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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 06:37:58 -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/20/n6gxdoatobjt73s1192887277.htm/, Retrieved Fri, 03 May 2024 01:26:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1154, Retrieved Fri, 03 May 2024 01:26:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [mannen boven de 2...] [2007-10-20 13:37:58] [a1ee67c0c4cd462b4e85e70c1c0a96bd] [Current]
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Dataseries X:
5
6,5
6,5
6,6
6,2
6,2
6,2
6,1
6,1
6,1
5,9
5,9
5,9
6,2
6,1
6,2
6,6
6,6
6,7
5,8
5,7
5,7
6,1
6,2
6,2
6,2
6,1
6,2
6,5
6,5
6,5
6
6,3
6
6,1
6,1
6,1
6,2
6,1
6,2
6,8
6,8
6,8
6,7
6,7
6,7
5,7
5,6
5,6
5,8
5,7
5,7
6,1
6,1
5,9
5,9
5,8
5,6
5,5
5,5
5,4




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=1154&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=1154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1154&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 Mean6.111475409836070.0497588919288567122.821774620183
Geometric Mean6.09916785631369
Harmonic Mean6.08669108573582
Quadratic Mean6.12361727450289
Winsorized Mean ( 1 / 20 )6.118032786885250.0477074530338798128.240608077327
Winsorized Mean ( 2 / 20 )6.121311475409840.046934133249965130.423447745557
Winsorized Mean ( 3 / 20 )6.116393442622950.0458186212573901133.491433717824
Winsorized Mean ( 4 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 5 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 6 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 7 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 8 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 9 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 10 / 20 )6.106557377049180.0368031874108912165.924687687297
Winsorized Mean ( 11 / 20 )6.106557377049180.0368031874108912165.924687687297
Winsorized Mean ( 12 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 13 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 14 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 15 / 20 )6.10163934426230.020710310422759294.618439787222
Winsorized Mean ( 16 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 17 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 18 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 19 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 20 / 20 )6.108196721311480.0115221530431512530.126331288595
Trimmed Mean ( 1 / 20 )6.118644067796610.0463434801747968132.028152497795
Trimmed Mean ( 2 / 20 )6.119298245614040.0446679896718386136.995156723429
Trimmed Mean ( 3 / 20 )6.118181818181820.0431184188139619141.892536564925
Trimmed Mean ( 4 / 20 )6.11886792452830.0417380562488354146.601650255312
Trimmed Mean ( 5 / 20 )6.117647058823530.0405555423888578150.846140834854
Trimmed Mean ( 6 / 20 )6.116326530612240.0390520038307014156.620043292216
Trimmed Mean ( 7 / 20 )6.114893617021280.0371235309908803164.717456928422
Trimmed Mean ( 8 / 20 )6.113333333333330.0360415024518942169.619269937290
Trimmed Mean ( 9 / 20 )6.111627906976740.0346169199127805176.550308992694
Trimmed Mean ( 10 / 20 )6.109756097560980.0327229460121920186.711676121232
Trimmed Mean ( 11 / 20 )6.110256410256410.0311270245470197196.300690450718
Trimmed Mean ( 12 / 20 )6.110810810810810.0289412223499261211.145567278585
Trimmed Mean ( 13 / 20 )6.108571428571430.0269987327967268226.254005125455
Trimmed Mean ( 14 / 20 )6.106060606060610.0242068868313189252.244770201536
Trimmed Mean ( 15 / 20 )6.103225806451610.019937467277887306.118411199641
Trimmed Mean ( 16 / 20 )6.103448275862070.0188869847415574323.156308928048
Trimmed Mean ( 17 / 20 )6.107407407407410.0184328502787713331.33277355598
Trimmed Mean ( 18 / 20 )6.1120.0176257387552031346.765607098072
Trimmed Mean ( 19 / 20 )6.117391304347830.0162151711436886377.263443607186
Trimmed Mean ( 20 / 20 )6.123809523809520.0136360200602632449.090680179838
Median6.1
Midrange5.9
Midmean - Weighted Average at Xnp6.09666666666666
Midmean - Weighted Average at X(n+1)p6.10322580645161
Midmean - Empirical Distribution Function6.10322580645161
Midmean - Empirical Distribution Function - Averaging6.10322580645161
Midmean - Empirical Distribution Function - Interpolation6.10322580645161
Midmean - Closest Observation6.07647058823529
Midmean - True Basic - Statistics Graphics Toolkit6.10322580645161
Midmean - MS Excel (old versions)6.10322580645161
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.11147540983607 & 0.0497588919288567 & 122.821774620183 \tabularnewline
Geometric Mean & 6.09916785631369 &  &  \tabularnewline
Harmonic Mean & 6.08669108573582 &  &  \tabularnewline
