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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 computationTue, 16 Nov 2010 15:35:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289921670w9if554zcwqome6.htm/, Retrieved Sun, 28 Apr 2024 23:52:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95934, Retrieved Sun, 28 Apr 2024 23:52:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [ws 6 deel 1 vraag...] [2010-11-14 08:37:37] [05ab9592748364013445d860bb938e43]
-    D    [Central Tendency] [Hapiness tutorial] [2010-11-16 07:14:13] [05ab9592748364013445d860bb938e43]
-   PD      [Central Tendency] [Central Tendency ...] [2010-11-16 11:05:47] [717f3d787904f94c39256c5c1fc72d4c]
-   PD          [Central Tendency] [Central Tendency ...] [2010-11-16 15:35:40] [c1f1b5e209adb4577289f490325e36f2] [Current]
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Dataseries X:
1,084
1,1154
1,1184
1,157
1,1625
1,1627
1,1578
1,1533
1,1684
1,1597
1,1888
1,1296
1,1424
1,1317
1,1581
1,1672
1,1391
1,1357
1,1065
1,1232
1,0845
1,0676
1,0863
1,0792
1,0799
1,0817
1,0869
1,0843
1,0747
1,0711
1,0688
1,0828
1,0746
1,0568
1,06
1,0593
1,037
1,0288
1,0295
1,0352
1,0324
1,0186
1,0094
1,0258
1,017
1,0117
1,0175
1,0064
1,0168
1,034
1,0423
1,0356
1,0348




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=95934&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=95934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95934&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 Mean1.084769811320750.00724955860970859149.632532092097
Geometric Mean1.08351876408222
Harmonic Mean1.08227735555168
Quadratic Mean1.08602875687282
Winsorized Mean ( 1 / 17 )1.084441509433960.00714126097927963151.855745446143
Winsorized Mean ( 2 / 17 )1.084483018867920.00711377052127657152.448411939118
Winsorized Mean ( 3 / 17 )1.084516981132080.00700268439916153154.871606274578
Winsorized Mean ( 4 / 17 )1.084516981132080.00699664222589815155.005350583416
Winsorized Mean ( 5 / 17 )1.08430.00693195520057347156.420514649359
Winsorized Mean ( 6 / 17 )1.084243396226420.0068713116557957157.792784047555
Winsorized Mean ( 7 / 17 )1.085154716981130.00669458035575092162.094509187411
Winsorized Mean ( 8 / 17 )1.085486792452830.0065933390089474164.633851069964
Winsorized Mean ( 9 / 17 )1.084977358490570.0064440765216631168.368168013398
Winsorized Mean ( 10 / 17 )1.083467924528300.00594744201919899182.173768324390
Winsorized Mean ( 11 / 17 )1.083115094339620.00576356568259183187.924481820524
Winsorized Mean ( 12 / 17 )1.082526415094340.00559154461638077193.600604012532
Winsorized Mean ( 13 / 17 )1.081643396226410.00539814346777204200.373221401772
Winsorized Mean ( 14 / 17 )1.081194339622640.00528228920163248204.682912720587
Winsorized Mean ( 15 / 17 )1.079779245283020.00490210135215911220.268649649081
Winsorized Mean ( 16 / 17 )1.079930188679250.00439026878192494245.98270454998
Winsorized Mean ( 17 / 17 )1.083618867924530.00349428940786535310.111367846462
Trimmed Mean ( 1 / 17 )1.084266666666670.00708125372009548153.117895435619
Trimmed Mean ( 2 / 17 )1.084077551020410.00699800765214942154.912312890575
Trimmed Mean ( 3 / 17 )1.083848936170210.00690332668089043157.003860062206
Trimmed Mean ( 4 / 17 )1.083586666666670.00682819289283909158.693036894587
Trimmed Mean ( 5 / 17 )1.08330.00672392300984354161.111303388527
Trimmed Mean ( 6 / 17 )1.083041463414630.00660201278954303164.047162273007
Trimmed Mean ( 7 / 17 )1.082769230769230.00645197158230478167.819900778677
Trimmed Mean ( 8 / 17 )1.082281081081080.00629651917501161171.885616639782
Trimmed Mean ( 9 / 17 )1.081674285714290.00610500874796467177.178171296626
Trimmed Mean ( 10 / 17 )1.081084848484850.00587824559159262183.91284127888
Trimmed Mean ( 11 / 17 )1.080677419354840.00571301797666215189.160514419776
Trimmed Mean ( 12 / 17 )1.080272413793100.00552169232409446195.641544364800
Trimmed Mean ( 13 / 17 )1.079903703703700.00528578020796172204.303558077783
Trimmed Mean ( 14 / 17 )1.079620.00498835644275747216.427998357552
Trimmed Mean ( 15 / 17 )1.079360869565220.0045537880644998237.024836087486
Trimmed Mean ( 16 / 17 )1.079290476190480.00401677971444495268.695460771519
Trimmed Mean ( 17 / 17 )1.079178947368420.00336754877229183320.464236850227
Median1.0799
Midrange1.0976
Midmean - Weighted Average at Xnp1.07791153846154
Midmean - Weighted Average at X(n+1)p1.07990370370370
