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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 computationSun, 18 Oct 2009 07:29:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255872689k20at1khzd9p6so.htm/, Retrieved Thu, 31 Oct 2024 23:08:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47296, Retrieved Thu, 31 Oct 2024 23:08:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 3 deel 2
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Central tendency] [2009-10-18 13:29:07] [e7a989b306049c061a54f626f1127c12] [Current]
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Dataseries X:
130.7
117.2
110.8
111.4
108.2
108.8
110.2
109.5
109.5
116
111.2
112.1
114
119.1
114.1
115.1
115.4
110.8
116
119.2
126.5
127.8
131.3
140.3
137.3
143
134.5
139.9
159.3
170.4
175
175.8
180.9
180.3
169.6
172.3
184.8
177.7
184.6
211.4
215.3
215.9
244.7
259.3
289
310.9
321
315.1
333.2
314.1
284.7
273.9
216
196.4
190.9
206.4
196.3
199.5
198.9
214.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47296&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47296&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean174.9658.4091925168419620.8063972432049
Geometric Mean164.457463497207
Harmonic Mean155.524206579724
Quadratic Mean186.507125422417
Winsorized Mean ( 1 / 20 )174.7716666666678.3452226232069520.9427207107273
Winsorized Mean ( 2 / 20 )174.5983333333338.2846326636126821.074963782063
Winsorized Mean ( 3 / 20 )174.5483333333338.270296550769221.1054503622484
Winsorized Mean ( 4 / 20 )174.3816666666678.2034974254531321.2569904789157
Winsorized Mean ( 5 / 20 )172.6066666666677.70502985863222.4018167137009
Winsorized Mean ( 6 / 20 )172.1766666666677.5959929842118622.6667753675567
Winsorized Mean ( 7 / 20 )170.9633333333337.2802433554449923.4831893641945
Winsorized Mean ( 8 / 20 )169.0433333333336.8245578349212224.7698587106024
Winsorized Mean ( 9 / 20 )166.9583333333336.335495598032826.3528449747759
Winsorized Mean ( 10 / 20 )162.4916666666675.3798616387741830.2036887892327
Winsorized Mean ( 11 / 20 )162.4916666666675.373972791961130.2367862579686
Winsorized Mean ( 12 / 20 )162.5716666666675.3234154384492830.5389779449608
Winsorized Mean ( 13 / 20 )162.4416666666675.2809685443560830.7598246992538
Winsorized Mean ( 14 / 20 )161.8816666666675.1443339966708231.4679542135929
Winsorized Mean ( 15 / 20 )160.6316666666674.9442276402456232.4887279378356
Winsorized Mean ( 16 / 20 )159.1116666666674.6140090608857734.4844720864335
Winsorized Mean ( 17 / 20 )159.484.5064697997986435.3891198842886
Winsorized Mean ( 18 / 20 )158.764.391815834900636.1490567838424
Winsorized Mean ( 19 / 20 )161.044.0429720007526739.832083915006
Winsorized Mean ( 20 / 20 )159.6733333333333.7187947341783942.9368504439949
Trimmed Mean ( 1 / 20 )173.3879310344838.1703220621238421.2216764181523
Trimmed Mean ( 2 / 20 )171.9053571428577.9488063384053521.6265625081695
Trimmed Mean ( 3 / 20 )170.4092592592597.7090081662874322.1052119265463
Trimmed Mean ( 4 / 20 )168.8173076923087.4094965363868622.7839107371564
Trimmed Mean ( 5 / 20 )167.1487.0518107328717323.702848294105
Trimmed Mean ( 6 / 20 )165.7833333333336.7805418394058924.4498651081046
Trimmed Mean ( 7 / 20 )164.3934782608706.4631279740857525.4355907727673
Trimmed Mean ( 8 / 20 )163.1136363636366.1506282795915526.5198332509973
Trimmed Mean ( 9 / 20 )162.0547619047625.8831825932931327.5454244934545
Trimmed Mean ( 10 / 20 )161.23755.6754731955661428.4095254164822
Trimmed Mean ( 11 / 20 )161.0394736842115.6584477052881428.4600091883345
Trimmed Mean ( 12 / 20 )160.8194444444445.6204428728010228.613304695738
Trimmed Mean ( 13 / 20 )160.5617647058825.5645587415020728.8543570415326
Trimmed Mean ( 14 / 20 )160.2906255.4810401932755829.2445629566177
Trimmed Mean ( 15 / 20 )160.0633333333335.3847474744861229.7253184279748
Trimmed Mean ( 16 / 20 )159.9821428571435.2876567198094230.255773272458
Trimmed Mean ( 17 / 20 )160.1076923076925.2249193533030530.6430935065968
Trimmed Mean ( 18 / 20 )160.25.135515017284431.1945344256265
Trimmed Mean ( 19 / 20 )160.4181818181825.0033955412448432.0618628880718
Trimmed Mean ( 20 / 20 )160.324.9010074152372532.7116419986561
Median170
Midrange220.7
Midmean - Weighted Average at Xnp158.641935483871
Midmean - Weighted Average at X(n+1)p158.641935483871
Midmean - Empirical Distribution Function158.641935483871
Midmean - Empirical Distribution Function - Averaging158.641935483871
Midmean - Empirical Distribution Function - Interpolation158.641935483871
Midmean - Closest Observation158.641935483871
Midmean - True Basic - Statistics Graphics Toolkit158.641935483871
