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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, 22 Oct 2009 14:19:23 -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/22/t1256242990edwcb414ue3y2t2.htm/, Retrieved Thu, 02 May 2024 16:08:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49821, Retrieved Thu, 02 May 2024 16:08:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKVN WS3
Estimated Impact129
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] [] [2009-10-20 15:12:09] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D        [Central Tendency] [] [2009-10-20 15:25:16] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D          [Central Tendency] [] [2009-10-20 17:39:50] [90f6d58d515a4caed6fb4b8be4e11eaa]
-   PD              [Central Tendency] [WS3 Q2 Yt-Xt Cent...] [2009-10-22 20:19:23] [f1100e00818182135823a11ccbd0f3b9] [Current]
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Dataseries X:
8318
6546
7378
6260
4924
3447
5488
3230
4722
6581
6753
7144
8216
6329
6724
6442
4339
4303
5563
3185
4846
6272
6829
7324
8093
6552
7450
5599
4384
4826
4542
4625
4863
6428
7302
7658
8121
6938
7998
6105
5100
5017
4181
4844
4742
7037
7264
7514
8590
7123
7924
6188
5761
4559
4757
4793
4393
7667
7807
7007




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49821&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49821&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6081.91666666667183.91436427077333.0692857558011
Geometric Mean5906.14129973422
Harmonic Mean5719.91782961124
Quadratic Mean6243.82538593129
Winsorized Mean ( 1 / 20 )6078.13333333333182.72013805605633.2647150883208
Winsorized Mean ( 2 / 20 )6081.96666666667180.17317151168833.7562280534765
Winsorized Mean ( 3 / 20 )6113.91666666667171.13619859593835.7254439261093
Winsorized Mean ( 4 / 20 )6120.18333333333169.24750453670536.1611437054071
Winsorized Mean ( 5 / 20 )6115.26666666667167.16656138924536.5818774750492
Winsorized Mean ( 6 / 20 )6112.36666666667164.96664954285037.0521355898604
Winsorized Mean ( 7 / 20 )6099.76666666667162.29217804507437.5850933799937
Winsorized Mean ( 8 / 20 )6100.96666666667155.57471903078139.2156688739354
Winsorized Mean ( 9 / 20 )6102.16666666667154.91283163410539.3909697621411
Winsorized Mean ( 10 / 20 )6089.16666666667149.07991669936140.8449830230738
Winsorized Mean ( 11 / 20 )6095.21666666667144.28033974166442.245649529106
Winsorized Mean ( 12 / 20 )6084.81666666667141.37324779827343.0407928050796
Winsorized Mean ( 13 / 20 )6076.36666666667139.05356031592643.698030117757
Winsorized Mean ( 14 / 20 )6079.63333333333136.93051140238644.3994057355678
Winsorized Mean ( 15 / 20 )6078.38333333333134.19093423719145.2965274285177
Winsorized Mean ( 16 / 20 )6051.18333333333128.72974031081447.006879053146
Winsorized Mean ( 17 / 20 )6045.8127.78649168682547.3117300599881
Winsorized Mean ( 18 / 20 )6025.1123.33565817017948.8512413148723
Winsorized Mean ( 19 / 20 )6034.91666666667118.94553967140350.7368051239133
Winsorized Mean ( 20 / 20 )6042.91666666667110.89373263983354.4928601717575
Trimmed Mean ( 1 / 20 )6088.62068965517178.25996674987434.1558500243548
Trimmed Mean ( 2 / 20 )6099.85714285714172.74011789460335.3123363420359
Trimmed Mean ( 3 / 20 )6109.7962962963167.59024057173336.4567547337647
Trimmed Mean ( 4 / 20 )6108.21153846154165.47637329254336.9128922572101
Trimmed Mean ( 5 / 20 )6104.62163.40682395263037.3584153484905
Trimmed Mean ( 6 / 20 )6101.95833333333161.32862577663137.8231594297582
Trimmed Mean ( 7 / 20 )6099.69565217391159.17251562078338.32128699094
Trimmed Mean ( 8 / 20 )6099.68181818182156.96916912482238.8591075062093
Trimmed Mean ( 9 / 20 )6099.45238095238155.6797921372139.1794740808528
Trimmed Mean ( 10 / 20 )6099153.86611729449139.6383564311749
Trimmed Mean ( 11 / 20 )6100.55263157895152.63840673647839.9673500399623
Trimmed Mean ( 12 / 20 )6101.36111111111151.80456396080440.19221130062
Trimmed Mean ( 13 / 20 )6103.79411764706150.92807827500440.4417401149535
Trimmed Mean ( 14 / 20 )6107.75149.78176328546640.7776612187385
Trimmed Mean ( 15 / 20 )6111.76666666667148.16818405542941.2488464080810
Trimmed Mean ( 16 / 20 )6116.53571428571146.01560475190941.8896029960506
Trimmed Mean ( 17 / 20 )6125.96153846154143.80008003388442.6005433169304
Trimmed Mean ( 18 / 20 )6137.75139.90989918981643.8693047135494
Trimmed Mean ( 19 / 20 )6154.81818181818134.56062275561745.7401136809266
Trimmed Mean ( 20 / 20 )6173.75126.87473878635348.6601987050875
Median6300.5
Midrange5887.5
Midmean - Weighted Average at Xnp6069.22580645161
Midmean - Weighted Average at X(n+1)p6111.76666666667
Midmean - Empirical Distribution Function6069.22580645161
Midmean - Empirical Distribution Function - Averaging6111.76666666667
Midmean - Empirical Distribution Function - Interpolation6111.76666666667
Midmean - Closest Observation6069.22580645161
