*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 03 Nov 2010 12:58:33 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi.htm/, Retrieved Wed, 03 Nov 2010 13:56:55 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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-4.5741188614556E-14 0.0069756137364543 2.9309887850104E-14 -0.014000228673371 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 1.9095836023553E-14 0.014000228673419 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 -0.014000228673371 1.9095836023553E-14 0.014000228673419 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 2.9309887850104E-14 -0.014000228673371 0.014000228673419 0.00099255591272929 0.0059347355197779 -3.68 etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.000733088002448934 0.000199733516466373 3.67033042535130 Geometric Mean NaN Harmonic Mean -8.47183323501395e-14 Quadratic Mean 0.00506264905259578 Winsorized Mean ( 1 / 210 ) 0.000724762236177459 0.000197392715767212 3.67167670478875 Winsorized Mean ( 2 / 210 ) 0.00071489852878372 0.000194918618177695 3.66767697958945 Winsorized Mean ( 3 / 210 ) 0.000723891588603011 0.000189407858291288 3.82186671204395 Winsorized Mean ( 4 / 210 ) 0.00072346009542562 0.000189311996337479 3.82152272133847 Winsorized Mean ( 5 / 210 ) 0.000729272893854099 0.000188022812798333 3.87864048516439 Winsorized Mean ( 6 / 210 ) 0.000717230365250099 0.000185413451213925 3.86827579420103 Winsorized Mean ( 7 / 210 ) 0.000709012543814188 0.000181127400794428 3.91444110998362 Winsorized Mean ( 8 / 210 ) 0.000701526428002302 0.000179611206700022 3.90580543882185 Winsorized Mean ( 9 / 210 ) 0.000650487010002302 0.000169894509312266 3.82877005640428 Winsorized Mean ( 10 / 210 ) 0.000646321754985263 0.000168361812918124 3.83888569375036 Winsorized Mean ( 11 / 210 ) 0.000556037806459115 0.000153961304725413 3.61154257201702 Winsorized Mean ( 12 / 210 ) 0.000552525305153743 0.000153469482877307 3.60022914520059 Winsorized Mean ( 13 / 210 ) 0.000552525305153743 0.000153469482877307 3.60022914520059 Winsorized Mean ( 14 / 210 ) 0.000552525305153743 0.000153469482877307 3.60022914520059 Winsorized Mean ( 15 / 210 ) 0.000547882326374934 0.000152825908272066 3.58500945663987 Winsorized Mean ( 16 / 210 ) 0.000514737925092775 0.000148410312743490 3.46834337572242 Winsorized Mean ( 17 / 210 ) 0.00049543038837545 0.000145983532115416 3.39374161726514 Winsorized Mean ( 18 / 210 ) 0.000475135020686821 0.000143544205352144 3.31002578279782 Winsorized Mean ( 19 / 210 ) 0.000465189545596402 0.000142389665044102 3.26701762696274 Winsorized Mean ( 20 / 210 ) 0.000447481773436913 0.000138638006133578 3.22769914193490 Winsorized Mean ( 21 / 210 ) 0.000434004325254817 0.000137199676598150 3.16330428770610 Winsorized Mean ( 22 / 210 ) 0.000424223319681982 0.000136184072893660 3.11507293524139 Winsorized Mean ( 23 / 210 ) 0.00042549477237934 0.000136076578045177 3.12687736928597 Winsorized Mean ( 24 / 210 ) 0.000425977858358856 0.000136035842473973 3.13136487128645 Winsorized Mean ( 25 / 210 ) 0.000383124139632411 0.000131827876422046 2.90624524972126 Winsorized Mean ( 26 / 210 ) 0.000383124139632411 0.000131827876422046 2.90624524972126 Winsorized Mean ( 27 / 210 ) 0.000347920433203007 0.000128665018242405 2.70407946119065 Winsorized Mean ( 28 / 210 ) 0.000347920433203007 0.000128665018242405 2.70407946119065 Winsorized Mean ( 29 / 210 ) 0.000347920433203007 0.000128665018242405 2.70407946119065 Winsorized Mean ( 30 / 210 ) 0.000338498823322888 0.000127862363500809 2.64736873349558 Winsorized Mean ( 31 / 210 ) 0.000363242671413206 0.000125726665590486 2.88914582843031 Winsorized Mean ( 32 / 210 ) 0.000363242671413206 0.000125726665590486 2.88914582843031 Winsorized Mean ( 33 / 210 ) 0.000363861535344391 0.000125674700187743 2.89526479713758 Winsorized Mean ( 34 / 210 ) 0.000363861535344391 0.000125674700187743 2.89526479713758 Winsorized Mean ( 35 / 210 ) 0.000370291948631324 0.000125138390330580 2.95905954721904 Winsorized Mean ( 36 / 210 ) 0.000371907499928513 0.000125004685246493 2.97514848499606 Winsorized Mean ( 37 / 210 ) 0.000383116615093835 0.000124087851594354 3.08746271428933 Winsorized Mean ( 38 / 210 ) 0.000383116615093835 0.000124087851594354 3.08746271428933 Winsorized Mean ( 39 / 210 ) 0.000383116615093835 0.000124087851594354 3.08746271428933 Winsorized Mean ( 40 / 210 ) 0.000374110009862286 0.000123316015900768 3.03375037808009 Winsorized Mean ( 41 / 210 ) 0.000374053468299864 0.000123311203937520 3.03341023650529 Winsorized Mean ( 42 / 210 ) 0.000378492028728691 0.000121376351254015 3.11833421270498 Winsorized Mean ( 43 / 210 ) 0.000378492028728691 0.000121376351254015 3.11833421270498 Winsorized Mean ( 44 / 210 ) 0.000380107040289190 0.000121247393081133 3.13497082807248 Winsorized Mean ( 45 / 210 ) 0.000381643489465555 0.000120716903584399 3.16147513839045 Winsorized Mean ( 46 / 210 ) 0.000381643489465555 0.000120716903584399 3.16147513839045 Winsorized Mean ( 47 / 210 ) 0.0003830620369625 0.000120449535603172 3.18026993665231 Winsorized Mean ( 48 / 210 ) 0.0003830620369625 0.000120449535603172 3.18026993665232 Winsorized Mean ( 49 / 210 ) 0.0003830620369625 0.000120449535603172 3.18026993665231 Winsorized Mean ( 50 / 210 ) 0.000406184997984112 0.000118646642569253 3.42348497343299 Winsorized Mean ( 51 / 210 ) 0.000411004132045714 0.000118277894530014 3.47490233639066 Winsorized Mean ( 52 / 210 ) 0.000411004132045714 0.000118277894530014 3.47490233639066 Winsorized Mean ( 53 / 210 ) 0.000368700133693974 0.000114731656266164 3.2135867788628 Winsorized Mean ( 54 / 210 ) 0.000368700133693974 0.000114731656266164 3.2135867788628 Winsorized Mean ( 55 / 210 ) 0.000367668693816653 0.000114647194226455 3.20695762593565 Winsorized Mean ( 56 / 210 ) 0.000367668693816654 0.000114647194226455 3.20695762593565 Winsorized Mean ( 57 / 210 ) 0.000360643872155241 0.000114074270478093 3.16148304647277 Winsorized Mean ( 58 / 210 ) 0.000357135822846922 0.000113789662825517 3.13856121882131 Winsorized Mean ( 59 / 210 ) 0.000358667976720121 0.000113247521409155 3.16711546758077 Winsorized Mean ( 60 / 210 ) 0.000356590787323254 0.000113079517390109 3.15345162018215 Winsorized Mean ( 61 / 210 ) 0.000342192642582958 0.000111611280956473 3.0659324008333 Winsorized Mean ( 62 / 210 ) 0.000351974102882525 0.000110842936602407 3.17543105290555 Winsorized Mean ( 63 / 210 ) 0.000351974102882525 0.000110842936602407 3.17543105290555 Winsorized Mean ( 64 / 210 ) 0.000351974102882525 0.000110842936602407 3.17543105290555 Winsorized Mean ( 65 / 210 ) 0.000483491145685177 0.000101221487499022 4.77656629665562 Winsorized Mean ( 66 / 210 ) 0.000483491145685177 0.000101221487499022 4.77656629665562 Winsorized Mean ( 67 / 210 ) 0.000461207898393485 9.93286783275799e-05 4.64325012835115 Winsorized Mean ( 68 / 210 ) 0.000873967513957304 8.05021219549107e-05 10.8564531310965 Winsorized Mean ( 69 / 210 ) 0.000873967513957304 8.05021219549107e-05 10.8564531310965 Winsorized Mean ( 70 / 210 ) 0.000871398177382893 8.0256108550221e-05 10.8577177877695 Winsorized Mean ( 71 / 210 ) 0.000871398177382893 8.0256108550221e-05 10.8577177877695 Winsorized Mean ( 72 / 210 ) 0.000864959658943281 7.96408112400218e-05 10.8607590188460 Winsorized Mean ( 73 / 210 ) 0.000864959658943281 7.96408112400218e-05 10.8607590188460 Winsorized Mean ( 74 / 210 ) 0.00086123668608108 7.92857529912732e-05 10.8624393865046 Winsorized Mean ( 75 / 210 ) 0.00086123668608108 7.92857529912732e-05 10.8624393865046 Winsorized Mean ( 76 / 210 ) 0.00086123668608108 7.92857529912732e-05 10.8624393865046 Winsorized Mean ( 77 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 78 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 79 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 80 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 81 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 82 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 83 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 84 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 85 / 210 ) 0.000818351378593419 7.52272212109842e-05 10.8783943553923 Winsorized Mean ( 86 / 210 ) 0.000812258697027607 7.46552104050007e-05 10.8801340538878 Winsorized Mean ( 87 / 210 ) 0.000812258697027607 7.46552104050007e-05 10.8801340538878 Winsorized Mean ( 88 / 210 ) 0.000809416818373815 7.438859853839e-05 10.8809257638601 Winsorized Mean ( 89 / 210 ) 0.000799531323498725 7.34619504805479e-05 10.8836114242629 Winsorized Mean ( 90 / 210 ) 0.000795328997370511 7.30683724136847e-05 10.8847230490871 Winsorized Mean ( 91 / 210 ) 0.000795328997370511 7.30683724136847e-05 10.8847230490871 Winsorized Mean ( 92 / 210 ) 0.000795328997370511 7.30683724136847e-05 10.8847230490871 Winsorized Mean ( 93 / 210 ) 0.000701663684917758 6.43261392277376e-05 10.9079091849989 Winsorized Mean ( 94 / 210 ) 0.000619922622331331 5.67493262416229e-05 10.9238763415776 Winsorized Mean ( 95 / 210 ) 0.000605995674538189 5.54638880375001e-05 10.9259501268369 Winsorized Mean ( 96 / 210 ) 0.000605995674538189 5.54638880375001e-05 10.9259501268369 Winsorized Mean ( 97 / 210 ) 0.000605995674538189 5.54638880375001e-05 10.9259501268369 Winsorized Mean ( 98 / 210 ) 0.000605995674538189 