R version 3.0.2 (2013-09-25) -- "Frisbee Sailing" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > x <- c(25.7300 + ,26.2400 + ,25.5150 + ,26.4400 + ,27.0800 + ,26.8000 + ,26.2850 + ,25.4600 + ,24.6500 + ,23.7050 + ,21.6500 + ,20.7500 + ,23.6300 + ,21.8650 + ,22.1050 + ,22.8900 + ,22.1000 + ,23.2300 + ,23.0150 + ,22.6900 + ,21.5300 + ,20.8050 + ,20.5050 + ,22.6250 + ,21.9250 + ,22.3300 + ,22.0300 + ,22.7250 + ,23.0150 + ,22.3650 + ,22.2450 + ,23.1250 + ,22.9500 + ,22.2200 + ,21.9150 + ,23.1400 + ,22.5100 + ,21.9850 + ,21.7450 + ,21.1350 + ,20.5350 + ,22.0000 + ,22.6150 + ,22.5350 + ,22.6900 + ,23.4350 + ,22.1650 + ,21.9650 + ,23.0700 + ,22.3750 + ,22.9900 + ,22.9900 + ,22.4150 + ,22.6550 + ,22.1100 + ,22.2850 + ,22.4850 + ,23.2300 + ,22.7400 + ,22.5900 + ,22.2150 + ,22.3300 + ,21.9850 + ,22.0500 + ,22.2900 + ,22.2050 + ,22.4650 + ,22.6350 + ,22.9500 + ,22.7200 + ,22.3550 + ,22.4650 + ,22.6200 + ,22.3000 + ,21.8650 + ,22.0100 + ,21.3100 + ,21.6800 + ,21.9200 + ,21.4400 + ,21.6450 + ,21.5600 + ,21.1000 + ,21.5150 + ,21.6650 + ,21.9300 + ,21.7750 + ,21.3600 + 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,37.7700 + ,37.8700 + ,38.0700 + ,38.2000 + ,38.1200 + ,38.3100 + ,38.3500 + ,38.4700 + ,38.5500 + ,38.6500 + ,38.8000 + ,38.4700 + ,37.9700 + ,38.1700 + ,38.2700 + ,38.4000 + ,38.1400 + ,38.4500 + ,38.4400 + ,38.4000 + ,38.6200 + ,38.6100 + ,38.8200 + ,38.9500 + ,38.6600 + ,38.4100 + ,38.3300 + ,38.0700 + ,38.2200 + ,38.6200 + ,38.9000 + ,38.9900 + ,38.8900 + ,38.6300 + ,38.7300 + ,40.1800 + ,40.5900 + ,40.7200 + ,40.7500 + ,40.7100 + ,40.7300 + ,40.7000 + ,41.0100 + ,41.0300 + ,40.5700 + ,40.7900 + ,40.7800 + ,40.9500 + ,40.7600 + ,40.4900 + ,40.9100 + ,40.7300 + ,40.8700 + ,40.8200 + ,41.1100 + ,40.8900 + ,40.5200 + ,40.8900 + ,40.7100 + ,40.5800 + ,40.8700 + ,40.5800 + ,40.5800 + ,40.7700 + ,40.5800 + ,40.6600 + ,40.9100 + ,40.8600 + ,40.8800 + ,40.7900 + ,40.8900 + ,40.9900 + ,40.9100 + ,41.0700 + ,40.8600 + ,40.4200 + ,40.3700 + ,40.6600 + ,40.9200 + ,41.5600 + ,41.7900 + ,41.6900 + ,41.7300 + ,41.8500 + ,41.9600 + ,42.0300 + ,42.1900 + ,42.3600 + ,42.2900 + ,42.2900 + ,42.2300 + ,42.1400 + ,41.9400 + ,41.9500 + ,42.2600 + ,41.9700 + ,42.3800 + ,42.1000 + ,42.1200 + ,42.0200 + ,42.4300 + ,42.4000 + ,41.1900 + ,40.8100 + ,40.9700 + ,41.0000 + ,40.6800 + ,40.3500 + ,39.6200 + ,39.2900 + ,39.2900 + ,39.4000 + ,39.1800 + ,39.9200 + ,39.3500 + ,39.4500 + ,39.5700 + ,39.6800 + ,39.9400 + ,40.1800 + ,40.8800 + ,41.3500 + ,41.2600 + ,41.2500 + ,41.4100 + ,41.1200 + ,41.4100 + ,41.6000 + ,41.6000 + ,41.6300 + ,41.7200 + ,41.6400 + ,41.7800 + ,41.8700 + ,41.8400 + ,41.7800 + ,41.9400 + ,42.1700 + ,41.9500 + ,41.4600 + ,41.5000 + ,41.6400 + ,41.6100 + ,41.7900 + ,42.0500 + ,42.2200 + ,41.8900 + ,42.2700 + ,41.7800) > ylimmax = '' > ylimmin = '' > main = 'Robustness of Central Tendency' > #'GNU S' R Code compiled by R2WASP v. 1.2.291 () > #Author: root > #To cite this work: Wessa, P., (2012), Central Tendency (v1.0.4) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > # > 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)) [1] 33.03119 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 0.1638966 > (armose <- arm / armse) [1] 201.5367 > (geo <- geomean(x)) [1] 32.36969 > (har <- harmean(x)) [1] 