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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 10:30:44 -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/t12561426806nno2dfd9rqwf8p.htm/, Retrieved Thu, 02 May 2024 05:56:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49488, Retrieved Thu, 02 May 2024 05:56:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid vrouwen] [2009-10-12 19:50:51] [a94022e7c2399c0f4d62eea578db3411]
- RMPD  [Central Tendency] [WS3Deel2Nieuwereeks] [2009-10-21 16:15:03] [a94022e7c2399c0f4d62eea578db3411]
-           [Central Tendency] [WS3-Deel3-CentTen] [2009-10-21 16:30:44] [30970b478e356ce7f8c2e9fca280b230] [Current]
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Dataseries X:
19
17.7
16.7
16.8
17.3
17.4
17.3
16.6
16.4
16.1
17.6
17.8
17.8
17.3
16.9
17.2
17.5
17.6
17.4
17.2
16.9
16.3
16.7
16.6
16.5
16.2
16
16.1
16.3
16.2
16
16.2
15.6
14.7
15.1
14.7
14.1
14.2
14.1
14.5
14.7
14.4
13.5
12.9
12.3
13
15.4
16
15.2
14
13.3
14
15.4
16.1
16.1
15.4
14.6
14.8
16.1
16.6




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49488&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49488&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49488&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.87333333333330.18564084556069585.5056078062498
Geometric Mean15.8069664050772
Harmonic Mean15.7382051290173
Quadratic Mean15.9372519588541
Winsorized Mean ( 1 / 20 )15.86333333333330.177871385431189.1842906316044
Winsorized Mean ( 2 / 20 )15.86666666666670.17694307339962689.6710244815958
Winsorized Mean ( 3 / 20 )15.87666666666670.17206565995892392.2709776631599
Winsorized Mean ( 4 / 20 )15.88333333333330.16758784974543294.7761628152655
Winsorized Mean ( 5 / 20 )15.9250.158250052436153100.631878188003
Winsorized Mean ( 6 / 20 )15.9150.156494526176361101.696847735521
Winsorized Mean ( 7 / 20 )15.9150.152137779511870104.609125038257
Winsorized Mean ( 8 / 20 )15.9150.152137779511870104.609125038257
Winsorized Mean ( 9 / 20 )15.9150.146692826377892108.492012820052
Winsorized Mean ( 10 / 20 )15.94833333333330.140267937041786113.699065300877
Winsorized Mean ( 11 / 20 )15.96666666666670.136887653771912116.640662811498
Winsorized Mean ( 12 / 20 )15.96666666666670.13002969384184122.792465281719
Winsorized Mean ( 13 / 20 )15.98833333333330.126224883761494126.665462917311
Winsorized Mean ( 14 / 20 )15.91833333333330.115457617304347137.871659791597
Winsorized Mean ( 15 / 20 )15.91833333333330.115457617304347137.871659791597
Winsorized Mean ( 16 / 20 )15.91833333333330.106921262192565148.879025620409
Winsorized Mean ( 17 / 20 )15.9750.088254415231815181.010773886372
Winsorized Mean ( 18 / 20 )16.0050.0832742728564712192.196214400883
Winsorized Mean ( 19 / 20 )16.03666666666670.0686416497679254233.628805847266
Winsorized Mean ( 20 / 20 )16.03666666666670.0686416497679254233.628805847266
Trimmed Mean ( 1 / 20 )15.88103448275860.17343992888766291.5650426323966
Trimmed Mean ( 2 / 20 )15.90.16793242301979394.6809419770355
Trimmed Mean ( 3 / 20 )15.91851851851850.16168820393128498.451947213686
Trimmed Mean ( 4 / 20 )15.93461538461540.156288123322242101.956662130754
Trimmed Mean ( 5 / 20 )15.950.151273505510343105.438159485961
Trimmed Mean ( 6 / 20 )15.956250.148183631825970107.678896807843
Trimmed Mean ( 7 / 20 )15.96521739130430.144670787068295110.355502412299
Trimmed Mean ( 8 / 20 )15.9750.141313866550642113.046230988769
Trimmed Mean ( 9 / 20 )15.98571428571430.136811688809071116.844652857281
Trimmed Mean ( 10 / 20 )15.99750.132311186223992120.908144326644
Trimmed Mean ( 11 / 20 )16.00526315789470.128064004735822124.978624484775
Trimmed Mean ( 12 / 20 )16.01111111111110.123170921234448129.990999098196
Trimmed Mean ( 13 / 20 )16.01764705882350.118326912650139135.367742638426
Trimmed Mean ( 14 / 20 )16.0218750.112588171093420142.30513600497
Trimmed Mean ( 15 / 20 )16.03666666666670.107477164998750149.209989553159
Trimmed Mean ( 16 / 20 )16.05357142857140.0996663936473862161.073064260437
Trimmed Mean ( 17 / 20 )16.07307692307690.0909027700868761176.816140011089
Trimmed Mean ( 18 / 20 )16.08750.085404514865552188.368261623238
Trimmed Mean ( 19 / 20 )16.10.0786795792469443204.627428795322
Trimmed Mean ( 20 / 20 )16.110.0746571109173555215.786544671325
Median16.1
Midrange15.65
Midmean - Weighted Average at Xnp15.9818181818182
Midmean - Weighted Average at X(n+1)p15.9818181818182
Midmean - Empirical Distribution Function15.9818181818182
Midmean - Empirical Distribution Function - Averaging15.9818181818182
Midmean - Empirical Distribution Function - Interpolation15.9818181818182
Midmean - Closest Observation15.9818181818182
Midmean - True Basic - Statistics Graphics Toolkit15.9818181818182
