Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Nov 2010 17:43:41 +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/Nov/11/t1289499670eggxr9f9av5lr5y.htm/, Retrieved Fri, 29 Mar 2024 08:28:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=93676, Retrieved Fri, 29 Mar 2024 08:28:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Tutorial - Centra...] [2010-11-11 17:43:41] [934c3727858e074bf543f25f5906ed72] [Current]
-    D      [Central Tendency] [Tutorial - Centra...] [2010-11-12 09:28:40] [8ef49741e164ec6343c90c7935194465]
-    D        [Central Tendency] [central tendancy ...] [2010-11-16 17:56:40] [8214fe6d084e5ad7598b249a26cc9f06]
-           [Central Tendency] [Central Tendancy ...] [2010-11-16 17:52:12] [8214fe6d084e5ad7598b249a26cc9f06]
Feedback Forum

Post a new message
Dataseries X:
167.16
179.84
174.44
180.35
193.17
195.16
202.43
189.91
195.98
212.09
205.81
204.31
196.07
199.98
199.1
198.31
195.72
223.04
238.41
259.73
326.54
335.15
321.81
368.62
369.59
425
439.72
362.23
328.76
348.55
328.18
329.34
295.55
237.38
226.85
220.14
239.36
224.69
230.98
233.47
256.7
253.41
224.95
210.37
191.09
198.85
211.04
206.25
201.19
194.37
191.08
192.87
181.61
157.67
196.14
246.35
271.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93676&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93676&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean241.9080701754398.9116592740889727.1451210975712
Geometric Mean234.077983653902
Harmonic Mean227.499215497756
Quadratic Mean250.932070475223
Winsorized Mean ( 1 / 19 )241.8163157894748.785687030247427.5238936871923
Winsorized Mean ( 2 / 19 )240.1275438596498.1051630961122729.6264912885996
Winsorized Mean ( 3 / 19 )240.3607017543868.0509741734514329.8548593718000
Winsorized Mean ( 4 / 19 )239.9480701754397.9205557830364930.2943476124917
Winsorized Mean ( 5 / 19 )238.8585964912287.585099099437231.4905043902394
Winsorized Mean ( 6 / 19 )238.3217543859657.119231508798233.4757696938832
Winsorized Mean ( 7 / 19 )237.7519298245616.9310055048443534.3026606541269
Winsorized Mean ( 8 / 19 )237.6719298245616.9116536266329734.3871297179491
Winsorized Mean ( 9 / 19 )237.8614035087726.8567271060199234.6902246262564
Winsorized Mean ( 10 / 19 )237.6263157894746.7830503162999935.0323681395148
Winsorized Mean ( 11 / 19 )236.9450877192986.5434894661533336.2108151843009
Winsorized Mean ( 12 / 19 )231.5829824561405.2810680154459743.8515432444367
Winsorized Mean ( 13 / 19 )226.3168421052634.1454881878564754.5935320158965
Winsorized Mean ( 14 / 19 )223.3915789473683.5701790477403862.5715337970952
Winsorized Mean ( 15 / 19 )222.6178947368423.4235447920848365.0255534122207
Winsorized Mean ( 16 / 19 )221.7140350877193.2584673375227168.0424298057504
Winsorized Mean ( 17 / 19 )220.2556140350882.8098918652382978.3857972471866
Winsorized Mean ( 18 / 19 )218.2187719298252.4305936065262389.7800320645539
Winsorized Mean ( 19 / 19 )217.9854385964912.3697710287510391.9858652805703
Trimmed Mean ( 1 / 19 )239.8430909090918.3492991736891428.7261344838259
Trimmed Mean ( 2 / 19 )237.7209433962267.7897924410482130.5169804196013
Trimmed Mean ( 3 / 19 )236.3760784313737.5602235628238531.2657524565428
Trimmed Mean ( 4 / 19 )234.8310204081637.2886473977118432.2187379350913
Trimmed Mean ( 5 / 19 )233.2795744680856.9900396293665933.3731404737721
Trimmed Mean ( 6 / 19 )231.8662222222226.7266178504467134.4699561320886
Trimmed Mean ( 7 / 19 )230.446.5327566134136435.2745423772317
Trimmed Mean ( 8 / 19 )228.9878048780496.3273320342952536.1902621257893
Trimmed Mean ( 9 / 19 )227.4012820512826.045749705198437.6134132472855
Trimmed Mean ( 10 / 19 )225.6108108108115.6619840931097139.8465991957423
Trimmed Mean ( 11 / 19 )223.6545.1309093694961343.5895440542469
Trimmed Mean ( 12 / 19 )221.5669696969704.426624412609750.053257074581
Trimmed Mean ( 13 / 19 )220.0322580645163.9415748642748555.8234374941896
Trimmed Mean ( 14 / 19 )219.0820689655173.7041050446897659.1457494650685
Trimmed Mean ( 15 / 19 )218.4322222222223.5693372194477361.196857789755
Trimmed Mean ( 16 / 19 )217.7963.4080754099638163.9058629287527
Trimmed Mean ( 17 / 19 )217.1891304347833.2128622379579667.5998889304461
Trimmed Mean ( 18 / 19 )216.6995238095243.0904479931210570.1191297481367
Trimmed Mean ( 19 / 19 )216.4463157894743.0483645515102571.0040784597892
Median212.09
Midrange298.695
Midmean - Weighted Average at Xnp217.630357142857
Midmean - Weighted Average at X(n+1)p219.082068965517
Midmean - Empirical Distribution Function219.082068965517
Midmean - Empirical Distribution Function - Averaging219.082068965517
Midmean - Empirical Distribution Function - Interpolation219.082068965517
Midmean - Closest Observation218.303333333333
