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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 08:59:09 -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/2008/Oct/20/t1224514792cle4l5xhqk4faci.htm/, Retrieved Sun, 19 May 2024 01:32:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17415, Retrieved Sun, 19 May 2024 01:32:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [] [2008-10-20 14:59:09] [6d40a467de0f28bd2350f82ac9522c51] [Current]
Feedback Forum
2008-10-23 14:03:24 [Dana Molenberghs] [reply
Er gebeurd duidelijk iets tussen 5-10 (op de x-as) dit wijst op outliers.
2008-10-25 12:19:45 [Kristof Van Esbroeck] [reply
Wat student opmerkt klopt, in de trimmed mean op grafiek twee zijn deze outliers afgezwakt.

Post a new message
Dataseries X:
299,63
305,945
382,252
348,846
335,367
373,617
312,612
312,232
337,161
331,476
350,103
345,127
297,256
295,979
361,007
321,803
354,937
349,432
290,979
349,576
327,625
349,377
336,777
339,134
323,321
318,86
373,583
333,03
408,556
414,646
291,514
348,857
349,368
375,765
364,136
349,53
348,167
332,856
360,551
346,969
392,815
372,02
371,027
342,672
367,343
390,786
343,785
362,6
349,468
340,624
369,536
407,782
392,239
404,824
373,669
344,902
396,7
398,911
366,009
392,484




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17415&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17415&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean352.1359166666673.9746509961766188.5954306442003
Geometric Mean350.801390149715
Harmonic Mean349.455459308134
Quadratic Mean353.456895517143
Winsorized Mean ( 1 / 20 )352.0433333333333.9464795234012389.2043988181974
Winsorized Mean ( 2 / 20 )352.1663666666673.9027219780346090.2360887218559
Winsorized Mean ( 3 / 20 )352.0823166666673.8522034650146791.3976428982124
Winsorized Mean ( 4 / 20 )351.8463833333333.7263238708474294.4218472489668
Winsorized Mean ( 5 / 20 )352.1883833333333.5666927011372398.7436857739494
Winsorized Mean ( 6 / 20 )352.4285833333333.35278487747545105.115179235329
Winsorized Mean ( 7 / 20 )352.43433.33592449288100105.648164624862
Winsorized Mean ( 8 / 20 )353.23473.16811889590457111.496667772358
Winsorized Mean ( 9 / 20 )353.45823.04318127040105116.147599697017
Winsorized Mean ( 10 / 20 )352.2888666666672.71639220180904129.689986016030
Winsorized Mean ( 11 / 20 )351.888652.36254241618277148.944902571763
Winsorized Mean ( 12 / 20 )352.239652.16145987047008162.963770372195
Winsorized Mean ( 13 / 20 )352.5273833333332.11160432034544166.947652046698
Winsorized Mean ( 14 / 20 )352.560052.10386176124041167.577574009489
Winsorized Mean ( 15 / 20 )352.753551.94777673221168181.105741826710
Winsorized Mean ( 16 / 20 )352.864751.84730110580120191.016369173317
Winsorized Mean ( 17 / 20 )352.55111.76148077902053200.144732885497
Winsorized Mean ( 18 / 20 )352.48511.56824831113164224.763576978220
Winsorized Mean ( 19 / 20 )352.53451.43336127449444245.949507826867
Winsorized Mean ( 20 / 20 )352.5928333333331.23983364980557284.387210646062
Trimmed Mean ( 1 / 20 )352.1125862068973.8213540314945592.143408672654
Trimmed Mean ( 2 / 20 )352.1867857142863.6670843920103896.0400001924168
Trimmed Mean ( 3 / 20 )352.1981296296303.50542030495032100.472439533787
Trimmed Mean ( 4 / 20 )352.2426730769233.32842501330153105.828634164579
Trimmed Mean ( 5 / 20 )352.361563.15796489933576111.578681597796
Trimmed Mean ( 6 / 20 )352.4048541666673.00064520056464117.443026619859
Trimmed Mean ( 7 / 20 )352.3996956521742.87130523365272122.731533910754
Trimmed Mean ( 8 / 20 )352.3929545454552.70815080804343130.123091187839
Trimmed Mean ( 9 / 20 )352.2426428571432.54608687954017138.346670605663
Trimmed Mean ( 10 / 20 )352.040052.36821386360735148.652136282895
Trimmed Mean ( 11 / 20 )352.0007631578952.23313294759668157.626425035160
Trimmed Mean ( 12 / 20 )352.017752.15521331628460163.333136140253
Trimmed Mean ( 13 / 20 )351.9851176470592.10293353959448167.378146298877
Trimmed Mean ( 14 / 20 )351.906906252.03987380191537172.514057447854
Trimmed Mean ( 15 / 20 )351.81361.94798588443988180.603772753292
Trimmed Mean ( 16 / 20 )351.6793214285711.86234282462656188.837048033351
Trimmed Mean ( 17 / 20 )351.5083461538461.76499231895675199.155737041176
Trimmed Mean ( 18 / 20 )351.3551.64486003325070213.607840726499
Trimmed Mean ( 19 / 20 )351.1837727272731.53449345948232228.859739060568
Trimmed Mean ( 20 / 20 )350.97051.41016213420189248.886629053217
Median349.4045
Midrange352.8125
Midmean - Weighted Average at Xnp351.207677419355
Midmean - Weighted Average at X(n+1)p351.8136
Midmean - Empirical Distribution Function351.207677419355
Midmean - Empirical Distribution Function - Averaging351.8136
Midmean - Empirical Distribution Function - Interpolation351.8136
Midmean - Closest Observation351.207677419355
Midmean - True Basic - Statistics Graphics Toolkit351.8136
