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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 computationThu, 12 Dec 2013 04:11:30 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386839501mte3gqaxldcu7ki.htm/, Retrieved Sun, 05 Dec 2021 17:44:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232229, Retrieved Sun, 05 Dec 2021 17:44:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-12-12 09:11:30] [9e6a405f514733ea23d87e4507d39d29] [Current]
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Dataseries X:
0.00550118759611825
0.100183846454512
0.407011937175347
-0.16737394013665
0.0874322043971727
0.411921594926703
-0.16303809760263
-0.347349364549994
-0.0296049307932174
0.323806680916916
-0.239140348405293
-0.0990421431826477
0.0467509732678099
0.163478509066741
-0.350096927982722
0.32436525705737
0.311383604987517
-0.0960371667588798
0.124548267674515
-0.511624147113553
0.314584415989742
0.287739894396906
0.282204368241592
-0.25961081368395
0.139880423671516
0.0468251561703096
0.141297672568196
0.131779095699905
0.188261365013337
0.34246868819404
0.195820162553774
-0.179557156234377
0.232001180091104
0.0900659140956214
-0.1338451790818
-0.00791389868766919
-0.0425554884595751
0.482693233899655
0.282396103736813
0.156155004245922
-0.114835337644616
0.00659340969595179
-0.224997452667842
-0.127774776710956
0.0620755029470993
-0.0998584806098916
0.267864642498592
0.389744472117138
0.0761067268738662
-0.135349114066045
-0.199236081602781
0.202107333568291
0.47797312151875
-0.330634318524646
-0.00413610310225685
0.14024473328936
-0.223728014463631
0.223086730239358
0.073422994370519
0.225451904074953
-0.0398059712998328
-0.0698047210357811
-0.259657758635374
0.167444170403979
-0.0135427590292624
0.192334314572137




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232229&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232229&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.05537661069989810.02749753302347282.0138755957717
Geometric MeanNaN
Harmonic Mean-0.909174873938727
Quadratic Mean0.228503829217612
Winsorized Mean ( 1 / 22 )0.05775247595368490.0268044160860132.15458810101897
Winsorized Mean ( 2 / 22 )0.05583417403976610.02633501104733762.12015001396443
Winsorized Mean ( 3 / 22 )0.05637078259767480.02611264033467162.1587546060146
Winsorized Mean ( 4 / 22 )0.05962587925410290.02498336265125152.38662345363329
Winsorized Mean ( 5 / 22 )0.0560479369077640.02429325755358462.3071396161728
Winsorized Mean ( 6 / 22 )0.05626312182976280.02363529997086362.38046997072689
Winsorized Mean ( 7 / 22 )0.05770388299914120.02334094252557082.47221734666133
Winsorized Mean ( 8 / 22 )0.05673990400241850.02311829898935252.45432866962015
Winsorized Mean ( 9 / 22 )0.05964323880132190.02243482395658792.65851155849199
Winsorized Mean ( 10 / 22 )0.05904251376765410.02130780446615922.77093371404946
Winsorized Mean ( 11 / 22 )0.06018241800725980.02081542408792392.89124150212124
Winsorized Mean ( 12 / 22 )0.06093589201431420.02067771181607072.94693593548175
Winsorized Mean ( 13 / 22 )0.0635652912766870.01932853809600513.2886755822379
Winsorized Mean ( 14 / 22 )0.05627690667175660.01808884220878343.11113923280453
Winsorized Mean ( 15 / 22 )0.05616807175236870.01764556827284493.18312626059239
Winsorized Mean ( 16 / 22 )0.0587315299901250.01706370246124253.4418983877341
Winsorized Mean ( 17 / 22 )0.05718542129591560.01567918291710413.64721947554633
Winsorized Mean ( 18 / 22 )0.05569337577211380.01540290110407613.61577182089259
Winsorized Mean ( 19 / 22 )0.05555494305090910.01512935924856433.67199576255557
Winsorized Mean ( 20 / 22 )0.06226994188857540.01375560758831844.52687687466868
Winsorized Mean ( 21 / 22 )0.06431649942348150.01157568076972155.55617425039173
Winsorized Mean ( 22 / 22 )0.0639111180309830.01126520781283665.67331904504743
Trimmed Mean ( 1 / 22 )0.05755917530323710.02606528080557712.20826991017574
Trimmed Mean ( 2 / 22 )0.0573534036430830.02517207941603092.27845315022156
Trimmed Mean ( 3 / 22 )0.05818897992490730.02439584909288022.38520002740505
Trimmed Mean ( 4 / 22 )0.05887864098006440.02355290850529182.49984586688458
Trimmed Mean ( 5 / 22 )0.05865847256003520.02295555016810262.55530676156666
Trimmed Mean ( 6 / 22 )0.05929660349725710.02243994132633132.64245804545299
Trimmed Mean ( 7 / 22 )0.05993830154230390.02198497575085062.72633011842121
Trimmed Mean ( 8 / 22 )0.06035964903901460.02148555914362052.80931246124617
