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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 27 Aug 2016 10:47:34 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/27/t1472291284s7twu7dfjek0bhp.htm/, Retrieved Sat, 18 May 2024 07:09:06 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 18 May 2024 07:09:06 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
6.8
6.3
6.4
6.2
6.9
6.4
6.3
6.8
6.9
6.7
6.9
6.9
6.3
6.1
6.2
6.8
6.5
7.6
6.3
7.1
6.8
7.3
6.4
6.8
7.2
6.4
6.6
6.8
6.1
6.5
6.4
6
6
7.3
6.1
6.7
6.4
5.8
6.9
7
7.3
5.9
6.2
6.8
7
5.9
6.1
5.7
7.1
5.8
7.4
6.8
6.8
7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.587037037037040.0624475347252838105.481138142833
Geometric Mean6.57130197310141
Harmonic Mean6.5555323182495
Quadratic Mean6.60270707670276
Winsorized Mean ( 1 / 18 )6.585185185185180.0609388122285866108.062250384592
Winsorized Mean ( 2 / 18 )6.581481481481480.0600532069043559109.594171914308
Winsorized Mean ( 3 / 18 )6.587037037037040.0587575944090873112.105287891403
Winsorized Mean ( 4 / 18 )6.587037037037040.0587575944090873112.105287891403
Winsorized Mean ( 5 / 18 )6.587037037037040.0547560689606589120.297843911507
Winsorized Mean ( 6 / 18 )6.575925925925930.0525343177701226125.173909266331
Winsorized Mean ( 7 / 18 )6.588888888888890.0499941762273403131.793128442141
Winsorized Mean ( 8 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 9 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 10 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 11 / 18 )6.574074074074070.0402807395876411163.206389489708
Winsorized Mean ( 12 / 18 )6.574074074074080.0402807395876411163.206389489708
Winsorized Mean ( 13 / 18 )6.574074074074070.0402807395876411163.206389489708
Winsorized Mean ( 14 / 18 )6.60.0359555591835041183.559932034877
Winsorized Mean ( 15 / 18 )6.60.0359555591835041183.559932034877
Winsorized Mean ( 16 / 18 )6.570370370370370.0315707617157928208.115674544642
Winsorized Mean ( 17 / 18 )6.570370370370370.0315707617157928208.115674544641
Winsorized Mean ( 18 / 18 )6.60370370370370.0264301570237528249.854879703097
Trimmed Mean ( 1 / 18 )6.584615384615380.0593697806555456110.908534811983
Trimmed Mean ( 2 / 18 )6.5840.0573823552486089114.739103535832
Trimmed Mean ( 3 / 18 )6.585416666666670.0554630398411057118.735227739645
Trimmed Mean ( 4 / 18 )6.584782608695650.0536554935983141122.723362830131
Trimmed Mean ( 5 / 18 )6.584090909090910.0512984862498312128.348639315114
Trimmed Mean ( 6 / 18 )6.583333333333330.0497282588574876132.386162004988
Trimmed Mean ( 7 / 18 )6.5850.0483775217987095136.116935203896
Trimmed Mean ( 8 / 18 )6.584210526315790.0473367999402607139.092852381764
Trimmed Mean ( 9 / 18 )6.586111111111110.0466586349853367141.155246251437
Trimmed Mean ( 10 / 18 )6.588235294117650.0456220046280389144.409158427654
Trimmed Mean ( 11 / 18 )6.5906250.0440764033772882149.527286597891
Trimmed Mean ( 12 / 18 )6.593333333333330.0439260960672447150.100599043445
Trimmed Mean ( 13 / 18 )6.596428571428570.0434863424576923151.68966159539
Trimmed Mean ( 14 / 18 )6.60.042607330535773154.902922032598
Trimmed Mean ( 15 / 18 )6.60.0425628265379374155.064889643014
Trimmed Mean ( 16 / 18 )6.60.0421294644505692156.659954881312
Trimmed Mean ( 17 / 18 )6.6050.042596639353481155.059180729952
Trimmed Mean ( 18 / 18 )6.611111111111110.0426942993308499154.847631059121
Median6.65
Midrange6.65
Midmean - Weighted Average at Xnp6.590625
Midmean - Weighted Average at X(n+1)p6.590625
Midmean - Empirical Distribution Function6.590625
Midmean - Empirical Distribution Function - Averaging6.590625
Midmean - Empirical Distribution Function - Interpolation6.63103448275862
Midmean - Closest Observation6.590625
Midmean - True Basic - Statistics Graphics Toolkit6.590625
Midmean - MS Excel (old versions)6.590625
Number of observations54

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.58703703703704 & 0.0624475347252838 & 105.481138142833 \tabularnewline
Geometric Mean & 6.57130197310141 &  &  \tabularnewline
Harmonic Mean & 6.5555323182495 &  &  \tabularnewline
Quadratic Mean & 6.60270707670276 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 6.58518518518518 & 0.0609388122285866 & 108.062250384592 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 6.58148148148148 & 0.0600532069043559 & 109.594171914308 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 6.58703703703704 & 0.0587575944090873 & 112.105287891403 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 6.58703703703704 & 0.0587575944090873 & 112.105287891403 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 6.58703703703704 & 0.0547560689606589 & 120.297843911507 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 6.57592592592593 & 0.0525343177701226 & 125.173909266331 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 6.58888888888889 & 0.0499941762273403 & 131.793128442141 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 6.57407407407407 & 0.047302141166612 & 138.980475554336 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 6.57407407407407 & 0.047302141166612 & 138.980475554336 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 6.57407407407407 & 0.047302141166612 & 138.980475554336 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 6.57407407407407 & 0.0402807395876411 & 163.206389489708 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 6.57407407407408 & 0.0402807395876411 & 163.206389489708 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 6.57407407407407 & 0.0402807395876411 & 163.206389489708 