Midmean - MS Excel (old versions)351.90690625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 352.135916666667 & 3.97465099617661 & 88.5954306442003 \tabularnewline
Geometric Mean & 350.801390149715 &  &  \tabularnewline
Harmonic Mean & 349.455459308134 &  &  \tabularnewline
Quadratic Mean & 353.456895517143 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 352.043333333333 & 3.94647952340123 & 89.2043988181974 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 352.166366666667 & 3.90272197803460 & 90.2360887218559 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 352.082316666667 & 3.85220346501467 & 91.3976428982124 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 351.846383333333 & 3.72632387084742 & 94.4218472489668 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 352.188383333333 & 3.56669270113723 & 98.7436857739494 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 352.428583333333 & 3.35278487747545 & 105.115179235329 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 352.4343 & 3.33592449288100 & 105.648164624862 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 353.2347 & 3.16811889590457 & 111.496667772358 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 353.4582 & 3.04318127040105 & 116.147599697017 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 352.288866666667 & 2.71639220180904 & 129.689986016030 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 351.88865 & 2.36254241618277 & 148.944902571763 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 352.23965 & 2.16145987047008 & 162.963770372195 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 352.527383333333 & 2.11160432034544 & 166.947652046698 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 352.56005 & 2.10386176124041 & 167.577574009489 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 352.75355 & 1.94777673221168 & 181.105741826710 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 352.86475 & 1.84730110580120 & 191.016369173317 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 352.5511 & 1.76148077902053 & 200.144732885497 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 352.4851 & 1.56824831113164 & 224.763576978220 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 352.5345 & 1.43336127449444 & 245.949507826867 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 352.592833333333 & 1.23983364980557 & 284.387210646062 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 352.112586206897 & 3.82135403149455 & 92.143408672654 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 352.186785714286 & 3.66708439201038 & 96.0400001924168 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 352.198129629630 & 3.50542030495032 & 100.472439533787 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 352.242673076923 & 3.32842501330153 & 105.828634164579 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 352.36156 & 3.15796489933576 & 111.578681597796 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 352.404854166667 & 3.00064520056464 & 117.443026619859 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 352.399695652174 & 2.87130523365272 & 122.731533910754 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 352.392954545455 & 2.70815080804343 & 130.123091187839 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 352.242642857143 & 2.54608687954017 & 138.346670605663 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 352.04005 & 2.36821386360735 & 148.652136282895 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 352.000763157895 & 2.23313294759668 & 157.626425035160 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 352.01775 & 2.15521331628460 & 163.333136140253 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 351.985117647059 & 2.10293353959448 & 167.378146298877 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 351.90690625 & 2.03987380191537 & 172.514057447854 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 351.8136 & 1.94798588443988 & 180.603772753292 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 351.679321428571 & 1.86234282462656 & 188.837048033351 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 351.508346153846 & 1.76499231895675 & 199.155737041176 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 351.355 & 1.64486003325070 & 213.607840726499 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 351.183772727273 & 1.53449345948232 & 228.859739060568 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 350.9705 & 1.41016213420189 & 248.886629053217 \tabularnewline
Median & 349.4045 &  &  \tabularnewline