5.54638880375001e-05 10.9259501268369 Winsorized Mean ( 99 / 210 ) 0.000161039306211702 1.45441453371814e-05 11.0724489117977 Winsorized Mean ( 100 / 210 ) 0.000143156537428458 1.29207562518025e-05 11.0795788294889 Winsorized Mean ( 101 / 210 ) 0.000111190699462502 1.00285750984754e-05 11.0873876269228 Winsorized Mean ( 102 / 210 ) 0.000104434410125389 9.41900420172188e-06 11.0876275122902 Winsorized Mean ( 103 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 104 / 210 ) 5.28677630773551e-17 1.39466787172322e-15 0.037907063143308 Winsorized Mean ( 105 / 210 ) 5.28677630773551e-17 1.39466787172322e-15 0.037907063143308 Winsorized Mean ( 106 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 107 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 108 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 109 / 210 ) 5.28677630773576e-17 1.39466787172322e-15 0.0379070631433098 Winsorized Mean ( 110 / 210 ) 5.28677630773576e-17 1.39466787172322e-15 0.0379070631433098 Winsorized Mean ( 111 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 112 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 113 / 210 ) 5.28677630773551e-17 1.39466787172322e-15 0.037907063143308 Winsorized Mean ( 114 / 210 ) 5.28677630773564e-17 1.39466787172322e-15 0.0379070631433089 Winsorized Mean ( 115 / 210 ) -4.33515657234548e-16 1.37122034012019e-15 -0.316153169954108 Winsorized Mean ( 116 / 210 ) 1.38865991016748e-16 1.33956589716980e-15 0.103664919590847 Winsorized Mean ( 117 / 210 ) 3.8628712221889e-16 1.32618592374933e-15 0.291276747325743 Winsorized Mean ( 118 / 210 ) 3.8628712221889e-16 1.32618592374933e-15 0.291276747325743 Winsorized Mean ( 119 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 120 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 121 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 122 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 123 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 124 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 125 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 126 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 127 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 128 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 129 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 130 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 131 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 132 / 210 ) 2.18520087386667e-16 1.31818430186098e-15 0.165773547051172 Winsorized Mean ( 133 / 210 ) 2.18520087386668e-16 1.31818430186098e-15 0.165773547051173 Winsorized Mean ( 134 / 210 ) 7.85262507576192e-16 1.28805258302830e-15 0.609650970715799 Winsorized Mean ( 135 / 210 ) 4.04614613418834e-16 1.27005417816126e-15 0.318580593155971 Winsorized Mean ( 136 / 210 ) 4.04614613418836e-16 1.27005417816126e-15 0.318580593155972 Winsorized Mean ( 137 / 210 ) 4.04614613418834e-16 1.27005417816126e-15 0.318580593155971 Winsorized Mean ( 138 / 210 ) 8.9099803373074e-16 1.24466615871583e-15 0.715853024115333 Winsorized Mean ( 139 / 210 ) 8.9099803373074e-16 1.24466615871583e-15 0.715853024115333 Winsorized Mean ( 140 / 210 ) 8.9099803373074e-16 1.24466615871583e-15 0.715853024115333 Winsorized Mean ( 141 / 210 ) 8.9099803373074e-16 1.24466615871583e-15 0.715853024115333 Winsorized Mean ( 142 / 210 ) 8.90998033730738e-16 1.24466615871583e-15 0.715853024115332 Winsorized Mean ( 143 / 210 ) 3.86992025726374e-16 1.22127155274451e-15 0.31687631211642 Winsorized Mean ( 144 / 210 ) 3.86992025726375e-16 1.22127155274451e-15 0.316876312116421 Winsorized Mean ( 145 / 210 ) 3.86992025726374e-16 1.22127155274451e-15 0.31687631211642 Winsorized Mean ( 146 / 210 ) 3.86992025726374e-16 1.22127155274451e-15 0.31687631211642 Winsorized Mean ( 147 / 210 ) 3.86992025726375e-16 1.22127155274451e-15 0.316876312116421 Winsorized Mean ( 148 / 210 ) 3.86992025726374e-16 1.22127155274451e-15 0.31687631211642 Winsorized Mean ( 149 / 210 ) 3.86992025726375e-16 1.22127155274451e-15 0.316876312116421 Winsorized Mean ( 150 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.859251639781619 Winsorized Mean ( 151 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.85925163978162 Winsorized Mean ( 152 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.85925163978162 Winsorized Mean ( 153 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.859251639781619 Winsorized Mean ( 154 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.859251639781619 Winsorized Mean ( 155 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.85925163978162 Winsorized Mean ( 156 / 210 ) 1.02140518265518e-15 1.18871484832403e-15 