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workshop2Q8

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

Title produced by software: Central Tendency

Date of computation: Sun, 21 Oct 2007 09:18:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Oct/21/o1pu9pczpb714hz1192983270.htm/, Retrieved Sun, 21 Oct 2007 18:14:32 +0200

User-defined keywords:

werkloosheid onder 25

Dataseries X:

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221 213 203 195 185 183 230 250 251 244 232 225 217 206 193 180 173 169 215 239 237 230 224 213 214 197 186 177 169 159 203 217 216 206 197 195 189 175 163 153 146 144 184 194 195 196 184 185 179 163 153 143 135 132 171 177 177 171 162 158 151 139 127 117 109 109 149 157 153 145 138 134 129 116 109 97 90 89 125 136 132 125 118 115 111 101 92 85 79 81 120 128 129 124 118 117 114 109 101 95 89 90 128 139 139 135 129 128 125 117 109 104 98 100 135 146 145 140 136 139 137 131 124 119 114 116 155 167 169 163 159 158 155 147 137 129 121 119 153 166 165 158 150 147 143 138 130 124 116 114 151 164 164 160 152 151 150 143 134 128 120 119 155 169 167 158 150 146 142 136 130 124 116 116 148 160 163 151 141 139 134 130 123 117 110 105 137 160 155 142 132 131 128 123 118 112 105 102 131 149 145 132 122 119 116 111 104 100 93 91 119 139 134 124 113 109 109 106 101 98 93 91 122 139 140 132 117 114 113 110 107 103 98 98 137 148 147 139 130 128 127 123 118 114 108 111 151 159 158 148 138 137 136 133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 140.868686868687 1.96707091651016 71.6134256707971 Geometric Mean 137.155715072968 Harmonic Mean 133.737557471298 Quadratic Mean 144.876912809874 Winsorized Mean ( 1 / 99 ) 140.872053872054 1.96573251216703 71.663897809146 Winsorized Mean ( 2 / 99 ) 140.858585858586 1.95565794912913 72.0261873612977 Winsorized Mean ( 3 / 99 ) 140.848484848485 1.94307754444648 72.4873205657925 Winsorized Mean ( 4 / 99 ) 140.821548821549 1.93852167878311 72.6437833338796 Winsorized Mean ( 5 / 99 ) 140.754208754209 1.92320916044713 73.1871559521298 Winsorized Mean ( 6 / 99 ) 140.713804713805 1.91679180768896 73.4111050294299 Winsorized Mean ( 7 / 99 ) 140.737373737374 1.91470425939383 73.5034525811987 Winsorized Mean ( 8 / 99 ) 140.602693602694 1.89395803875515 74.2374913940057 Winsorized Mean ( 9 / 99 ) 140.602693602694 1.88675522401118 74.5208980016902 Winsorized Mean ( 10 / 99 ) 140.535353535354 1.86895468489842 75.194628671798 Winsorized Mean ( 11 / 99 ) 140.387205387205 1.84780255339339 75.9752199332075 Winsorized Mean ( 12 / 99 ) 140.387205387205 1.84780255339339 75.9752199332075 Winsorized Mean ( 13 / 99 ) 140.430976430976 1.83423536187041 76.5610451909379 Winsorized Mean ( 14 / 99 ) 140.383838383838 1.82770411940174 76.808842795512 Winsorized Mean ( 15 / 99 ) 140.434343434343 1.81243194774662 77.4839262842086 Winsorized Mean ( 16 / 99 ) 140.434343434343 1.80074582409305 77.9867661251269 Winsorized Mean ( 17 / 99 ) 140.434343434343 1.80074582409305 77.9867661251269 Winsorized Mean ( 18 / 99 ) 