Midrange & 352.8125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 351.207677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 351.8136 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 351.207677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 351.8136 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 351.8136 &  &  \tabularnewline
Midmean - Closest Observation & 351.207677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 351.8136 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 351.90690625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17415&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]352.135916666667[/C][C]3.97465099617661[/C][C]88.5954306442003[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]350.801390149715[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]349.455459308134[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]353.456895517143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]352.043333333333[/C][C]3.94647952340123[/C][C]89.2043988181974[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]352.166366666667[/C][C]3.90272197803460[/C][C]90.2360887218559[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]352.082316666667[/C][C]3.85220346501467[/C][C]91.3976428982124[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]351.846383333333[/C][C]3.72632387084742[/C][C]94.4218472489668[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]352.188383333333[/C][C]3.56669270113723[/C][C]98.7436857739494[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]352.428583333333[/C][C]3.35278487747545[/C][C]105.115179235329[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]352.4343[/C][C]3.33592449288100[/C][C]105.648164624862[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]353.2347[/C][C]3.16811889590457[/C][C]111.496667772358[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]353.4582[/C][C]3.04318127040105[/C][C]116.147599697017[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]352.288866666667[/C][C]2.71639220180904[/C][C]129.689986016030[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]351.88865[/C][C]2.36254241618277[/C][C]148.944902571763[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]352.23965[/C][C]2.16145987047008[/C][C]162.963770372195[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]352.527383333333[/C][C]2.11160432034544[/C][C]166.947652046698[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]352.56005[/C][C]2.10386176124041[/C][C]167.577574009489[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]352.75355[/C][C]1.94777673221168[/C][C]181.105741826710[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]352.86475[/C][C]1.84730110580120[/C][C]191.016369173317[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]352.5511[/C][C]1.76148077902053[/C][C]200.144732885497[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]352.4851[/C][C]1.56824831113164[/C][C]224.763576978220[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]352.5345[/C][C]1.43336127449444[/C][C]245.949507826867[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]352.592833333333[/C][C]1.23983364980557[/C][C]284.387210646062[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]352.112586206897[/C][C]3.82135403149455[/C][C]92.143408672654[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]352.186785714286[/C][C]3.66708439201038[/C][C]96.0400001924168[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]352.198129629630[/C][C]3.50542030495032[/C][C]100.472439533787[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]352.242673076923[/C][C]3.32842501330153[/C][C]105.828634164579[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]352.36156[/C][C]3.15796489933576[/C][C]111.578681597796[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]352.404854166667[/C][C]3.00064520056464[/C][C]117.443026619859[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]352.399695652174[/C][C]2.87130523365272[/C][C]122.731533910754[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]352.392954545455[/C][C]2.70815080804343[/C][C]130.123091187839[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]352.242642857143[/C][C]2.54608687954017[/C][C]138.346670605663[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]352.04005[/C][C]2.36821386360735[/C][C]148.652136282895[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]352.000763157895[/C][C]2.23313294759668[/C][C]157.626425035160[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]352.01775[/C][C]2.15521331628460[/C][C]163.333136140253[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]351.985117647059[/C][C]2.10293353959448[/C][C]167.378146298877[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]351.90690625[/C][C]2.03987380191537[/C][C]172.514057447854[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]351.8136[/C][C]1.94798588443988[/C][C]180.603772753292[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]351.679321428571[/C][C]1.86234282462656[/C][C]188.837048033351[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]351.508346153846[/C][C]1.76499231895675[/C][C]199.155737041176[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]351.355[/C][C]1.64486003325070[/C][C]213.607840726499[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]351.183772727273[/C][C]1.53449345948232[/C][C]228.859739060568[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]350.9705[/C][C]1.41016213420189[/C][C]248.886629053217[/C][/ROW]
