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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 computationMon, 15 Dec 2008 14:25:04 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/15/t12293763485ld03sd24boehoo.htm/, Retrieved Wed, 15 May 2024 22:34:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33829, Retrieved Wed, 15 May 2024 22:34:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency] [2008-12-15 21:25:04] [0bb3b56b7083c5944c3818446f605d68] [Current]
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Dataseries X:
7,6
7,7
7,6
8,2
8
8,1
8,3
8,2
8,1
7,7
7,6
7,7
8,2
8,4
8,4
8,6
8,4
8,5
8,7
8,7
8,6
7,4
7,3
7,4
9
9,2
9,2
8,5
8,3
8,3
8,6
8,6
8,5
8,1
8,1
8
8,6
8,7
8,7
8,6
8,4
8,4
8,7
8,7
8,5
8,3
8,3
8,3
8,1
8,2
8,1
8,1
7,9
7,7
8,1
8
7,7
7,8
7,6
7,4
7,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33829&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33829&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.203278688524590.0568752451800278144.232849679306
Geometric Mean8.19138851885783
Harmonic Mean8.17943833581142
Quadratic Mean8.21510005127503
Winsorized Mean ( 1 / 20 )8.204918032786880.0564634525398721145.313785532206
Winsorized Mean ( 2 / 20 )8.19836065573770.0546969696405723149.886926270527
Winsorized Mean ( 3 / 20 )8.183606557377050.0516493181451325158.445587498008
Winsorized Mean ( 4 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 5 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 6 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 7 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 8 / 20 )8.209836065573770.0460876403208398178.135309345865
Winsorized Mean ( 9 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 10 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 11 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 12 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 13 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 14 / 20 )8.218032786885250.0394295523632974208.423182468968
Winsorized Mean ( 15 / 20 )8.218032786885250.0313196281549882262.392412394474
Winsorized Mean ( 16 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 17 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 18 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 19 / 20 )8.244262295081970.0178831346141570461.007674155486
Winsorized Mean ( 20 / 20 )8.244262295081970.0178831346141570461.007674155486
Trimmed Mean ( 1 / 20 )8.201694915254240.0541385717654054151.494482543685
Trimmed Mean ( 2 / 20 )8.198245614035090.0512678374160828159.910111821165
Trimmed Mean ( 3 / 20 )8.198181818181820.0489272743538444167.558522857664
Trimmed Mean ( 4 / 20 )8.203773584905660.0475038967274098172.696855417591
Trimmed Mean ( 5 / 20 )8.205882352941180.0468967798305759174.977522605744
Trimmed Mean ( 6 / 20 )8.208163265306120.0460918868100433178.082604843974
Trimmed Mean ( 7 / 20 )8.210638297872340.0450340648691845182.320612667826
Trimmed Mean ( 8 / 20 )8.213333333333330.0436468842536384188.176853257256
Trimmed Mean ( 9 / 20 )8.213953488372090.0425621030656805192.987491141981
Trimmed Mean ( 10 / 20 )8.21707317073170.0417458102212563196.835877113907
Trimmed Mean ( 11 / 20 )8.220512820512820.0406059845445199202.445844195699
Trimmed Mean ( 12 / 20 )8.224324324324320.0390205546445184210.769026715505
Trimmed Mean ( 13 / 20 )8.228571428571430.0367986637890925223.610603790740
Trimmed Mean ( 14 / 20 )8.233333333333330.0336162238368694244.921421670902
Trimmed Mean ( 15 / 20 )8.235483870967740.0306026870338876269.109828880329
Trimmed Mean ( 16 / 20 )8.237931034482760.0291140923266743282.953387041888
Trimmed Mean ( 17 / 20 )8.237037037037040.0283185723983799290.870490262011
Trimmed Mean ( 18 / 20 )8.2360.0270061721340389304.967322252207
Trimmed Mean ( 19 / 20 )8.234782608695650.0248383673412886331.534778254409
Trimmed Mean ( 20 / 20 )8.233333333333330.0251976315339486326.750286916476
Median8.2
Midrange8.25
Midmean - Weighted Average at Xnp8.23548387096774
Midmean - Weighted Average at X(n+1)p8.23548387096774
Midmean - Empirical Distribution Function8.23548387096774
Midmean - Empirical Distribution Function - Averaging8.23548387096774
Midmean - Empirical Distribution Function - Interpolation8.23548387096774
Midmean - Closest Observation8.221875
Midmean - True Basic - Statistics Graphics Toolkit8.23548387096774
Midmean - MS Excel (old versions)8.23548387096774
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.20327868852459 & 0.0568752451800278 & 144.232849679306 \tabularnewline
Geometric Mean & 8.19138851885783 &  &  \tabularnewline
Harmonic Mean & 8.17943833581142 &  &  \tabularnewline
Quadratic Mean & 8.21510005127503 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.20491803278688 & 0.0564634525398721 & 145.313785532206 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.1983606557377 & 0.0546969696405723 & 149.886926270527 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.18360655737705 & 0.0516493181451325 & 158.445587498008 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.19672131147541 & 0.0486409401150089 & 168.514862009137 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.19672131147541 & 0.0486409401150089 & 168.514862009137 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.19672131147541 & 0.0486409401150089 & 168.514862009137 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.19672131147541 & 0.0486409401150089 & 168.514862009137 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.20983606557377 & 0.0460876403208398 & 178.135309345865 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.19508196721311 & 0.0436344871318308 & 187.812038272702 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.19508196721311 & 0.0436344871318308 & 187.812038272702 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.19508196721311 & 0.0436344871318308 & 187.812038272702 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.19508196721311 & 0.0436344871318308 & 187.812038272702 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.19508196721311 & 0.0436344871318308 & 187.812038272702 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.21803278688525 & 0.0394295523632974 & 208.423182468968 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.21803278688525 & 0.0313196281549882 & 262.392412394474 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.24426229508197 & 0.0271128576523417 & 304.072053222686 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.24426229508197 & 0.0271128576523417 & 304.072053222686 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.24426229508197 & 0.0271128576523417 & 304.072053222686 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.24426229508197 & 0.0178831346141570 & 461.007674155486 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.24426229508197 & 0.0178831346141570 & 461.007674155486 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.20169491525424 & 0.0541385717654054 & 151.494482543685 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.19824561403509 & 0.0512678374160828 & 159.910111821165 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.19818181818182 & 0.0489272743538444 & 167.558522857664 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.20377358490566 & 0.0475038967274098 & 172.696855417591 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.20588235294118 & 0.0468967798305759 & 174.977522605744 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.20816326530612 & 0.0460918868100433 & 178.082604843974 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.21063829787234 & 0.0450340648691845 & 182.320612667826 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.21333333333333 & 0.0436468842536384 & 188.176853257256 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.21395348837209 & 0.0425621030656805 & 192.987491141981 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.2170731707317 & 0.0417458102212563 & 196.835877113907 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.22051282051282 & 0.0406059845445199 & 202.445844195699 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.22432432432432 & 0.0390205546445184 & 210.769026715505 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.22857142857143 & 0.0367986637890925 & 223.610603790740 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.23333333333333 & 0.0336162238368694 & 244.921421670902 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.23548387096774 & 0.0306026870338876 & 269.109828880329 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.23793103448276 & 0.0291140923266743 & 282.953387041888 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.23703703703704 & 0.0283185723983799 & 290.870490262011 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.236 & 0.0270061721340389 & 304.967322252207 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.23478260869565 & 0.0248383673412886 & 331.534778254409 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.23333333333333 & 0.0251976315339486 & 326.750286916476 \tabularnewline
Median & 8.2 &  &  \tabularnewline
Midrange & 8.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.23548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.23548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.23548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.23548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.23548387096774 &  &  \tabularnewline
Midmean - Closest Observation & 8.221875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.23548387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.23548387096774 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33829&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]8.20327868852459[/C][C]0.0568752451800278[/C][C]144.232849679306[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.19138851885783[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.17943833581142[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.21510005127503[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.20491803278688[/C][C]0.0564634525398721[/C][C]145.313785532206[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.1983606557377[/C][C]0.0546969696405723[/C][C]149.886926270527[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.18360655737705[/C][C]0.0516493181451325[/C][C]158.445587498008[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.19672131147541[/C][C]0.0486409401150089[/C][C]168.514862009137[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.19672131147541[/C][C]0.0486409401150089[/C][C]168.514862009137[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.19672131147541[/C][C]0.0486409401150089[/C][C]168.514862009137[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.19672131147541[/C][C]0.0486409401150089[/C][C]168.514862009137[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.20983606557377[/C][C]0.0460876403208398[/C][C]178.135309345865[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.19508196721311[/C][C]0.0436344871318308[/C][C]187.812038272702[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.19508196721311[/C][C]0.0436344871318308[/C][C]187.812038272702[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.19508196721311[/C][C]0.0436344871318308[/C][C]187.812038272702[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.19508196721311[/C][C]0.0436344871318308[/C][C]187.812038272702[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.19508196721311[/C][C]0.0436344871318308[/C][C]187.812038272702[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.21803278688525[/C][C]0.0394295523632974[/C][C]208.423182468968[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.21803278688525[/C][C]0.0313196281549882[/C][C]262.392412394474[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.24426229508197[/C][C]0.0271128576523417[/C][C]304.072053222686[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.24426229508197[/C][C]0.0271128576523417[/C][C]304.072053222686[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.24426229508197[/C][C]0.0271128576523417[/C][C]304.072053222686[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.24426229508197[/C][C]0.0178831346141570[/C][C]461.007674155486[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.24426229508197[/C][C]0.0178831346141570[/C][C]461.007674155486[