140.010101010101 1.74473510149925 80.2471967749088 Winsorized Mean ( 19 / 99 ) 140.010101010101 1.74473510149925 80.2471967749088 Winsorized Mean ( 20 / 99 ) 139.942760942761 1.70843121756029 81.9130202634702 Winsorized Mean ( 21 / 99 ) 139.942760942761 1.70843121756029 81.9130202634702 Winsorized Mean ( 22 / 99 ) 139.572390572391 1.64869057373154 84.656510321698 Winsorized Mean ( 23 / 99 ) 139.572390572391 1.64869057373154 84.656510321698 Winsorized Mean ( 24 / 99 ) 139.491582491583 1.63923031983097 85.0957798938017 Winsorized Mean ( 25 / 99 ) 139.491582491583 1.62284117768517 85.9551657978965 Winsorized Mean ( 26 / 99 ) 139.491582491583 1.62284117768517 85.9551657978965 Winsorized Mean ( 27 / 99 ) 139.582491582492 1.61581665582472 86.3851050670401 Winsorized Mean ( 28 / 99 ) 139.582491582492 1.59777858518429 87.3603469697223 Winsorized Mean ( 29 / 99 ) 139.484848484848 1.58659764448139 87.9144431923328 Winsorized Mean ( 30 / 99 ) 139.181818181818 1.53377578891114 90.7445659190033 Winsorized Mean ( 31 / 99 ) 138.868686868687 1.49996920672384 92.5810251611746 Winsorized Mean ( 32 / 99 ) 138.760942760943 1.48859691398245 93.2159280041195 Winsorized Mean ( 33 / 99 ) 138.872053872054 1.48017174212812 93.8215815905191 Winsorized Mean ( 34 / 99 ) 138.872053872054 1.45964904201713 95.1407152503884 Winsorized Mean ( 35 / 99 ) 138.989898989899 1.45105078679260 95.78568872639 Winsorized Mean ( 36 / 99 ) 138.989898989899 1.42972840932338 97.2141968247496 Winsorized Mean ( 37 / 99 ) 138.616161616162 1.39151093918749 99.615574489914 Winsorized Mean ( 38 / 99 ) 138.488215488216 1.37873248873101 100.446037661505 Winsorized Mean ( 39 / 99 ) 138.225589225589 1.35298060901403 102.163762218528 Winsorized Mean ( 40 / 99 ) 138.225589225589 1.35298060901403 102.163762218528 Winsorized Mean ( 41 / 99 ) 138.225589225589 1.35298060901403 102.163762218528 Winsorized Mean ( 42 / 99 ) 137.942760942761 1.32593337483322 104.034458714874 Winsorized Mean ( 43 / 99 ) 137.797979797980 1.28827725310602 106.962984455210 Winsorized Mean ( 44 / 99 ) 137.501683501683 1.26130455285956 109.015450067113 Winsorized Mean ( 45 / 99 ) 137.653198653199 1.25026741821127 110.099004939388 Winsorized Mean ( 46 / 99 ) 137.343434343434 1.22276020766361 112.322459859782 Winsorized Mean ( 47 / 99 ) 137.343434343434 1.22276020766361 112.322459859782 Winsorized Mean ( 48 / 99 ) 137.343434343434 1.22276020766361 112.322459859782 Winsorized Mean ( 49 / 99 ) 137.343434343434 1.22276020766361 112.322459859782 Winsorized Mean ( 50 / 99 ) 137.175084175084 1.18148469461797 116.103987465906 Winsorized Mean ( 51 / 99 ) 137.175084175084 1.18148469461797 116.103987465906 Winsorized Mean ( 52 / 99 ) 137 1.16666666666667 117.428571428571 Winsorized Mean ( 53 / 99 ) 137 1.13894964647534 120.286265880119 Winsorized Mean ( 54 / 99 ) 136.818181818182 1.12397101007662 121.727500613077 Winsorized Mean ( 55 / 99 ) 136.818181818182 1.12397101007662 121.727500613077 Winsorized Mean ( 56 / 99 ) 136.818181818182 1.09526744121816 124.917601554933 