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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 computationWed, 21 Oct 2009 14:31:51 -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/21/t125615717177s8l6vd2c8xvja.htm/, Retrieved Wed, 01 May 2024 23:36:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49614, Retrieved Wed, 01 May 2024 23:36:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- R  D      [Univariate Data Series] [SHWW3-2.2] [2009-10-21 19:42:11] [ff6896cd60d3b2257a9a5027c462fa18]
- RMPD          [Central Tendency] [SHWW3-2.3.1] [2009-10-21 20:31:51] [be285953263a374c1f072a85fb5ca13a] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,07
1,25
1,18
1,15
1,23
1,04
1,01
1,14
1,05
1,05
1,12
0,92
1,00
1,19
1,09
1,10
1,08
1,03
1,04
1,21
1,01
1,08
1,11
0,91
1,00
1,13
1,14
1,09
1,03
1,00
0,97
1,12
0,97
1,00
1,09
0,96
0,97
1,03
1,12
1,06
1,02
1,01
1,01
1,05
1,11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49614&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49614&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.065333333333330.011688723738127491.141972143488
Geometric Mean1.06254187061873
Harmonic Mean1.05977913923127
Quadratic Mean1.06815105049177
Winsorized Mean ( 1 / 15 )1.065111111111110.011470745496464992.8545674245292
Winsorized Mean ( 2 / 15 )1.0660.010732749842976899.322169583367
Winsorized Mean ( 3 / 15 )1.065333333333330.0101980390271856104.464527983606
Winsorized Mean ( 4 / 15 )1.064444444444440.00995725995511277106.901341256827
Winsorized Mean ( 5 / 15 )1.061111111111110.00914651902777647116.012562581316
Winsorized Mean ( 6 / 15 )1.063777777777780.00803583444586198132.379255066108
Winsorized Mean ( 7 / 15 )1.063777777777780.00803583444586198132.379255066108
Winsorized Mean ( 8 / 15 )1.0620.00766469012729639138.557460557718
Winsorized Mean ( 9 / 15 )1.060.0072752520869928145.699418704012
Winsorized Mean ( 10 / 15 )1.062222222222220.00687470027915186154.511786563773
Winsorized Mean ( 11 / 15 )1.062222222222220.00687470027915186154.511786563773
Winsorized Mean ( 12 / 15 )1.059555555555560.00637985747248699166.078248632492
Winsorized Mean ( 13 / 15 )1.059555555555560.00637985747248699166.078248632492
Winsorized Mean ( 14 / 15 )1.059555555555560.00528916899351641200.325525021867
Winsorized Mean ( 15 / 15 )1.059555555555560.00416764298325981254.233762299572
Trimmed Mean ( 1 / 15 )1.064651162790700.010841395775955698.2024072169668
Trimmed Mean ( 2 / 15 )1.064146341463410.00999985127789468106.416216790722
Trimmed Mean ( 3 / 15 )1.063076923076920.0094315764911536112.714658474545
Trimmed Mean ( 4 / 15 )1.062162162162160.00896385078474432118.493958419061
Trimmed Mean ( 5 / 15 )1.061428571428570.00843305677548962125.865222977459
Trimmed Mean ( 6 / 15 )1.061515151515150.00804957664190272131.872171511400
Trimmed Mean ( 7 / 15 )1.060967741935480.0079291871162599133.805360673079
Trimmed Mean ( 8 / 15 )1.060344827586210.00772818331784764137.204926950610
Trimmed Mean ( 9 / 15 )1.060.00754851356096398140.424997774613
Trimmed Mean ( 10 / 15 )1.060.00739369100427295143.365471912122
Trimmed Mean ( 11 / 15 )1.059565217391300.00726348441708927145.875609631432
Trimmed Mean ( 12 / 15 )1.059047619047620.00700016196767591151.289016445319
Trimmed Mean ( 13 / 15 )1.059047619047620.00674925756549872156.913202492275
Trimmed Mean ( 14 / 15 )1.058823529411760.00623571030797477169.799987029168
Trimmed Mean ( 15 / 15 )1.058666666666670.00592546294487706178.663958667052
Median1.05
Midrange1.08
Midmean - Weighted Average at Xnp1.05478260869565
Midmean - Weighted Average at X(n+1)p1.06230769230769
Midmean - Empirical Distribution Function1.06230769230769
Midmean - Empirical Distribution Function - Averaging1.06230769230769
Midmean - Empirical Distribution Function - Interpolation1.06230769230769
Midmean - Closest Observation1.06230769230769