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 6.6 & 0.0359555591835041 & 183.559932034877 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 6.6 & 0.0359555591835041 & 183.559932034877 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 6.57037037037037 & 0.0315707617157928 & 208.115674544642 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 6.57037037037037 & 0.0315707617157928 & 208.115674544641 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 6.6037037037037 & 0.0264301570237528 & 249.854879703097 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 6.58461538461538 & 0.0593697806555456 & 110.908534811983 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 6.584 & 0.0573823552486089 & 114.739103535832 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 6.58541666666667 & 0.0554630398411057 & 118.735227739645 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 6.58478260869565 & 0.0536554935983141 & 122.723362830131 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 6.58409090909091 & 0.0512984862498312 & 128.348639315114 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 6.58333333333333 & 0.0497282588574876 & 132.386162004988 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 6.585 & 0.0483775217987095 & 136.116935203896 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 6.58421052631579 & 0.0473367999402607 & 139.092852381764 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 6.58611111111111 & 0.0466586349853367 & 141.155246251437 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 6.58823529411765 & 0.0456220046280389 & 144.409158427654 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 6.590625 & 0.0440764033772882 & 149.527286597891 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 6.59333333333333 & 0.0439260960672447 & 150.100599043445 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 6.59642857142857 & 0.0434863424576923 & 151.68966159539 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 6.6 & 0.042607330535773 & 154.902922032598 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 6.6 & 0.0425628265379374 & 155.064889643014 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 6.6 & 0.0421294644505692 & 156.659954881312 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 6.605 & 0.042596639353481 & 155.059180729952 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 6.61111111111111 & 0.0426942993308499 & 154.847631059121 \tabularnewline
Median & 6.65 &  &  \tabularnewline
Midrange & 6.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.590625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.590625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.590625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.590625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.63103448275862 &  &  \tabularnewline
Midmean - Closest Observation & 6.590625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.590625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.590625 &  &  \tabularnewline
Number of observations & 54 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]6.58703703703704[/C][C]0.0624475347252838[/C][C]105.481138142833[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.57130197310141[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.5555323182495[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.60270707670276[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]6.58518518518518[/C][C]0.0609388122285866[/C][C]108.062250384592[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]6.58148148148148[/C][C]0.0600532069043559[/C][C]109.594171914308[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]6.58703703703704[/C][C]0.0587575944090873[/C][C]112.105287891403[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]6.58703703703704[/C][C]0.0587575944090873[/C][C]112.105287891403[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]6.58703703703704[/C][C]0.0547560689606589[/C][C]120.297843911507[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]6.57592592592593[/C][C]0.0525343177701226[/C][C]125.173909266331[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]6.58888888888889[/C][C]0.0499941762273403[/C][C]131.793128442141[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]6.57407407407407[/C][C]0.047302141166612[/C][C]138.980475554336[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]6.57407407407407[/C][C]0.047302141166612[/C][C]138.980475554336[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]6.57407407407407[/C][C]0.047302141166612[/C][C]138.980475554336[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]6.57407407407407[/C][C]0.0402807395876411[/C][C]163.206389489708[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]6.57407407407408[/C][C]0.0402807395876411[/C][C]163.206389489708[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]6.57407407407407[/C][C]0.0402807395876411[/C][C]163.206389489708[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]6.6[/C][C]0.0359555591835041[/C][C]183.559932034877[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]6.6[/C][C]0.0359555591835041[/C][C]183.559932034877[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]6.57037037037037[/C][C]0.0315707617157928[/C][C]208.115674544642[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]6.57037037037037[/C][C]0.0315707617157928[/C][C]208.115674544641[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]6.6037037037037[/C][C]0.0264301570237528[/C][C]249.854879703097[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