Trimmed Mean ( 9 / 22 )0.06098179271717960.02090205391136062.91750241271911
Trimmed Mean ( 10 / 22 )0.06119518537043220.02032609220817223.01067144356594
Trimmed Mean ( 11 / 22 )0.0615180861108490.01985587296548363.0982312496554
Trimmed Mean ( 12 / 22 )0.06170889583993310.01934994050671143.18910002945641
Trimmed Mean ( 13 / 22 )0.06181518386595570.01870180410866023.30530592165336
Trimmed Mean ( 14 / 22 )0.0615813638475180.01817195889555233.38881263167452
Trimmed Mean ( 15 / 22 )0.06227599514434380.01775131626637833.50824661167787
Trimmed Mean ( 16 / 22 )0.06306643228918770.01726047468664373.65380636593899
Trimmed Mean ( 17 / 22 )0.06362522828867620.01671044876527633.80751164629925
Trimmed Mean ( 18 / 22 )0.06445861507597470.01629752581847673.95511661057762
Trimmed Mean ( 19 / 22 )0.06560644403243260.01572981566161274.17083362219812
Trimmed Mean ( 20 / 22 )0.06694935711903290.01492645505238334.48528179558235
Trimmed Mean ( 21 / 22 )0.06759277671322090.01420547789307094.75821913363371
Trimmed Mean ( 22 / 22 )0.06806081632604070.01390158761930764.8959024098451
Median0.0747648606221926
Midrange-0.014465456606949
Midmean - Weighted Average at Xnp0.0582173323513037
Midmean - Weighted Average at X(n+1)p0.0630664322891877
Midmean - Empirical Distribution Function0.0630664322891877
Midmean - Empirical Distribution Function - Averaging0.0630664322891877
Midmean - Empirical Distribution Function - Interpolation0.0636252282886762
Midmean - Closest Observation0.0630664322891877
Midmean - True Basic - Statistics Graphics Toolkit0.0630664322891877
Midmean - MS Excel (old versions)0.0630664322891877
Number of observations66

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0553766106998981 & 0.0274975330234728 & 2.0138755957717 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.909174873938727 &  &  \tabularnewline
Quadratic Mean & 0.228503829217612 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 0.0577524759536849 & 0.026804416086013 & 2.15458810101897 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 0.0558341740397661 & 0.0263350110473376 & 2.12015001396443 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 0.0563707825976748 & 0.0261126403346716 & 2.1587546060146 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 0.0596258792541029 & 0.0249833626512515 & 2.38662345363329 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 0.056047936907764 & 0.0242932575535846 & 2.3071396161728 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 0.0562631218297628 & 0.0236352999708636 & 2.38046997072689 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 0.0577038829991412 & 0.0233409425255708 & 2.47221734666133 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 0.0567399040024185 & 0.0231182989893525 & 2.45432866962015 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 0.0596432388013219 & 0.0224348239565879 & 2.65851155849199 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 0.0590425137676541 & 0.0213078044661592 & 2.77093371404946 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 0.0601824180072598 & 0.0208154240879239 & 2.89124150212124 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 0.0609358920143142 & 0.0206777118160707 & 2.94693593548175 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 0.063565291276687 & 0.0193285380960051 & 3.2886755822379 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 0.0562769066717566 & 0.0180888422087834 & 3.11113923280453 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 0.0561680717523687 & 0.0176455682728449 & 3.18312626059239 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 0.058731529990125 & 0.0170637024612425 & 3.4418983877341 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 0.0571854212959156 & 0.0156791829171041 & 3.64721947554633 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 0.0556933757721138 & 0.0154029011040761 & 3.61577182089259 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 0.0555549430509091 & 0.0151293592485643 & 3.67199576255557 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 0.0622699418885754 & 0.0137556075883184 & 4.52687687466868 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 0.0643164994234815 & 0.0115756807697215 & 5.55617425039173 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 0.063911118030983 & 0.0112652078128366 & 5.67331904504743 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 0.0575591753032371 & 0.0260652808055771 & 2.20826991017574 