Midmean - MS Excel (old versions)160.290625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 174.965 & 8.40919251684196 & 20.8063972432049 \tabularnewline
Geometric Mean & 164.457463497207 &  &  \tabularnewline
Harmonic Mean & 155.524206579724 &  &  \tabularnewline
Quadratic Mean & 186.507125422417 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 174.771666666667 & 8.34522262320695 & 20.9427207107273 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 174.598333333333 & 8.28463266361268 & 21.074963782063 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 174.548333333333 & 8.2702965507692 & 21.1054503622484 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 174.381666666667 & 8.20349742545313 & 21.2569904789157 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 172.606666666667 & 7.705029858632 & 22.4018167137009 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 172.176666666667 & 7.59599298421186 & 22.6667753675567 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 170.963333333333 & 7.28024335544499 & 23.4831893641945 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 169.043333333333 & 6.82455783492122 & 24.7698587106024 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 166.958333333333 & 6.3354955980328 & 26.3528449747759 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 162.491666666667 & 5.37986163877418 & 30.2036887892327 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 162.491666666667 & 5.3739727919611 & 30.2367862579686 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 162.571666666667 & 5.32341543844928 & 30.5389779449608 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 162.441666666667 & 5.28096854435608 & 30.7598246992538 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 161.881666666667 & 5.14433399667082 & 31.4679542135929 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 160.631666666667 & 4.94422764024562 & 32.4887279378356 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 159.111666666667 & 4.61400906088577 & 34.4844720864335 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 159.48 & 4.50646979979864 & 35.3891198842886 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 158.76 & 4.3918158349006 & 36.1490567838424 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 161.04 & 4.04297200075267 & 39.832083915006 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 159.673333333333 & 3.71879473417839 & 42.9368504439949 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 173.387931034483 & 8.17032206212384 & 21.2216764181523 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 171.905357142857 & 7.94880633840535 & 21.6265625081695 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 170.409259259259 & 7.70900816628743 & 22.1052119265463 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 168.817307692308 & 7.40949653638686 & 22.7839107371564 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 167.148 & 7.05181073287173 & 23.702848294105 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 165.783333333333 & 6.78054183940589 & 24.4498651081046 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 164.393478260870 & 6.46312797408575 & 25.4355907727673 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 163.113636363636 & 6.15062827959155 & 26.5198332509973 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 162.054761904762 & 5.88318259329313 & 27.5454244934545 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 161.2375 & 5.67547319556614 & 28.4095254164822 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 161.039473684211 & 5.65844770528814 & 28.4600091883345 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 160.819444444444 & 5.62044287280102 & 28.613304695738 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 160.561764705882 & 5.56455874150207 & 28.8543570415326 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 160.290625 & 5.48104019327558 & 29.2445629566177 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 160.063333333333 & 5.38474747448612 & 29.7253184279748 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 159.982142857143 & 5.28765671980942 & 30.255773272458 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 160.107692307692 & 5.22491935330305 & 30.6430935065968 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 160.2 & 5.1355150172844 & 31.1945344256265 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 160.418181818182 & 5.00339554124484 & 32.0618628880718 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 160.32 & 4.90100741523725 & 32.7116419986561 \tabularnewline
Median & 170 &  &  \tabularnewline
