Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 28 Oct 2009 08:09:28 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256739079cmwewl3zp6e1epi.htm/, Retrieved Sun, 05 May 2024 22:52:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51355, Retrieved Sun, 05 May 2024 22:52:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [KDGP1W52] [2009-10-28 14:09:28] [d00efe1a3b3f6588aa0a3288268f2e7e] [Current]
-  M      [Central Tendency] [Nicolas Van hoeij...] [2010-01-23 13:50:14] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8
13
9
8
8
6
8
6
12
16




Summary of computational 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 computational 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=51355&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]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=51355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51355&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.918918918918920.64988158769821913.7239138448411
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5061114775343
Winsorized Mean ( 1 / 24 )8.90540540540540.64110954095958613.890614374692
Winsorized Mean ( 2 / 24 )8.878378378378380.63670078873318113.9443495838027
Winsorized Mean ( 3 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 4 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 5 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 6 / 24 )8.878378378378380.60540350465137714.6652246149302
Winsorized Mean ( 7 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 8 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 9 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 10 / 24 )8.837837837837840.56689722582910115.5898413948177
Winsorized Mean ( 11 / 24 )8.986486486486490.53582961977694116.7711641066566
Winsorized Mean ( 12 / 24 )8.986486486486490.53582961977694116.7711641066566
Winsorized Mean ( 13 / 24 )9.162162162162160.44465105439311520.6052860364116
Winsorized Mean ( 14 / 24 )9.351351351351350.40972644743766522.8234018326924
Winsorized Mean ( 15 / 24 )9.554054054054050.37466109177258325.5005237102478
Winsorized Mean ( 16 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 17 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 18 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 19 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 20 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 21 / 24 )10.05405405405410.29864056539257633.6660695804589
Winsorized Mean ( 22 / 24 )10.35135135135140.25917623070160839.9394316497679
Winsorized Mean ( 23 / 24 )10.04054054054050.21806526098526246.0437416541056
Winsorized Mean ( 24 / 24 )10.04054054054050.21806526098526246.0437416541056
Trimmed Mean ( 1 / 24 )8.958333333333330.62749891669534714.2762530659199
Trimmed Mean ( 2 / 24 )9.014285714285710.61131256034533214.7457884869788
Trimmed Mean ( 3 / 24 )9.088235294117650.59472929858400815.2812974167505
Trimmed Mean ( 4 / 24 )9.136363636363640.58372901544024415.6517209093556
Trimmed Mean ( 5 / 24 )9.18750.57038129477444416.1076460328756
Trimmed Mean ( 6 / 24 )9.241935483870970.55414666050514516.6777789032352
Trimmed Mean ( 7 / 24 )9.316666666666670.53756705883966617.3311710854765
Trimmed Mean ( 8 / 24 )9.379310344827590.52281729379411117.9399389732529
Trimmed Mean ( 9 / 24 )9.446428571428570.50447326448738618.7253304315887
Trimmed Mean ( 10 / 24 )9.518518518518520.48148148148148219.7692307692308
Trimmed Mean ( 11 / 24 )9.615384615384610.45635602233404121.0699194155619
Trimmed Mean ( 12 / 24 )9.70.43260011227790622.4225554379159
Trimmed Mean ( 13 / 24 )9.791666666666670.40163488294247724.3795225029521
Trimmed Mean ( 14 / 24 )9.86956521739130.38524563423581125.6188891977166
Trimmed Mean ( 15 / 24 )9.931818181818180.37269053085549726.6489684055564
Trimmed Mean ( 16 / 24 )9.976190476190480.36465199109384427.3581132692158
Trimmed Mean ( 17 / 24 )100.36162028533979027.6533159377486
Trimmed Mean ( 18 / 24 )10.02631578947370.3567811728085528.1021437049141
Trimmed Mean ( 19 / 24 )10.05555555555560.34947680724292128.7731699132926
Trimmed Mean ( 20 / 24 )10.08823529411760.33872900493725329.7826142641266
Trimmed Mean ( 21 / 24 )10.1250.32300878845529131.3458963405308
Trimmed Mean ( 22 / 24 )10.13333333333330.31342869666436132.3305856840056
Trimmed Mean ( 23 / 24 )10.10714285714290.31005753739075532.5976363683918
Trimmed Mean ( 24 / 24 )10.11538461538460.31538461538461532.0731707317073
Median10.5
Midrange7.5
Midmean - Weighted Average at Xnp10.1777777777778
Midmean - Weighted Average at X(n+1)p10.1777777777778
Midmean - Empirical Distribution Function10.1777777777778
Midmean - Empirical Distribution Function - Averaging10.1777777777778
Midmean - Empirical Distribution Function - Interpolation10.1777777777778
Midmean - Closest Observation10.1777777777778
Midmean - True Basic - Statistics Graphics Toolkit10.1777777777778
Midmean - MS Excel (old versions)10.1777777777778
