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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 computationMon, 22 Oct 2007 02:46:22 -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/mfven2l0ar41nsq1193046090.htm/, Retrieved Mon, 06 May 2024 09:43:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1529, Retrieved Mon, 06 May 2024 09:43:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCosumptieprijsindex
Estimated Impact479
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Cosumptieprijsindex] [2007-10-22 09:46:22] [a1c3b9772d97ad2d7bb67d4cdac038f3] [Current]
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Dataseries X:
1,5
1,1
1,4
1,3
1,3
1,8
1,8
1,8
1,7
1,6
1,5
1,2
1,2
1,6
1,6
1,9
2,2
2,0
1,7
2,4
2,6
2,9
2,6
2,5
3,2
3,1
3,1
2,9
2,5
2,8
3,1
2,6
2,3
2,3
2,6
2,9
2,0
2,2
2,4
2,3
2,6
1,9
1,1
1,3
1,6
1,7
1,9
1,6
1,8
1,8
1,5
1,6
1,0
1,5
1,8
1,7
1,2
1,4
1,1
1,3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1529&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]2 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=1529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1529&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.948333333333330.078058780787325724.9598227602561
Geometric Mean1.85818756107037
Harmonic Mean1.77219223111154
Quadratic Mean2.03850435368679
Winsorized Mean ( 1 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 2 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 3 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 4 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 5 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 6 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 7 / 20 )1.941666666666670.068448985773961628.3666243511425
Winsorized Mean ( 8 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 9 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 10 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 11 / 20 )1.933333333333330.060256826355281532.0848848217490
Winsorized Mean ( 12 / 20 )1.933333333333330.060256826355281532.0848848217490
Winsorized Mean ( 13 / 20 )1.933333333333330.053131680924762536.3875808121155
Winsorized Mean ( 14 / 20 )1.933333333333330.053131680924762536.3875808121155
Winsorized Mean ( 15 / 20 )1.908333333333330.048729141078077339.1620556224389
Winsorized Mean ( 16 / 20 )1.908333333333330.048729141078077339.1620556224389
Winsorized Mean ( 17 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 18 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 19 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 20 / 20 )1.8750.034659359290683454.0979417500084
Trimmed Mean ( 1 / 20 )1.943103448275860.07601350172063225.5626093298166
Trimmed Mean ( 2 / 20 )1.93750.074405108224302326.0398787964826
Trimmed Mean ( 3 / 20 )1.931481481481480.072386882480423326.6827554288422
Trimmed Mean ( 4 / 20 )1.9250.069845498531819327.5608312699355
Trimmed Mean ( 5 / 20 )1.920.068392624020490428.0732027393008
Trimmed Mean ( 6 / 20 )1.914583333333330.066510649665392228.7861168544495
Trimmed Mean ( 7 / 20 )1.908695652173910.064067151286568529.7921105253523
Trimmed Mean ( 8 / 20 )1.902272727272730.062242164688856430.5624448761067
Trimmed Mean ( 9 / 20 )1.90.061343835893189730.9729571412559
Trimmed Mean ( 10 / 20 )1.89750.060073405951087131.5863562246659
Trimmed Mean ( 11 / 20 )1.894736842105260.058300658948847932.4994069752741
Trimmed Mean ( 12 / 20 )1.888888888888890.056593479036798433.3764405552924
Trimmed Mean ( 13 / 20 )1.882352941176470.054145540358704334.7646902903956
Trimmed Mean ( 14 / 20 )1.8750.052747114276670435.5469683168866
Trimmed Mean ( 15 / 20 )1.866666666666670.050590384196802436.897657456111
Trimmed Mean ( 16 / 20 )1.860714285714290.048886891837174738.0616197059874
Trimmed Mean ( 17 / 20 )1.853846153846150.046153846153846140.1666666666667
Trimmed Mean ( 18 / 20 )1.845833333333330.045035882097817340.9858372336132
Trimmed Mean ( 19 / 20 )1.836363636363640.042916134134696942.7895865596843
Trimmed Mean ( 20 / 20 )1.8250.038983802304357946.8143149750168
Median1.8
Midrange2.1
Midmean - Weighted Average at Xnp1.84375
Midmean - Weighted Average at X(n+1)p1.84375
Midmean - Empirical Distribution Function1.84375
Midmean - Empirical Distribution Function - Averaging1.84375
Midmean - Empirical Distribution Function - Interpolation1.84375
Midmean - Closest Observation1.84375
Midmean - True Basic - Statistics Graphics Toolkit1.84375
Midmean - MS Excel (old versions)1.88235294117647
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.94833333333333 & 0.0780587807873257 & 24.9598227602561 \tabularnewline
Geometric Mean & 1.85818756107037 &  &  \tabularnewline
Harmonic Mean & 1.77219223111154 &  &  \tabularnewline
Quadratic Mean & 2.03850435368679 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.94833333333333 & 0.077295078693324 & 25.2064344363183 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.94833333333333 & 0.077295078693324 & 25.2064344363183 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.94833333333333 & 0.077295078693324 & 25.2064344363183 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.94166666666667 & 0.0729248381216298 & 26.6255876143078 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.94166666666667 & 0.0729248381216298 & 26.6255876143078 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.94166666666667 & 0.0729248381216298 & 26.6255876143078 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.94166666666667 & 0.0684489857739616 & 28.3666243511425 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.915 & 0.0631483322377304 & 30.3254247917542 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.915 & 0.0631483322377304 & 30.3254247917542 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.915 & 0.0631483322377304 & 30.3254247917542 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.93333333333333 & 0.0602568263552815 & 32.0848848217490 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.93333333333333 & 0.0602568263552815 & 32.0848848217490 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.93333333333333 & 0.0531316809247625 & 36.3875808121155 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.93333333333333 & 0.0531316809247625 & 36.3875808121155 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.90833333333333 & 0.0487291410780773 & 39.1620556224389 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.90833333333333 & 0.0487291410780773 & 39.1620556224389 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.90833333333333 & 0.0400770209507425 & 47.6166463490091 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.90833333333333 & 0.0400770209507425 & 47.6166463490091 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.90833333333333 & 0.0400770209507425 & 47.6166463490091 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.875 & 0.0346593592906834 & 54.0979417500084 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.94310344827586 & 0.076013501720632 & 25.5626093298166 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.9375 & 0.0744051082243023 & 26.0398787964826 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.93148148148148 & 0.0723868824804233 & 26.6827554288422 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.925 & 0.0698454985318193 & 27.5608312699355 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.92 & 0.0683926240204904 & 28.0732027393008 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.91458333333333 & 0.0665106496653922 & 28.7861168544495 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.90869565217391 & 0.0640671512865685 & 29.7921105253523 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.90227272727273 & 0.0622421646888564 & 30.5624448761067 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.9 & 0.0613438358931897 & 30.9729571412559 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.8975 & 0.0600734059510871 & 31.5863562246659 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.89473684210526 & 0.0583006589488479 & 32.4994069752741 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.88888888888889 & 0.0565934790367984 & 33.3764405552924 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.88235294117647 & 0.0541455403587043 & 34.7646902903956 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.875 & 0.0527471142766704 & 35.5469683168866 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.86666666666667 & 0.0505903841968024 & 36.897657456111 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.86071428571429 & 0.0488868918371747 & 38.0616197059874 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.85384615384615 & 0.0461538461538461 & 40.1666666666667 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.84583333333333 & 0.0450358820978173 & 40.9858372336132 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.83636363636364 & 0.0429161341346969 & 42.7895865596843 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.825 & 0.0389838023043579 & 46.8143149750168 \tabularnewline
Median & 1.8 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.84375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.84375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.84375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.84375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.84375 &  &  \tabularnewline
Midmean - Closest Observation & 1.84375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.84375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.88235294117647 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1529&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]1.94833333333333[/C][C]0.0780587807873257[/C][C]24.9598227602561[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.85818756107037[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.77219223111154[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.03850435368679[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.94833333333333[/C][C]0.077295078693324[/C][C]25.2064344363183[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.94833333333333[/C][C]0.077295078693324[/C][C]25.2064344363183[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.94833333333333[/C][C]0.077295078693324[/C][C]25.2064344363183[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.94166666666667[/C][C]0.0729248381216298[/C][C]26.6255876143078[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.94166666666667[/C][C]0.0729248381216298[/C][C]26.6255876143078[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.94166666666667[/C][C]0.0729248381216298[/C][C]26.6255876143078[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.94166666666667[/C][C]0.0684489857739616[/C][C]28.3666243511425[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.915[/C][C]0.0631483322377304[/C][C]30.3254247917542[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.915[/C][C]0.0631483322377304[/C][C]30.3254247917542[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.915[/C][C]0.0631483322377304[/C][C]30.3254247917542[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.93333333333333[/C][C]0.0602568263552815[/C][C]32.0848848217490[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.93333333333333[/C][C]0.0602568263552815[/C][C]32.0848848217490[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.93333333333333[/C][C]0.0531316809247625[/C][C]36.3875808121155[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.93333333333333[/C][C]0.0531316809247625[/C][C]36.3875808121155[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.90833333333333[/C][C]0.0487291410780773[/C][C]39.1620556224389[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.90833333333333[/C][C]0.0487291410780773[/C][C]39.1620556224389[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.90833333333333[/C][C]0.0400770209507425[/C][C]47.6166463490091[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.90833333333333[/C][C]0.0400770209507425[/C][C]47.6166463490091[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.90833333333333[/C][C]0.0400770209507425[/C][C]47.6166463490091[