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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 computationMon, 22 Dec 2008 04:31:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229945698z4k6dnpk2av0xz8.htm/, Retrieved Mon, 13 May 2024 07:50:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36008, Retrieved Mon, 13 May 2024 07:50:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [ARMA backward sel...] [2008-12-21 12:09:36] [82d201ca7b4e7cd2c6f885d29b5b6937]
- RMP     [Central Tendency] [Central tendency ...] [2008-12-22 11:31:32] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataseries X:
1995
1947
1766
1635
1833
1910
1960
1970
2061
2093
2121
2175
2197
2350
2440
2409
2473
2408
2455
2448
2498
2646
2757
2849
2921
2982
3081
3106
3119
3061
3097
3162
3257
3277
3295
3364
3494
3667
3813
3918
3896
3801
3570
3702
3862
3970
4139
4200
4291
4444
4503
4357
4591
4697
4621
4563
4203
4296
4435
4105
4117




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36008&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36008&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3186.44262295082116.83292102058527.2734995848421
Geometric Mean3051.68979680338
Harmonic Mean2915.01459376087
Quadratic Mean3312.46320363107
Winsorized Mean ( 1 / 20 )3187.34426229508116.11370177791927.4501993605479
Winsorized Mean ( 2 / 20 )3188.55737704918115.47393793105927.6127880816954
Winsorized Mean ( 3 / 20 )3190.96721311475114.47336046132227.8751947200232
Winsorized Mean ( 4 / 20 )3189.45901639344113.25196188549228.1625056492910
Winsorized Mean ( 5 / 20 )3185.68852459016112.13777031220228.4087022215701
Winsorized Mean ( 6 / 20 )3185.7868852459111.79382397565928.4969846450511
Winsorized Mean ( 7 / 20 )3179.70491803279109.64075053187329.0011232375541
Winsorized Mean ( 8 / 20 )3180.36065573770106.69104835616329.8090674404175
Winsorized Mean ( 9 / 20 )3184.34426229508105.74355484304830.1138378317383
Winsorized Mean ( 10 / 20 )3174.50819672131102.49021177560930.9737695114880
Winsorized Mean ( 11 / 20 )3183.70491803279100.75276601787531.5991812817125
Winsorized Mean ( 12 / 20 )3176.0327868852598.04024479554332.3951943766426
Winsorized Mean ( 13 / 20 )3203.9508196721392.028106380930434.8149162866622
Winsorized Mean ( 14 / 20 )3214.5081967213189.543290574215435.8989286199736
Winsorized Mean ( 15 / 20 )3181.5573770491884.158247778663737.8044631515699
Winsorized Mean ( 16 / 20 )3176.0491803278780.810104012480639.3026245806756
Winsorized Mean ( 17 / 20 )3172.1475409836179.537600951142339.8823638511824
Winsorized Mean ( 18 / 20 )3164.1803278688577.712056115388440.7167238397427
Winsorized Mean ( 19 / 20 )3154.5245901639374.593629896054842.2894635179937
Winsorized Mean ( 20 / 20 )3158.786885245972.770479493115743.4075315601669
Trimmed Mean ( 1 / 20 )3187.13559322034115.01780274781227.7099328719437
Trimmed Mean ( 2 / 20 )3186.91228070175113.60239129838128.0532147631578
Trimmed Mean ( 3 / 20 )3186112.20138820510028.3953706007283
Trimmed Mean ( 4 / 20 )3184.09433962264110.85052261019928.7242158597607
Trimmed Mean ( 5 / 20 )3182.49019607843109.53598521445429.0542892351551
Trimmed Mean ( 6 / 20 )3181.69387755102108.14868435926929.4196262895021
Trimmed Mean ( 7 / 20 )3180.8085106383106.38779637565029.8982460300899
Trimmed Mean ( 8 / 20 )3181.02222222222104.64159846920730.3992128250822
Trimmed Mean ( 9 / 20 )3181.13953488372103.06247812856830.8661269615052
Trimmed Mean ( 10 / 20 )3180.60975609756101.11348296169431.4558421185283
Trimmed Mean ( 11 / 20 )3181.564102564199.252148223363332.0553676622103
Trimmed Mean ( 12 / 20 )3181.2432432432497.061862300397532.7754193856037
Trimmed Mean ( 13 / 20 )318294.658723578864333.6154965933905
Trimmed Mean ( 14 / 20 )3178.8787878787992.809451231180534.2516709851076
Trimmed Mean ( 15 / 20 )3173.8709677419490.65605261167135.0100283026589
Trimmed Mean ( 16 / 20 )3172.7931034482888.948016856672235.6701949697294
Trimmed Mean ( 17 / 20 )3172.3333333333387.151961466534936.4000222135157
Trimmed Mean ( 18 / 20 )3172.3684.495204597657537.5448525760236
Trimmed Mean ( 19 / 20 )3173.5652173913080.67675280420939.3367991036166
Trimmed Mean ( 20 / 20 )3176.4761904761975.49164630693642.0771879521767
Median3119
Midrange3166
Midmean - Weighted Average at Xnp3147.33333333333
Midmean - Weighted Average at X(n+1)p3173.87096774194
Midmean - Empirical Distribution Function3173.87096774194
Midmean - Empirical Distribution Function - Averaging3173.87096774194
Midmean - Empirical Distribution Function - Interpolation3173.87096774194
Midmean - Closest Observation3149.9375
Midmean - True Basic - Statistics Graphics Toolkit3173.87096774194
Midmean - MS Excel (old versions)3173.87096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3186.44262295082 & 116.832921020585 & 27.2734995848421 \tabularnewline