31.66681 > (qua <- quamean(x)) [1] 33.63958 > (win <- winmean(x)) [,1] [,2] [1,] 33.03141 0.16387670 [2,] 33.03139 0.16387114 [3,] 33.03126 0.16384075 [4,] 33.03129 0.16383435 [5,] 33.03197 0.16379775 [6,] 33.03205 0.16377882 [7,] 33.03163 0.16375415 [8,] 33.03412 0.16362395 [9,] 33.03445 0.16359114 [10,] 33.03408 0.16357425 [11,] 33.03445 0.16353629 [12,] 33.03445 0.16351516 [13,] 33.03428 0.16350864 [14,] 33.03497 0.16347356 [15,] 33.03512 0.16345732 [16,] 33.03501 0.16345332 [17,] 33.03591 0.16339837 [18,] 33.03609 0.16337903 [19,] 33.03666 0.16333992 [20,] 33.03639 0.16330690 [21,] 33.03945 0.16315676 [22,] 33.03982 0.16311399 [23,] 33.03982 0.16310091 [24,] 33.03997 0.16307958 [25,] 33.03981 0.16307339 [26,] 33.04007 0.16306091 [27,] 33.04016 0.16305659 [28,] 33.04025 0.16303624 [29,] 33.04063 0.16300131 [30,] 33.04073 0.16297957 [31,] 33.04104 0.16292980 [32,] 33.04242 0.16286390 [33,] 33.04220 0.16283725 [34,] 33.04197 0.16280983 [35,] 33.04244 0.16278775 [36,] 33.04232 0.16277326 [37,] 33.04207 0.16274350 [38,] 33.04220 0.16273752 [39,] 33.04207 0.16270007 [40,] 33.04260 0.16267495 [41,] 33.04273 0.16266852 [42,] 33.04273 0.16262171 [43,] 33.04245 0.16256341 [44,] 33.04245 0.16251455 [45,] 33.04215 0.16250365 [46,] 33.04078 0.16244092 [47,] 33.04063 0.16242226 [48,] 33.04206 0.16235493 [49,] 33.04206 0.16232790 [50,] 33.04222 0.16232013 [51,] 33.04188 0.16230787 [52,] 33.04240 0.16228363 [53,] 33.04258 0.16224623 [54,] 33.04150 0.16217773 [55,] 33.04132 0.16212589 [56,] 33.04280 0.16199534 [57,] 33.04262 0.16197298 [58,] 33.04070 0.16190411 [59,] 33.04109 0.16188593 [60,] 33.04089 0.16186248 [61,] 33.04149 0.16183431 [62,] 33.04416 0.16171060 [63,] 33.04333 0.16157837 [64,] 33.04290 0.16156330 [65,] 33.04333 0.16143810 [66,] 33.04333 0.16126038 [67,] 33.04333 0.16126038 [68,] 33.04513 0.16114139 [69,] 33.04445 0.16109876 [70,] 33.04422 0.16107186 [71,] 33.04422 0.16107186 [72,] 33.04255 0.16099405 [73,] 33.04110 0.16082659 [74,] 33.03939 0.16074732 [75,] 33.03790 0.16065594 [76,] 33.03790 0.16061564 [77,] 33.03790 0.16061564 [78,] 33.03867 0.16058037 [79,] 33.03867 0.16053854 [80,] 33.03602 0.16044746 [81,] 33.03495 0.16032526 [82,] 33.03332 0.16018342 [83,] 33.03387 0.16011490 [84,] 33.03220 0.15992632 [85,] 33.03192 0.15989459 [86,] 33.03192 0.15989459 [87,] 33.02876 0.15976533 [88,] 33.03138 0.15960110 [89,] 33.03020 0.15956166 [90,] 33.03199 0.15948116 [91,] 33.03169 0.15944747 [92,] 33.03138 0.15941343 [93,] 33.03200 0.15938576 [94,] 33.02982 0.15928884 [95,] 33.03139 0.15921826 [96,] 33.03393 0.15910440 [97,] 33.03297 0.15904735 [98,] 33.03362 0.15901835 [99,] 33.03362 0.15896732 [100,] 33.03428 0.15888627 [101,] 33.03294 0.15884198 [102,] 33.03396 0.15874441 [103,] 33.03396 0.15869152 [104,] 33.03258 0.15864609 [105,] 33.03258 0.15859226 [106,] 33.03188 0.15856916 [107,] 33.03471 0.15844326 [108,] 33.03542 0.15841155 [109,] 33.03434 0.15834810 [110,] 33.03580 0.15828357 [111,] 33.03690 0.15823479 [112,] 33.03616 0.15821044 [113,] 33.03728 0.15816083 [114,] 33.03690 0.15811939 [115,] 33.03690 0.15811939 [116,] 33.03690 0.15806029 [117,] 33.03690 0.15806029 [118,] 33.03690 0.15806029 [119,] 33.03808 0.15800814 [120,] 33.03650 0.15795612 [121,] 33.03690 0.15793845 [122,] 33.03851 0.15786726 [123,] 33.03892 0.15778685 [124,] 33.03810 0.15776003 [125,] 33.04058 0.15758750 [126,] 33.04266 0.15749602 [127,] 33.04308 0.15747759 [128,] 33.04181 0.15740374 [129,] 33.04267 0.15736634 [130,] 33.04439 0.15729102 [131,] 33.04569 0.15723416 [132,] 33.04656 0.15712937 [133,] 33.04568 0.15710069 [134,] 33.04834 0.15698466 [135,] 33.04790 0.15693611 [136,] 33.04835 0.15684804 [137,] 33.06013 0.15619988 [138,] 33.06561 0.15596405 [139,] 33.06469 0.15593413 [140,] 33.06840 0.15577513 [141,] 33.06747 0.15574479 [142,] 33.06982 0.15564419 [143,] 33.06982 0.15564419 [144,] 33.07077 0.15553173 [145,] 33.07317 0.15535719 [146,] 33.07752 0.15509960 [147,] 33.07898 0.15503761 [148,] 33.08779 0.15466444 [149,] 33.08582 0.15460039 [150,] 33.09426 0.15424511 [151,] 33.09476 0.15422414 [152,] 33.09677 0.15413975 [153,] 33.10537 0.15370481 [154,] 33.10588 0.15360802 [155,] 33.10588 0.15322854 [156,] 33.11569 0.15274660 [157,] 33.11829 0.15263958 [158,] 33.12038 0.15255354 [159,] 33.12617 0.15231604 [160,] 33.12988 0.15208682 [161,] 33.14586 0.15143730 [162,] 33.14639 0.15133750 [163,] 33.14532 0.15122401 [164,] 33.14966 0.15104894 [165,] 33.15075 0.15084643 [166,] 33.15075 0.15084643 [167,] 33.15572 0.15052677 [168,] 33.15461 0.15045063 [169,] 33.15517 0.15042825 [170,] 33.16417 0.15006903 [171,] 33.16191 0.14991438 [172,] 33.16760 0.14968831 [173,] 33.17046 0.14957491 [174,] 33.16989 0.14951497 [175,] 33.17104 0.14938602 [176,] 33.17104 0.14930248 [177,] 33.17397 0.14918689 [178,] 33.17456 0.14907930 [179,] 33.17575 0.14899026 [180,] 33.17872 0.14883056 [181,] 33.17932 0.14880703 [182,] 33.17992 0.14869736 [183,] 33.18174 0.14862612 [184,] 33.18296 0.14849156 [185,] 33.18724 0.14832400 [186,] 33.18540 0.14822086 [187,] 33.19220 0.14795554 [188,] 33.19345 0.14790714 [189,] 33.19470 0.14785853 [190,] 33.19533 0.14783411 [191,] 33.19343 0.14772838 [192,] 33.19343 0.14772838 [193,] 33.19407 0.14761303 [194,] 33.19279 0.14757189 [195,] 33.19408 0.14743046 [196,] 33.19602 0.14735508 [197,] 33.19276 0.14720478 [198,] 33.19211 0.14713759 [199,] 33.19079 0.14709559 [200,] 33.18947 0.14705343 [201,] 33.19479 0.14675389 [202,] 33.19278 0.14664304 [203,] 33.19211 0.14657443 [204,] 33.19481 0.14647029 [205,] 33.19617 0.14641801 [206,] 33.19481 0.14637472 [207,] 33.19481 0.14627849 [208,] 33.19412 0.14620836 [209,] 33.19412 0.14620836 [210,] 33.19620 0.14612814 [211,] 33.19620 0.14603020 [212,] 33.19620 0.14603020 [213,] 33.19479 0.14598558 [214,] 33.19904 0.14582239 [215,] 33.19904 0.14572277 [216,] 33.20119 0.14564057 [217,] 33.20190 0.14551264 [218,] 33.20190 0.14541181 [219,] 33.20480 0.14519979 [220,] 33.20553 0.14517199 [221,] 33.21065 0.14487481 [222,] 33.21359 0.14476298 [223,] 33.21506 0.14460417 [224,] 33.21729 0.14431368 [225,] 33.21878 0.14415388 [226,] 33.22476 0.14392758 [227,] 33.22626 0.14387085 [228,] 33.22702 0.14373785 [229,] 33.22853 0.14357581 [230,] 33.23766 0.14312725 [231,] 33.24225 0.14295536 [232,] 33.24148 0.14287821 [233,] 33.24303 0.14282051 [234,] 33.24457 0.14254928 [235,] 33.24380 0.14241782 [236,] 33.24926 0.14205305 [237,] 33.24534 0.14166121 [238,] 33.24849 0.14154412 [239,] 33.24612 0.14141579 [240,] 33.25883 0.14094506 [241,] 33.25643 0.14081584 [242,] 33.26364 0.14038639 [243,] 33.27168 0.14003623 [244,] 33.27087 0.14001100 [245,] 33.27412 0.13983708 [246,] 33.28633 0.13939094 [247,] 33.28796 0.13922074 [248,] 33.28796 0.13910971 [249,] 33.28961 0.13882709 [250,] 33.29375 0.13867696 [251,] 33.29873 0.13849642 [252,] 33.29373 0.13834038 [253,] 33.29122 0.13820585 [254,] 33.29122 0.13797972 [255,] 33.29122 0.13797972 [256,] 33.28867 0.13773021 [257,] 33.28867 0.13761607 [258,] 33.28953 0.13747074 [259,] 33.29124 0.13717927 [260,] 33.30243 0.13666205 [261,] 33.32834 0.13539300 [262,] 33.32487 0.13517089 [263,] 33.33009 0.13498599 [264,] 33.33271 0.13489333 [265,] 33.33359 0.13474629 [266,] 33.33447 0.13471522 [267,] 33.33358 0.13451276 [268,] 33.33358 0.13439561 [269,] 33.33269 0.13430946 [270,] 33.33537 0.13421505 [271,] 33.33179 0.13410480 [272,] 33.32909 0.13396264 [273,] 33.32999 0.13393083 [274,] 33.33271 0.13383511 [275,] 33.33271 0.13383511 [276,] 33.32906 0.13372318 [277,] 33.32814 0.13363485 [278,] 33.32446 0.13340153 [279,] 33.32262 0.13334522 [280,] 33.32910 0.13299583 [281,] 33.32538 0.13282166 [282,] 33.32725 0.13245096 [283,] 33.32912 0.13238541 [284,] 33.32818 0.13235688 [285,] 33.33007 0.13210615 [286,] 33.32439 0.13193417 [287,] 33.32724 0.13183462 [288,] 33.33010 0.13148661 [289,] 33.32914 0.13127114 [290,] 33.32914 0.13127114 [291,] 33.32914 0.13114599 [292,] 33.32817 0.13105411 [293,] 33.33690 0.13075082 [294,] 33.33787 0.13059093 [295,] 33.34471 0.13022787 [296,] 33.34373 0.13013500 [297,] 33.34176 0.12994879 [298,] 33.33979 0.12988954 [299,] 33.33880 0.12985983 [300,] 33.33781 0.12983004 [301,] 33.33681 0.12973586 [302,] 33.33581 0.12938367 [303,] 33.33080 0.12891132 [304,] 33.32979 0.12881670 [305,] 33.32576 0.12869664 [306,] 33.32778 0.12856178 [307,] 33.32981 0.12842658 [308,] 33.33083 0.12839148 [309,] 33.33083 0.12839148 [310,] 33.33083 0.12819417 [311,] 33.32671 0.12800623 [312,] 33.32362 0.12784853 [313,] 33.32672 0.12760922 [314,] 33.32776 0.12757352 [315,] 33.32255 0.12735315 [316,] 33.32464 0.12728131 [317,] 33.32569 0.12724530 [318,] 33.32254 0.12695105 [319,] 33.32042 0.12688899 [320,] 33.31831 0.12669198 [321,] 33.32362 0.12623983 [322,] 33.32149 0.12617740 [323,] 33.32042 0.12607826 [324,] 33.32042 0.12580618 [325,] 33.31934 0.12570660 [326,] 33.32042 0.12546474 [327,] 33.31934 0.12543319 [328,] 33.31934 0.12529582 [329,] 33.31825 0.12519526 [330,] 33.31934 0.12515799 [331,] 33.32153 0.12508325 [332,] 33.31714 0.12495544 [333,] 33.31714 0.12495544 [334,] 33.31824 0.12477815 [335,] 33.31714 0.12467600 [336,] 33.31936 0.12460023 [337,] 33.32159 0.12452427 [338,] 33.32383 0.12437762 [339,] 33.32383 0.12430691 [340,] 33.32945 0.12411573 [341,] 33.32945 0.12397362 [342,] 33.32832 0.12372718 [343,] 33.33059 0.12357884 [344,] 33.33059 0.12350729 [345,] 33.33287 0.12342993 [346,] 33.33631 0.12331364 [347,] 33.33401 0.12324715 [348,] 33.33516 0.12320818 [349,] 33.33632 0.12316911 [350,] 33.33863 0.12287280 [351,] 33.33863 0.12279998 [352,] 33.33747 0.12269330 [353,] 33.33747 0.12254694 [354,] 33.33278 0.12241178 [355,] 33.33161 0.12230442 [356,] 33.33279 0.12226464 [357,] 33.33515 0.12218490 [358,] 33.33515 0.12203675 [359,] 33.33634 0.12199669 [360,] 33.33753 0.12195653 [361,] 33.33753 0.12195653 [362,] 33.33873 0.12176647 [363,] 33.34113 0.12168556 [364,] 33.34233 0.12164502 [365,] 33.34354 0.12145358 [366,] 33.34596 0.12137213 [367,] 33.34718 0.12133131 [368,] 33.34718 0.12117941 [369,] 33.35450 0.12093349 [370,] 33.35083 0.12075159 [371,] 33.34838 0.12068107 [372,] 33.35084 0.12059850 [373,] 33.35331 0.12051575 [374,] 33.35454 0.12032030 [375,] 33.36075 0.12011265 [376,] 33.35826 0.12004121 [377,] 33.35951 0.11984448 [378,] 33.36326 0.11971909 [379,] 33.36075 0.11964715 [380,] 33.36452 0.11936515 [381,] 33.36831 0.11908267 [382,] 33.36831 0.11908267 [383,] 33.36957 0.11904043 [384,] 33.37084 0.11899809 [385,] 33.37212 0.11887673 [386,] 33.37084 0.11884014 [387,] 33.37212 0.11879750 [388,] 33.36955 0.11872398 [389,] 33.36312 0.11846035 [390,] 33.36441 0.11841737 [391,] 33.36570 0.11837429 [392,] 33.36570 0.11829407 [393,] 33.36440 0.11809619 [394,] 33.36571 0.11805281 [395,] 33.36309 0.11797828 [396,] 33.36440 0.11793468 [397,] 33.36966 0.11775995 [398,] 33.37097 0.11763488 [399,] 33.36569 0.11740298 [400,] 33.36569 0.11723973 [401,] 33.36835 0.11715160 [402,] 33.36968 0.11710744 [403,] 33.36834 0.11698733 [404,] 33.36701 0.11686698 [405,] 33.36299 0.11650536 [406,] 33.36299 0.11650536 [407,] 33.37107 0.11623740 [408,] 33.37647 0.11605853 [409,] 33.37782 0.11601374 [410,] 33.37511 0.11593675 [411,] 33.38871 0.11532007 [412,] 33.39143 0.11523007 [413,] 33.39143 0.11523007 [414,] 33.39143 0.11523007 [415,] 33.39143 0.11506153 [416,] 33.39143 0.11497708 [417,] 33.39695 0.11471050 [418,] 33.39834 0.11466493 [419,] 33.41081 0.11425433 [420,] 33.41359 0.11416298 [421,] 33.41359 0.11373650 [422,] 33.42058 0.11350740 [423,] 33.42758 0.11319244 [424,] 33.42898 0.11297498 [425,] 33.42476 0.11259767 [426,] 33.42617 0.11255154 [427,] 33.43747 0.11218201 [428,] 33.43889 0.11196298 [429,] 33.44173 0.11169724 [430,] 33.43641 0.11152405 [431,] 33.43461 0.11123527 [432,] 33.43604 0.11101464 [433,] 33.45037 0.11054798 [434,] 33.46186 0.11017458 [435,] 33.46330 0.11012784 [436,] 33.46618 0.10994655 [437,] 33.46907 0.10976492 [438,] 33.47777 0.10930723 [439,] 33.48068 0.10921320 [440,] 33.48359 0.10894240 [441,] 33.48651 0.10884806 [442,] 33.48651 0.10867074 [443,] 33.48504 0.10854044 [444,] 33.48945 0.10839809 [445,] 33.49092 0.10835056 [446,] 33.49682 0.10816010 [447,] 33.50718 0.10764744 [448,] 33.51162 0.10750433 [449,] 33.53540 0.10674107 [450,] 33.53391 0.10660885 [451,] 33.54883 0.10595097 [452,] 33.54434 0.10573346 [453,] 33.54434 0.10573346 [454,] 33.54284 0.10532860 [455,] 33.54736 0.10491221 [456,] 33.54736 0.10491221 [457,] 33.54131 0.10455915 [458,] 33.54586 0.10441403 [459,] 33.54434 0.10427977 [460,] 33.54890 0.10376813 [461,] 33.55196 0.10367092 [462,] 33.55348 0.10325498 [463,] 33.55348 0.10325498 [464,] 33.55041 0.10298414 [465,] 33.56118 0.10264153 [466,] 33.55810 0.10255463 [467,] 33.55810 0.10236935 [468,] 33.55810 0.10218374 [469,] 33.56896 0.10183879 [470,] 33.57519 0.10164150 [471,] 33.57830 0.10154271 [472,] 33.57205 0.10136674 [473,] 33.57519 0.10108025 [474,] 33.57675 0.10103057 [475,] 33.57990 0.10093103 [476,] 33.58462 0.10059313 [477,] 33.58304 0.10054871 [478,] 33.58304 0.10026516 [479,] 33.58304 0.09988650 [480,] 33.57828 0.09927891 [481,] 33.57828 0.09927891 [482,] 33.58785 0.09897663 [483,] 33.59904 0.09843325 [484,] 33.59904 0.09843325 [485,] 33.60546 0.09823103 [486,] 33.60224 0.09814076 [487,] 33.61030 0.09750347 [488,] 33.60868 0.09736212 [489,] 33.61839 0.09705697 [490,] 33.62326 0.09671145 [491,] 33.62488 0.09646736 [492,] 33.62488 0.09646736 [493,] 33.63467 0.09596669 [494,] 33.63467 0.09557853 [495,] 33.63303 0.09543543 [496,] 33.63795 0.09508658 [497,] 33.65933 0.09441845 [498,] 33.67581 0.09390472 [499,] 33.67581 0.09390472 [500,] 33.67912 0.09340978 [501,] 33.68244 0.09330663 [502,] 33.67912 0.09301675 [503,] 33.70075 0.09224616 > (tri <- trimean(x)) [,1] [,2] [1,] 33.03387 0.16371153 [2,] 33.03634 0.16354500 [3,] 33.03882 0.16337991 [4,] 33.04136 0.16322373 [5,] 33.04389 0.16306788 [6,] 33.04630 0.16291822 [7,] 33.04869 0.16277053 [8,] 33.05115 0.16262523 [9,] 33.05331 0.16249552 [10,] 33.05543 0.16236846 [11,] 33.05760 0.16224207 [12,] 33.05974 0.16211818 [13,] 33.06188 0.16199505 [14,] 33.06405 0.16187137 [15,] 33.06617 0.16174925 [16,] 33.06828 0.16162721 [17,] 33.07041 0.16150436 [18,] 33.07249 0.16138387 [19,] 33.07456 0.16126348 [20,] 33.07661 0.16114422 [21,] 33.07868 0.16102568 [22,] 33.08060 0.16091380 [23,] 33.08251 0.16080302 [24,] 33.08443 0.16069186 [25,] 33.08635 0.16058066 [26,] 33.08827 0.16046872 [27,] 33.08827 0.16035629 [28,] 33.09212 0.16024302 [29,] 33.09405 0.16012953 [30,] 33.09597 0.16001634 [31,] 33.09789 0.15990293 [32,] 33.09980 0.15979028 [33,] 33.10168 0.15967891 [34,] 33.10356 0.15956742 [35,] 33.10546 0.15945581 [36,] 33.10735 0.15934389 [37,] 33.10925 0.15923140 [38,] 33.11116 0.15911878 [39,] 33.11308 0.15900531 [40,] 33.11500 0.15889189 [41,] 33.11691 0.15877814 [42,] 33.11883 0.15866353 [43,] 33.12075 0.15854915 [44,] 33.12269 0.15843527 [45,] 33.12462 0.15832163 [46,] 33.12658 0.15820721 [47,] 33.12856 0.15809331 [48,] 33.13056 0.15797881 [49,] 33.13253 0.15786491 [50,] 33.13451 0.15775059 [51,] 33.13649 0.15763539 [52,] 33.13848 0.15751939 [53,] 33.14047 0.15740287 [54,] 33.14047 0.15728610 [55,] 33.14448 0.15716975 [56,] 33.14650 0.15705345 [57,] 33.14850 0.15693887 [58,] 33.15052 0.15682369 [59,] 33.15257 0.15670884 [60,] 33.15462 0.15659328 [61,] 33.15462 0.15647710 [62,] 33.15874 0.15636039 [63,] 33.16076 0.15624505 [64,] 33.16280 0.15613120 [65,] 33.16485 0.15601654 [66,] 33.16689 0.15590319 [67,] 33.16895 0.15579210 [68,] 33.17101 0.15567994 [69,] 33.17305 0.15556890 [70,] 33.17510 0.15545755 [71,] 33.17716 0.15534560 [72,] 33.17923 0.15523256 [73,] 33.18133 0.15511978 [74,] 33.18346 0.15500880 [75,] 33.18563 0.15489809 [76,] 33.18782 0.15478784 [77,] 33.19001 0.15467718 [78,] 33.19221 0.15456542 [79,] 33.19441 0.15445316 [80,] 33.19662 0.15434047 [81,] 33.19887 0.15422812 [82,] 33.20114 0.15411662 [83,] 33.20344 0.15400627 [84,] 33.20573 0.15389590 [85,] 33.20806 0.15378737 [86,] 33.21040 0.15367823 [87,] 33.21275 0.15356799 [88,] 33.21514 0.15345858 [89,] 33.21751 0.15335059 [90,] 33.21990 0.15324208 [91,] 33.22227 0.15313369 [92,] 33.22465 0.15302469 [93,] 33.22705 0.15291506 [94,] 33.22945 0.15280473 [95,] 33.23187 0.15269465 [96,] 33.23429 0.15258448 [97,] 33.23669 0.15247483 [98,] 33.23910 0.15236486 [99,] 33.24151 0.15225417 [100,] 33.24393 0.15214305 [101,] 33.24393 0.15203192 [102,] 33.24880 0.15192023 [103,] 33.25123 0.15180875 [104,] 33.25368 0.15169683 [105,] 33.25615 0.15158434 [106,] 33.25863 