Midmean - True Basic - Statistics Graphics Toolkit1.06230769230769
Midmean - MS Excel (old versions)1.06230769230769
Number of observations45

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.06533333333333 & 0.0116887237381274 & 91.141972143488 \tabularnewline
Geometric Mean & 1.06254187061873 &  &  \tabularnewline
Harmonic Mean & 1.05977913923127 &  &  \tabularnewline
Quadratic Mean & 1.06815105049177 &  &  \tabularnewline
Winsorized Mean ( 1 / 15 ) & 1.06511111111111 & 0.0114707454964649 & 92.8545674245292 \tabularnewline
Winsorized Mean ( 2 / 15 ) & 1.066 & 0.0107327498429768 & 99.322169583367 \tabularnewline
Winsorized Mean ( 3 / 15 ) & 1.06533333333333 & 0.0101980390271856 & 104.464527983606 \tabularnewline
Winsorized Mean ( 4 / 15 ) & 1.06444444444444 & 0.00995725995511277 & 106.901341256827 \tabularnewline
Winsorized Mean ( 5 / 15 ) & 1.06111111111111 & 0.00914651902777647 & 116.012562581316 \tabularnewline
Winsorized Mean ( 6 / 15 ) & 1.06377777777778 & 0.00803583444586198 & 132.379255066108 \tabularnewline
Winsorized Mean ( 7 / 15 ) & 1.06377777777778 & 0.00803583444586198 & 132.379255066108 \tabularnewline
Winsorized Mean ( 8 / 15 ) & 1.062 & 0.00766469012729639 & 138.557460557718 \tabularnewline
Winsorized Mean ( 9 / 15 ) & 1.06 & 0.0072752520869928 & 145.699418704012 \tabularnewline
Winsorized Mean ( 10 / 15 ) & 1.06222222222222 & 0.00687470027915186 & 154.511786563773 \tabularnewline
Winsorized Mean ( 11 / 15 ) & 1.06222222222222 & 0.00687470027915186 & 154.511786563773 \tabularnewline
Winsorized Mean ( 12 / 15 ) & 1.05955555555556 & 0.00637985747248699 & 166.078248632492 \tabularnewline
Winsorized Mean ( 13 / 15 ) & 1.05955555555556 & 0.00637985747248699 & 166.078248632492 \tabularnewline
Winsorized Mean ( 14 / 15 ) & 1.05955555555556 & 0.00528916899351641 & 200.325525021867 \tabularnewline
Winsorized Mean ( 15 / 15 ) & 1.05955555555556 & 0.00416764298325981 & 254.233762299572 \tabularnewline
Trimmed Mean ( 1 / 15 ) & 1.06465116279070 & 0.0108413957759556 & 98.2024072169668 \tabularnewline
Trimmed Mean ( 2 / 15 ) & 1.06414634146341 & 0.00999985127789468 & 106.416216790722 \tabularnewline
Trimmed Mean ( 3 / 15 ) & 1.06307692307692 & 0.0094315764911536 & 112.714658474545 \tabularnewline
Trimmed Mean ( 4 / 15 ) & 1.06216216216216 & 0.00896385078474432 & 118.493958419061 \tabularnewline
Trimmed Mean ( 5 / 15 ) & 1.06142857142857 & 0.00843305677548962 & 125.865222977459 \tabularnewline
Trimmed Mean ( 6 / 15 ) & 1.06151515151515 & 0.00804957664190272 & 131.872171511400 \tabularnewline
Trimmed Mean ( 7 / 15 ) & 1.06096774193548 & 0.0079291871162599 & 133.805360673079 \tabularnewline
Trimmed Mean ( 8 / 15 ) & 1.06034482758621 & 0.00772818331784764 & 137.204926950610 \tabularnewline
Trimmed Mean ( 9 / 15 ) & 1.06 & 0.00754851356096398 & 140.424997774613 \tabularnewline
Trimmed Mean ( 10 / 15 ) & 1.06 & 0.00739369100427295 & 143.365471912122 \tabularnewline
Trimmed Mean ( 11 / 15 ) & 1.05956521739130 & 0.00726348441708927 & 145.875609631432 \tabularnewline
Trimmed Mean ( 12 / 15 ) & 1.05904761904762 & 0.00700016196767591 & 151.289016445319 \tabularnewline
Trimmed Mean ( 13 / 15 ) & 1.05904761904762 & 0.00674925756549872 & 156.913202492275 \tabularnewline
Trimmed Mean ( 14 / 15 ) & 1.05882352941176 & 0.00623571030797477 & 169.799987029168 \tabularnewline
Trimmed Mean ( 15 / 15 ) & 1.05866666666667 & 0.00592546294487706 & 178.663958667052 \tabularnewline
Median & 1.05 &  &  \tabularnewline
Midrange & 1.08 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.05478260869565 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.06230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.06230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.06230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.06230769230769 &  &  \tabularnewline