0.85925163978162 Winsorized Mean ( 157 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 158 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 159 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 160 / 210 ) 5.78725779820581e-16 1.16850867635988e-15 0.49526870576898 Winsorized Mean ( 161 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 162 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 163 / 210 ) 5.78725779820578e-16 1.16850867635988e-15 0.495268705768978 Winsorized Mean ( 164 / 210 ) 5.78725779820581e-16 1.16850867635988e-15 0.49526870576898 Winsorized Mean ( 165 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 166 / 210 ) 5.7872577982058e-16 1.16850867635988e-15 0.495268705768979 Winsorized Mean ( 167 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 168 / 210 ) 6.96444665606216e-16 1.16252326117730e-15 0.599080198103668 Winsorized Mean ( 169 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 170 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 171 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 172 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 173 / 210 ) 6.96444665606213e-16 1.16252326117730e-15 0.599080198103666 Winsorized Mean ( 174 / 210 ) 6.96444665606216e-16 1.16252326117730e-15 0.599080198103668 Winsorized Mean ( 175 / 210 ) 6.96444665606215e-16 1.16252326117730e-15 0.599080198103667 Winsorized Mean ( 176 / 210 ) 2.80551596064014e-15 1.05869114183476e-15 2.64998529767431 Winsorized Mean ( 177 / 210 ) 2.80551596064015e-15 1.05869114183476e-15 2.64998529767431 Winsorized Mean ( 178 / 210 ) 2.80551596064014e-15 1.05869114183476e-15 2.64998529767431 Winsorized Mean ( 179 / 210 ) 2.80551596064014e-15 1.05869114183476e-15 2.64998529767431 Winsorized Mean ( 180 / 210 ) 2.29798543509729e-15 1.03533193010473e-15 2.21956395652246 Winsorized Mean ( 181 / 210 ) 2.29798543509729e-15 1.03533193010473e-15 2.21956395652247 Winsorized Mean ( 182 / 210 ) 3.83749469591091e-15 9.63658382310202e-16 3.98221482462612 Winsorized Mean ( 183 / 210 ) 3.45050267018419e-15 9.45831162484674e-16 3.64811692302441 Winsorized Mean ( 184 / 210 ) 3.06139593393467e-15 9.28190654503974e-16 3.29824041976665 Winsorized Mean ( 185 / 210 ) 3.06139593393467e-15 9.28190654503974e-16 3.29824041976665 Winsorized Mean ( 186 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 187 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 188 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 189 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 190 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 191 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 192 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 193 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 194 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 195 / 210 ) 3.45473209123038e-15 9.10417225925394e-16 3.79466907353254 Winsorized Mean ( 196 / 210 ) 3.73105426624816e-15 8.9810018794317e-16 4.15438535292262 Winsorized Mean ( 197 / 210 ) 3.73105426624816e-15 8.9810018794317e-16 4.15438535292263 Winsorized Mean ( 198 / 210 ) 3.73105426624816e-15 8.9810018794317e-16 4.15438535292263 Winsorized Mean ( 199 / 210 ) 4.15188166034411e-15 8.79589848311579e-16 4.72024736110118 Winsorized Mean ( 200 / 210 ) 4.15188166034411e-15 8.79589848311579e-16 4.72024736110118 Winsorized Mean ( 201 / 210 ) 4.15188166034411e-15 8.79589848311579e-16 4.72024736110118 Winsorized Mean ( 202 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636165 Winsorized Mean ( 203 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636166 Winsorized Mean ( 204 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636166 Winsorized Mean ( 205 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636166 Winsorized Mean ( 206 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636165 Winsorized Mean ( 207 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636165 Winsorized Mean ( 208 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636166 Winsorized Mean ( 209 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636165 Winsorized Mean ( 210 / 210 ) 4.29427216889919e-15 8.73395112774227e-16 4.91675772636166 Trimmed Mean ( 1 / 210 ) 0.000696463995841368 0.000189680872758648 3.67176714084165 Trimmed Mean ( 2 / 210 ) 0.00066798493607821 0.000181527297471026 3.67980433457854 Trimmed Mean ( 3 / 210 ) 0.000644302593606678 0.000174296186040552 3.69659605435527 Trimmed Mean ( 4 / 210 ) 0.000617431711051646 0.000168800972576450 3.65774972518011 Trimmed Mean ( 5 / 210 ) 0.000590497081150193 0.000163065690977869 3.62122208300908 Trimmed Mean ( 6 / 210 ) 0.000562202983414446 