]6.58461538461538[/C][C]0.0593697806555456[/C][C]110.908534811983[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]6.584[/C][C]0.0573823552486089[/C][C]114.739103535832[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]6.58541666666667[/C][C]0.0554630398411057[/C][C]118.735227739645[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]6.58478260869565[/C][C]0.0536554935983141[/C][C]122.723362830131[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]6.58409090909091[/C][C]0.0512984862498312[/C][C]128.348639315114[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]6.58333333333333[/C][C]0.0497282588574876[/C][C]132.386162004988[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]6.585[/C][C]0.0483775217987095[/C][C]136.116935203896[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]6.58421052631579[/C][C]0.0473367999402607[/C][C]139.092852381764[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]6.58611111111111[/C][C]0.0466586349853367[/C][C]141.155246251437[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]6.58823529411765[/C][C]0.0456220046280389[/C][C]144.409158427654[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]6.590625[/C][C]0.0440764033772882[/C][C]149.527286597891[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]6.59333333333333[/C][C]0.0439260960672447[/C][C]150.100599043445[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]6.59642857142857[/C][C]0.0434863424576923[/C][C]151.68966159539[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]6.6[/C][C]0.042607330535773[/C][C]154.902922032598[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]6.6[/C][C]0.0425628265379374[/C][C]155.064889643014[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]6.6[/C][C]0.0421294644505692[/C][C]156.659954881312[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]6.605[/C][C]0.042596639353481[/C][C]155.059180729952[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]6.61111111111111[/C][C]0.0426942993308499[/C][C]154.847631059121[/C][/ROW]
[ROW][C]Median[/C][C]6.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.63103448275862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.590625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]54[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean6.587037037037040.0624475347252838105.481138142833
Geometric Mean6.57130197310141
Harmonic Mean6.5555323182495
Quadratic Mean6.60270707670276
Winsorized Mean ( 1 / 18 )6.585185185185180.0609388122285866108.062250384592
Winsorized Mean ( 2 / 18 )6.581481481481480.0600532069043559109.594171914308
Winsorized Mean ( 3 / 18 )6.587037037037040.0587575944090873112.105287891403
Winsorized Mean ( 4 / 18 )6.587037037037040.0587575944090873112.105287891403
Winsorized Mean ( 5 / 18 )6.587037037037040.0547560689606589120.297843911507
Winsorized Mean ( 6 / 18 )6.575925925925930.0525343177701226125.173909266331
Winsorized Mean ( 7 / 18 )6.588888888888890.0499941762273403131.793128442141
Winsorized Mean ( 8 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 9 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 10 / 18 )6.574074074074070.047302141166612138.980475554336
Winsorized Mean ( 11 / 18 )6.574074074074070.0402807395876411163.206389489708
Winsorized Mean ( 12 / 18 )6.574074074074080.0402807395876411163.206389489708
Winsorized Mean ( 13 / 18 )6.574074074074070.0402807395876411163.206389489708
Winsorized Mean ( 14 / 18 )6.60.0359555591835041183.559932034877
Winsorized Mean ( 15 / 18 )6.60.0359555591835041183.559932034877
Winsorized Mean ( 16 / 18 )6.570370370370370.0315707617157928208.115674544642
Winsorized Mean ( 17 / 18 )6.570370370370370.0315707617157928208.115674544641
Winsorized Mean ( 18 / 18 )6.60370370370370.0264301570237528249.854879703097
Trimmed Mean ( 1 / 18 )6.584615384615380.0593697806555456110.908534811983
Trimmed Mean ( 2 / 18 )6.5840.0573823552486089114.739103535832
Trimmed Mean ( 3 / 18 )6.585416666666670.0554630398411057118.735227739645
Trimmed Mean ( 4 / 18 )6.584782608695650.0536554935983141122.723362830131
Trimmed Mean ( 5 / 18 )6.584090909090910.0512984862498312128.348639315114
Trimmed Mean ( 6 / 18 )6.583333333333330.0497282588574876132.386162004988
Trimmed Mean ( 7 / 18 )6.5850.0483775217987095136.116935203896
Trimmed Mean ( 8 / 18 )6.584210526315790.0473367999402607139.092852381764
Trimmed Mean ( 9 / 18 )6.586111111111110.0466586349853367141.155246251437
Trimmed Mean ( 10 / 18 )6.588235294117650.0456220046280389144.409158427654
Trimmed Mean ( 11 / 18 )6.5906250.0440764033772882149.527286597891
Trimmed Mean ( 12 / 18 )6.593333333333330.0439260960672447150.100599043445
Trimmed Mean ( 13 / 18 )6.596428571428570.0434863424576923151.68966159539
Trimmed Mean ( 14 / 18 )6.60.042607330535773154.902922032598
Trimmed Mean ( 15 / 18 )6.60.0425628265379374155.064889643014
Trimmed Mean ( 16 / 18 )6.60.0421294644505692156.659954881312
Trimmed Mean ( 17 / 18 )6.6050.042596639353481155.059180729952
Trimmed Mean ( 18 / 18 )6.611111111111110.0426942993308499154.847631059121
Median6.65
Midrange6.65
Midmean - Weighted Average at Xnp6.590625
Midmean - Weighted Average at X(n+1)p6.590625
Midmean - Empirical Distribution Function6.590625
Midmean - Empirical Distribution Function - Averaging6.590625
Midmean - Empirical Distribution Function - Interpolation6.63103448275862
Midmean - Closest Observation6.590625
Midmean - True Basic - Statistics Graphics Toolkit6.590625
Midmean - MS Excel (old versions)6.590625
Number of observations54



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')