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.875[/C][C]0.0346593592906834[/C][C]54.0979417500084[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.94310344827586[/C][C]0.076013501720632[/C][C]25.5626093298166[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.9375[/C][C]0.0744051082243023[/C][C]26.0398787964826[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.93148148148148[/C][C]0.0723868824804233[/C][C]26.6827554288422[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.925[/C][C]0.0698454985318193[/C][C]27.5608312699355[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.92[/C][C]0.0683926240204904[/C][C]28.0732027393008[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.91458333333333[/C][C]0.0665106496653922[/C][C]28.7861168544495[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.90869565217391[/C][C]0.0640671512865685[/C][C]29.7921105253523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.90227272727273[/C][C]0.0622421646888564[/C][C]30.5624448761067[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.9[/C][C]0.0613438358931897[/C][C]30.9729571412559[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.8975[/C][C]0.0600734059510871[/C][C]31.5863562246659[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.89473684210526[/C][C]0.0583006589488479[/C][C]32.4994069752741[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.88888888888889[/C][C]0.0565934790367984[/C][C]33.3764405552924[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.88235294117647[/C][C]0.0541455403587043[/C][C]34.7646902903956[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.875[/C][C]0.0527471142766704[/C][C]35.5469683168866[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.86666666666667[/C][C]0.0505903841968024[/C][C]36.897657456111[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.86071428571429[/C][C]0.0488868918371747[/C][C]38.0616197059874[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.85384615384615[/C][C]0.0461538461538461[/C][C]40.1666666666667[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.84583333333333[/C][C]0.0450358820978173[/C][C]40.9858372336132[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.83636363636364[/C][C]0.0429161341346969[/C][C]42.7895865596843[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.825[/C][C]0.0389838023043579[/C][C]46.8143149750168[/C][/ROW]
[ROW][C]Median[/C][C]1.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.88235294117647[/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=1529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1529&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 Mean1.948333333333330.078058780787325724.9598227602561
Geometric Mean1.85818756107037
Harmonic Mean1.77219223111154
Quadratic Mean2.03850435368679
Winsorized Mean ( 1 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 2 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 3 / 20 )1.948333333333330.07729507869332425.2064344363183
Winsorized Mean ( 4 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 5 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 6 / 20 )1.941666666666670.072924838121629826.6255876143078
Winsorized Mean ( 7 / 20 )1.941666666666670.068448985773961628.3666243511425
Winsorized Mean ( 8 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 9 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 10 / 20 )1.9150.063148332237730430.3254247917542
Winsorized Mean ( 11 / 20 )1.933333333333330.060256826355281532.0848848217490
Winsorized Mean ( 12 / 20 )1.933333333333330.060256826355281532.0848848217490
Winsorized Mean ( 13 / 20 )1.933333333333330.053131680924762536.3875808121155
Winsorized Mean ( 14 / 20 )1.933333333333330.053131680924762536.3875808121155
Winsorized Mean ( 15 / 20 )1.908333333333330.048729141078077339.1620556224389
Winsorized Mean ( 16 / 20 )1.908333333333330.048729141078077339.1620556224389
Winsorized Mean ( 17 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 18 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 19 / 20 )1.908333333333330.040077020950742547.6166463490091
Winsorized Mean ( 20 / 20 )1.8750.034659359290683454.0979417500084
Trimmed Mean ( 1 / 20 )1.943103448275860.07601350172063225.5626093298166
Trimmed Mean ( 2 / 20 )1.93750.074405108224302326.0398787964826
Trimmed Mean ( 3 / 20 )1.931481481481480.072386882480423326.6827554288422
Trimmed Mean ( 4 / 20 )1.9250.069845498531819327.5608312699355
Trimmed Mean ( 5 / 20 )1.920.068392624020490428.0732027393008
Trimmed Mean ( 6 / 20 )1.914583333333330.066510649665392228.7861168544495
Trimmed Mean ( 7 / 20 )1.908695652173910.064067151286568529.7921105253523
Trimmed Mean ( 8 / 20 )1.902272727272730.062242164688856430.5624448761067
Trimmed Mean ( 9 / 20 )1.90.061343835893189730.9729571412559
Trimmed Mean ( 10 / 20 )1.89750.060073405951087131.5863562246659
Trimmed Mean ( 11 / 20 )1.894736842105260.058300658948847932.4994069752741
Trimmed Mean ( 12 / 20 )1.888888888888890.056593479036798433.3764405552924
Trimmed Mean ( 13 / 20 )1.882352941176470.054145540358704334.7646902903956
Trimmed Mean ( 14 / 20 )1.8750.052747114276670435.5469683168866
Trimmed Mean ( 15 / 20 )1.866666666666670.050590384196802436.897657456111
Trimmed Mean ( 16 / 20 )1.860714285714290.048886891837174738.0616197059874
Trimmed Mean ( 17 / 20 )1.853846153846150.046153846153846140.1666666666667
Trimmed Mean ( 18 / 20 )1.845833333333330.045035882097817340.9858372336132
Trimmed Mean ( 19 / 20 )1.836363636363640.042916134134696942.7895865596843
Trimmed Mean ( 20 / 20 )1.8250.038983802304357946.8143149750168
Median1.8
Midrange2.1
Midmean - Weighted Average at Xnp1.84375
Midmean - Weighted Average at X(n+1)p1.84375
Midmean - Empirical Distribution Function1.84375
Midmean - Empirical Distribution Function - Averaging1.84375
Midmean - Empirical Distribution Function - Interpolation1.84375
Midmean - Closest Observation1.84375
Midmean - True Basic - Statistics Graphics Toolkit1.84375
Midmean - MS Excel (old versions)1.88235294117647
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')