0.000157352725587739 3.57288366829697 Trimmed Mean ( 7 / 210 ) 0.000535777861510641 0.000151899489077972 3.52718672566186 Trimmed Mean ( 8 / 210 ) 0.000510385155635528 0.000146966881034309 3.47279027794283 Trimmed Mean ( 9 / 210 ) 0.000485789771323627 0.000142043223044188 3.42001371774352 Trimmed Mean ( 10 / 210 ) 0.000466890088196566 0.000138342681366132 3.37488100986646 Trimmed Mean ( 11 / 210 ) 0.000448297662197079 0.000134691343482536 3.32833314009675 Trimmed Mean ( 12 / 210 ) 0.000438115200318129 0.000132630509039689 3.30327617295826 Trimmed Mean ( 13 / 210 ) 0.000428170613391193 0.000130559266793169 3.27951147327978 Trimmed Mean ( 14 / 210 ) 0.000418159949474708 0.000128423551904870 3.25610017222121 Trimmed Mean ( 15 / 210 ) 0.000408082547798781 0.000126219588519900 3.23311581493898 Trimmed Mean ( 16 / 210 ) 0.000398263834253298 0.000124002715161704 3.2117347893064 Trimmed Mean ( 17 / 210 ) 0.000390568922631143 0.000122097307404474 3.19883321699551 Trimmed Mean ( 18 / 210 ) 0.000384026763449235 0.000120331714938766 3.19140106699764 Trimmed Mean ( 19 / 210 ) 0.000378640295538229 0.000118702484028774 3.1898262166649 Trimmed Mean ( 20 / 210 ) 0.000373776243126395 0.000117111515895611 3.19162671807242 Trimmed Mean ( 21 / 210 ) 0.000369827732574046 0.000115737690367451 3.19539582481641 Trimmed Mean ( 22 / 210 ) 0.000366542241481174 0.000114422817868685 3.20340163184784 Trimmed Mean ( 23 / 210 ) 0.000363713857353955 0.000113138135861848 3.21477682642821 Trimmed Mean ( 24 / 210 ) 0.000360806194387722 0.000111825783794053 3.22650270935914 Trimmed Mean ( 25 / 210 ) 0.000357856614768339 0.000110480300408608 3.23909885694389 Trimmed Mean ( 26 / 210 ) 0.000356754985656618 0.000109344380670110 3.26267324822975 Trimmed Mean ( 27 / 210 ) 0.000355645706342733 0.000108179083694947 3.28756441814218 Trimmed Mean ( 28 / 210 ) 0.000355959741836218 0.000107155093204450 3.32191155073753 Trimmed Mean ( 29 / 210 ) 0.000356275973382104 0.000106105300699777 3.35775848173865 Trimmed Mean ( 30 / 210 ) 0.000356594424096734 0.000105028670601173 3.39521029882246 Trimmed Mean ( 31 / 210 ) 0.000357263451590133 0.000103964639883750 3.43639387381723 Trimmed Mean ( 32 / 210 ) 0.000357048763998173 0.000102978209869905 3.46722636224926 Trimmed Mean ( 33 / 210 ) 0.000356832553799178 0.000101966667821674 3.49950195904441 Trimmed Mean ( 34 / 210 ) 0.000356593782184086 0.000100931461225565 3.53302902637224 Trimmed Mean ( 35 / 210 ) 0.000356353305057459 9.98691334895293e-05 3.56820263284672 Trimmed Mean ( 36 / 210 ) 0.000355903671393786 9.88032925881783e-05 3.60214383621026 Trimmed Mean ( 37 / 210 ) 0.000355399953769041 9.77149591884055e-05 3.6371089618304 Trimmed Mean ( 38 / 210 ) 0.000354548090336774 9.66381834517997e-05 3.66881989781619 Trimmed Mean ( 39 / 210 ) 0.000353690053981084 9.55320298252794e-05 3.70231905077235 Trimmed Mean ( 40 / 210 ) 0.000352825777360989 9.43951716499653e-05 3.73775237857856 Trimmed Mean ( 41 / 210 ) 0.000352214049875779 9.32601581730115e-05 3.77668295632063 Trimmed Mean ( 42 / 210 ) 0.000351599432096489 9.2093073407101e-05 3.81787054214415 Trimmed Mean ( 43 / 210 ) 0.000351599432096489 9.09752418235846e-05 3.8647815059211 Trimmed Mean ( 44 / 210 ) 0.000350110911987696 8.98253458033224e-05 3.89768510053146 Trimmed Mean ( 45 / 210 ) 0.000349315560100914 8.86472564332107e-05 3.94051180099519 Trimmed Mean ( 46 / 210 ) 0.000348474312868377 8.74564234620477e-05 3.98454795055276 Trimmed Mean ( 47 / 210 ) 0.000347626787671418 8.62296657385236e-05 4.03140595170037 Trimmed Mean ( 48 / 210 ) 0.000346737306156820 8.49762970496343e-05 4.08040027861289 Trimmed Mean ( 49 / 210 ) 0.000345841136811285 8.36835547634219e-05 4.13272521451792 Trimmed Mean ( 50 / 210 ) 0.000344938203923519 8.23492203750105e-05 4.18872458479514 Trimmed Mean ( 51 / 210 ) 0.000343476632701619 8.1045982943218e-05 4.23804635625511 Trimmed Mean ( 52 / 210 ) 0.000341890771052965 7.97150265033888e-05 4.28891246794519 Trimmed Mean ( 53 / 210 ) 0.0003402928035902 7.83392753006532e-05 4.34383394898935 Trimmed Mean ( 54 / 210 ) 0.000339645922293107 7.70646747044874e-05 4.40728418819018 Trimmed Mean ( 55 / 210 ) 0.000338994064986036 7.57472534744816e-05 4.47533144023815 Trimmed Mean ( 56 / 210 ) 0.000338359982284622 7.4387870904072e-05 4.54859076046092 Trimmed Mean ( 57 / 210 ) 0.000337720984213429 7.29802475903079e-05 4.62756698373109 Trimmed Mean ( 58 / 210 ) 0.000337228069359059 7.15453773389779e-05 4.71348509018677 Trimmed Mean ( 59 / 210 ) 0.000336805726797860 7.00689082571018e-05 4.80677857234522 Trimmed Mean ( 60 / 210 ) 0.000336347992751632 6.85587103605126e-05 4.90598482647883 