Midmean - Empirical Distribution Function1.07990370370370
Midmean - Empirical Distribution Function - Averaging1.07990370370370
Midmean - Empirical Distribution Function - Interpolation1.07990370370370
Midmean - Closest Observation1.07829285714286
Midmean - True Basic - Statistics Graphics Toolkit1.07990370370370
Midmean - MS Excel (old versions)1.07990370370370
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.08476981132075 & 0.00724955860970859 & 149.632532092097 \tabularnewline
Geometric Mean & 1.08351876408222 &  &  \tabularnewline
Harmonic Mean & 1.08227735555168 &  &  \tabularnewline
Quadratic Mean & 1.08602875687282 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 1.08444150943396 & 0.00714126097927963 & 151.855745446143 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 1.08448301886792 & 0.00711377052127657 & 152.448411939118 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 1.08451698113208 & 0.00700268439916153 & 154.871606274578 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 1.08451698113208 & 0.00699664222589815 & 155.005350583416 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 1.0843 & 0.00693195520057347 & 156.420514649359 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 1.08424339622642 & 0.0068713116557957 & 157.792784047555 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 1.08515471698113 & 0.00669458035575092 & 162.094509187411 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 1.08548679245283 & 0.0065933390089474 & 164.633851069964 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 1.08497735849057 & 0.0064440765216631 & 168.368168013398 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 1.08346792452830 & 0.00594744201919899 & 182.173768324390 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 1.08311509433962 & 0.00576356568259183 & 187.924481820524 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 1.08252641509434 & 0.00559154461638077 & 193.600604012532 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 1.08164339622641 & 0.00539814346777204 & 200.373221401772 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 1.08119433962264 & 0.00528228920163248 & 204.682912720587 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 1.07977924528302 & 0.00490210135215911 & 220.268649649081 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 1.07993018867925 & 0.00439026878192494 & 245.98270454998 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 1.08361886792453 & 0.00349428940786535 & 310.111367846462 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 1.08426666666667 & 0.00708125372009548 & 153.117895435619 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 1.08407755102041 & 0.00699800765214942 & 154.912312890575 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 1.08384893617021 & 0.00690332668089043 & 157.003860062206 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 1.08358666666667 & 0.00682819289283909 & 158.693036894587 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 1.0833 & 0.00672392300984354 & 161.111303388527 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 1.08304146341463 & 0.00660201278954303 & 164.047162273007 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 1.08276923076923 & 0.00645197158230478 & 167.819900778677 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 1.08228108108108 & 0.00629651917501161 & 171.885616639782 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 1.08167428571429 & 0.00610500874796467 & 177.178171296626 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 1.08108484848485 & 0.00587824559159262 & 183.91284127888 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 1.08067741935484 & 0.00571301797666215 & 189.160514419776 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 1.08027241379310 & 0.00552169232409446 & 195.641544364800 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 1.07990370370370 & 0.00528578020796172 & 204.303558077783 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 1.07962 & 0.00498835644275747 & 216.427998357552 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 1.07936086956522 & 0.0045537880644998 & 237.024836087486 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 1.07929047619048 & 0.00401677971444495 & 268.695460771519 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 1.07917894736842 & 0.00336754877229183 & 320.464236850227 \tabularnewline