0.15147142 [107,] 33.26112 0.15135762 [108,] 33.26112 0.15124435 [109,] 33.26606 0.15113033 [110,] 33.26854 0.15101594 [111,] 33.27103 0.15090122 [112,] 33.27350 0.15078595 [113,] 33.27599 0.15066978 [114,] 33.27848 0.15055306 [115,] 33.27848 0.15043563 [116,] 33.28349 0.15031698 [117,] 33.28600 0.15019784 [118,] 33.28853 0.15007744 [119,] 33.29106 0.14995579 [120,] 33.29358 0.14983354 [121,] 33.29614 0.14971063 [122,] 33.29614 0.14958666 [123,] 33.30124 0.14946229 [124,] 33.30379 0.14933761 [125,] 33.30636 0.14921195 [126,] 33.30891 0.14908709 [127,] 33.31145 0.14896207 [128,] 33.31399 0.14883595 [129,] 33.31656 0.14870937 [130,] 33.31912 0.14858192 [131,] 33.32168 0.14845405 [132,] 33.32423 0.14832551 [133,] 33.32678 0.14819688 [134,] 33.32935 0.14806720 [135,] 33.33191 0.14793755 [136,] 33.33447 0.14780709 [137,] 33.33704 0.14767627 [138,] 33.33952 0.14755175 [139,] 33.34195 0.14742867 [140,] 33.34440 0.14730460 [141,] 33.34682 0.14718106 [142,] 33.34926 0.14705652 [143,] 33.35169 0.14693180 [144,] 33.35412 0.14680574 [145,] 33.35656 0.14667959 [146,] 33.35898 0.14655406 [147,] 33.36137 0.14643012 [148,] 33.36376 0.14630553 [149,] 33.36609 0.14618384 [150,] 33.36843 0.14606150 [151,] 33.37072 0.14594184 [152,] 33.37300 0.14582109 [153,] 33.37528 0.14569995 [154,] 33.37750 0.14558233 [155,] 33.37972 0.14546445 [156,] 33.38194 0.14534935 [157,] 33.38410 0.14523827 [158,] 33.38624 0.14512711 [159,] 33.38837 0.14501562 [160,] 33.39046 0.14490546 [161,] 33.39253 0.14479651 [162,] 33.39448 0.14469335 [163,] 33.39644 0.14459004 [164,] 33.39840 0.14448670 [165,] 33.40034 0.14438402 [166,] 33.40228 0.14428226 [167,] 33.40423 0.14417929 [168,] 33.40614 0.14407847 [169,] 33.40807 0.14397722 [170,] 33.41000 0.14387500 [171,] 33.41187 0.14377536 [172,] 33.41376 0.14367607 [173,] 33.41562 0.14357796 [174,] 33.41746 0.14347984 [175,] 33.41931 0.14338114 [176,] 33.42116 0.14328255 [177,] 33.42302 0.14318361 [178,] 33.42486 0.14308466 [179,] 33.42670 0.14298558 [180,] 33.42854 0.14288621 [181,] 33.43037 0.14278725 [182,] 33.43219 0.14268732 [183,] 33.43402 0.14258726 [184,] 33.43585 0.14248670 [185,] 33.43767 0.14238625 [186,] 33.43946 0.14228628 [187,] 33.44128 0.14218607 [188,] 33.44305 0.14208732 [189,] 33.44482 0.14198783 [190,] 33.44659 0.14188759 [191,] 33.44836 0.14178635 [192,] 33.45015 0.14168486 [193,] 33.45194 0.14158211 [194,] 33.45374 0.14147921 [195,] 33.45374 0.14137542 [196,] 33.45736 0.14127174 [197,] 33.45917 0.14116751 [198,] 33.46100 0.14106340 [199,] 33.46284 0.14095864 [200,] 33.46470 0.14085295 [201,] 33.46658 0.14074634 [202,] 33.46658 0.14064134 [203,] 33.47029 0.14053608 [204,] 33.47217 0.14043013 [205,] 33.47403 0.14032389 [206,] 33.47590 0.14021681 [207,] 33.47778 0.14010879 [208,] 33.47966 0.14000032 [209,] 33.47966 0.13989114 [210,] 33.48347 0.13978058 [211,] 33.48536 0.13966942 [212,] 33.48727 0.13955779 [213,] 33.48918 0.13944475 [214,] 33.49111 0.13933068 [215,] 33.49302 0.13921679 [216,] 33.49302 0.13910240 [217,] 33.49684 0.13898738 [218,] 33.49875 0.13887213 [219,] 33.50067 0.13875637 [220,] 33.50257 0.13864119 [221,] 33.50448 0.13852482 [222,] 33.50636 0.13840986 [223,] 33.50636 0.13829452 [224,] 33.51010 0.13817922 [225,] 33.51197 0.13806522 [226,] 33.51383 0.13795128 [227,] 33.51565 