Midmean - True Basic - Statistics Graphics Toolkit6111.76666666667
Midmean - MS Excel (old versions)6107.75
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6081.91666666667 & 183.914364270773 & 33.0692857558011 \tabularnewline
Geometric Mean & 5906.14129973422 &  &  \tabularnewline
Harmonic Mean & 5719.91782961124 &  &  \tabularnewline
Quadratic Mean & 6243.82538593129 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6078.13333333333 & 182.720138056056 & 33.2647150883208 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6081.96666666667 & 180.173171511688 & 33.7562280534765 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6113.91666666667 & 171.136198595938 & 35.7254439261093 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6120.18333333333 & 169.247504536705 & 36.1611437054071 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6115.26666666667 & 167.166561389245 & 36.5818774750492 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6112.36666666667 & 164.966649542850 & 37.0521355898604 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6099.76666666667 & 162.292178045074 & 37.5850933799937 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6100.96666666667 & 155.574719030781 & 39.2156688739354 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6102.16666666667 & 154.912831634105 & 39.3909697621411 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6089.16666666667 & 149.079916699361 & 40.8449830230738 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6095.21666666667 & 144.280339741664 & 42.245649529106 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6084.81666666667 & 141.373247798273 & 43.0407928050796 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6076.36666666667 & 139.053560315926 & 43.698030117757 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6079.63333333333 & 136.930511402386 & 44.3994057355678 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6078.38333333333 & 134.190934237191 & 45.2965274285177 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6051.18333333333 & 128.729740310814 & 47.006879053146 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6045.8 & 127.786491686825 & 47.3117300599881 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6025.1 & 123.335658170179 & 48.8512413148723 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6034.91666666667 & 118.945539671403 & 50.7368051239133 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6042.91666666667 & 110.893732639833 & 54.4928601717575 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6088.62068965517 & 178.259966749874 & 34.1558500243548 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6099.85714285714 & 172.740117894603 & 35.3123363420359 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6109.7962962963 & 167.590240571733 & 36.4567547337647 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6108.21153846154 & 165.476373292543 & 36.9128922572101 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6104.62 & 163.406823952630 & 37.3584153484905 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6101.95833333333 & 161.328625776631 & 37.8231594297582 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6099.69565217391 & 159.172515620783 & 38.32128699094 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6099.68181818182 & 156.969169124822 & 38.8591075062093 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6099.45238095238 & 155.67979213721 & 39.1794740808528 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6099 & 153.866117294491 & 39.6383564311749 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6100.55263157895 & 152.638406736478 & 39.9673500399623 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6101.36111111111 & 151.804563960804 & 40.19221130062 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6103.79411764706 & 150.928078275004 & 40.4417401149535 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6107.75 & 149.781763285466 & 40.7776612187385 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6111.76666666667 & 148.168184055429 & 41.2488464080810 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6116.53571428571 & 146.015604751909 & 41.8896029960506 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6125.96153846154 & 143.800080033884 & 42.6005433169304 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6137.75 & 139.909899189816 & 43.8693047135494 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6154.81818181818 & 134.560622755617 & 45.7401136809266 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6173.75 & 126.874738786353 & 48.6601987050875 \tabularnewline
Median & 6300.5 &  &  \tabularnewline