Quadratic Mean & 6.12361727450289 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.11803278688525 & 0.0477074530338798 & 128.240608077327 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.12131147540984 & 0.046934133249965 & 130.423447745557 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.11639344262295 & 0.0458186212573901 & 133.491433717824 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.12295081967213 & 0.0444390318899576 & 137.783173018578 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.12295081967213 & 0.0444390318899576 & 137.783173018578 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.12295081967213 & 0.0444390318899576 & 137.783173018578 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.12295081967213 & 0.0399038080152068 & 153.442769605817 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.12295081967213 & 0.0399038080152068 & 153.442769605817 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.12295081967213 & 0.0399038080152068 & 153.442769605817 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.10655737704918 & 0.0368031874108912 & 165.924687687297 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.10655737704918 & 0.0368031874108912 & 165.924687687297 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.12622950819672 & 0.0333798832897689 & 183.530585023778 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.12622950819672 & 0.0333798832897689 & 183.530585023778 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.12622950819672 & 0.0333798832897689 & 183.530585023778 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.1016393442623 & 0.020710310422759 & 294.618439787222 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6.07540983606557 & 0.0169627907966694 & 358.160983584048 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6.07540983606557 & 0.0169627907966694 & 358.160983584048 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6.07540983606557 & 0.0169627907966694 & 358.160983584048 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.07540983606557 & 0.0169627907966694 & 358.160983584048 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6.10819672131148 & 0.0115221530431512 & 530.126331288595 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.11864406779661 & 0.0463434801747968 & 132.028152497795 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.11929824561404 & 0.0446679896718386 & 136.995156723429 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.11818181818182 & 0.0431184188139619 & 141.892536564925 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.1188679245283 & 0.0417380562488354 & 146.601650255312 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.11764705882353 & 0.0405555423888578 & 150.846140834854 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.11632653061224 & 0.0390520038307014 & 156.620043292216 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.11489361702128 & 0.0371235309908803 & 164.717456928422 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.11333333333333 & 0.0360415024518942 & 169.619269937290 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.11162790697674 & 0.0346169199127805 & 176.550308992694 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.10975609756098 & 0.0327229460121920 & 186.711676121232 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.11025641025641 & 0.0311270245470197 & 196.300690450718 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.11081081081081 & 0.0289412223499261 & 211.145567278585 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.10857142857143 & 0.0269987327967268 & 226.254005125455 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6.10606060606061 & 0.0242068868313189 & 252.244770201536 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6.10322580645161 & 0.019937467277887 & 306.118411199641 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6.10344827586207 & 0.0188869847415574 & 323.156308928048 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6.10740740740741 & 0.0184328502787713 & 331.33277355598 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6.112 & 0.0176257387552031 & 346.765607098072 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6.11739130434783 & 0.0162151711436886 & 377.263443607186 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6.12380952380952 & 0.0136360200602632 & 449.090680179838 \tabularnewline
Median & 6.1 &  &  \tabularnewline
Midrange & 5.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.09666666666666 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.10322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.10322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.10322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.10322580645161 &  &  \tabularnewline