Midmean - True Basic - Statistics Graphics Toolkit219.082068965517
Midmean - MS Excel (old versions)219.082068965517
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 241.908070175439 & 8.91165927408897 & 27.1451210975712 \tabularnewline
Geometric Mean & 234.077983653902 &  &  \tabularnewline
Harmonic Mean & 227.499215497756 &  &  \tabularnewline
Quadratic Mean & 250.932070475223 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 241.816315789474 & 8.7856870302474 & 27.5238936871923 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 240.127543859649 & 8.10516309611227 & 29.6264912885996 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 240.360701754386 & 8.05097417345143 & 29.8548593718000 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 239.948070175439 & 7.92055578303649 & 30.2943476124917 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 238.858596491228 & 7.5850990994372 & 31.4905043902394 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 238.321754385965 & 7.1192315087982 & 33.4757696938832 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 237.751929824561 & 6.93100550484435 & 34.3026606541269 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 237.671929824561 & 6.91165362663297 & 34.3871297179491 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 237.861403508772 & 6.85672710601992 & 34.6902246262564 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 237.626315789474 & 6.78305031629999 & 35.0323681395148 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 236.945087719298 & 6.54348946615333 & 36.2108151843009 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 231.582982456140 & 5.28106801544597 & 43.8515432444367 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 226.316842105263 & 4.14548818785647 & 54.5935320158965 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 223.391578947368 & 3.57017904774038 & 62.5715337970952 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 222.617894736842 & 3.42354479208483 & 65.0255534122207 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 221.714035087719 & 3.25846733752271 & 68.0424298057504 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 220.255614035088 & 2.80989186523829 & 78.3857972471866 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 218.218771929825 & 2.43059360652623 & 89.7800320645539 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 217.985438596491 & 2.36977102875103 & 91.9858652805703 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 239.843090909091 & 8.34929917368914 & 28.7261344838259 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 237.720943396226 & 7.78979244104821 & 30.5169804196013 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 236.376078431373 & 7.56022356282385 & 31.2657524565428 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 234.831020408163 & 7.28864739771184 & 32.2187379350913 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 233.279574468085 & 6.99003962936659 & 33.3731404737721 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 231.866222222222 & 6.72661785044671 & 34.4699561320886 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 230.44 & 6.53275661341364 & 35.2745423772317 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 228.987804878049 & 6.32733203429525 & 36.1902621257893 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 227.401282051282 & 6.0457497051984 & 37.6134132472855 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 225.610810810811 & 5.66198409310971 & 39.8465991957423 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 223.654 & 5.13090936949613 & 43.5895440542469 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 221.566969696970 & 4.4266244126097 & 50.053257074581 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 220.032258064516 & 3.94157486427485 & 55.8234374941896 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 219.082068965517 & 3.70410504468976 & 59.1457494650685 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 218.432222222222 & 3.56933721944773 & 61.196857789755 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 217.796 & 3.40807540996381 & 63.9058629287527 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 217.189130434783 & 3.21286223795796 & 67.5998889304461 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 216.699523809524 & 3.09044799312105 & 70.1191297481367 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 216.446315789474 & 3.04836455151025 & 71.0040784597892 \tabularnewline
Median & 212.09 &  &  \tabularnewline