Geometric Mean & 3051.68979680338 &  &  \tabularnewline
Harmonic Mean & 2915.01459376087 &  &  \tabularnewline
Quadratic Mean & 3312.46320363107 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3187.34426229508 & 116.113701777919 & 27.4501993605479 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3188.55737704918 & 115.473937931059 & 27.6127880816954 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3190.96721311475 & 114.473360461322 & 27.8751947200232 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3189.45901639344 & 113.251961885492 & 28.1625056492910 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3185.68852459016 & 112.137770312202 & 28.4087022215701 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3185.7868852459 & 111.793823975659 & 28.4969846450511 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3179.70491803279 & 109.640750531873 & 29.0011232375541 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3180.36065573770 & 106.691048356163 & 29.8090674404175 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3184.34426229508 & 105.743554843048 & 30.1138378317383 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3174.50819672131 & 102.490211775609 & 30.9737695114880 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3183.70491803279 & 100.752766017875 & 31.5991812817125 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3176.03278688525 & 98.040244795543 & 32.3951943766426 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3203.95081967213 & 92.0281063809304 & 34.8149162866622 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3214.50819672131 & 89.5432905742154 & 35.8989286199736 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3181.55737704918 & 84.1582477786637 & 37.8044631515699 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3176.04918032787 & 80.8101040124806 & 39.3026245806756 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3172.14754098361 & 79.5376009511423 & 39.8823638511824 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3164.18032786885 & 77.7120561153884 & 40.7167238397427 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3154.52459016393 & 74.5936298960548 & 42.2894635179937 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3158.7868852459 & 72.7704794931157 & 43.4075315601669 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3187.13559322034 & 115.017802747812 & 27.7099328719437 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3186.91228070175 & 113.602391298381 & 28.0532147631578 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3186 & 112.201388205100 & 28.3953706007283 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3184.09433962264 & 110.850522610199 & 28.7242158597607 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3182.49019607843 & 109.535985214454 & 29.0542892351551 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3181.69387755102 & 108.148684359269 & 29.4196262895021 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3180.8085106383 & 106.387796375650 & 29.8982460300899 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3181.02222222222 & 104.641598469207 & 30.3992128250822 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3181.13953488372 & 103.062478128568 & 30.8661269615052 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3180.60975609756 & 101.113482961694 & 31.4558421185283 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3181.5641025641 & 99.2521482233633 & 32.0553676622103 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3181.24324324324 & 97.0618623003975 & 32.7754193856037 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3182 & 94.6587235788643 & 33.6154965933905 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3178.87878787879 & 92.8094512311805 & 34.2516709851076 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3173.87096774194 & 90.656052611671 & 35.0100283026589 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3172.79310344828 & 88.9480168566722 & 35.6701949697294 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3172.33333333333 & 87.1519614665349 & 36.4000222135157 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3172.36 & 84.4952045976575 & 37.5448525760236 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3173.56521739130 & 80.676752804209 & 39.3367991036166 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3176.47619047619 & 75.491646306936 & 42.0771879521767 \tabularnewline
Median & 3119 &  &  \tabularnewline
Midrange & 3166 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3147.33333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3173.87096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3173.87096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3173.87096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3173.87096774194 &  &  \tabularnewline