Midmean - Closest Observation & 6.07647058823529 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.10322580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.10322580645161 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1154&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]6.11147540983607[/C][C]0.0497588919288567[/C][C]122.821774620183[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.09916785631369[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.08669108573582[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.12361727450289[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.11803278688525[/C][C]0.0477074530338798[/C][C]128.240608077327[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.12131147540984[/C][C]0.046934133249965[/C][C]130.423447745557[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.11639344262295[/C][C]0.0458186212573901[/C][C]133.491433717824[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.12295081967213[/C][C]0.0444390318899576[/C][C]137.783173018578[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.12295081967213[/C][C]0.0444390318899576[/C][C]137.783173018578[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.12295081967213[/C][C]0.0444390318899576[/C][C]137.783173018578[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.12295081967213[/C][C]0.0399038080152068[/C][C]153.442769605817[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.12295081967213[/C][C]0.0399038080152068[/C][C]153.442769605817[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.12295081967213[/C][C]0.0399038080152068[/C][C]153.442769605817[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.10655737704918[/C][C]0.0368031874108912[/C][C]165.924687687297[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.10655737704918[/C][C]0.0368031874108912[/C][C]165.924687687297[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.12622950819672[/C][C]0.0333798832897689[/C][C]183.530585023778[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.12622950819672[/C][C]0.0333798832897689[/C][C]183.530585023778[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.12622950819672[/C][C]0.0333798832897689[/C][C]183.530585023778[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.1016393442623[/C][C]0.020710310422759[/C][C]294.618439787222[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6.07540983606557[/C][C]0.0169627907966694[/C][C]358.160983584048[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6.07540983606557[/C][C]0.0169627907966694[/C][C]358.160983584048[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6.07540983606557[/C][C]0.0169627907966694[/C][C]358.160983584048[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.07540983606557[/C][C]0.0169627907966694[/C][C]358.160983584048[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6.10819672131148[/C][C]0.0115221530431512[/C][C]530.126331288595[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.11864406779661[/C][C]0.0463434801747968[/C][C]132.028152497795[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.11929824561404[/C][C]0.0446679896718386[/C][C]136.995156723429[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.11818181818182[/C][C]0.0431184188139619[/C][C]141.892536564925[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.1188679245283[/C][C]0.0417380562488354[/C][C]146.601650255312[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.11764705882353[/C][C]0.0405555423888578[/C][C]150.846140834854[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.11632653061224[/C][C]0.0390520038307014[/C][C]156.620043292216[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.11489361702128[/C][C]0.0371235309908803[/C][C]164.717456928422[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.11333333333333[/C][C]0.0360415024518942[/C][C]169.619269937290[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.11162790697674[/C][C]0.0346169199127805[/C][C]176.550308992694[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.10975609756098[/C][C]0.0327229460121920[/C][C]186.711676121232[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.11025641025641[/C][C]0.0311270245470197[/C][C]196.300690450718[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.11081081081081[/C][C]0.0289412223499261[/C][C]211.145567278585[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.10857142857143[/C][C]0.0269987327967268[/C][C]226.254005125455[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6.10606060606061[/C][C]0.0242068868313189[/C][C]252.244770201536[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6.10322580645161[/C][C]0.019937467277887[/C][C]306.118411199641[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6.10344827586207[/C][C]0.0188869847415574[/C][C]323.156308928048[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6.10740740740741[/C][C]0.0184328502787713[/C][C]331.33277355598[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6.112[/C][C]0.0176257387552031[/C][C]346.765607098072[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6.11739130434783[/C][C]0.0162151711436886[/C][C]377.263443607186[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6.12380952380952[/C][C]0.0136360200602632[/C][C]449.090680179838[/C][/ROW]