Midrange & 298.695 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 217.630357142857 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 219.082068965517 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 219.082068965517 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 219.082068965517 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 219.082068965517 &  &  \tabularnewline
Midmean - Closest Observation & 218.303333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 219.082068965517 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 219.082068965517 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93676&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]241.908070175439[/C][C]8.91165927408897[/C][C]27.1451210975712[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]234.077983653902[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]227.499215497756[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]250.932070475223[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]241.816315789474[/C][C]8.7856870302474[/C][C]27.5238936871923[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]240.127543859649[/C][C]8.10516309611227[/C][C]29.6264912885996[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]240.360701754386[/C][C]8.05097417345143[/C][C]29.8548593718000[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]239.948070175439[/C][C]7.92055578303649[/C][C]30.2943476124917[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]238.858596491228[/C][C]7.5850990994372[/C][C]31.4905043902394[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]238.321754385965[/C][C]7.1192315087982[/C][C]33.4757696938832[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]237.751929824561[/C][C]6.93100550484435[/C][C]34.3026606541269[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]237.671929824561[/C][C]6.91165362663297[/C][C]34.3871297179491[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]237.861403508772[/C][C]6.85672710601992[/C][C]34.6902246262564[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]237.626315789474[/C][C]6.78305031629999[/C][C]35.0323681395148[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]236.945087719298[/C][C]6.54348946615333[/C][C]36.2108151843009[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]231.582982456140[/C][C]5.28106801544597[/C][C]43.8515432444367[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]226.316842105263[/C][C]4.14548818785647[/C][C]54.5935320158965[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]223.391578947368[/C][C]3.57017904774038[/C][C]62.5715337970952[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]222.617894736842[/C][C]3.42354479208483[/C][C]65.0255534122207[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]221.714035087719[/C][C]3.25846733752271[/C][C]68.0424298057504[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]220.255614035088[/C][C]2.80989186523829[/C][C]78.3857972471866[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]218.218771929825[/C][C]2.43059360652623[/C][C]89.7800320645539[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]217.985438596491[/C][C]2.36977102875103[/C][C]91.9858652805703[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]239.843090909091[/C][C]8.34929917368914[/C][C]28.7261344838259[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]237.720943396226[/C][C]7.78979244104821[/C][C]30.5169804196013[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]236.376078431373[/C][C]7.56022356282385[/C][C]31.2657524565428[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]234.831020408163[/C][C]7.28864739771184[/C][C]32.2187379350913[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]233.279574468085[/C][C]6.99003962936659[/C][C]33.3731404737721[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]231.866222222222[/C][C]6.72661785044671[/C][C]34.4699561320886[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]230.44[/C][C]6.53275661341364[/C][C]35.2745423772317[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]228.987804878049[/C][C]6.32733203429525[/C][C]36.1902621257893[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]227.401282051282[/C][C]6.0457497051984[/C][C]37.6134132472855[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]225.610810810811[/C][C]5.66198409310971[/C][C]39.8465991957423[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]223.654[/C][C]5.13090936949613[/C][C]43.5895440542469[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]221.566969696970[/C][C]4.4266244126097[/C][C]50.053257074581[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]220.032258064516[/C][C]3.94157486427485[/C][C]55.8234374941896[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]219.082068965517[/C][C]3.70410504468976[/C][C]59.1457494650685[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]218.432222222222[/C][C]3.56933721944773[/C][C]61.196857789755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]217.796[/C][C]3.40807540996381[/C][C]63.9058629287527[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]217.189130434783[/C][C]3.21286223795796[/C][C]67.5998889304461[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]216.699523809524[/C][C]3.09044799312105[/C][C]70.1191297481367[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]216.446315789474[/C][C]3.04836455151025[/C][C]71.0040784597892[/C][/ROW]