Median & 1.0799 &  &  \tabularnewline
Midrange & 1.0976 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.07791153846154 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.07990370370370 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.07990370370370 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.07990370370370 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.07990370370370 &  &  \tabularnewline
Midmean - Closest Observation & 1.07829285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.07990370370370 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.07990370370370 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95934&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]1.08476981132075[/C][C]0.00724955860970859[/C][C]149.632532092097[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.08351876408222[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.08227735555168[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.08602875687282[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]1.08444150943396[/C][C]0.00714126097927963[/C][C]151.855745446143[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]1.08448301886792[/C][C]0.00711377052127657[/C][C]152.448411939118[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]1.08451698113208[/C][C]0.00700268439916153[/C][C]154.871606274578[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]1.08451698113208[/C][C]0.00699664222589815[/C][C]155.005350583416[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]1.0843[/C][C]0.00693195520057347[/C][C]156.420514649359[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]1.08424339622642[/C][C]0.0068713116557957[/C][C]157.792784047555[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]1.08515471698113[/C][C]0.00669458035575092[/C][C]162.094509187411[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]1.08548679245283[/C][C]0.0065933390089474[/C][C]164.633851069964[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]1.08497735849057[/C][C]0.0064440765216631[/C][C]168.368168013398[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]1.08346792452830[/C][C]0.00594744201919899[/C][C]182.173768324390[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]1.08311509433962[/C][C]0.00576356568259183[/C][C]187.924481820524[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]1.08252641509434[/C][C]0.00559154461638077[/C][C]193.600604012532[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]1.08164339622641[/C][C]0.00539814346777204[/C][C]200.373221401772[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]1.08119433962264[/C][C]0.00528228920163248[/C][C]204.682912720587[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]1.07977924528302[/C][C]0.00490210135215911[/C][C]220.268649649081[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]1.07993018867925[/C][C]0.00439026878192494[/C][C]245.98270454998[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]1.08361886792453[/C][C]0.00349428940786535[/C][C]310.111367846462[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]1.08426666666667[/C][C]0.00708125372009548[/C][C]153.117895435619[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]1.08407755102041[/C][C]0.00699800765214942[/C][C]154.912312890575[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]1.08384893617021[/C][C]0.00690332668089043[/C][C]157.003860062206[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]1.08358666666667[/C][C]0.00682819289283909[/C][C]158.693036894587[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]1.0833[/C][C]0.00672392300984354[/C][C]161.111303388527[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]1.08304146341463[/C][C]0.00660201278954303[/C][C]164.047162273007[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]1.08276923076923[/C][C]0.00645197158230478[/C][C]167.819900778677[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]1.08228108108108[/C][C]0.00629651917501161[/C][C]171.885616639782[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]1.08167428571429[/C][C]0.00610500874796467[/C][C]177.178171296626[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]1.08108484848485[/C][C]0.00587824559159262[/C][C]183.91284127888[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]1.08067741935484[/C][C]0.00571301797666215[/C][C]189.160514419776[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