2 / 20 )551409.7540983614547.14532052057121.265038882732
Winsorized Mean ( 3 / 20 )550779.7540983614350.63120730747126.597665454441
Winsorized Mean ( 4 / 20 )550953.7213114754220.81548035416130.532529525609
Winsorized Mean ( 5 / 20 )550900.7704918034106.74989215532134.145196313058
Winsorized Mean ( 6 / 20 )551270.7049180334014.7856053616137.310122907144
Winsorized Mean ( 7 / 20 )551293.311475413959.71160873356139.225621951729
Winsorized Mean ( 8 / 20 )551331.2131147543857.15851033286142.937141846207
Winsorized Mean ( 9 / 20 )551014.8852459023738.09180442443147.405391326590
Winsorized Mean ( 10 / 20 )551141.6065573773576.60143987489154.096456041425
Winsorized Mean ( 11 / 20 )551290.9180327873486.67138322318158.113816141502
Winsorized Mean ( 12 / 20 )551354.2622950823445.76597541436160.009201503819
Winsorized Mean ( 13 / 20 )550381.3934426233215.93233141831171.142094025309
Winsorized Mean ( 14 / 20 )551584.2459016392990.5928441322184.439766511143
Winsorized Mean ( 15 / 20 )552078.2622950822890.71120249505190.983541288582
Winsorized Mean ( 16 / 20 )551145.8032786892653.39330325517207.713572881391
Winsorized Mean ( 17 / 20 )551374.3278688522591.29202553405212.779695393543
Winsorized Mean ( 18 / 20 )551256.5901639342559.79557087806215.351802478056
Winsorized Mean ( 19 / 20 )551889.1967213112350.9898193107234.747591073416
Winsorized Mean ( 20 / 20 )552150.8360655742297.74236158187240.301456463312
Trimmed Mean ( 1 / 20 )551082.5593220344491.7015473359122.689041895246
Trimmed Mean ( 2 / 20 )551164.4736842114295.59096166822128.309347561846
Trimmed Mean ( 3 / 20 )551028.4545454554123.83069967818133.620532624789
Trimmed Mean ( 4 / 20 )551123.8679245284006.96912394638137.541331334677
Trimmed Mean ( 5 / 20 )551174.7450980393911.30481411211140.918381791514
Trimmed Mean ( 6 / 20 )551242.9591836733828.05398632833144.000832055244
Trimmed Mean ( 7 / 20 )551236.9574468083748.4669714976147.056639857914
Trimmed Mean ( 8 / 20 )551226.0444444443659.76966749918150.617687593742
Trimmed Mean ( 9 / 20 )551207.3953488373570.85449928761154.362883018282
Trimmed Mean ( 10 / 20 )551239.2195121953483.78036266048158.230187362107
Trimmed Mean ( 11 / 20 )551254.4871794873408.00491537216161.752843927248
Trimmed Mean ( 12 / 20 )551249.0270270273325.72800955268165.752889425606
Trimmed Mean ( 13 / 20 )551233.7428571433220.05684597843171.187581220992
Trimmed Mean ( 14 / 20 )551354.939393943134.05444935979175.923854643485
Trimmed Mean ( 15 / 20 )551322.7096774193071.69562020913179.484811597278
Trimmed Mean ( 16 / 20 )551216.758620693002.10699517534183.609964437159
Trimmed Mean ( 17 / 20 )551226.7777777782963.48271490142186.006408947830
Trimmed Mean ( 18 / 20 )551205.62910.33637574766189.395839117874
Trimmed Mean ( 19 / 20 )551198.0869565222822.83437781204195.264054911982
Trimmed Mean ( 20 / 20 )551092.4285714292750.64759177719200.350066732965
Median551531
Midrange547583
Midmean - Weighted Average at Xnp550373.5
Midmean - Weighted Average at X(n+1)p551322.709677419
Midmean - Empirical Distribution Function551322.709677419
Midmean - Empirical Distribution Function - Averaging551322.709677419
Midmean - Empirical Distribution Function - Interpolation551322.709677419
Midmean - Closest Observation550456.28125
Midmean - True Basic - Statistics Graphics Toolkit551322.709677419
Midmean - MS Excel (old versions)551322.709677419
Number of observations61



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')