[ROW][C]Median[/C][C]212.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]298.695[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]217.630357142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]218.303333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]219.082068965517[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93676&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 Mean241.9080701754398.9116592740889727.1451210975712
Geometric Mean234.077983653902
Harmonic Mean227.499215497756
Quadratic Mean250.932070475223
Winsorized Mean ( 1 / 19 )241.8163157894748.785687030247427.5238936871923
Winsorized Mean ( 2 / 19 )240.1275438596498.1051630961122729.6264912885996
Winsorized Mean ( 3 / 19 )240.3607017543868.0509741734514329.8548593718000
Winsorized Mean ( 4 / 19 )239.9480701754397.9205557830364930.2943476124917
Winsorized Mean ( 5 / 19 )238.8585964912287.585099099437231.4905043902394
Winsorized Mean ( 6 / 19 )238.3217543859657.119231508798233.4757696938832
Winsorized Mean ( 7 / 19 )237.7519298245616.9310055048443534.3026606541269
Winsorized Mean ( 8 / 19 )237.6719298245616.9116536266329734.3871297179491
Winsorized Mean ( 9 / 19 )237.8614035087726.8567271060199234.6902246262564
Winsorized Mean ( 10 / 19 )237.6263157894746.7830503162999935.0323681395148
Winsorized Mean ( 11 / 19 )236.9450877192986.5434894661533336.2108151843009
Winsorized Mean ( 12 / 19 )231.5829824561405.2810680154459743.8515432444367
Winsorized Mean ( 13 / 19 )226.3168421052634.1454881878564754.5935320158965
Winsorized Mean ( 14 / 19 )223.3915789473683.5701790477403862.5715337970952
Winsorized Mean ( 15 / 19 )222.6178947368423.4235447920848365.0255534122207
Winsorized Mean ( 16 / 19 )221.7140350877193.2584673375227168.0424298057504
Winsorized Mean ( 17 / 19 )220.2556140350882.8098918652382978.3857972471866
Winsorized Mean ( 18 / 19 )218.2187719298252.4305936065262389.7800320645539
Winsorized Mean ( 19 / 19 )217.9854385964912.3697710287510391.9858652805703
Trimmed Mean ( 1 / 19 )239.8430909090918.3492991736891428.7261344838259
Trimmed Mean ( 2 / 19 )237.7209433962267.7897924410482130.5169804196013
Trimmed Mean ( 3 / 19 )236.3760784313737.5602235628238531.2657524565428
Trimmed Mean ( 4 / 19 )234.8310204081637.2886473977118432.2187379350913
Trimmed Mean ( 5 / 19 )233.2795744680856.9900396293665933.3731404737721
Trimmed Mean ( 6 / 19 )231.8662222222226.7266178504467134.4699561320886
Trimmed Mean ( 7 / 19 )230.446.5327566134136435.2745423772317
Trimmed Mean ( 8 / 19 )228.9878048780496.3273320342952536.1902621257893
Trimmed Mean ( 9 / 19 )227.4012820512826.045749705198437.6134132472855
Trimmed Mean ( 10 / 19 )225.6108108108115.6619840931097139.8465991957423
Trimmed Mean ( 11 / 19 )223.6545.1309093694961343.5895440542469
Trimmed Mean ( 12 / 19 )221.5669696969704.426624412609750.053257074581
Trimmed Mean ( 13 / 19 )220.0322580645163.9415748642748555.8234374941896
Trimmed Mean ( 14 / 19 )219.0820689655173.7041050446897659.1457494650685
Trimmed Mean ( 15 / 19 )218.4322222222223.5693372194477361.196857789755
Trimmed Mean ( 16 / 19 )217.7963.4080754099638163.9058629287527
Trimmed Mean ( 17 / 19 )217.1891304347833.2128622379579667.5998889304461
Trimmed Mean ( 18 / 19 )216.6995238095243.0904479931210570.1191297481367
Trimmed Mean ( 19 / 19 )216.4463157894743.0483645515102571.0040784597892
Median212.09
Midrange298.695
Midmean - Weighted Average at Xnp217.630357142857
Midmean - Weighted Average at X(n+1)p219.082068965517
Midmean - Empirical Distribution Function219.082068965517
Midmean - Empirical Distribution Function - Averaging219.082068965517
Midmean - Empirical Distribution Function - Interpolation219.082068965517
Midmean - Closest Observation218.303333333333
Midmean - True Basic - Statistics Graphics Toolkit219.082068965517
Midmean - MS Excel (old versions)219.082068965517
Number of observations57



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>80) denom <- n/80
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>80) denom <- n/80
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')