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.91891891891892 & 0.649881587698219 & 13.7239138448411 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.5061114775343 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.9054054054054 & 0.641109540959586 & 13.890614374692 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.87837837837838 & 0.636700788733181 & 13.9443495838027 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.95945945945946 & 0.617359387671828 & 14.5125507741077 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.95945945945946 & 0.617359387671828 & 14.5125507741077 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.95945945945946 & 0.617359387671828 & 14.5125507741077 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.87837837837838 & 0.605403504651377 & 14.6652246149302 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.97297297297297 & 0.5848807689382 & 15.3415421561263 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.97297297297297 & 0.5848807689382 & 15.3415421561263 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.97297297297297 & 0.5848807689382 & 15.3415421561263 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.83783783783784 & 0.566897225829101 & 15.5898413948177 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.98648648648649 & 0.535829619776941 & 16.7711641066566 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.98648648648649 & 0.535829619776941 & 16.7711641066566 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.16216216216216 & 0.444651054393115 & 20.6052860364116 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9.35135135135135 & 0.409726447437665 & 22.8234018326924 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.55405405405405 & 0.374661091772583 & 25.5005237102478 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9.77027027027027 & 0.3401696645829 & 28.7217564865760 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9.77027027027027 & 0.3401696645829 & 28.7217564865760 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.77027027027027 & 0.3401696645829 & 28.7217564865760 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9.77027027027027 & 0.3401696645829 & 28.7217564865760 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.77027027027027 & 0.3401696645829 & 28.7217564865760 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 10.0540540540541 & 0.298640565392576 & 33.6660695804589 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 10.3513513513514 & 0.259176230701608 & 39.9394316497679 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 10.0405405405405 & 0.218065260985262 & 46.0437416541056 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 10.0405405405405 & 0.218065260985262 & 46.0437416541056 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.95833333333333 & 0.627498916695347 & 14.2762530659199 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9.01428571428571 & 0.611312560345332 & 14.7457884869788 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9.08823529411765 & 0.594729298584008 & 15.2812974167505 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9.13636363636364 & 0.583729015440244 & 15.6517209093556 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9.1875 & 0.570381294774444 & 16.1076460328756 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9.24193548387097 & 0.554146660505145 & 16.6777789032352 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9.31666666666667 & 0.537567058839666 & 17.3311710854765 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9.37931034482759 & 0.522817293794111 & 17.9399389732529 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9.44642857142857 & 0.504473264487386 & 18.7253304315887 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9.51851851851852 & 0.481481481481482 & 19.7692307692308 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9.61538461538461 & 0.456356022334041 & 21.0699194155619 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9.7 & 0.432600112277906 & 22.4225554379159 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9.79166666666667 & 0.401634882942477 & 24.3795225029521 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9.8695652173913 & 0.385245634235811 & 25.6188891977166 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9.93181818181818 & 0.372690530855497 & 26.6489684055564 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9.97619047619048 & 0.364651991093844 & 27.3581132692158 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 10 & 0.361620285339790 & 27.6533159377486 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 10.0263157894737 & 0.35678117280855 & 28.1021437049141 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 10.0555555555556 & 0.349476807242921 & 28.7731699132926 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 10.0882352941176 & 0.338729004937253 & 29.7826142641266 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 10.125 & 0.323008788455291 & 31.3458963405308 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 10.1333333333333 & 0.313428696664361 & 32.3305856840056 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 10.1071428571429 & 0.310057537390755 & 32.5976363683918 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 10.1153846153846 & 0.315384615384615 & 32.0731707317073 \tabularnewline
Median & 10.5 &  &  \tabularnewline