Midrange & 5887.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6069.22580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6111.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6069.22580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6111.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6111.76666666667 &  &  \tabularnewline
Midmean - Closest Observation & 6069.22580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6111.76666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6107.75 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49821&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]6081.91666666667[/C][C]183.914364270773[/C][C]33.0692857558011[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5906.14129973422[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5719.91782961124[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6243.82538593129[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6078.13333333333[/C][C]182.720138056056[/C][C]33.2647150883208[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6081.96666666667[/C][C]180.173171511688[/C][C]33.7562280534765[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6113.91666666667[/C][C]171.136198595938[/C][C]35.7254439261093[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6120.18333333333[/C][C]169.247504536705[/C][C]36.1611437054071[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6115.26666666667[/C][C]167.166561389245[/C][C]36.5818774750492[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6112.36666666667[/C][C]164.966649542850[/C][C]37.0521355898604[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6099.76666666667[/C][C]162.292178045074[/C][C]37.5850933799937[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6100.96666666667[/C][C]155.574719030781[/C][C]39.2156688739354[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6102.16666666667[/C][C]154.912831634105[/C][C]39.3909697621411[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6089.16666666667[/C][C]149.079916699361[/C][C]40.8449830230738[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6095.21666666667[/C][C]144.280339741664[/C][C]42.245649529106[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6084.81666666667[/C][C]141.373247798273[/C][C]43.0407928050796[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6076.36666666667[/C][C]139.053560315926[/C][C]43.698030117757[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6079.63333333333[/C][C]136.930511402386[/C][C]44.3994057355678[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6078.38333333333[/C][C]134.190934237191[/C][C]45.2965274285177[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6051.18333333333[/C][C]128.729740310814[/C][C]47.006879053146[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6045.8[/C][C]127.786491686825[/C][C]47.3117300599881[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6025.1[/C][C]123.335658170179[/C][C]48.8512413148723[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6034.91666666667[/C][C]118.945539671403[/C][C]50.7368051239133[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6042.91666666667[/C][C]110.893732639833[/C][C]54.4928601717575[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6088.62068965517[/C][C]178.259966749874[/C][C]34.1558500243548[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6099.85714285714[/C][C]172.740117894603[/C][C]35.3123363420359[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6109.7962962963[/C][C]167.590240571733[/C][C]36.4567547337647[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6108.21153846154[/C][C]165.476373292543[/C][C]36.9128922572101[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6104.62[/C][C]163.406823952630[/C][C]37.3584153484905[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6101.95833333333[/C][C]161.328625776631[/C][C]37.8231594297582[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6099.69565217391[/C][C]159.172515620783[/C][C]38.32128699094[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6099.68181818182[/C][C]156.969169124822[/C][C]38.8591075062093[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6099.45238095238[/C][C]155.67979213721[/C][C]39.1794740808528[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6099[/C][C]153.866117294491[/C][C]39.6383564311749[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6100.55263157895[/C][C]152.638406736478[/C][C]39.9673500399623[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6101.36111111111[/C][C]151.804563960804[/C][C]40.19221130062[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6103.79411764706[/C][C]150.928078275004[/C][C]40.4417401149535[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6107.75[/C][C]149.781763285466[/C][C]40.7776612187385[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6111.76666666667[/C][C]148.168184055429[/C][C]41.2488464080810[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6116.53571428571[/C][C]146.015604751909[/C][C]41.8896029960506[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6125.96153846154[/C][C]143.800080033884[/C][C]42.6005433169304[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6137.75[/C][C]139.909899189816[/C][C]43.8693047135494[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6154.81818181818[/C][C]134.560622755617[/C][C]45.7401136809266[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6173.75[/C][C]126.874738786353[/C][C]48.6601987050875[/C][/ROW]
