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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 10:49:38 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/emt4vvy5vp94sxy1193075097.htm/, Retrieved Sun, 05 May 2024 23:22:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1449, Retrieved Sun, 05 May 2024 23:22:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTotale werkloosheid, central tendency
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-10-22 17:49:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8,5
8,6
8,5
8,5
9
9
8,8
8
7,9
8,1
9,3
9,4
9,4
9,3
9
9,1
9,7
9,7
9,6
8,3
8,2
8,4
10,6
10,9
10,9
9,6
9,3
9,3
9,6
9,5
9,5
9
8,9
9
10,1
10,2
10,2
9,5
9,3
9,3
9,4
9,3
9,1
9
8,9
9
9,8
10
9,8
9,4
9
8,9
9,3
9,1
8,8
8,9
8,7
8,6
9,1
9,3
8,9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1449&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1449&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.20163934426230.0805884031874242114.180688291615
Geometric Mean9.18079092966321
Harmonic Mean9.16022344314658
Quadratic Mean9.22278895267444
Winsorized Mean ( 1 / 20 )9.203278688524590.0801626493130645114.807566458818
Winsorized Mean ( 2 / 20 )9.196721311475410.0761063109306226120.840455923018
Winsorized Mean ( 3 / 20 )9.181967213114750.0694831896453081132.146599198829
Winsorized Mean ( 4 / 20 )9.188524590163930.0679962374664524135.132838705926
Winsorized Mean ( 5 / 20 )9.188524590163930.0642781847200562142.949347903674
Winsorized Mean ( 6 / 20 )9.188524590163930.0600590947898089152.991393265606
Winsorized Mean ( 7 / 20 )9.16557377049180.05526316799793165.853209335287
Winsorized Mean ( 8 / 20 )9.16557377049180.05526316799793165.853209335287
Winsorized Mean ( 9 / 20 )9.16557377049180.0496372219482638184.651223633042
Winsorized Mean ( 10 / 20 )9.16557377049180.0496372219482638184.651223633042
Winsorized Mean ( 11 / 20 )9.16557377049180.0431597139305433212.364099197736
Winsorized Mean ( 12 / 20 )9.185245901639340.0397970305049904230.802293163244
Winsorized Mean ( 13 / 20 )9.185245901639340.0397970305049904230.802293163244
Winsorized Mean ( 14 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 15 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 16 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 17 / 20 )9.157377049180330.0280961479958482325.929983374715
Winsorized Mean ( 18 / 20 )9.157377049180330.0280961479958482325.929983374715
Winsorized Mean ( 19 / 20 )9.188524590163930.0236202146286268389.011054075174
Winsorized Mean ( 20 / 20 )9.188524590163930.0236202146286268389.011054075174
Trimmed Mean ( 1 / 20 )9.194915254237290.0748824806462472122.791274739883
Trimmed Mean ( 2 / 20 )9.18596491228070.0682046252488313134.682433614546
Trimmed Mean ( 3 / 20 )9.180.062678700757271146.461236258715
Trimmed Mean ( 4 / 20 )9.179245283018870.0592256815401053154.987583837310
Trimmed Mean ( 5 / 20 )9.17647058823530.055489849649026165.372057164988
Trimmed Mean ( 6 / 20 )9.17346938775510.0521457525455152175.919781381006
Trimmed Mean ( 7 / 20 )9.170212765957450.0493167839264252185.945068511327
Trimmed Mean ( 8 / 20 )9.171111111111110.0472070682755661194.274108647793
Trimmed Mean ( 9 / 20 )9.172093023255810.0444388640723082206.398008021347
Trimmed Mean ( 10 / 20 )9.173170731707320.0424873568344666215.903539668202
Trimmed Mean ( 11 / 20 )9.174358974358970.0398577004478753230.177829409826
Trimmed Mean ( 12 / 20 )9.175675675675680.038243216714939239.929495054515
Trimmed Mean ( 13 / 20 )9.174285714285710.0369744079430232248.125290563763
Trimmed Mean ( 14 / 20 )9.172727272727270.035160004199613260.885272386521
Trimmed Mean ( 15 / 20 )9.170967741935480.0347629602619530263.814349319751
Trimmed Mean ( 16 / 20 )9.168965517241380.0340614658385469269.188811799902
Trimmed Mean ( 17 / 20 )9.166666666666670.0329032077861883278.594923821212
Trimmed Mean ( 18 / 20 )9.1680.0325166623953526281.947756154406
Trimmed Mean ( 19 / 20 )9.16956521739130.031706897922026289.197802949415
Trimmed Mean ( 20 / 20 )9.166666666666670.0318727629155839287.601884121088
Median9.1
Midrange9.4
Midmean - Weighted Average at Xnp9.17272727272727
Midmean - Weighted Average at X(n+1)p9.17272727272727
Midmean - Empirical Distribution Function9.17272727272727
Midmean - Empirical Distribution Function - Averaging9.17272727272727
Midmean - Empirical Distribution Function - Interpolation9.17272727272727
Midmean - Closest Observation9.17272727272727
Midmean - True Basic - Statistics Graphics Toolkit9.17272727272727
Midmean - MS Excel (old versions)9.17272727272727
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.2016393442623 & 0.0805884031874242 & 114.180688291615 \tabularnewline
Geometric Mean & 9.18079092966321 &  &  \tabularnewline