Midrange & 7.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.1777777777778 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.1777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.1777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.1777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.1777777777778 &  &  \tabularnewline
Midmean - Closest Observation & 10.1777777777778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.1777777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.1777777777778 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51355&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]8.91891891891892[/C][C]0.649881587698219[/C][C]13.7239138448411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.5061114775343[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.9054054054054[/C][C]0.641109540959586[/C][C]13.890614374692[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.87837837837838[/C][C]0.636700788733181[/C][C]13.9443495838027[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.95945945945946[/C][C]0.617359387671828[/C][C]14.5125507741077[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.95945945945946[/C][C]0.617359387671828[/C][C]14.5125507741077[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.95945945945946[/C][C]0.617359387671828[/C][C]14.5125507741077[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.87837837837838[/C][C]0.605403504651377[/C][C]14.6652246149302[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.97297297297297[/C][C]0.5848807689382[/C][C]15.3415421561263[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.97297297297297[/C][C]0.5848807689382[/C][C]15.3415421561263[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.97297297297297[/C][C]0.5848807689382[/C][C]15.3415421561263[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.83783783783784[/C][C]0.566897225829101[/C][C]15.5898413948177[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.98648648648649[/C][C]0.535829619776941[/C][C]16.7711641066566[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.98648648648649[/C][C]0.535829619776941[/C][C]16.7711641066566[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.16216216216216[/C][C]0.444651054393115[/C][C]20.6052860364116[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9.35135135135135[/C][C]0.409726447437665[/C][C]22.8234018326924[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.55405405405405[/C][C]0.374661091772583[/C][C]25.5005237102478[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9.77027027027027[/C][C]0.3401696645829[/C][C]28.7217564865760[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9.77027027027027[/C][C]0.3401696645829[/C][C]28.7217564865760[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.77027027027027[/C][C]0.3401696645829[/C][C]28.7217564865760[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9.77027027027027[/C][C]0.3401696645829[/C][C]28.7217564865760[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.77027027027027[/C][C]0.3401696645829[/C][C]28.7217564865760[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]10.0540540540541[/C][C]0.298640565392576[/C][C]33.6660695804589[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]10.3513513513514[/C][C]0.259176230701608[/C][C]39.9394316497679[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]10.0405405405405[/C][C]0.218065260985262[/C][C]46.0437416541056[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]10.0405405405405[/C][C]0.218065260985262[/C][C]46.0437416541056[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.95833333333333[/C][C]0.627498916695347[/C][C]14.2762530659199[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9.01428571428571[/C][C]0.611312560345332[/C][C]14.7457884869788[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9.08823529411765[/C][C]0.594729298584008[/C][C]15.2812974167505[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9.13636363636364[/C][C]0.583729015440244[/C][C]15.6517209093556[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9.1875[/C][C]0.570381294774444[/C][C]16.1076460328756[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9.24193548387097[/C][C]0.554146660505145[/C][C]16.6777789032352[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9.31666666666667[/C][C]0.537567058839666[/C][C]17.3311710854765[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9.37931034482759[/C][C]0.522817293794111[/C][C]17.9399389732529[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9.44642857142857[/C][C]0.504473264487386[/C][C]18.7253304315887[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9.51851851851852[/C][C]0.481481481481482[/C][C]19.7692307692308[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9.61538461538461[/C][C]0.456356022334041[/C][C]21.0699194155619[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9.7[/C][C]0.432600112277906[/C][C]22.4225554379159[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9.79166666666667[/C][C]0.401634882942477[/C][C]24.3795225029521[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9.8695652173913[/C][C]0.385245634235811[/C][C]25.6188891977166[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9.93181818181818[/C][C]0.372690530855497[/C][C]26.6489684055564[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9.97619047619048[/C][C]0.364651991093844[/C][C]27.3581132