Midmean - MS Excel (old versions)15.9818181818182
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.8733333333333 & 0.185640845560695 & 85.5056078062498 \tabularnewline
Geometric Mean & 15.8069664050772 &  &  \tabularnewline
Harmonic Mean & 15.7382051290173 &  &  \tabularnewline
Quadratic Mean & 15.9372519588541 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 15.8633333333333 & 0.1778713854311 & 89.1842906316044 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 15.8666666666667 & 0.176943073399626 & 89.6710244815958 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 15.8766666666667 & 0.172065659958923 & 92.2709776631599 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 15.8833333333333 & 0.167587849745432 & 94.7761628152655 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 15.925 & 0.158250052436153 & 100.631878188003 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 15.915 & 0.156494526176361 & 101.696847735521 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 15.915 & 0.152137779511870 & 104.609125038257 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 15.915 & 0.152137779511870 & 104.609125038257 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 15.915 & 0.146692826377892 & 108.492012820052 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 15.9483333333333 & 0.140267937041786 & 113.699065300877 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 15.9666666666667 & 0.136887653771912 & 116.640662811498 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 15.9666666666667 & 0.13002969384184 & 122.792465281719 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 15.9883333333333 & 0.126224883761494 & 126.665462917311 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 15.9183333333333 & 0.115457617304347 & 137.871659791597 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 15.9183333333333 & 0.115457617304347 & 137.871659791597 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 15.9183333333333 & 0.106921262192565 & 148.879025620409 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 15.975 & 0.088254415231815 & 181.010773886372 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 16.005 & 0.0832742728564712 & 192.196214400883 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 16.0366666666667 & 0.0686416497679254 & 233.628805847266 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 16.0366666666667 & 0.0686416497679254 & 233.628805847266 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 15.8810344827586 & 0.173439928887662 & 91.5650426323966 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 15.9 & 0.167932423019793 & 94.6809419770355 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 15.9185185185185 & 0.161688203931284 & 98.451947213686 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 15.9346153846154 & 0.156288123322242 & 101.956662130754 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 15.95 & 0.151273505510343 & 105.438159485961 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 15.95625 & 0.148183631825970 & 107.678896807843 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 15.9652173913043 & 0.144670787068295 & 110.355502412299 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 15.975 & 0.141313866550642 & 113.046230988769 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 15.9857142857143 & 0.136811688809071 & 116.844652857281 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 15.9975 & 0.132311186223992 & 120.908144326644 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 16.0052631578947 & 0.128064004735822 & 124.978624484775 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 16.0111111111111 & 0.123170921234448 & 129.990999098196 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 16.0176470588235 & 0.118326912650139 & 135.367742638426 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 16.021875 & 0.112588171093420 & 142.30513600497 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 16.0366666666667 & 0.107477164998750 & 149.209989553159 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 16.0535714285714 & 0.0996663936473862 & 161.073064260437 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 16.0730769230769 & 0.0909027700868761 & 176.816140011089 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 16.0875 & 0.085404514865552 & 188.368261623238 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 16.1 & 0.0786795792469443 & 204.627428795322 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 16.11 & 0.0746571109173555 & 215.786544671325 \tabularnewline
Median & 16.1 &  &  \tabularnewline