[ROW][C]Median[/C][C]6.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.09666666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.10322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.10322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.10322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.10322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.07647058823529[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.10322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.10322580645161[/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=1154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1154&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 Mean6.111475409836070.0497588919288567122.821774620183
Geometric Mean6.09916785631369
Harmonic Mean6.08669108573582
Quadratic Mean6.12361727450289
Winsorized Mean ( 1 / 20 )6.118032786885250.0477074530338798128.240608077327
Winsorized Mean ( 2 / 20 )6.121311475409840.046934133249965130.423447745557
Winsorized Mean ( 3 / 20 )6.116393442622950.0458186212573901133.491433717824
Winsorized Mean ( 4 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 5 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 6 / 20 )6.122950819672130.0444390318899576137.783173018578
Winsorized Mean ( 7 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 8 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 9 / 20 )6.122950819672130.0399038080152068153.442769605817
Winsorized Mean ( 10 / 20 )6.106557377049180.0368031874108912165.924687687297
Winsorized Mean ( 11 / 20 )6.106557377049180.0368031874108912165.924687687297
Winsorized Mean ( 12 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 13 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 14 / 20 )6.126229508196720.0333798832897689183.530585023778
Winsorized Mean ( 15 / 20 )6.10163934426230.020710310422759294.618439787222
Winsorized Mean ( 16 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 17 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 18 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 19 / 20 )6.075409836065570.0169627907966694358.160983584048
Winsorized Mean ( 20 / 20 )6.108196721311480.0115221530431512530.126331288595
Trimmed Mean ( 1 / 20 )6.118644067796610.0463434801747968132.028152497795
Trimmed Mean ( 2 / 20 )6.119298245614040.0446679896718386136.995156723429
Trimmed Mean ( 3 / 20 )6.118181818181820.0431184188139619141.892536564925
Trimmed Mean ( 4 / 20 )6.11886792452830.0417380562488354146.601650255312
Trimmed Mean ( 5 / 20 )6.117647058823530.0405555423888578150.846140834854
Trimmed Mean ( 6 / 20 )6.116326530612240.0390520038307014156.620043292216
Trimmed Mean ( 7 / 20 )6.114893617021280.0371235309908803164.717456928422
Trimmed Mean ( 8 / 20 )6.113333333333330.0360415024518942169.619269937290
Trimmed Mean ( 9 / 20 )6.111627906976740.0346169199127805176.550308992694
Trimmed Mean ( 10 / 20 )6.109756097560980.0327229460121920186.711676121232
Trimmed Mean ( 11 / 20 )6.110256410256410.0311270245470197196.300690450718
Trimmed Mean ( 12 / 20 )6.110810810810810.0289412223499261211.145567278585
Trimmed Mean ( 13 / 20 )6.108571428571430.0269987327967268226.254005125455
Trimmed Mean ( 14 / 20 )6.106060606060610.0242068868313189252.244770201536
Trimmed Mean ( 15 / 20 )6.103225806451610.019937467277887306.118411199641
Trimmed Mean ( 16 / 20 )6.103448275862070.0188869847415574323.156308928048
Trimmed Mean ( 17 / 20 )6.107407407407410.0184328502787713331.33277355598
Trimmed Mean ( 18 / 20 )6.1120.0176257387552031346.765607098072
Trimmed Mean ( 19 / 20 )6.117391304347830.0162151711436886377.263443607186
Trimmed Mean ( 20 / 20 )6.123809523809520.0136360200602632449.090680179838
Median6.1
Midrange5.9
Midmean - Weighted Average at Xnp6.09666666666666
Midmean - Weighted Average at X(n+1)p6.10322580645161
Midmean - Empirical Distribution Function6.10322580645161
Midmean - Empirical Distribution Function - Averaging6.10322580645161
Midmean - Empirical Distribution Function - Interpolation6.10322580645161
Midmean - Closest Observation6.07647058823529
Midmean - True Basic - Statistics Graphics Toolkit6.10322580645161
Midmean - MS Excel (old versions)6.10322580645161
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')