Midrange & 220.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 158.641935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 158.641935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 158.641935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 158.641935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 158.641935483871 &  &  \tabularnewline
Midmean - Closest Observation & 158.641935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 158.641935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 160.290625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47296&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]174.965[/C][C]8.40919251684196[/C][C]20.8063972432049[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]164.457463497207[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]155.524206579724[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]186.507125422417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]174.771666666667[/C][C]8.34522262320695[/C][C]20.9427207107273[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]174.598333333333[/C][C]8.28463266361268[/C][C]21.074963782063[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]174.548333333333[/C][C]8.2702965507692[/C][C]21.1054503622484[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]174.381666666667[/C][C]8.20349742545313[/C][C]21.2569904789157[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]172.606666666667[/C][C]7.705029858632[/C][C]22.4018167137009[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]172.176666666667[/C][C]7.59599298421186[/C][C]22.6667753675567[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]170.963333333333[/C][C]7.28024335544499[/C][C]23.4831893641945[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]169.043333333333[/C][C]6.82455783492122[/C][C]24.7698587106024[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]166.958333333333[/C][C]6.3354955980328[/C][C]26.3528449747759[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]162.491666666667[/C][C]5.37986163877418[/C][C]30.2036887892327[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]162.491666666667[/C][C]5.3739727919611[/C][C]30.2367862579686[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]162.571666666667[/C][C]5.32341543844928[/C][C]30.5389779449608[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]162.441666666667[/C][C]5.28096854435608[/C][C]30.7598246992538[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]161.881666666667[/C][C]5.14433399667082[/C][C]31.4679542135929[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]160.631666666667[/C][C]4.94422764024562[/C][C]32.4887279378356[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]159.111666666667[/C][C]4.61400906088577[/C][C]34.4844720864335[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]159.48[/C][C]4.50646979979864[/C][C]35.3891198842886[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]158.76[/C][C]4.3918158349006[/C][C]36.1490567838424[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]161.04[/C][C]4.04297200075267[/C][C]39.832083915006[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]159.673333333333[/C][C]3.71879473417839[/C][C]42.9368504439949[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]173.387931034483[/C][C]8.17032206212384[/C][C]21.2216764181523[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]171.905357142857[/C][C]7.94880633840535[/C][C]21.6265625081695[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]170.409259259259[/C][C]7.70900816628743[/C][C]22.1052119265463[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]168.817307692308[/C][C]7.40949653638686[/C][C]22.7839107371564[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]167.148[/C][C]7.05181073287173[/C][C]23.702848294105[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]165.783333333333[/C][C]6.78054183940589[/C][C]24.4498651081046[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]164.393478260870[/C][C]6.46312797408575[/C][C]25.4355907727673[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]163.113636363636[/C][C]6.15062827959155[/C][C]26.5198332509973[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]162.054761904762[/C][C]5.88318259329313[/C][C]27.5454244934545[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]161.2375[/C][C]5.67547319556614[/C][C]28.4095254164822[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]161.039473684211[/C][C]5.65844770528814[/C][C]28.4600091883345[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]160.819444444444[/C][C]5.62044287280102[/C][C]28.613304695738[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]160.561764705882[/C][C]5.56455874150207[/C][C]28.8543570415326[