Midrange & 15.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.9818181818182 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.9818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.9818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.9818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.9818181818182 &  &  \tabularnewline
Midmean - Closest Observation & 15.9818181818182 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.9818181818182 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.9818181818182 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49488&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]15.8733333333333[/C][C]0.185640845560695[/C][C]85.5056078062498[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.8069664050772[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.7382051290173[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.9372519588541[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]15.8633333333333[/C][C]0.1778713854311[/C][C]89.1842906316044[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]15.8666666666667[/C][C]0.176943073399626[/C][C]89.6710244815958[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]15.8766666666667[/C][C]0.172065659958923[/C][C]92.2709776631599[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]15.8833333333333[/C][C]0.167587849745432[/C][C]94.7761628152655[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]15.925[/C][C]0.158250052436153[/C][C]100.631878188003[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]15.915[/C][C]0.156494526176361[/C][C]101.696847735521[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]15.915[/C][C]0.152137779511870[/C][C]104.609125038257[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]15.915[/C][C]0.152137779511870[/C][C]104.609125038257[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]15.915[/C][C]0.146692826377892[/C][C]108.492012820052[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]15.9483333333333[/C][C]0.140267937041786[/C][C]113.699065300877[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]15.9666666666667[/C][C]0.136887653771912[/C][C]116.640662811498[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]15.9666666666667[/C][C]0.13002969384184[/C][C]122.792465281719[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]15.9883333333333[/C][C]0.126224883761494[/C][C]126.665462917311[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]15.9183333333333[/C][C]0.115457617304347[/C][C]137.871659791597[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]15.9183333333333[/C][C]0.115457617304347[/C][C]137.871659791597[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]15.9183333333333[/C][C]0.106921262192565[/C][C]148.879025620409[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]15.975[/C][C]0.088254415231815[/C][C]181.010773886372[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]16.005[/C][C]0.0832742728564712[/C][C]192.196214400883[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]16.0366666666667[/C][C]0.0686416497679254[/C][C]233.628805847266[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]16.0366666666667[/C][C]0.0686416497679254[/C][C]233.628805847266[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]15.8810344827586[/C][C]0.173439928887662[/C][C]91.5650426323966[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]15.9[/C][C]0.167932423019793[/C][C]94.6809419770355[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]15.9185185185185[/C][C]0.161688203931284[/C][C]98.451947213686[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]15.9346153846154[/C][C]0.156288123322242[/C][C]101.956662130754[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]15.95[/C][C]0.151273505510343[/C][C]105.438159485961[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]15.95625[/C][C]0.148183631825970[/C][C]107.678896807843[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]15.9652173913043[/C][C]0.144670787068295[/C][C]110.355502412299[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]15.975[/C][C]0.141313866550642[/C][C]113.046230988769[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]15.9857142857143[/C][C]0.136811688809071[/C][C]116.844652857281[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]15.9975[/C][C]0.132311186223992[/C][C]120.908144326644[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]16.0052631578947[/C][C]0.128064004735822[/C][C]124.978624484775[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]16.0111111111111[/C][C]0.123170921234448[/C][C]129.990999098196[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]16.0176470588235[/C][C]0.118326912650139[/C][C]135.367742638426[