Trimmed Mean ( 61 / 210 ) 0.000335929588533124 6.69959724901938e-05 5.01417586829258 Trimmed Mean ( 62 / 210 ) 0.000335801754539364 6.54333230924779e-05 5.13196852412295 Trimmed Mean ( 63 / 210 ) 0.000335475699129219 6.38391973879297e-05 5.25501122908304 Trimmed Mean ( 64 / 210 ) 0.000335147045667998 6.21766510263269e-05 5.39023958569415 Trimmed Mean ( 65 / 210 ) 0.000334815762979087 6.04395188379543e-05 5.53968280053269 Trimmed Mean ( 66 / 210 ) 0.000331922173510294 5.90403613143274e-05 5.62195362835196 Trimmed Mean ( 67 / 210 ) 0.000329005248642559 5.75824221793874e-05 5.71364031227453 Trimmed Mean ( 68 / 210 ) 0.000326488852807672 5.61450372123117e-05 5.81509727338961 Trimmed Mean ( 69 / 210 ) 0.000316179444733656 5.52870863849125e-05 5.71886611156162 Trimmed Mean ( 70 / 210 ) 0.000305785878226383 5.43962103239871e-05 5.6214555463534 Trimmed Mean ( 71 / 210 ) 0.000295354503856694 5.34801745847759e-05 5.52269146744281 Trimmed Mean ( 72 / 210 ) 0.00028483727455392 5.25273650336343e-05 5.42264540342988 Trimmed Mean ( 73 / 210 ) 0.000274349524836137 5.15605015969991e-05 5.3209242799939 Trimmed Mean ( 74 / 210 ) 0.000263774739850987 5.05530685901473e-05 5.21777900347667 Trimmed Mean ( 75 / 210 ) 0.000253177864115487 4.9517041557661e-05 5.11294407240928 Trimmed Mean ( 76 / 210 ) 0.000242492311595589 4.84350599107738e-05 5.0065450944482 Trimmed Mean ( 77 / 210 ) 0.000231716964516701 4.73034059671847e-05 4.8985260105255 Trimmed Mean ( 78 / 210 ) 0.000221590938957264 4.62945433978151e-05 4.78654551256946 Trimmed Mean ( 79 / 210 ) 0.000211379099621900 4.52396976954738e-05 4.67242511311140 Trimmed Mean ( 80 / 210 ) 0.000201080351015596 4.41350069282777e-05 4.55602853631279 Trimmed Mean ( 81 / 210 ) 0.000201080351015596 4.29760316562022e-05 4.67889526478829 Trimmed Mean ( 82 / 210 ) 0.000180217649976217 4.17576223860507e-05 4.31580247338074 Trimmed Mean ( 83 / 210 ) 0.000169651411303255 4.04737445849352e-05 4.19164110074464 Trimmed Mean ( 84 / 210 ) 0.000158993690044381 3.91172432537152e-05 4.06454230460835 Trimmed Mean ( 85 / 210 ) 0.000148243292948473 3.76795192501397e-05 3.93432017973327 Trimmed Mean ( 86 / 210 ) 0.000148243292948473 3.61500729841402e-05 4.10077437502021 Trimmed Mean ( 87 / 210 ) 0.000126557471716251 3.45477019477807e-05 3.66326744127712 Trimmed Mean ( 88 / 210 ) 0.000115620417385750 3.28280396971528e-05 3.52200187560324 Trimmed Mean ( 89 / 210 ) 0.000104631586617888 3.09869901161460e-05 3.37662955407109 Trimmed Mean ( 90 / 210 ) 9.37005795208856e-05 2.90436747934533e-05 3.22619572720207 Trimmed Mean ( 91 / 210 ) 9.37005795208856e-05 2.69385259947376e-05 3.4783113054957 Trimmed Mean ( 92 / 210 ) 7.16763690951126e-05 2.45994070094355e-05 2.91374377714146 Trimmed Mean ( 93 / 210 ) 6.05154516496195e-05 2.19501389567533e-05 2.75695073133015 Trimmed Mean ( 94 / 210 ) 5.06890665243598e-05 1.96584218339408e-05 2.57849113995732 Trimmed Mean ( 95 / 210 ) 4.20184393445147e-05 1.76756210067729e-05 2.37719734590451 Trimmed Mean ( 96 / 210 ) 3.3479490578064e-05 1.55042807564758e-05 2.15937076372152 Trimmed Mean ( 97 / 210 ) 2.48622028321045e-05 1.29096220793962e-05 1.92586604620942 Trimmed Mean ( 98 / 210 ) 1.61654930792699e-05 9.55051302592315e-06 1.69263086028903 Trimmed Mean ( 99 / 210 ) 7.38825823613119e-06 3.74182176591233e-06 1.97450832731734 Trimmed Mean ( 100 / 210 ) 5.11435266355403e-06 2.97628341382999e-06 1.71836883536998 Trimmed Mean ( 101 / 210 ) 3.0824233083697e-06 2.17814262630189e-06 1.41516137242267 Trimmed Mean ( 102 / 210 ) 1.49946849088484e-06 1.49946848952227e-06 1.00000000090870 Trimmed Mean ( 103 / 210 ) 1.48099561964148e-15 1.36247921560819e-15 1.08698584365589 Trimmed Mean ( 104 / 210 ) 1.50169502951668e-15 1.36015066342906e-15 1.10406521122504 Trimmed Mean ( 105 / 210 ) 1.52259157662879e-15 1.35774164985427e-15 1.12141479698454 Trimmed Mean ( 106 / 210 ) 1.5436880906989e-15 1.35524984950799e-15 1.13904317440753 Trimmed Mean ( 107 / 210 ) 1.56498745586585e-15 1.35267285274753e-15 1.15695931406257 Trimmed Mean ( 108 / 210 ) 1.58649261200059e-15 1.35000816173474e-15 1.17517260781740 Trimmed Mean ( 109 / 210 ) 1.60820655605897e-15 1.34725318627472e-15 1.19369289487881 Trimmed Mean ( 110 / 210 ) 1.63013234347401e-15 1.34440523940504e-15 1.21253048983610 Trimmed Mean ( 111 / 210 ) 1.65227308958921e-15 1.34146153271676e-15 1.23169621289325 Trimmed Mean ( 112 / 210 ) 1.67463197113411e-15 1.33841917138696e-15 1.25120142249512 Trimmed Mean ( 113 / 210 ) 1.69721222774381e-15 1.33527514890078e-15 1.27105805057556 Trimmed Mean ( 114 / 210 ) 1.72001716352375e-15 1.33202634143868e-15 1.29127864068065 Trimmed Mean ( 