]1.08027241379310[/C][C]0.00552169232409446[/C][C]195.641544364800[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]1.07990370370370[/C][C]0.00528578020796172[/C][C]204.303558077783[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]1.07962[/C][C]0.00498835644275747[/C][C]216.427998357552[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]1.07936086956522[/C][C]0.0045537880644998[/C][C]237.024836087486[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]1.07929047619048[/C][C]0.00401677971444495[/C][C]268.695460771519[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]1.07917894736842[/C][C]0.00336754877229183[/C][C]320.464236850227[/C][/ROW]
[ROW][C]Median[/C][C]1.0799[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.0976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.07791153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.07829285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.07990370370370[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95934&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 Mean1.084769811320750.00724955860970859149.632532092097
Geometric Mean1.08351876408222
Harmonic Mean1.08227735555168
Quadratic Mean1.08602875687282
Winsorized Mean ( 1 / 17 )1.084441509433960.00714126097927963151.855745446143
Winsorized Mean ( 2 / 17 )1.084483018867920.00711377052127657152.448411939118
Winsorized Mean ( 3 / 17 )1.084516981132080.00700268439916153154.871606274578
Winsorized Mean ( 4 / 17 )1.084516981132080.00699664222589815155.005350583416
Winsorized Mean ( 5 / 17 )1.08430.00693195520057347156.420514649359
Winsorized Mean ( 6 / 17 )1.084243396226420.0068713116557957157.792784047555
Winsorized Mean ( 7 / 17 )1.085154716981130.00669458035575092162.094509187411
Winsorized Mean ( 8 / 17 )1.085486792452830.0065933390089474164.633851069964
Winsorized Mean ( 9 / 17 )1.084977358490570.0064440765216631168.368168013398
Winsorized Mean ( 10 / 17 )1.083467924528300.00594744201919899182.173768324390
Winsorized Mean ( 11 / 17 )1.083115094339620.00576356568259183187.924481820524
Winsorized Mean ( 12 / 17 )1.082526415094340.00559154461638077193.600604012532
Winsorized Mean ( 13 / 17 )1.081643396226410.00539814346777204200.373221401772
Winsorized Mean ( 14 / 17 )1.081194339622640.00528228920163248204.682912720587
Winsorized Mean ( 15 / 17 )1.079779245283020.00490210135215911220.268649649081
Winsorized Mean ( 16 / 17 )1.079930188679250.00439026878192494245.98270454998
Winsorized Mean ( 17 / 17 )1.083618867924530.00349428940786535310.111367846462
Trimmed Mean ( 1 / 17 )1.084266666666670.00708125372009548153.117895435619
Trimmed Mean ( 2 / 17 )1.084077551020410.00699800765214942154.912312890575
Trimmed Mean ( 3 / 17 )1.083848936170210.00690332668089043157.003860062206
Trimmed Mean ( 4 / 17 )1.083586666666670.00682819289283909158.693036894587
Trimmed Mean ( 5 / 17 )1.08330.00672392300984354161.111303388527
Trimmed Mean ( 6 / 17 )1.083041463414630.00660201278954303164.047162273007
Trimmed Mean ( 7 / 17 )1.082769230769230.00645197158230478167.819900778677
Trimmed Mean ( 8 / 17 )1.082281081081080.00629651917501161171.885616639782
Trimmed Mean ( 9 / 17 )1.081674285714290.00610500874796467177.178171296626
Trimmed Mean ( 10 / 17 )1.081084848484850.00587824559159262183.91284127888
Trimmed Mean ( 11 / 17 )1.080677419354840.00571301797666215189.160514419776
Trimmed Mean ( 12 / 17 )1.080272413793100.00552169232409446195.641544364800
Trimmed Mean ( 13 / 17 )1.079903703703700.00528578020796172204.303558077783
Trimmed Mean ( 14 / 17 )1.079620.00498835644275747216.427998357552
Trimmed Mean ( 15 / 17 )1.079360869565220.0045537880644998237.024836087486
Trimmed Mean ( 16 / 17 )1.079290476190480.00401677971444495268.695460771519
Trimmed Mean ( 17 / 17 )1.079178947368420.00336754877229183320.464236850227
Median1.0799
Midrange1.0976
Midmean - Weighted Average at Xnp1.07791153846154
Midmean - Weighted Average at X(n+1)p1.07990370370370
Midmean - Empirical Distribution Function1.07990370370370
Midmean - Empirical Distribution Function - Averaging1.07990370370370
Midmean - Empirical Distribution Function - Interpolation1.07990370370370
Midmean - Closest Observation1.07829285714286
Midmean - True Basic - Statistics Graphics Toolkit1.07990370370370
Midmean - MS Excel (old versions)1.07990370370370
Number of observations53



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')