[ROW][C]Median[/C][C]6300.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5887.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6069.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6111.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6069.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6111.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6111.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6069.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6111.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6107.75[/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=49821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49821&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 Mean6081.91666666667183.91436427077333.0692857558011
Geometric Mean5906.14129973422
Harmonic Mean5719.91782961124
Quadratic Mean6243.82538593129
Winsorized Mean ( 1 / 20 )6078.13333333333182.72013805605633.2647150883208
Winsorized Mean ( 2 / 20 )6081.96666666667180.17317151168833.7562280534765
Winsorized Mean ( 3 / 20 )6113.91666666667171.13619859593835.7254439261093
Winsorized Mean ( 4 / 20 )6120.18333333333169.24750453670536.1611437054071
Winsorized Mean ( 5 / 20 )6115.26666666667167.16656138924536.5818774750492
Winsorized Mean ( 6 / 20 )6112.36666666667164.96664954285037.0521355898604
Winsorized Mean ( 7 / 20 )6099.76666666667162.29217804507437.5850933799937
Winsorized Mean ( 8 / 20 )6100.96666666667155.57471903078139.2156688739354
Winsorized Mean ( 9 / 20 )6102.16666666667154.91283163410539.3909697621411
Winsorized Mean ( 10 / 20 )6089.16666666667149.07991669936140.8449830230738
Winsorized Mean ( 11 / 20 )6095.21666666667144.28033974166442.245649529106
Winsorized Mean ( 12 / 20 )6084.81666666667141.37324779827343.0407928050796
Winsorized Mean ( 13 / 20 )6076.36666666667139.05356031592643.698030117757
Winsorized Mean ( 14 / 20 )6079.63333333333136.93051140238644.3994057355678
Winsorized Mean ( 15 / 20 )6078.38333333333134.19093423719145.2965274285177
Winsorized Mean ( 16 / 20 )6051.18333333333128.72974031081447.006879053146
Winsorized Mean ( 17 / 20 )6045.8127.78649168682547.3117300599881
Winsorized Mean ( 18 / 20 )6025.1123.33565817017948.8512413148723
Winsorized Mean ( 19 / 20 )6034.91666666667118.94553967140350.7368051239133
Winsorized Mean ( 20 / 20 )6042.91666666667110.89373263983354.4928601717575
Trimmed Mean ( 1 / 20 )6088.62068965517178.25996674987434.1558500243548
Trimmed Mean ( 2 / 20 )6099.85714285714172.74011789460335.3123363420359
Trimmed Mean ( 3 / 20 )6109.7962962963167.59024057173336.4567547337647
Trimmed Mean ( 4 / 20 )6108.21153846154165.47637329254336.9128922572101
Trimmed Mean ( 5 / 20 )6104.62163.40682395263037.3584153484905
Trimmed Mean ( 6 / 20 )6101.95833333333161.32862577663137.8231594297582
Trimmed Mean ( 7 / 20 )6099.69565217391159.17251562078338.32128699094
Trimmed Mean ( 8 / 20 )6099.68181818182156.96916912482238.8591075062093
Trimmed Mean ( 9 / 20 )6099.45238095238155.6797921372139.1794740808528
Trimmed Mean ( 10 / 20 )6099153.86611729449139.6383564311749
Trimmed Mean ( 11 / 20 )6100.55263157895152.63840673647839.9673500399623
Trimmed Mean ( 12 / 20 )6101.36111111111151.80456396080440.19221130062
Trimmed Mean ( 13 / 20 )6103.79411764706150.92807827500440.4417401149535
Trimmed Mean ( 14 / 20 )6107.75149.78176328546640.7776612187385
Trimmed Mean ( 15 / 20 )6111.76666666667148.16818405542941.2488464080810
Trimmed Mean ( 16 / 20 )6116.53571428571146.01560475190941.8896029960506
Trimmed Mean ( 17 / 20 )6125.96153846154143.80008003388442.6005433169304
Trimmed Mean ( 18 / 20 )6137.75139.90989918981643.8693047135494
Trimmed Mean ( 19 / 20 )6154.81818181818134.56062275561745.7401136809266
Trimmed Mean ( 20 / 20 )6173.75126.87473878635348.6601987050875
Median6300.5
Midrange5887.5
Midmean - Weighted Average at Xnp6069.22580645161
Midmean - Weighted Average at X(n+1)p6111.76666666667
Midmean - Empirical Distribution Function6069.22580645161
Midmean - Empirical Distribution Function - Averaging6111.76666666667
Midmean - Empirical Distribution Function - Interpolation6111.76666666667
Midmean - Closest Observation6069.22580645161
Midmean - True Basic - Statistics Graphics Toolkit6111.76666666667
Midmean - MS Excel (old versions)6107.75
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = 36 ;
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')