Midmean - Closest Observation & 3149.9375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3173.87096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3173.87096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36008&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]3186.44262295082[/C][C]116.832921020585[/C][C]27.2734995848421[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3051.68979680338[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2915.01459376087[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3312.46320363107[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3187.34426229508[/C][C]116.113701777919[/C][C]27.4501993605479[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3188.55737704918[/C][C]115.473937931059[/C][C]27.6127880816954[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3190.96721311475[/C][C]114.473360461322[/C][C]27.8751947200232[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3189.45901639344[/C][C]113.251961885492[/C][C]28.1625056492910[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3185.68852459016[/C][C]112.137770312202[/C][C]28.4087022215701[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3185.7868852459[/C][C]111.793823975659[/C][C]28.4969846450511[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3179.70491803279[/C][C]109.640750531873[/C][C]29.0011232375541[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3180.36065573770[/C][C]106.691048356163[/C][C]29.8090674404175[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3184.34426229508[/C][C]105.743554843048[/C][C]30.1138378317383[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3174.50819672131[/C][C]102.490211775609[/C][C]30.9737695114880[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3183.70491803279[/C][C]100.752766017875[/C][C]31.5991812817125[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3176.03278688525[/C][C]98.040244795543[/C][C]32.3951943766426[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3203.95081967213[/C][C]92.0281063809304[/C][C]34.8149162866622[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3214.50819672131[/C][C]89.5432905742154[/C][C]35.8989286199736[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3181.55737704918[/C][C]84.1582477786637[/C][C]37.8044631515699[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3176.04918032787[/C][C]80.8101040124806[/C][C]39.3026245806756[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3172.14754098361[/C][C]79.5376009511423[/C][C]39.8823638511824[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3164.18032786885[/C][C]77.7120561153884[/C][C]40.7167238397427[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3154.52459016393[/C][C]74.5936298960548[/C][C]42.2894635179937[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3158.7868852459[/C][C]72.7704794931157[/C][C]43.4075315601669[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3187.13559322034[/C][C]115.017802747812[/C][C]27.7099328719437[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3186.91228070175[/C][C]113.602391298381[/C][C]28.0532147631578[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3186[/C][C]112.201388205100[/C][C]28.3953706007283[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3184.09433962264[/C][C]110.850522610199[/C][C]28.7242158597607[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3182.49019607843[/C][C]109.535985214454[/C][C]29.0542892351551[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3181.69387755102[/C][C]108.148684359269[/C][C]29.4196262895021[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3180.8085106383[/C][C]106.387796375650[/C][C]29.8982460300899[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3181.02222222222[/C][C]104.641598469207[/C][C]30.3992128250822[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3181.13953488372[/C][C]103.062478128568[/C][C]30.8661269615052[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3180.60975609756[/C][C]101.113482961694[/C][C]31.4558421185283[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3181.5641025641[/C][C]99.2521482233633[/C][C]32.0553676622103[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3181.24324324324[/C][C]97.0618623003975[/C][C]32.7754193856037[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3182[/C][C]94.6587235788643[/C][C]33.6154965933905[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3178.87878787879[/C][C]92.8094512311805[/C][C]34.2516709851076[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3173.87096774194[/C][C]90.656052611671[/C][C]35.0100283026589[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3172.79310344828[/C][C]88.9480168566722[/C][C]35.6701949697294[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3172.33333333333[/C][C]87.1519614665349[/C][C]36.4000222135157[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3172.36[/C][C]84.4952045976575[/C][C]37.5448525760236[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3173.56521739130[/C][C]80.676752804209[/C][C]39.3367991036166[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3176.47619047619[/C][C]75.491646306936[/C][C]42.0771879521767[/C][/ROW]