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]16.021875[/C][C]0.112588171093420[/C][C]142.30513600497[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]16.0366666666667[/C][C]0.107477164998750[/C][C]149.209989553159[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]16.0535714285714[/C][C]0.0996663936473862[/C][C]161.073064260437[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]16.0730769230769[/C][C]0.0909027700868761[/C][C]176.816140011089[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]16.0875[/C][C]0.085404514865552[/C][C]188.368261623238[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]16.1[/C][C]0.0786795792469443[/C][C]204.627428795322[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]16.11[/C][C]0.0746571109173555[/C][C]215.786544671325[/C][/ROW]
[ROW][C]Median[/C][C]16.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.9818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.9818181818182[/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=49488&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49488&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 Mean15.87333333333330.18564084556069585.5056078062498
Geometric Mean15.8069664050772
Harmonic Mean15.7382051290173
Quadratic Mean15.9372519588541
Winsorized Mean ( 1 / 20 )15.86333333333330.177871385431189.1842906316044
Winsorized Mean ( 2 / 20 )15.86666666666670.17694307339962689.6710244815958
Winsorized Mean ( 3 / 20 )15.87666666666670.17206565995892392.2709776631599
Winsorized Mean ( 4 / 20 )15.88333333333330.16758784974543294.7761628152655
Winsorized Mean ( 5 / 20 )15.9250.158250052436153100.631878188003
Winsorized Mean ( 6 / 20 )15.9150.156494526176361101.696847735521
Winsorized Mean ( 7 / 20 )15.9150.152137779511870104.609125038257
Winsorized Mean ( 8 / 20 )15.9150.152137779511870104.609125038257
Winsorized Mean ( 9 / 20 )15.9150.146692826377892108.492012820052
Winsorized Mean ( 10 / 20 )15.94833333333330.140267937041786113.699065300877
Winsorized Mean ( 11 / 20 )15.96666666666670.136887653771912116.640662811498
Winsorized Mean ( 12 / 20 )15.96666666666670.13002969384184122.792465281719
Winsorized Mean ( 13 / 20 )15.98833333333330.126224883761494126.665462917311
Winsorized Mean ( 14 / 20 )15.91833333333330.115457617304347137.871659791597
Winsorized Mean ( 15 / 20 )15.91833333333330.115457617304347137.871659791597
Winsorized Mean ( 16 / 20 )15.91833333333330.106921262192565148.879025620409
Winsorized Mean ( 17 / 20 )15.9750.088254415231815181.010773886372
Winsorized Mean ( 18 / 20 )16.0050.0832742728564712192.196214400883
Winsorized Mean ( 19 / 20 )16.03666666666670.0686416497679254233.628805847266
Winsorized Mean ( 20 / 20 )16.03666666666670.0686416497679254233.628805847266
Trimmed Mean ( 1 / 20 )15.88103448275860.17343992888766291.5650426323966
Trimmed Mean ( 2 / 20 )15.90.16793242301979394.6809419770355
Trimmed Mean ( 3 / 20 )15.91851851851850.16168820393128498.451947213686
Trimmed Mean ( 4 / 20 )15.93461538461540.156288123322242101.956662130754
Trimmed Mean ( 5 / 20 )15.950.151273505510343105.438159485961
Trimmed Mean ( 6 / 20 )15.956250.148183631825970107.678896807843
Trimmed Mean ( 7 / 20 )15.96521739130430.144670787068295110.355502412299
Trimmed Mean ( 8 / 20 )15.9750.141313866550642113.046230988769
Trimmed Mean ( 9 / 20 )15.98571428571430.136811688809071116.844652857281
Trimmed Mean ( 10 / 20 )15.99750.132311186223992120.908144326644
Trimmed Mean ( 11 / 20 )16.00526315789470.128064004735822124.978624484775
Trimmed Mean ( 12 / 20 )16.01111111111110.123170921234448129.990999098196
Trimmed Mean ( 13 / 20 )16.01764705882350.118326912650139135.367742638426
Trimmed Mean ( 14 / 20 )16.0218750.112588171093420142.30513600497
Trimmed Mean ( 15 / 20 )16.03666666666670.107477164998750149.209989553159
Trimmed Mean ( 16 / 20 )16.05357142857140.0996663936473862161.073064260437
Trimmed Mean ( 17 / 20 )16.07307692307690.0909027700868761176.816140011089
Trimmed Mean ( 18 / 20 )16.08750.085404514865552188.368261623238
Trimmed Mean ( 19 / 20 )16.10.0786795792469443204.627428795322
Trimmed Mean ( 20 / 20 )16.110.0746571109173555215.786544671325
Median16.1
Midrange15.65
Midmean - Weighted Average at Xnp15.9818181818182
Midmean - Weighted Average at X(n+1)p15.9818181818182
Midmean - Empirical Distribution Function15.9818181818182
Midmean - Empirical Distribution Function - Averaging15.9818181818182
Midmean - Empirical Distribution Function - Interpolation15.9818181818182
Midmean - Closest Observation15.9818181818182
Midmean - True Basic - Statistics Graphics Toolkit15.9818181818182
Midmean - MS Excel (old versions)15.9818181818182
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')