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 0.057353403643083 & 0.0251720794160309 & 2.27845315022156 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 0.0581889799249073 & 0.0243958490928802 & 2.38520002740505 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 0.0588786409800644 & 0.0235529085052918 & 2.49984586688458 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 0.0586584725600352 & 0.0229555501681026 & 2.55530676156666 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 0.0592966034972571 & 0.0224399413263313 & 2.64245804545299 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 0.0599383015423039 & 0.0219849757508506 & 2.72633011842121 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 0.0603596490390146 & 0.0214855591436205 & 2.80931246124617 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 0.0609817927171796 & 0.0209020539113606 & 2.91750241271911 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 0.0611951853704322 & 0.0203260922081722 & 3.01067144356594 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 0.061518086110849 & 0.0198558729654836 & 3.0982312496554 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 0.0617088958399331 & 0.0193499405067114 & 3.18910002945641 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 0.0618151838659557 & 0.0187018041086602 & 3.30530592165336 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 0.061581363847518 & 0.0181719588955523 & 3.38881263167452 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 0.0622759951443438 & 0.0177513162663783 & 3.50824661167787 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 0.0630664322891877 & 0.0172604746866437 & 3.65380636593899 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 0.0636252282886762 & 0.0167104487652763 & 3.80751164629925 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 0.0644586150759747 & 0.0162975258184767 & 3.95511661057762 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 0.0656064440324326 & 0.0157298156616127 & 4.17083362219812 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 0.0669493571190329 & 0.0149264550523833 & 4.48528179558235 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 0.0675927767132209 & 0.0142054778930709 & 4.75821913363371 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 0.0680608163260407 & 0.0139015876193076 & 4.8959024098451 \tabularnewline
Median & 0.0747648606221926 &  &  \tabularnewline
Midrange & -0.014465456606949 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.0582173323513037 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0630664322891877 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0630664322891877 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0630664322891877 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0636252282886762 &  &  \tabularnewline
Midmean - Closest Observation & 0.0630664322891877 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0630664322891877 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0630664322891877 &  &  \tabularnewline
Number of observations & 66 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232229&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]0.0553766106998981[/C][C]0.0274975330234728[/C][C]2.0138755957717[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.909174873938727[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.228503829217612[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]0.0577524759536849[/C][C]0.026804416086013[/C][C]2.15458810101897[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]0.0558341740397661[/C][C]0.0263350110473376[/C][C]2.12015001396443[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]0.0563707825976748[/C][C]0.0261126403346716[/C][C]2.1587546060146[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]0.0596258792541029[/C][C]0.0249833626512515[/C][C]2.38662345363329[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]0.056047936907764[/C][C]0.0242932575535846[/C][C]2.3071396161728[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]0.0562631218297628[/C][C]0.0236352999708636[/C][C]2.38046997072689[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]0.0577038829991412[/C][C]0.0233409425255708[/C][C]2.47221734666133[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]0.0567399040024185[/C][C]0.0231182989893525[/C][C]2.45432866962015[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]0.0596432388013219[/C][C]0.0224348239565879[/C][C]2.65851155849