Winsorized Mean ( 57 / 99 ) 136.818181818182 1.09526744121816 124.917601554933 Winsorized Mean ( 58 / 99 ) 136.818181818182 1.09526744121816 124.917601554933 Winsorized Mean ( 59 / 99 ) 136.818181818182 1.09526744121816 124.917601554933 Winsorized Mean ( 60 / 99 ) 136.616161616162 1.07908163360931 126.604102378435 Winsorized Mean ( 61 / 99 ) 136.616161616162 1.07908163360931 126.604102378435 Winsorized Mean ( 62 / 99 ) 136.407407407407 1.06262470270594 128.368376022174 Winsorized Mean ( 63 / 99 ) 136.407407407407 1.03113611752829 132.288458418454 Winsorized Mean ( 64 / 99 ) 136.622895622896 1.01619073094925 134.446114751778 Winsorized Mean ( 65 / 99 ) 136.622895622896 1.01619073094925 134.446114751778 Winsorized Mean ( 66 / 99 ) 136.400673400673 0.999062941758313 136.528608658643 Winsorized Mean ( 67 / 99 ) 136.400673400673 0.999062941758313 136.528608658643 Winsorized Mean ( 68 / 99 ) 136.400673400673 0.999062941758313 136.528608658643 Winsorized Mean ( 69 / 99 ) 136.168350168350 0.981455023980067 138.741304330127 Winsorized Mean ( 70 / 99 ) 136.168350168350 0.981455023980067 138.741304330127 Winsorized Mean ( 71 / 99 ) 136.168350168350 0.981455023980067 138.741304330127 Winsorized Mean ( 72 / 99 ) 136.410774410774 0.964799786821119 141.387649825493 Winsorized Mean ( 73 / 99 ) 136.410774410774 0.964799786821119 141.387649825493 Winsorized Mean ( 74 / 99 ) 136.161616161616 0.946110539366786 143.917238521354 Winsorized Mean ( 75 / 99 ) 136.161616161616 0.946110539366786 143.917238521354 Winsorized Mean ( 76 / 99 ) 136.161616161616 0.946110539366786 143.917238521354 Winsorized Mean ( 77 / 99 ) 135.643097643098 0.9081370985133 149.364118991678 Winsorized Mean ( 78 / 99 ) 135.643097643098 0.9081370985133 149.364118991678 Winsorized Mean ( 79 / 99 ) 135.643097643098 0.9081370985133 149.364118991678 Winsorized Mean ( 80 / 99 ) 135.912457912458 0.889633295732017 152.773573746051 Winsorized Mean ( 81 / 99 ) 135.367003367003 0.850752937391871 159.114353201053 Winsorized Mean ( 82 / 99 ) 135.367003367003 0.850752937391871 159.114353201053 Winsorized Mean ( 83 / 99 ) 135.367003367003 0.850752937391871 159.114353201053 Winsorized Mean ( 84 / 99 ) 135.649831649832 0.8314309605248 163.152249663892 Winsorized Mean ( 85 / 99 ) 135.649831649832 0.8314309605248 163.152249663892 Winsorized Mean ( 86 / 99 ) 135.360269360269 0.811188504714947 166.866601996333 Winsorized Mean ( 87 / 99 ) 135.06734006734 0.79107035460001 170.739984480438 Winsorized Mean ( 88 / 99 ) 135.06734006734 0.79107035460001 170.739984480438 Winsorized Mean ( 89 / 99 ) 135.367003367003 0.770693798255356 175.643042247697 Winsorized Mean ( 90 / 99 ) 135.367003367003 0.770693798255356 175.643042247697 Winsorized Mean ( 91 / 99 ) 135.367003367003 0.770693798255356 175.643042247697 Winsorized Mean ( 92 / 99 ) 135.367003367003 0.728820188989853 185.734431361764 Winsorized Mean ( 93 / 99 ) 135.680134680135 0.708172628705172 191.591893248138 Winsorized Mean ( 94 / 99 ) 135.680134680135 0.708172628705172 191.591893248138 Winsorized