Midmean - Closest Observation & 1.06230769230769 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.06230769230769 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.06230769230769 &  &  \tabularnewline
Number of observations & 45 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49614&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]1.06533333333333[/C][C]0.0116887237381274[/C][C]91.141972143488[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.06254187061873[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.05977913923127[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.06815105049177[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 15 )[/C][C]1.06511111111111[/C][C]0.0114707454964649[/C][C]92.8545674245292[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 15 )[/C][C]1.066[/C][C]0.0107327498429768[/C][C]99.322169583367[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 15 )[/C][C]1.06533333333333[/C][C]0.0101980390271856[/C][C]104.464527983606[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 15 )[/C][C]1.06444444444444[/C][C]0.00995725995511277[/C][C]106.901341256827[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 15 )[/C][C]1.06111111111111[/C][C]0.00914651902777647[/C][C]116.012562581316[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 15 )[/C][C]1.06377777777778[/C][C]0.00803583444586198[/C][C]132.379255066108[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 15 )[/C][C]1.06377777777778[/C][C]0.00803583444586198[/C][C]132.379255066108[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 15 )[/C][C]1.062[/C][C]0.00766469012729639[/C][C]138.557460557718[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 15 )[/C][C]1.06[/C][C]0.0072752520869928[/C][C]145.699418704012[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 15 )[/C][C]1.06222222222222[/C][C]0.00687470027915186[/C][C]154.511786563773[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 15 )[/C][C]1.06222222222222[/C][C]0.00687470027915186[/C][C]154.511786563773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 15 )[/C][C]1.05955555555556[/C][C]0.00637985747248699[/C][C]166.078248632492[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 15 )[/C][C]1.05955555555556[/C][C]0.00637985747248699[/C][C]166.078248632492[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 15 )[/C][C]1.05955555555556[/C][C]0.00528916899351641[/C][C]200.325525021867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 15 )[/C][C]1.05955555555556[/C][C]0.00416764298325981[/C][C]254.233762299572[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 15 )[/C][C]1.06465116279070[/C][C]0.0108413957759556[/C][C]98.2024072169668[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 15 )[/C][C]1.06414634146341[/C][C]0.00999985127789468[/C][C]106.416216790722[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 15 )[/C][C]1.06307692307692[/C][C]0.0094315764911536[/C][C]112.714658474545[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 15 )[/C][C]1.06216216216216[/C][C]0.00896385078474432[/C][C]118.493958419061[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 15 )[/C][C]1.06142857142857[/C][C]0.00843305677548962[/C][C]125.865222977459[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 15 )[/C][C]1.06151515151515[/C][C]0.00804957664190272[/C][C]131.872171511400[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 15 )[/C][C]1.06096774193548[/C][C]0.0079291871162599[/C][C]133.805360673079[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 15 )[/C][C]1.06034482758621[/C][C]0.00772818331784764[/C][C]137.204926950610[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 15 )[/C][C]1.06[/C][C]0.00754851356096398[/C][C]140.424997774613[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 15 )[/C][C]1.06[/C][C]0.00739369100427295[/C][C]143.365471912122[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 15 )[/C][C]1.05956521739130[/C][C]0.00726348441708927[/C][C]145.875609631432[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 15 )[/C][C]1.05904761904762[/C][C]0.00700016196767591[/C][C]151.289016445319[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 15 )[/C][C]1.05904761904762[/C][C]0.00674925756549872[/C][C]156.913202492275[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 15 )[/C][C]1.05882352941176[/C][C]0.00623571030797477[/C][C]169.799987029168[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 15 )[/C][C]1.05866666666667[/C][C]0.00592546294487706[/C][C]178.663958667052[/C][/ROW]