Harmonic Mean & 9.16022344314658 &  &  \tabularnewline
Quadratic Mean & 9.22278895267444 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 9.20327868852459 & 0.0801626493130645 & 114.807566458818 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 9.19672131147541 & 0.0761063109306226 & 120.840455923018 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 9.18196721311475 & 0.0694831896453081 & 132.146599198829 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 9.18852459016393 & 0.0679962374664524 & 135.132838705926 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 9.18852459016393 & 0.0642781847200562 & 142.949347903674 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9.18852459016393 & 0.0600590947898089 & 152.991393265606 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9.1655737704918 & 0.05526316799793 & 165.853209335287 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9.1655737704918 & 0.05526316799793 & 165.853209335287 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9.1655737704918 & 0.0496372219482638 & 184.651223633042 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9.1655737704918 & 0.0496372219482638 & 184.651223633042 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9.1655737704918 & 0.0431597139305433 & 212.364099197736 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 9.18524590163934 & 0.0397970305049904 & 230.802293163244 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9.18524590163934 & 0.0397970305049904 & 230.802293163244 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9.18524590163934 & 0.032377222106476 & 283.694687315442 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9.18524590163934 & 0.032377222106476 & 283.694687315442 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9.18524590163934 & 0.032377222106476 & 283.694687315442 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9.15737704918033 & 0.0280961479958482 & 325.929983374715 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9.15737704918033 & 0.0280961479958482 & 325.929983374715 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9.18852459016393 & 0.0236202146286268 & 389.011054075174 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9.18852459016393 & 0.0236202146286268 & 389.011054075174 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 9.19491525423729 & 0.0748824806462472 & 122.791274739883 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 9.1859649122807 & 0.0682046252488313 & 134.682433614546 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9.18 & 0.062678700757271 & 146.461236258715 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9.17924528301887 & 0.0592256815401053 & 154.987583837310 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9.1764705882353 & 0.055489849649026 & 165.372057164988 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9.1734693877551 & 0.0521457525455152 & 175.919781381006 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9.17021276595745 & 0.0493167839264252 & 185.945068511327 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9.17111111111111 & 0.0472070682755661 & 194.274108647793 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9.17209302325581 & 0.0444388640723082 & 206.398008021347 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9.17317073170732 & 0.0424873568344666 & 215.903539668202 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9.17435897435897 & 0.0398577004478753 & 230.177829409826 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9.17567567567568 & 0.038243216714939 & 239.929495054515 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9.17428571428571 & 0.0369744079430232 & 248.125290563763 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9.17272727272727 & 0.035160004199613 & 260.885272386521 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9.17096774193548 & 0.0347629602619530 & 263.814349319751 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9.16896551724138 & 0.0340614658385469 & 269.188811799902 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9.16666666666667 & 0.0329032077861883 & 278.594923821212 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9.168 & 0.0325166623953526 & 281.947756154406 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.1695652173913 & 0.031706897922026 & 289.197802949415 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.16666666666667 & 0.0318727629155839 & 287.601884121088 \tabularnewline
Median & 9.1 &  &  \tabularnewline