692158[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]10[/C][C]0.361620285339790[/C][C]27.6533159377486[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]10.0263157894737[/C][C]0.35678117280855[/C][C]28.1021437049141[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]10.0555555555556[/C][C]0.349476807242921[/C][C]28.7731699132926[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]10.0882352941176[/C][C]0.338729004937253[/C][C]29.7826142641266[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]10.125[/C][C]0.323008788455291[/C][C]31.3458963405308[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]10.1333333333333[/C][C]0.313428696664361[/C][C]32.3305856840056[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]10.1071428571429[/C][C]0.310057537390755[/C][C]32.5976363683918[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]10.1153846153846[/C][C]0.315384615384615[/C][C]32.0731707317073[/C][/ROW]
[ROW][C]Median[/C][C]10.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.1777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51355&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 Mean8.918918918918920.64988158769821913.7239138448411
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5061114775343
Winsorized Mean ( 1 / 24 )8.90540540540540.64110954095958613.890614374692
Winsorized Mean ( 2 / 24 )8.878378378378380.63670078873318113.9443495838027
Winsorized Mean ( 3 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 4 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 5 / 24 )8.959459459459460.61735938767182814.5125507741077
Winsorized Mean ( 6 / 24 )8.878378378378380.60540350465137714.6652246149302
Winsorized Mean ( 7 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 8 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 9 / 24 )8.972972972972970.584880768938215.3415421561263
Winsorized Mean ( 10 / 24 )8.837837837837840.56689722582910115.5898413948177
Winsorized Mean ( 11 / 24 )8.986486486486490.53582961977694116.7711641066566
Winsorized Mean ( 12 / 24 )8.986486486486490.53582961977694116.7711641066566
Winsorized Mean ( 13 / 24 )9.162162162162160.44465105439311520.6052860364116
Winsorized Mean ( 14 / 24 )9.351351351351350.40972644743766522.8234018326924
Winsorized Mean ( 15 / 24 )9.554054054054050.37466109177258325.5005237102478
Winsorized Mean ( 16 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 17 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 18 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 19 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 20 / 24 )9.770270270270270.340169664582928.7217564865760
Winsorized Mean ( 21 / 24 )10.05405405405410.29864056539257633.6660695804589
Winsorized Mean ( 22 / 24 )10.35135135135140.25917623070160839.9394316497679
Winsorized Mean ( 23 / 24 )10.04054054054050.21806526098526246.0437416541056
Winsorized Mean ( 24 / 24 )10.04054054054050.21806526098526246.0437416541056
Trimmed Mean ( 1 / 24 )8.958333333333330.62749891669534714.2762530659199
Trimmed Mean ( 2 / 24 )9.014285714285710.61131256034533214.7457884869788
Trimmed Mean ( 3 / 24 )9.088235294117650.59472929858400815.2812974167505
Trimmed Mean ( 4 / 24 )9.136363636363640.58372901544024415.6517209093556
Trimmed Mean ( 5 / 24 )9.18750.57038129477444416.1076460328756
Trimmed Mean ( 6 / 24 )9.241935483870970.55414666050514516.6777789032352
Trimmed Mean ( 7 / 24 )9.316666666666670.53756705883966617.3311710854765
Trimmed Mean ( 8 / 24 )9.379310344827590.52281729379411117.9399389732529
Trimmed Mean ( 9 / 24 )9.446428571428570.50447326448738618.7253304315887
Trimmed Mean ( 10 / 24 )9.518518518518520.48148148148148219.7692307692308
Trimmed Mean ( 11 / 24 )9.615384615384610.45635602233404121.0699194155619
Trimmed Mean ( 12 / 24 )9.70.43260011227790622.4225554379159
Trimmed Mean ( 13 / 24 )9.791666666666670.40163488294247724.3795225029521
Trimmed Mean ( 14 / 24 )9.86956521739130.38524563423581125.6188891977166
Trimmed Mean ( 15 / 24 )9.931818181818180.37269053085549726.6489684055564
Trimmed Mean ( 16 / 24 )9.976190476190480.36465199109384427.3581132692158
Trimmed Mean ( 17 / 24 )100.36162028533979027.6533159377486
Trimmed Mean ( 18 / 24 )10.02631578947370.3567811728085528.1021437049141
Trimmed Mean ( 19 / 24 )10.05555555555560.34947680724292128.7731699132926
Trimmed Mean ( 20 / 24 )10.08823529411760.33872900493725329.7826142641266
Trimmed Mean ( 21 / 24 )10.1250.32300878845529131.3458963405308
Trimmed Mean ( 22 / 24 )10.13333333333330.31342869666436132.3305856840056
Trimmed Mean ( 23 / 24 )10.10714285714290.31005753739075532.5976363683918
Trimmed Mean ( 24 / 24 )10.11538461538460.31538461538461532.0731707317073
Median10.5
Midrange7.5
Midmean - Weighted Average at Xnp10.1777777777778
Midmean - Weighted Average at X(n+1)p10.1777777777778
Midmean - Empirical Distribution Function10.1777777777778
Midmean - Empirical Distribution Function - Averaging10.1777777777778
Midmean - Empirical Distribution Function - Interpolation10.1777777777778
Midmean - Closest Observation10.1777777777778
Midmean - True Basic - Statistics Graphics Toolkit10.1777777777778
Midmean - MS Excel (old versions)10.1777777777778
Number of observations74



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')