199[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]0.0590425137676541[/C][C]0.0213078044661592[/C][C]2.77093371404946[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]0.0601824180072598[/C][C]0.0208154240879239[/C][C]2.89124150212124[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]0.0609358920143142[/C][C]0.0206777118160707[/C][C]2.94693593548175[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]0.063565291276687[/C][C]0.0193285380960051[/C][C]3.2886755822379[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]0.0562769066717566[/C][C]0.0180888422087834[/C][C]3.11113923280453[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]0.0561680717523687[/C][C]0.0176455682728449[/C][C]3.18312626059239[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]0.058731529990125[/C][C]0.0170637024612425[/C][C]3.4418983877341[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]0.0571854212959156[/C][C]0.0156791829171041[/C][C]3.64721947554633[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]0.0556933757721138[/C][C]0.0154029011040761[/C][C]3.61577182089259[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]0.0555549430509091[/C][C]0.0151293592485643[/C][C]3.67199576255557[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]0.0622699418885754[/C][C]0.0137556075883184[/C][C]4.52687687466868[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]0.0643164994234815[/C][C]0.0115756807697215[/C][C]5.55617425039173[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]0.063911118030983[/C][C]0.0112652078128366[/C][C]5.67331904504743[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]0.0575591753032371[/C][C]0.0260652808055771[/C][C]2.20826991017574[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]0.057353403643083[/C][C]0.0251720794160309[/C][C]2.27845315022156[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]0.0581889799249073[/C][C]0.0243958490928802[/C][C]2.38520002740505[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]0.0588786409800644[/C][C]0.0235529085052918[/C][C]2.49984586688458[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]0.0586584725600352[/C][C]0.0229555501681026[/C][C]2.55530676156666[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]0.0592966034972571[/C][C]0.0224399413263313[/C][C]2.64245804545299[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]0.0599383015423039[/C][C]0.0219849757508506[/C][C]2.72633011842121[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]0.0603596490390146[/C][C]0.0214855591436205[/C][C]2.80931246124617[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]0.0609817927171796[/C][C]0.0209020539113606[/C][C]2.91750241271911[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]0.0611951853704322[/C][C]0.0203260922081722[/C][C]3.01067144356594[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]0.061518086110849[/C][C]0.0198558729654836[/C][C]3.0982312496554[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]0.0617088958399331[/C][C]0.0193499405067114[/C][C]3.18910002945641[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]0.0618151838659557[/C][C]0.0187018041086602[/C][C]3.30530592165336[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]0.061581363847518[/C][C]0.0181719588955523[/C][C]3.38881263167452[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]0.0622759951443438[/C][C]0.0177513162663783[/C][C]3.50824661167787[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]0.0630664322891877[/C][C]0.0172604746866437[/C][C]3.65380636593899[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]0.0636252282886762[/C][C]0.0167104487652763[/C][C]3.80751164629925[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]0.0644586150759747[/C][C]0.0162975258184767[/C][C]3.95511661057762[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]0.0656064440324326[/C][C]0.0157298156616127[/C][C]4.17083362219812[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]0.0669493571190329[/C][C]0.0149264550523833[/C][C]4.48528179558235[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]0.0675927767132209[/C][C]0.0142054778930709[/C][C]4.75821913363371[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]0.0680608163260407[/C][C]0.0139015876193076[/C][C]4.8959024098451[/C][/ROW]