Midrange & 9.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.17272727272727 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.17272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.17272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.17272727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.17272727272727 &  &  \tabularnewline
Midmean - Closest Observation & 9.17272727272727 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.17272727272727 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.17272727272727 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1449&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]9.2016393442623[/C][C]0.0805884031874242[/C][C]114.180688291615[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.18079092966321[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.16022344314658[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.22278895267444[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]9.20327868852459[/C][C]0.0801626493130645[/C][C]114.807566458818[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]9.19672131147541[/C][C]0.0761063109306226[/C][C]120.840455923018[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]9.18196721311475[/C][C]0.0694831896453081[/C][C]132.146599198829[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]9.18852459016393[/C][C]0.0679962374664524[/C][C]135.132838705926[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]9.18852459016393[/C][C]0.0642781847200562[/C][C]142.949347903674[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9.18852459016393[/C][C]0.0600590947898089[/C][C]152.991393265606[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9.1655737704918[/C][C]0.05526316799793[/C][C]165.853209335287[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9.1655737704918[/C][C]0.05526316799793[/C][C]165.853209335287[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9.1655737704918[/C][C]0.0496372219482638[/C][C]184.651223633042[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9.1655737704918[/C][C]0.0496372219482638[/C][C]184.651223633042[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9.1655737704918[/C][C]0.0431597139305433[/C][C]212.364099197736[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]9.18524590163934[/C][C]0.0397970305049904[/C][C]230.802293163244[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9.18524590163934[/C][C]0.0397970305049904[/C][C]230.802293163244[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9.18524590163934[/C][C]0.032377222106476[/C][C]283.694687315442[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9.18524590163934[/C][C]0.032377222106476[/C][C]283.694687315442[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9.18524590163934[/C][C]0.032377222106476[/C][C]283.694687315442[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9.15737704918033[/C][C]0.0280961479958482[/C][C]325.929983374715[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9.15737704918033[/C][C]0.0280961479958482[/C][C]325.929983374715[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9.18852459016393[/C][C]0.0236202146286268[/C][C]389.011054075174[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9.18852459016393[/C][C]0.0236202146286268[/C][C]389.011054075174[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]9.19491525423729[/C][C]0.0748824806462472[/C][C]122.791274739883[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]9.1859649122807[/C][C]0.0682046252488313[/C][C]134.682433614546[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9.18[/C][C]0.062678700757271[/C][C]146.461236258715[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9.17924528301887[/C][C]0.0592256815401053[/C][C]154.987583837310[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9.1764705882353[/C][C]0.055489849649026[/C][C]165.372057164988[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9.1734693877551[/C][C]0.0521457525455152[/C][C]175.919781381006[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9.17021276595745[/C][C]0.0493167839264252[/C][C]185.945068511327[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9.17111111111111[/C][C]0.0472070682755661[/C][C]194.274108647793[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9.17209302325581[/C][C]0.0444388640723082[/C][C]206.398008021347[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9.17317073170732[/C][C]0.0424873568344666[/C][C]215.903539668202[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9.17435897435897[/C][C]0.0398577004478753[/C][C]230.177829409826[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9.17567567567568[/C][C]0.038243216714939[/C][C]239.929495054515[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9.17428571428571[/C][C]0.0369744079430232[/C][C]248.125290563763[