Mean ( 95 / 99 ) 135.680134680135 0.708172628705172 191.591893248138 Winsorized Mean ( 96 / 99 ) 135.680134680135 0.665237110419385 203.957555216061 Winsorized Mean ( 97 / 99 ) 135.680134680135 0.665237110419385 203.957555216061 Winsorized Mean ( 98 / 99 ) 135.680134680135 0.665237110419385 203.957555216061 Winsorized Mean ( 99 / 99 ) 135.680134680135 0.665237110419385 203.957555216061 Trimmed Mean ( 1 / 99 ) 140.705084745763 1.93339856352805 72.7760366641656 Trimmed Mean ( 2 / 99 ) 140.535836177474 1.89945769147890 73.9873474454986 Trimmed Mean ( 3 / 99 ) 140.371134020619 1.86930449505841 75.0927066145169 Trimmed Mean ( 4 / 99 ) 140.207612456747 1.84234685040642 76.1027232335853 Trimmed Mean ( 5 / 99 ) 140.048780487805 1.81538504951823 77.1454962268039 Trimmed Mean ( 6 / 99 ) 139.901754385965 1.79070869266245 78.1264730322815 Trimmed Mean ( 7 / 99 ) 139.759717314488 1.76612849011277 79.1333802137826 Trimmed Mean ( 8 / 99 ) 139.612099644128 1.74070528564558 80.2043291276329 Trimmed Mean ( 9 / 99 ) 139.480286738351 1.71732271506096 81.2196132474731 Trimmed Mean ( 10 / 99 ) 139.346570397112 1.69381976362387 82.2676493625181 Trimmed Mean ( 11 / 99 ) 139.218181818182 1.67150643541939 83.2890492481122 Trimmed Mean ( 12 / 99 ) 139.102564102564 1.65069837021198 84.2689170915584 Trimmed Mean ( 13 / 99 ) 138.985239852399 1.62887007624586 85.3261668191027 Trimmed Mean ( 14 / 99 ) 138.862453531599 1.60739699890484 86.3896433962542 Trimmed Mean ( 15 / 99 ) 138.741573033708 1.58552369746408 87.5052030162743 Trimmed Mean ( 16 / 99 ) 138.615094339623 1.56400851535902 88.6280943987083 Trimmed Mean ( 17 / 99 ) 138.486692015209 1.54247754639557 89.7819824598563 Trimmed Mean ( 18 / 99 ) 138.356321839080 1.51982605449165 91.0343137164848 Trimmed Mean ( 19 / 99 ) 138.250965250965 1.50095341114189 92.1087651520024 Trimmed Mean ( 20 / 99 ) 138.143968871595 1.48111322793535 93.2703633092019 Trimmed Mean ( 21 / 99 ) 138.039215686275 1.46316835362526 94.3426744736913 Trimmed Mean ( 22 / 99 ) 137.932806324111 1.44429284856497 95.5019658659658 Trimmed Mean ( 23 / 99 ) 137.844621513944 1.42900483712498 96.4619698497831 Trimmed Mean ( 24 / 99 ) 137.755020080321 1.41293081841182 97.4959412628304 Trimmed Mean ( 25 / 99 ) 137.668016194332 1.39671199829236 98.5657861911737 Trimmed Mean ( 26 / 99 ) 137.579591836735 1.38077960750787 99.6390670087081 Trimmed Mean ( 27 / 99 ) 137.489711934156 1.36400247161597 100.798726391799 Trimmed Mean ( 28 / 99 ) 137.394190871369 1.34676981429546 102.017575247812 Trimmed Mean ( 29 / 99 ) 137.297071129707 1.32979733677337 103.246613098840 Trimmed Mean ( 30 / 99 ) 137.202531645570 1.31265439000965 104.522967118985 Trimmed Mean ( 31 / 99 ) 137.119148936170 1.29803706931323 105.635772797088 Trimmed Mean ( 32 / 99 ) 137.047210300429 1.28479744214527 106.668339930376 Trimmed Mean ( 33 / 99 ) 136.978354978355 1.27155158620499 107.725362041484 Trimmed Mean ( 34 / 99 ) 136.903930131004 1.25805370321813 108.822007980106 Trimmed Mean ( 35 / 99 ) 136.828193832599 1.24502283495778 