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]160.290625[/C][C]5.48104019327558[/C][C]29.2445629566177[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]160.063333333333[/C][C]5.38474747448612[/C][C]29.7253184279748[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]159.982142857143[/C][C]5.28765671980942[/C][C]30.255773272458[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]160.107692307692[/C][C]5.22491935330305[/C][C]30.6430935065968[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]160.2[/C][C]5.1355150172844[/C][C]31.1945344256265[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]160.418181818182[/C][C]5.00339554124484[/C][C]32.0618628880718[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]160.32[/C][C]4.90100741523725[/C][C]32.7116419986561[/C][/ROW]
[ROW][C]Median[/C][C]170[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]220.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]158.641935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]160.290625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47296&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 Mean174.9658.4091925168419620.8063972432049
Geometric Mean164.457463497207
Harmonic Mean155.524206579724
Quadratic Mean186.507125422417
Winsorized Mean ( 1 / 20 )174.7716666666678.3452226232069520.9427207107273
Winsorized Mean ( 2 / 20 )174.5983333333338.2846326636126821.074963782063
Winsorized Mean ( 3 / 20 )174.5483333333338.270296550769221.1054503622484
Winsorized Mean ( 4 / 20 )174.3816666666678.2034974254531321.2569904789157
Winsorized Mean ( 5 / 20 )172.6066666666677.70502985863222.4018167137009
Winsorized Mean ( 6 / 20 )172.1766666666677.5959929842118622.6667753675567
Winsorized Mean ( 7 / 20 )170.9633333333337.2802433554449923.4831893641945
Winsorized Mean ( 8 / 20 )169.0433333333336.8245578349212224.7698587106024
Winsorized Mean ( 9 / 20 )166.9583333333336.335495598032826.3528449747759
Winsorized Mean ( 10 / 20 )162.4916666666675.3798616387741830.2036887892327
Winsorized Mean ( 11 / 20 )162.4916666666675.373972791961130.2367862579686
Winsorized Mean ( 12 / 20 )162.5716666666675.3234154384492830.5389779449608
Winsorized Mean ( 13 / 20 )162.4416666666675.2809685443560830.7598246992538
Winsorized Mean ( 14 / 20 )161.8816666666675.1443339966708231.4679542135929
Winsorized Mean ( 15 / 20 )160.6316666666674.9442276402456232.4887279378356
Winsorized Mean ( 16 / 20 )159.1116666666674.6140090608857734.4844720864335
Winsorized Mean ( 17 / 20 )159.484.5064697997986435.3891198842886
Winsorized Mean ( 18 / 20 )158.764.391815834900636.1490567838424
Winsorized Mean ( 19 / 20 )161.044.0429720007526739.832083915006
Winsorized Mean ( 20 / 20 )159.6733333333333.7187947341783942.9368504439949
Trimmed Mean ( 1 / 20 )173.3879310344838.1703220621238421.2216764181523
Trimmed Mean ( 2 / 20 )171.9053571428577.9488063384053521.6265625081695
Trimmed Mean ( 3 / 20 )170.4092592592597.7090081662874322.1052119265463
Trimmed Mean ( 4 / 20 )168.8173076923087.4094965363868622.7839107371564
Trimmed Mean ( 5 / 20 )167.1487.0518107328717323.702848294105
Trimmed Mean ( 6 / 20 )165.7833333333336.7805418394058924.4498651081046
Trimmed Mean ( 7 / 20 )164.3934782608706.4631279740857525.4355907727673
Trimmed Mean ( 8 / 20 )163.1136363636366.1506282795915526.5198332509973
Trimmed Mean ( 9 / 20 )162.0547619047625.8831825932931327.5454244934545
Trimmed Mean ( 10 / 20 )161.23755.6754731955661428.4095254164822
Trimmed Mean ( 11 / 20 )161.0394736842115.6584477052881428.4600091883345
Trimmed Mean ( 12 / 20 )160.8194444444445.6204428728010228.613304695738
Trimmed Mean ( 13 / 20 )160.5617647058825.5645587415020728.8543570415326
Trimmed Mean ( 14 / 20 )160.2906255.4810401932755829.2445629566177
Trimmed Mean ( 15 / 20 )160.0633333333335.3847474744861229.7253184279748
Trimmed Mean ( 16 / 20 )159.9821428571435.2876567198094230.255773272458
Trimmed Mean ( 17 / 20 )160.1076923076925.2249193533030530.6430935065968
Trimmed Mean ( 18 / 20 )160.25.135515017284431.1945344256265
Trimmed Mean ( 19 / 20 )160.4181818181825.0033955412448432.0618628880718
Trimmed Mean ( 20 / 20 )160.324.9010074152372532.7116419986561
Median170
Midrange220.7
Midmean - Weighted Average at Xnp158.641935483871
Midmean - Weighted Average at X(n+1)p158.641935483871
Midmean - Empirical Distribution Function158.641935483871
Midmean - Empirical Distribution Function - Averaging158.641935483871
Midmean - Empirical Distribution Function - Interpolation158.641935483871
Midmean - Closest Observation158.641935483871
Midmean - True Basic - Statistics Graphics Toolkit158.641935483871
Midmean - MS Excel (old versions)160.290625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')