[ROW][C]Median[/C][C]3119[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3166[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3147.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3173.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3173.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3173.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3173.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3149.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3173.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3173.87096774194[/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=36008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36008&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 Mean3186.44262295082116.83292102058527.2734995848421
Geometric Mean3051.68979680338
Harmonic Mean2915.01459376087
Quadratic Mean3312.46320363107
Winsorized Mean ( 1 / 20 )3187.34426229508116.11370177791927.4501993605479
Winsorized Mean ( 2 / 20 )3188.55737704918115.47393793105927.6127880816954
Winsorized Mean ( 3 / 20 )3190.96721311475114.47336046132227.8751947200232
Winsorized Mean ( 4 / 20 )3189.45901639344113.25196188549228.1625056492910
Winsorized Mean ( 5 / 20 )3185.68852459016112.13777031220228.4087022215701
Winsorized Mean ( 6 / 20 )3185.7868852459111.79382397565928.4969846450511
Winsorized Mean ( 7 / 20 )3179.70491803279109.64075053187329.0011232375541
Winsorized Mean ( 8 / 20 )3180.36065573770106.69104835616329.8090674404175
Winsorized Mean ( 9 / 20 )3184.34426229508105.74355484304830.1138378317383
Winsorized Mean ( 10 / 20 )3174.50819672131102.49021177560930.9737695114880
Winsorized Mean ( 11 / 20 )3183.70491803279100.75276601787531.5991812817125
Winsorized Mean ( 12 / 20 )3176.0327868852598.04024479554332.3951943766426
Winsorized Mean ( 13 / 20 )3203.9508196721392.028106380930434.8149162866622
Winsorized Mean ( 14 / 20 )3214.5081967213189.543290574215435.8989286199736
Winsorized Mean ( 15 / 20 )3181.5573770491884.158247778663737.8044631515699
Winsorized Mean ( 16 / 20 )3176.0491803278780.810104012480639.3026245806756
Winsorized Mean ( 17 / 20 )3172.1475409836179.537600951142339.8823638511824
Winsorized Mean ( 18 / 20 )3164.1803278688577.712056115388440.7167238397427
Winsorized Mean ( 19 / 20 )3154.5245901639374.593629896054842.2894635179937
Winsorized Mean ( 20 / 20 )3158.786885245972.770479493115743.4075315601669
Trimmed Mean ( 1 / 20 )3187.13559322034115.01780274781227.7099328719437
Trimmed Mean ( 2 / 20 )3186.91228070175113.60239129838128.0532147631578
Trimmed Mean ( 3 / 20 )3186112.20138820510028.3953706007283
Trimmed Mean ( 4 / 20 )3184.09433962264110.85052261019928.7242158597607
Trimmed Mean ( 5 / 20 )3182.49019607843109.53598521445429.0542892351551
Trimmed Mean ( 6 / 20 )3181.69387755102108.14868435926929.4196262895021
Trimmed Mean ( 7 / 20 )3180.8085106383106.38779637565029.8982460300899
Trimmed Mean ( 8 / 20 )3181.02222222222104.64159846920730.3992128250822
Trimmed Mean ( 9 / 20 )3181.13953488372103.06247812856830.8661269615052
Trimmed Mean ( 10 / 20 )3180.60975609756101.11348296169431.4558421185283
Trimmed Mean ( 11 / 20 )3181.564102564199.252148223363332.0553676622103
Trimmed Mean ( 12 / 20 )3181.2432432432497.061862300397532.7754193856037
Trimmed Mean ( 13 / 20 )318294.658723578864333.6154965933905
Trimmed Mean ( 14 / 20 )3178.8787878787992.809451231180534.2516709851076
Trimmed Mean ( 15 / 20 )3173.8709677419490.65605261167135.0100283026589
Trimmed Mean ( 16 / 20 )3172.7931034482888.948016856672235.6701949697294
Trimmed Mean ( 17 / 20 )3172.3333333333387.151961466534936.4000222135157
Trimmed Mean ( 18 / 20 )3172.3684.495204597657537.5448525760236
Trimmed Mean ( 19 / 20 )3173.5652173913080.67675280420939.3367991036166
Trimmed Mean ( 20 / 20 )3176.4761904761975.49164630693642.0771879521767
Median3119
Midrange3166
Midmean - Weighted Average at Xnp3147.33333333333
Midmean - Weighted Average at X(n+1)p3173.87096774194
Midmean - Empirical Distribution Function3173.87096774194
Midmean - Empirical Distribution Function - Averaging3173.87096774194
Midmean - Empirical Distribution Function - Interpolation3173.87096774194
Midmean - Closest Observation3149.9375
Midmean - True Basic - Statistics Graphics Toolkit3173.87096774194
Midmean - MS Excel (old versions)3173.87096774194
Number of observations61



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')