109.900148005911 Trimmed Mean ( 36 / 99 ) 136.746666666667 1.23172804151483 111.020178203047 Trimmed Mean ( 37 / 99 ) 136.663677130045 1.21891540840652 112.11908241336 Trimmed Mean ( 38 / 99 ) 136.592760180995 1.20765885490783 113.105418492890 Trimmed Mean ( 39 / 99 ) 136.525114155251 1.19650507526164 114.103247013305 Trimmed Mean ( 40 / 99 ) 136.465437788018 1.18619806760683 115.044393946231 Trimmed Mean ( 41 / 99 ) 136.404651162791 1.17528888501661 116.060530225182 Trimmed Mean ( 42 / 99 ) 136.342723004695 1.16373644542443 117.159450957101 Trimmed Mean ( 43 / 99 ) 136.289099526066 1.15305140027833 118.198633203314 Trimmed Mean ( 44 / 99 ) 136.239234449761 1.14378549899066 119.112573616281 Trimmed Mean ( 45 / 99 ) 136.198067632850 1.13543782817646 119.952025776336 Trimmed Mean ( 46 / 99 ) 136.151219512195 1.12712217814861 120.795440061196 Trimmed Mean ( 47 / 99 ) 136.113300492611 1.11976555515831 121.555177211508 Trimmed Mean ( 48 / 99 ) 136.074626865672 1.11194196801103 122.375655187359 Trimmed Mean ( 49 / 99 ) 136.035175879397 1.10362022883004 123.262669825841 Trimmed Mean ( 50 / 99 ) 135.994923857868 1.09476631481476 124.222788021094 Trimmed Mean ( 51 / 99 ) 135.958974358974 1.08749739739628 125.020045734814 Trimmed Mean ( 52 / 99 ) 135.922279792746 1.07974654747371 125.883504893593 Trimmed Mean ( 53 / 99 ) 135.890052356021 1.07226734711758 126.731502848906 Trimmed Mean ( 54 / 99 ) 135.857142857143 1.06568500686686 127.483395169991 Trimmed Mean ( 55 / 99 ) 135.828877005348 1.05942305451886 128.210233320847 Trimmed Mean ( 56 / 99 ) 135.8 1.05271737234642 128.999486060834 Trimmed Mean ( 57 / 99 ) 135.8 1.04697166265152 129.707426518190 Trimmed Mean ( 58 / 99 ) 135.740331491713 1.0408004955711 130.419164930576 Trimmed Mean ( 59 / 99 ) 135.709497206704 1.03417368818572 131.225053157930 Trimmed Mean ( 60 / 99 ) 135.677966101695 1.02705823370804 132.103479285542 Trimmed Mean ( 61 / 99 ) 135.651428571429 1.02028260264321 132.95476000473 Trimmed Mean ( 62 / 99 ) 135.624277456647 1.01299822960521 133.884022195679 Trimmed Mean ( 63 / 99 ) 135.602339181287 1.00605253077526 134.786539502855 Trimmed Mean ( 64 / 99 ) 135.579881656805 1.00019671912700 135.553215746541 Trimmed Mean ( 65 / 99 ) 135.550898203593 0.994598306120164 136.287079285671 Trimmed Mean ( 66 / 99 ) 135.521212121212 0.988536955580819 137.092711968048 Trimmed Mean ( 67 / 99 ) 135.496932515337 0.982902163167436 137.853936630574 Trimmed Mean ( 68 / 99 ) 135.472049689441 0.976790524717104 138.690994907712 Trimmed Mean ( 69 / 99 ) 135.446540880503 0.970164252462849 139.611968320478 Trimmed Mean ( 70 / 99 ) 135.426751592357 0.96395955092204 140.490077060619 Trimmed Mean ( 71 / 99 ) 135.406451612903 0.95722055984177 141.457943230227 Trimmed Mean ( 72 / 99 ) 135.385620915033 0.949902869358164 142.525752139807 Trimmed Mean ( 73 / 99 ) 135.357615894040 0.942840776758645 143.563599740966 Trimmed Mean ( 74 / 99 ) 135.328859060403 0.935157034327293 144.712443036641 Trimmed Mean ( 75 / 99 ) 135.306122448980 0.927911966385134 