[ROW][C]Median[/C][C]0.0747648606221926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.014465456606949[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.0582173323513037[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0636252282886762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0630664322891877[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]66[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232229&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 Mean0.05537661069989810.02749753302347282.0138755957717
Geometric MeanNaN
Harmonic Mean-0.909174873938727
Quadratic Mean0.228503829217612
Winsorized Mean ( 1 / 22 )0.05775247595368490.0268044160860132.15458810101897
Winsorized Mean ( 2 / 22 )0.05583417403976610.02633501104733762.12015001396443
Winsorized Mean ( 3 / 22 )0.05637078259767480.02611264033467162.1587546060146
Winsorized Mean ( 4 / 22 )0.05962587925410290.02498336265125152.38662345363329
Winsorized Mean ( 5 / 22 )0.0560479369077640.02429325755358462.3071396161728
Winsorized Mean ( 6 / 22 )0.05626312182976280.02363529997086362.38046997072689
Winsorized Mean ( 7 / 22 )0.05770388299914120.02334094252557082.47221734666133
Winsorized Mean ( 8 / 22 )0.05673990400241850.02311829898935252.45432866962015
Winsorized Mean ( 9 / 22 )0.05964323880132190.02243482395658792.65851155849199
Winsorized Mean ( 10 / 22 )0.05904251376765410.02130780446615922.77093371404946
Winsorized Mean ( 11 / 22 )0.06018241800725980.02081542408792392.89124150212124
Winsorized Mean ( 12 / 22 )0.06093589201431420.02067771181607072.94693593548175
Winsorized Mean ( 13 / 22 )0.0635652912766870.01932853809600513.2886755822379
Winsorized Mean ( 14 / 22 )0.05627690667175660.01808884220878343.11113923280453
Winsorized Mean ( 15 / 22 )0.05616807175236870.01764556827284493.18312626059239
Winsorized Mean ( 16 / 22 )0.0587315299901250.01706370246124253.4418983877341
Winsorized Mean ( 17 / 22 )0.05718542129591560.01567918291710413.64721947554633
Winsorized Mean ( 18 / 22 )0.05569337577211380.01540290110407613.61577182089259
Winsorized Mean ( 19 / 22 )0.05555494305090910.01512935924856433.67199576255557
Winsorized Mean ( 20 / 22 )0.06226994188857540.01375560758831844.52687687466868
Winsorized Mean ( 21 / 22 )0.06431649942348150.01157568076972155.55617425039173
Winsorized Mean ( 22 / 22 )0.0639111180309830.01126520781283665.67331904504743
Trimmed Mean ( 1 / 22 )0.05755917530323710.02606528080557712.20826991017574
Trimmed Mean ( 2 / 22 )0.0573534036430830.02517207941603092.27845315022156
Trimmed Mean ( 3 / 22 )0.05818897992490730.02439584909288022.38520002740505
Trimmed Mean ( 4 / 22 )0.05887864098006440.02355290850529182.49984586688458
Trimmed Mean ( 5 / 22 )0.05865847256003520.02295555016810262.55530676156666
Trimmed Mean ( 6 / 22 )0.05929660349725710.02243994132633132.64245804545299
Trimmed Mean ( 7 / 22 )0.05993830154230390.02198497575085062.72633011842121
Trimmed Mean ( 8 / 22 )0.06035964903901460.02148555914362052.80931246124617
Trimmed Mean ( 9 / 22 )0.06098179271717960.02090205391136062.91750241271911
Trimmed Mean ( 10 / 22 )0.06119518537043220.02032609220817223.01067144356594
Trimmed Mean ( 11 / 22 )0.0615180861108490.01985587296548363.0982312496554
Trimmed Mean ( 12 / 22 )0.06170889583993310.01934994050671143.18910002945641
Trimmed Mean ( 13 / 22 )0.06181518386595570.01870180410866023.30530592165336
Trimmed Mean ( 14 / 22 )0.0615813638475180.01817195889555233.38881263167452
Trimmed Mean ( 15 / 22 )0.06227599514434380.01775131626637833.50824661167787
Trimmed Mean ( 16 / 22 )0.06306643228918770.01726047468664373.65380636593899
Trimmed Mean ( 17 / 22 )0.06362522828867620.01671044876527633.80751164629925
Trimmed Mean ( 18 / 22 )0.06445861507597470.01629752581847673.95511661057762
Trimmed Mean ( 19 / 22 )0.06560644403243260.01572981566161274.17083362219812
Trimmed Mean ( 20 / 22 )0.06694935711903290.01492645505238334.48528179558235
Trimmed Mean ( 21 / 22 )0.06759277671322090.01420547789307094.75821913363371
Trimmed Mean ( 22 / 22 )0.06806081632604070.01390158761930764.8959024098451
Median0.0747648606221926
Midrange-0.014465456606949
Midmean - Weighted Average at Xnp0.0582173323513037
Midmean - Weighted Average at X(n+1)p0.0630664322891877
Midmean - Empirical Distribution Function0.0630664322891877
Midmean - Empirical Distribution Function - Averaging0.0630664322891877
Midmean - Empirical Distribution Function - Interpolation0.0636252282886762
Midmean - Closest Observation0.0630664322891877
Midmean - True Basic - Statistics Graphics Toolkit0.0630664322891877
Midmean - MS Excel (old versions)0.0630664322891877
Number of observations66



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')