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9.17272727272727[/C][C]0.035160004199613[/C][C]260.885272386521[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9.17096774193548[/C][C]0.0347629602619530[/C][C]263.814349319751[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9.16896551724138[/C][C]0.0340614658385469[/C][C]269.188811799902[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9.16666666666667[/C][C]0.0329032077861883[/C][C]278.594923821212[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9.168[/C][C]0.0325166623953526[/C][C]281.947756154406[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.1695652173913[/C][C]0.031706897922026[/C][C]289.197802949415[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.16666666666667[/C][C]0.0318727629155839[/C][C]287.601884121088[/C][/ROW]
[ROW][C]Median[/C][C]9.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.17272727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1449&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 Mean9.20163934426230.0805884031874242114.180688291615
Geometric Mean9.18079092966321
Harmonic Mean9.16022344314658
Quadratic Mean9.22278895267444
Winsorized Mean ( 1 / 20 )9.203278688524590.0801626493130645114.807566458818
Winsorized Mean ( 2 / 20 )9.196721311475410.0761063109306226120.840455923018
Winsorized Mean ( 3 / 20 )9.181967213114750.0694831896453081132.146599198829
Winsorized Mean ( 4 / 20 )9.188524590163930.0679962374664524135.132838705926
Winsorized Mean ( 5 / 20 )9.188524590163930.0642781847200562142.949347903674
Winsorized Mean ( 6 / 20 )9.188524590163930.0600590947898089152.991393265606
Winsorized Mean ( 7 / 20 )9.16557377049180.05526316799793165.853209335287
Winsorized Mean ( 8 / 20 )9.16557377049180.05526316799793165.853209335287
Winsorized Mean ( 9 / 20 )9.16557377049180.0496372219482638184.651223633042
Winsorized Mean ( 10 / 20 )9.16557377049180.0496372219482638184.651223633042
Winsorized Mean ( 11 / 20 )9.16557377049180.0431597139305433212.364099197736
Winsorized Mean ( 12 / 20 )9.185245901639340.0397970305049904230.802293163244
Winsorized Mean ( 13 / 20 )9.185245901639340.0397970305049904230.802293163244
Winsorized Mean ( 14 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 15 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 16 / 20 )9.185245901639340.032377222106476283.694687315442
Winsorized Mean ( 17 / 20 )9.157377049180330.0280961479958482325.929983374715
Winsorized Mean ( 18 / 20 )9.157377049180330.0280961479958482325.929983374715
Winsorized Mean ( 19 / 20 )9.188524590163930.0236202146286268389.011054075174
Winsorized Mean ( 20 / 20 )9.188524590163930.0236202146286268389.011054075174
Trimmed Mean ( 1 / 20 )9.194915254237290.0748824806462472122.791274739883
Trimmed Mean ( 2 / 20 )9.18596491228070.0682046252488313134.682433614546
Trimmed Mean ( 3 / 20 )9.180.062678700757271146.461236258715
Trimmed Mean ( 4 / 20 )9.179245283018870.0592256815401053154.987583837310
Trimmed Mean ( 5 / 20 )9.17647058823530.055489849649026165.372057164988
Trimmed Mean ( 6 / 20 )9.17346938775510.0521457525455152175.919781381006
Trimmed Mean ( 7 / 20 )9.170212765957450.0493167839264252185.945068511327
Trimmed Mean ( 8 / 20 )9.171111111111110.0472070682755661194.274108647793
Trimmed Mean ( 9 / 20 )9.172093023255810.0444388640723082206.398008021347
Trimmed Mean ( 10 / 20 )9.173170731707320.0424873568344666215.903539668202
Trimmed Mean ( 11 / 20 )9.174358974358970.0398577004478753230.177829409826
Trimmed Mean ( 12 / 20 )9.175675675675680.038243216714939239.929495054515
Trimmed Mean ( 13 / 20 )9.174285714285710.0369744079430232248.125290563763
Trimmed Mean ( 14 / 20 )9.172727272727270.035160004199613260.885272386521
Trimmed Mean ( 15 / 20 )9.170967741935480.0347629602619530263.814349319751
Trimmed Mean ( 16 / 20 )9.168965517241380.0340614658385469269.188811799902
Trimmed Mean ( 17 / 20 )9.166666666666670.0329032077861883278.594923821212
Trimmed Mean ( 18 / 20 )9.1680.0325166623953526281.947756154406
Trimmed Mean ( 19 / 20 )9.16956521739130.031706897922026289.197802949415
Trimmed Mean ( 20 / 20 )9.166666666666670.0318727629155839287.601884121088
Median9.1
Midrange9.4
Midmean - Weighted Average at Xnp9.17272727272727
Midmean - Weighted Average at X(n+1)p9.17272727272727
Midmean - Empirical Distribution Function9.17272727272727
Midmean - Empirical Distribution Function - Averaging9.17272727272727
Midmean - Empirical Distribution Function - Interpolation9.17272727272727
Midmean - Closest Observation9.17272727272727
Midmean - True Basic - Statistics Graphics Toolkit9.17272727272727
Midmean - MS Excel (old versions)9.17272727272727
Number of observations61



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