[ROW][C]Median[/C][C]1.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.05478260869565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.06230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]45[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49614&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 Mean1.065333333333330.011688723738127491.141972143488
Geometric Mean1.06254187061873
Harmonic Mean1.05977913923127
Quadratic Mean1.06815105049177
Winsorized Mean ( 1 / 15 )1.065111111111110.011470745496464992.8545674245292
Winsorized Mean ( 2 / 15 )1.0660.010732749842976899.322169583367
Winsorized Mean ( 3 / 15 )1.065333333333330.0101980390271856104.464527983606
Winsorized Mean ( 4 / 15 )1.064444444444440.00995725995511277106.901341256827
Winsorized Mean ( 5 / 15 )1.061111111111110.00914651902777647116.012562581316
Winsorized Mean ( 6 / 15 )1.063777777777780.00803583444586198132.379255066108
Winsorized Mean ( 7 / 15 )1.063777777777780.00803583444586198132.379255066108
Winsorized Mean ( 8 / 15 )1.0620.00766469012729639138.557460557718
Winsorized Mean ( 9 / 15 )1.060.0072752520869928145.699418704012
Winsorized Mean ( 10 / 15 )1.062222222222220.00687470027915186154.511786563773
Winsorized Mean ( 11 / 15 )1.062222222222220.00687470027915186154.511786563773
Winsorized Mean ( 12 / 15 )1.059555555555560.00637985747248699166.078248632492
Winsorized Mean ( 13 / 15 )1.059555555555560.00637985747248699166.078248632492
Winsorized Mean ( 14 / 15 )1.059555555555560.00528916899351641200.325525021867
Winsorized Mean ( 15 / 15 )1.059555555555560.00416764298325981254.233762299572
Trimmed Mean ( 1 / 15 )1.064651162790700.010841395775955698.2024072169668
Trimmed Mean ( 2 / 15 )1.064146341463410.00999985127789468106.416216790722
Trimmed Mean ( 3 / 15 )1.063076923076920.0094315764911536112.714658474545
Trimmed Mean ( 4 / 15 )1.062162162162160.00896385078474432118.493958419061
Trimmed Mean ( 5 / 15 )1.061428571428570.00843305677548962125.865222977459
Trimmed Mean ( 6 / 15 )1.061515151515150.00804957664190272131.872171511400
Trimmed Mean ( 7 / 15 )1.060967741935480.0079291871162599133.805360673079
Trimmed Mean ( 8 / 15 )1.060344827586210.00772818331784764137.204926950610
Trimmed Mean ( 9 / 15 )1.060.00754851356096398140.424997774613
Trimmed Mean ( 10 / 15 )1.060.00739369100427295143.365471912122
Trimmed Mean ( 11 / 15 )1.059565217391300.00726348441708927145.875609631432
Trimmed Mean ( 12 / 15 )1.059047619047620.00700016196767591151.289016445319
Trimmed Mean ( 13 / 15 )1.059047619047620.00674925756549872156.913202492275
Trimmed Mean ( 14 / 15 )1.058823529411760.00623571030797477169.799987029168
Trimmed Mean ( 15 / 15 )1.058666666666670.00592546294487706178.663958667052
Median1.05
Midrange1.08
Midmean - Weighted Average at Xnp1.05478260869565
Midmean - Weighted Average at X(n+1)p1.06230769230769
Midmean - Empirical Distribution Function1.06230769230769
Midmean - Empirical Distribution Function - Averaging1.06230769230769
Midmean - Empirical Distribution Function - Interpolation1.06230769230769
Midmean - Closest Observation1.06230769230769
Midmean - True Basic - Statistics Graphics Toolkit1.06230769230769
Midmean - MS Excel (old versions)1.06230769230769
Number of observations45



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')