115 / 210 ) 1.7430501486615e-15 1.32866950190256e-15 1.31187638924922 Trimmed Mean ( 116 / 210 ) 1.77300943329586e-15 1.32570984399559e-15 1.33740383789574 Trimmed Mean ( 117 / 210 ) 1.79542127517664e-15 1.32338494132534e-15 1.35668860896858 Trimmed Mean ( 118 / 210 ) 1.81467925852437e-15 1.32127847126195e-15 1.3734267968441 Trimmed Mean ( 119 / 210 ) 1.83413375190625e-15 1.31909000027897e-15 1.39045383674985 Trimmed Mean ( 120 / 210 ) 1.85606515911693e-15 1.31698644608598e-15 1.40932745711473 Trimmed Mean ( 121 / 210 ) 1.87822266330915e-15 1.31479966762925e-15 1.42852383488644 Trimmed Mean ( 122 / 210 ) 1.90060977894378e-15 1.31252707824941e-15 1.44805376623447 Trimmed Mean ( 123 / 210 ) 1.92323009369961e-15 1.31016599168785e-15 1.46792857233454 Trimmed Mean ( 124 / 210 ) 1.94608727039005e-15 1.30771361718956e-15 1.48816013292914 Trimmed Mean ( 125 / 210 ) 1.96918504894040e-15 1.30516705430175e-15 1.50876092255783 Trimmed Mean ( 126 / 210 ) 1.99252724842778e-15 1.30252328734500e-15 1.52974404971234 Trimmed Mean ( 127 / 210 ) 2.01611776918631e-15 1.29977917953121e-15 1.5511232992003 Trimmed Mean ( 128 / 210 ) 2.03996059497968e-15 1.29693146670053e-15 1.57291317803357 Trimmed Mean ( 129 / 210 ) 2.06405979524395e-15 1.29397675064664e-15 1.59512896519391 Trimmed Mean ( 130 / 210 ) 2.08841952740298e-15 1.29091149199659e-15 1.61778676566967 Trimmed Mean ( 131 / 210 ) 2.11304403925938e-15 1.28773200260852e-15 1.64090356920465 Trimmed Mean ( 132 / 210 ) 2.13793767146394e-15 1.28443443744633e-15 1.66449731425336 Trimmed Mean ( 133 / 210 ) 2.16310486006635e-15 1.28101478588667e-15 1.68858695769786 Trimmed Mean ( 134 / 210 ) 2.18855013915055e-15 1.27746886240874e-15 1.71319255095104 Trimmed Mean ( 135 / 210 ) 2.20687665672709e-15 1.27452508194300e-15 1.73152862034126 Trimmed Mean ( 136 / 210 ) 2.23036983047598e-15 1.27186519874531e-15 1.75362124278283 Trimmed Mean ( 137 / 210 ) 2.25412697246925e-15 1.26909776852341e-15 1.77616494834115 Trimmed Mean ( 138 / 210 ) 2.27815255674493e-15 1.26621909896593e-15 1.79917721870204 Trimmed Mean ( 139 / 210 ) 2.29614307365655e-15 1.26383599949076e-15 1.81680461276759 Trimmed Mean ( 140 / 210 ) 2.31433919647573e-15 1.26135116495891e-15 1.83480957624607 Trimmed Mean ( 141 / 210 ) 2.33274447013192e-15 1.25876108140066e-15 1.85320670030266 Trimmed Mean ( 142 / 210 ) 2.35136252151823e-15 1.25606208343081e-15 1.87201138585102 Trimmed Mean ( 143 / 210 ) 2.37019706187415e-15 1.25325034587289e-15 1.89123990245007 Trimmed Mean ( 144 / 210 ) 2.39574442155953e-15 1.25084324089554e-15 1.91530348746522 Trimmed Mean ( 145 / 210 ) 2.42159233841768e-15 1.24832920713517e-15 1.93986676317145 Trimmed Mean ( 146 / 210 ) 2.44774614778302e-15 1.245704423191e-15 1.96494939105448 Trimmed Mean ( 147 / 210 ) 2.47421131202176e-15 1.24296489742133e-15 1.99057215304695 Trimmed Mean ( 148 / 210 ) 2.50099342433522e-15 1.24010645820958e-15 2.01675703547747 Trimmed Mean ( 149 / 210 ) 2.52809821270065e-15 1.23712474352399e-15 2.04352732085794 Trimmed Mean ( 150 / 210 ) 2.55553154395535e-15 1.23401518970743e-15 2.07090768839015 Trimmed Mean ( 151 / 210 ) 2.57517584492322e-15 1.23159569232081e-15 2.09092631695599 Trimmed Mean ( 152 / 210 ) 2.59506118025879e-15 1.22906384712273e-15 2.11141283370583 Trimmed Mean ( 153 / 210 ) 2.61519201356147e-15 1.22641548562478e-15 2.13238665380125 Trimmed Mean ( 154 / 210 ) 2.63557291932753e-15 1.22364624670991e-15 2.15386834750154 Trimmed Mean ( 155 / 210 ) 2.65620858641567e-15 1.22075156521118e-15 2.17587973025141 Trimmed Mean ( 156 / 210 ) 2.67710382164329e-15 1.21772665963126e-15 2.19844396151592 Trimmed Mean ( 157 / 210 ) 2.69826355351935e-15 1.21456651892213e-15 2.22158565338516 Trimmed Mean ( 158 / 210 ) 2.72535002350658e-15 1.21174204042895e-15 2.24911733073304 Trimmed Mean ( 159 / 210 ) 2.75278375592954e-15 1.20878563709648e-15 2.27731342220591 Trimmed Mean ( 160 / 210 ) 2.78057147199666e-15 1.20569212379466e-15 2.30620356318279 Trimmed Mean ( 161 / 210 ) 2.80872006749323e-15 1.20245605861309e-15 2.33581929865513 Trimmed Mean ( 162 / 210 ) 2.80872006749323e-15 1.19907172640931e-15 2.34241205561914 Trimmed Mean ( 163 / 210 ) 2.86612838725597e-15 1.19553312101082e-15 2.39736426945049 Trimmed Mean ( 164 / 210 ) 2.89540282845949e-15 1.19183392593334e-15 2.42936768744190 Trimmed Mean ( 165 / 210 ) 2.92506759554572e-15 1.18796749346086e-15 2.46224548369100 Trimmed Mean ( 166 / 210 ) 2.95513054742505e-15 1.18392682191308e-15 2.49604155656337 Trimmed Mean ( 167 / 210 ) 2.98559975541086e-15 1.17970453090373e-15 2.5308029910877 Trimmed Mean ( 168 / 210 ) 3.01497300292760e-15 1.17546675618370e-15 2.56491558529148 