145.817844095805 Trimmed Mean ( 76 / 99 ) 135.282758620690 0.920014963660786 147.044085111826 Trimmed Mean ( 77 / 99 ) 135.258741258741 0.91140671330442 148.406566776696 Trimmed Mean ( 78 / 99 ) 135.248226950355 0.9043492809318 149.553087288355 Trimmed Mean ( 79 / 99 ) 135.237410071942 0.896626675167155 150.829117421396 Trimmed Mean ( 80 / 99 ) 135.226277372263 0.88817627495798 152.251620747988 Trimmed Mean ( 81 / 99 ) 135.207407407407 0.880040723233343 153.637671346212 Trimmed Mean ( 82 / 99 ) 135.203007518797 0.873573399968691 154.770059989971 Trimmed Mean ( 83 / 99 ) 135.198473282443 0.866443642547449 156.038392624064 Trimmed Mean ( 84 / 99 ) 135.193798449612 0.858586187970052 157.460951904258 Trimmed Mean ( 85 / 99 ) 135.193798449612 0.851153104707593 158.836051589164 Trimmed Mean ( 86 / 99 ) 135.168 0.842939250862813 160.353192548152 Trimmed Mean ( 87 / 99 ) 135.162601626016 0.835246955202377 161.823519121081 Trimmed Mean ( 88 / 99 ) 135.165289256198 0.828083777205756 163.226587667607 Trimmed Mean ( 89 / 99 ) 135.168067226891 0.820121484337237 164.814688809334 Trimmed Mean ( 90 / 99 ) 135.162393162393 0.812693765234045 166.314052038369 Trimmed Mean ( 91 / 99 ) 135.156521739130 0.80441111343164 168.019212418074 Trimmed Mean ( 92 / 99 ) 135.150442477876 0.795175604064084 169.963014190994 Trimmed Mean ( 93 / 99 ) 135.144144144144 0.787998308662428 171.503089103759 Trimmed Mean ( 94 / 99 ) 135.128440366972 0.781420867681677 172.926582787419 Trimmed Mean ( 95 / 99 ) 135.112149532710 0.773996253061854 174.564345755189 Trimmed Mean ( 96 / 99 ) 135.095238095238 0.765621657145883 176.451693645726 Trimmed Mean ( 97 / 99 ) 135.077669902913 0.759568610270358 177.83471838684 Trimmed Mean ( 98 / 99 ) 135.059405940594 0.752661519414649 179.442421934405 Trimmed Mean ( 99 / 99 ) 135.040404040404 0.744791464288559 181.313039307449 Median 135 Midrange 165 Midmean - Weighted Average at Xnp 135.086092715232 Midmean - Weighted Average at X(n+1)p 135.086092715232 Midmean - Empirical Distribution Function 135.086092715232 Midmean - Empirical Distribution Function - Averaging 135.086092715232 Midmean - Empirical Distribution Function - Interpolation 135.086092715232 Midmean - Closest Observation 135.086092715232 Midmean - True Basic - Statistics Graphics Toolkit 135.086092715232 Midmean - MS Excel (old versions) 135.086092715232 Number of observations 297

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/o1pu9pczpb714hz1192983270/1ca1z1192983530.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/o1pu9pczpb714hz1192983270/1ca1z1192983530.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/o1pu9pczpb714hz1192983270/2x0n61192983530.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/21/o1pu9pczpb714hz1192983270/2x0n61192983530.ps (open in new window)

Parameters:

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')

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Software written by Ed van Stee & Patrick Wessa

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