[ROW][C]Median[/C][C]349.4045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]352.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]351.207677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]351.8136[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]351.207677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]351.8136[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]351.8136[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]351.207677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]351.8136[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]351.90690625[/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=17415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17415&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 Mean352.1359166666673.9746509961766188.5954306442003
Geometric Mean350.801390149715
Harmonic Mean349.455459308134
Quadratic Mean353.456895517143
Winsorized Mean ( 1 / 20 )352.0433333333333.9464795234012389.2043988181974
Winsorized Mean ( 2 / 20 )352.1663666666673.9027219780346090.2360887218559
Winsorized Mean ( 3 / 20 )352.0823166666673.8522034650146791.3976428982124
Winsorized Mean ( 4 / 20 )351.8463833333333.7263238708474294.4218472489668
Winsorized Mean ( 5 / 20 )352.1883833333333.5666927011372398.7436857739494
Winsorized Mean ( 6 / 20 )352.4285833333333.35278487747545105.115179235329
Winsorized Mean ( 7 / 20 )352.43433.33592449288100105.648164624862
Winsorized Mean ( 8 / 20 )353.23473.16811889590457111.496667772358
Winsorized Mean ( 9 / 20 )353.45823.04318127040105116.147599697017
Winsorized Mean ( 10 / 20 )352.2888666666672.71639220180904129.689986016030
Winsorized Mean ( 11 / 20 )351.888652.36254241618277148.944902571763
Winsorized Mean ( 12 / 20 )352.239652.16145987047008162.963770372195
Winsorized Mean ( 13 / 20 )352.5273833333332.11160432034544166.947652046698
Winsorized Mean ( 14 / 20 )352.560052.10386176124041167.577574009489
Winsorized Mean ( 15 / 20 )352.753551.94777673221168181.105741826710
Winsorized Mean ( 16 / 20 )352.864751.84730110580120191.016369173317
Winsorized Mean ( 17 / 20 )352.55111.76148077902053200.144732885497
Winsorized Mean ( 18 / 20 )352.48511.56824831113164224.763576978220
Winsorized Mean ( 19 / 20 )352.53451.43336127449444245.949507826867
Winsorized Mean ( 20 / 20 )352.5928333333331.23983364980557284.387210646062
Trimmed Mean ( 1 / 20 )352.1125862068973.8213540314945592.143408672654
Trimmed Mean ( 2 / 20 )352.1867857142863.6670843920103896.0400001924168
Trimmed Mean ( 3 / 20 )352.1981296296303.50542030495032100.472439533787
Trimmed Mean ( 4 / 20 )352.2426730769233.32842501330153105.828634164579
Trimmed Mean ( 5 / 20 )352.361563.15796489933576111.578681597796
Trimmed Mean ( 6 / 20 )352.4048541666673.00064520056464117.443026619859
Trimmed Mean ( 7 / 20 )352.3996956521742.87130523365272122.731533910754
Trimmed Mean ( 8 / 20 )352.3929545454552.70815080804343130.123091187839
Trimmed Mean ( 9 / 20 )352.2426428571432.54608687954017138.346670605663
Trimmed Mean ( 10 / 20 )352.040052.36821386360735148.652136282895
Trimmed Mean ( 11 / 20 )352.0007631578952.23313294759668157.626425035160
Trimmed Mean ( 12 / 20 )352.017752.15521331628460163.333136140253
Trimmed Mean ( 13 / 20 )351.9851176470592.10293353959448167.378146298877
Trimmed Mean ( 14 / 20 )351.906906252.03987380191537172.514057447854
Trimmed Mean ( 15 / 20 )351.81361.94798588443988180.603772753292
Trimmed Mean ( 16 / 20 )351.6793214285711.86234282462656188.837048033351
Trimmed Mean ( 17 / 20 )351.5083461538461.76499231895675199.155737041176
Trimmed Mean ( 18 / 20 )351.3551.64486003325070213.607840726499
Trimmed Mean ( 19 / 20 )351.1837727272731.53449345948232228.859739060568
Trimmed Mean ( 20 / 20 )350.97051.41016213420189248.886629053217
Median349.4045
Midrange352.8125
Midmean - Weighted Average at Xnp351.207677419355
Midmean - Weighted Average at X(n+1)p351.8136
Midmean - Empirical Distribution Function351.207677419355
Midmean - Empirical Distribution Function - Averaging351.8136
Midmean - Empirical Distribution Function - Interpolation351.8136
Midmean - Closest Observation351.207677419355
Midmean - True Basic - Statistics Graphics Toolkit351.8136
Midmean - MS Excel (old versions)351.90690625
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')