Trimmed Mean ( 169 / 210 ) 3.044748623698e-15 1.17103777797650e-15 2.60004303956716 Trimmed Mean ( 170 / 210 ) 3.07493494268592e-15 1.16640924426089e-15 2.63624020284098 Trimmed Mean ( 171 / 210 ) 3.10554051610422e-15 1.16157232505830e-15 2.67356620772482 Trimmed Mean ( 172 / 210 ) 3.10554051610422e-15 1.15651767604999e-15 2.6852512334364 Trimmed Mean ( 173 / 210 ) 3.16804485618386e-15 1.15123539858719e-15 2.7518653961403 Trimmed Mean ( 174 / 210 ) 3.19996196601176e-15 1.14571499564257e-15 2.79298252897272 Trimmed Mean ( 175 / 210 ) 3.23233503455149e-15 1.13994532318207e-15 2.83551760669422 Trimmed Mean ( 176 / 210 ) 3.26517390263855e-15 1.13391453635405e-15 2.87955908311861 Trimmed Mean ( 177 / 210 ) 3.27113537545350e-15 1.13077457056858e-15 2.89282714750888 Trimmed Mean ( 178 / 210 ) 3.27718387706866e-15 1.12747219188826e-15 2.90666492765568 Trimmed Mean ( 179 / 210 ) 3.28332132723700e-15 1.12400015750362e-15 2.921103974335 Trimmed Mean ( 180 / 210 ) 3.28954970259301e-15 1.12035081460391e-15 2.93617825748269 Trimmed Mean ( 181 / 210 ) 3.30249923593717e-15 1.11717319217746e-15 2.95612109121626 Trimmed Mean ( 182 / 210 ) 3.30249923593717e-15 1.11382545434984e-15 2.96500607257614 Trimmed Mean ( 183 / 210 ) 3.30880104460249e-15 1.11233855556421e-15 2.97463486098815 Trimmed Mean ( 184 / 210 ) 3.30693911609716e-15 1.11122950300626e-15 2.97592811129543 Trimmed Mean ( 185 / 210 ) 3.31017264880541e-15 1.11049396400382e-15 2.98081102293503 Trimmed Mean ( 186 / 210 ) 3.3134563138037e-15 1.10966780764029e-15 2.98598940240483 Trimmed Mean ( 187 / 210 ) 3.31158711563966e-15 1.10922872207622e-15 2.98548626602558 Trimmed Mean ( 188 / 210 ) 3.30968848128407e-15 1.10870640085266e-15 2.98518027742848 Trimmed Mean ( 189 / 210 ) 3.30775970987521e-15 1.10809691147365e-15 2.98508160759717 Trimmed Mean ( 190 / 210 ) 3.3058000781238e-15 1.10739611114914e-15 2.98520109005384 Trimmed Mean ( 191 / 210 ) 3.30380883940867e-15 1.10659963311013e-15 2.98555027541732 Trimmed Mean ( 192 / 210 ) 3.30178522282825e-15 1.10570287183649e-15 2.98614149146978 Trimmed Mean ( 193 / 210 ) 3.29972843220552e-15 1.10470096709310e-15 2.98698790939634 Trimmed Mean ( 194 / 210 ) 3.29763764504358e-15 1.10358878665770e-15 2.98810361695565 Trimmed Mean ( 195 / 210 ) 3.29551201142894e-15 1.10236090761049e-15 2.98950369944848 Trimmed Mean ( 196 / 210 ) 3.2933506528796e-15 1.10101159603965e-15 2.99120432947829 Trimmed Mean ( 197 / 210 ) 3.28738919325442e-15 1.09989957327353e-15 2.98880849955281 Trimmed Mean ( 198 / 210 ) 3.28132582833651e-15 1.09866701629565e-15 2.9866427039924 Trimmed Mean ( 199 / 210 ) 3.27515792264415e-15 1.09730779016167e-15 2.98472128969540 Trimmed Mean ( 200 / 210 ) 3.26309028107213e-15 1.09636730949787e-15 2.97627469626637 Trimmed Mean ( 201 / 210 ) 3.26309028107213e-15 1.09530720169576e-15 2.97915532374861 Trimmed Mean ( 202 / 210 ) 3.23831423819862e-15 1.09412118947262e-15 2.95973998982648 Trimmed Mean ( 203 / 210 ) 3.22361185364370e-15 1.09298960068473e-15 2.94935272176807 Trimmed Mean ( 204 / 210 ) 3.20864456125895e-15 1.09172540429453e-15 2.93905825460970 Trimmed Mean ( 205 / 210 ) 3.19340513628539e-15 1.09032145081640e-15 2.9288657339487 Trimmed Mean ( 206 / 210 ) 3.17788608883525e-15 1.08877013965548e-15 2.91878512561048 Trimmed Mean ( 207 / 210 ) 3.16207965161752e-15 1.08706338382804e-15 2.90882730359512 Trimmed Mean ( 208 / 210 ) 3.14597776697515e-15 1.08519257126203e-15 2.89900414938938 Trimmed Mean ( 209 / 210 ) 3.12957207318859e-15 1.08314852227142e-15 2.88932866438827 Trimmed Mean ( 210 / 210 ) 3.11285388999658e-15 1.08092144274003e-15 2.87981509748368 Median -5.3290705182008e-15 Midrange 0.0122330260772245 Midmean - Weighted Average at Xnp 1.84097663154561e-15 Midmean - Weighted Average at X(n+1)p 1.84097663154561e-15 Midmean - Empirical Distribution Function 1.84097663154561e-15 Midmean - Empirical Distribution Function - Averaging 1.84097663154561e-15 Midmean - Empirical Distribution Function - Interpolation 1.84097663154561e-15 Midmean - Closest Observation 1.84097663154561e-15 Midmean - True Basic - Statistics Graphics Toolkit 1.84097663154561e-15 Midmean - MS Excel (old versions) 1.84097663154561e-15 Number of observations 630

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi/17wlb1288789106.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi/17wlb1288789106.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi/2i5kw1288789106.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/03/t12887890107i4jubhgd9pvdgi/2i5kw1288789106.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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