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.20169491525424[/C][C]0.0541385717654054[/C][C]151.494482543685[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.19824561403509[/C][C]0.0512678374160828[/C][C]159.910111821165[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.19818181818182[/C][C]0.0489272743538444[/C][C]167.558522857664[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.20377358490566[/C][C]0.0475038967274098[/C][C]172.696855417591[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.20588235294118[/C][C]0.0468967798305759[/C][C]174.977522605744[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.20816326530612[/C][C]0.0460918868100433[/C][C]178.082604843974[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.21063829787234[/C][C]0.0450340648691845[/C][C]182.320612667826[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.21333333333333[/C][C]0.0436468842536384[/C][C]188.176853257256[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.21395348837209[/C][C]0.0425621030656805[/C][C]192.987491141981[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.2170731707317[/C][C]0.0417458102212563[/C][C]196.835877113907[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.22051282051282[/C][C]0.0406059845445199[/C][C]202.445844195699[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.22432432432432[/C][C]0.0390205546445184[/C][C]210.769026715505[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.22857142857143[/C][C]0.0367986637890925[/C][C]223.610603790740[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.23333333333333[/C][C]0.0336162238368694[/C][C]244.921421670902[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.23548387096774[/C][C]0.0306026870338876[/C][C]269.109828880329[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.23793103448276[/C][C]0.0291140923266743[/C][C]282.953387041888[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.23703703703704[/C][C]0.0283185723983799[/C][C]290.870490262011[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.236[/C][C]0.0270061721340389[/C][C]304.967322252207[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.23478260869565[/C][C]0.0248383673412886[/C][C]331.534778254409[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.23333333333333[/C][C]0.0251976315339486[/C][C]326.750286916476[/C][/ROW]
[ROW][C]Median[/C][C]8.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.221875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.23548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33829&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 Mean8.203278688524590.0568752451800278144.232849679306
Geometric Mean8.19138851885783
Harmonic Mean8.17943833581142
Quadratic Mean8.21510005127503
Winsorized Mean ( 1 / 20 )8.204918032786880.0564634525398721145.313785532206
Winsorized Mean ( 2 / 20 )8.19836065573770.0546969696405723149.886926270527
Winsorized Mean ( 3 / 20 )8.183606557377050.0516493181451325158.445587498008
Winsorized Mean ( 4 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 5 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 6 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 7 / 20 )8.196721311475410.0486409401150089168.514862009137
Winsorized Mean ( 8 / 20 )8.209836065573770.0460876403208398178.135309345865
Winsorized Mean ( 9 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 10 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 11 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 12 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 13 / 20 )8.195081967213110.0436344871318308187.812038272702
Winsorized Mean ( 14 / 20 )8.218032786885250.0394295523632974208.423182468968
Winsorized Mean ( 15 / 20 )8.218032786885250.0313196281549882262.392412394474
Winsorized Mean ( 16 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 17 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 18 / 20 )8.244262295081970.0271128576523417304.072053222686
Winsorized Mean ( 19 / 20 )8.244262295081970.0178831346141570461.007674155486
Winsorized Mean ( 20 / 20 )8.244262295081970.0178831346141570461.007674155486
Trimmed Mean ( 1 / 20 )8.201694915254240.0541385717654054151.494482543685
Trimmed Mean ( 2 / 20 )8.198245614035090.0512678374160828159.910111821165
Trimmed Mean ( 3 / 20 )8.198181818181820.0489272743538444167.558522857664
Trimmed Mean ( 4 / 20 )8.203773584905660.0475038967274098172.696855417591
Trimmed Mean ( 5 / 20 )8.205882352941180.0468967798305759174.977522605744
Trimmed Mean ( 6 / 20 )8.208163265306120.0460918868100433178.082604843974
Trimmed Mean ( 7 / 20 )8.210638297872340.0450340648691845182.320612667826
Trimmed Mean ( 8 / 20 )8.213333333333330.0436468842536384188.176853257256
Trimmed Mean ( 9 / 20 )8.213953488372090.0425621030656805192.987491141981
Trimmed Mean ( 10 / 20 )8.21707317073170.0417458102212563196.835877113907
Trimmed Mean ( 11 / 20 )8.220512820512820.0406059845445199202.445844195699
Trimmed Mean ( 12 / 20 )8.224324324324320.0390205546445184210.769026715505
Trimmed Mean ( 13 / 20 )8.228571428571430.0367986637890925223.610603790740
Trimmed Mean ( 14 / 20 )8.233333333333330.0336162238368694244.921421670902
Trimmed Mean ( 15 / 20 )8.235483870967740.0306026870338876269.109828880329
Trimmed Mean ( 16 / 20 )8.237931034482760.0291140923266743282.953387041888
Trimmed Mean ( 17 / 20 )8.237037037037040.0283185723983799290.870490262011
Trimmed Mean ( 18 / 20 )8.2360.0270061721340389304.967322252207
Trimmed Mean ( 19 / 20 )8.234782608695650.0248383673412886331.534778254409
Trimmed Mean ( 20 / 20 )8.233333333333330.0251976315339486326.750286916476
Median8.2
Midrange8.25
Midmean - Weighted Average at Xnp8.23548387096774
Midmean - Weighted Average at X(n+1)p8.23548387096774
Midmean - Empirical Distribution Function8.23548387096774
Midmean - Empirical Distribution Function - Averaging8.23548387096774
Midmean - Empirical Distribution Function - Interpolation8.23548387096774
Midmean - Closest Observation8.221875
Midmean - True Basic - Statistics Graphics Toolkit8.23548387096774
Midmean - MS Excel (old versions)8.23548387096774
Number of observations61



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')