0.13783807 [228,] 33.51748 0.13772394 [229,] 33.51931 0.13760960 [230,] 33.51931 0.13749531 [231,] 33.52291 0.13738386 [232,] 33.52466 0.13727262 [233,] 33.52643 0.13716062 [234,] 33.52819 0.13704771 [235,] 33.52995 0.13693586 [236,] 33.53172 0.13682375 [237,] 33.53172 0.13671363 [238,] 33.53524 0.13660565 [239,] 33.53700 0.13649734 [240,] 33.53878 0.13638873 [241,] 33.54050 0.13628319 [242,] 33.54223 0.13617738 [243,] 33.54393 0.13607419 [244,] 33.54393 0.13597290 [245,] 33.54725 0.13587043 [246,] 33.54890 0.13576818 [247,] 33.55049 0.13566876 [248,] 33.55207 0.13556953 [249,] 33.55366 0.13546991 [250,] 33.55524 0.13537150 [251,] 33.55524 0.13527312 [252,] 33.55835 0.13517505 [253,] 33.55993 0.13507694 [254,] 33.56153 0.13497863 [255,] 33.56314 0.13488097 [256,] 33.56475 0.13478190 [257,] 33.56639 0.13468366 [258,] 33.56803 0.13458503 [259,] 33.56967 0.13448632 [260,] 33.57131 0.13438885 [261,] 33.57289 0.13429483 [262,] 33.57432 0.13421126 [263,] 33.57578 0.13412836 [264,] 33.57722 0.13404589 [265,] 33.57865 0.13396299 [266,] 33.58007 0.13388012 [267,] 33.58150 0.13379623 [268,] 33.58294 0.13371285 [269,] 33.58438 0.13362920 [270,] 33.58584 0.13354500 [271,] 33.58729 0.13346035 [272,] 33.58876 0.13337531 [273,] 33.59026 0.13329017 [274,] 33.59175 0.13320398 [275,] 33.59324 0.13311731 [276,] 33.59473 0.13302927 [277,] 33.59625 0.13294080 [278,] 33.59778 0.13285172 [279,] 33.59934 0.13276331 [280,] 33.60092 0.13267397 [281,] 33.60246 0.13258646 [282,] 33.60404 0.13249908 [283,] 33.60560 0.13241367 [284,] 33.60717 0.13232749 [285,] 33.60875 0.13224014 [286,] 33.61032 0.13215367 [287,] 33.61193 0.13206727 [288,] 33.61354 0.13198039 [289,] 33.61513 0.13189528 [290,] 33.61674 0.13181069 [291,] 33.61835 0.13172469 [292,] 33.61997 0.13163839 [293,] 33.62160 0.13155147 [294,] 33.62319 0.13146597 [295,] 33.62478 0.13138050 [296,] 33.62635 0.13129698 [297,] 33.62792 0.13121286 [298,] 33.62951 0.13112897 [299,] 33.63112 0.13104415 [300,] 33.63274 0.13095813 [301,] 33.63437 0.13087090 [302,] 33.63602 0.13078302 [303,] 33.63768 0.13069686 [304,] 33.63938 0.13061345 [305,] 33.64108 0.13052942 [306,] 33.64282 0.13044495 [307,] 33.64456 0.13036027 [308,] 33.64629 0.13027535 [309,] 33.64802 0.13018928 [310,] 33.64976 0.13010169 [311,] 33.65151 0.13001438 [312,] 33.65329 0.12992720 [313,] 33.65509 0.12983988 [314,] 33.65689 0.12975326 [315,] 33.65868 0.12966545 [316,] 33.66052 0.12957802 [317,] 33.66235 0.12948972 [318,] 33.66418 0.12940020 [319,] 33.66604 0.12931176 [320,] 33.66792 0.12922226 [321,] 33.66982 0.12913295 [322,] 33.67170 0.12904632 [323,] 33.67360 0.12895864 [324,] 33.67552 0.12887027 [325,] 33.67744 0.12878281 [326,] 33.67938 0.12869465 [327,] 33.68132 0.12860713 [328,] 33.68328 0.12851827 [329,] 33.68524 0.12842905 [330,] 33.68722 0.12833911 [331,] 33.68921 0.12824787 [332,] 33.69119 0.12815568 [333,] 33.69320 0.12806292 [334,] 33.69523 0.12796845 [335,] 33.69725 0.12787394 [336,] 33.69930 0.12777863 [337,] 33.70134 0.12768233 [338,] 33.70338 0.12758501 [339,] 33.70542 0.12748735 [340,] 33.70746 0.12738856 [341,] 33.70949 0.12728988 [342,] 33.71153 0.12719075 [343,] 33.71358 0.12709212 [344,] 33.71563 0.12699312 [345,] 33.71769 0.12689296 [346,] 33.71975 0.12679173 [347,] 33.72179 0.12668982 [348,] 33.72387 0.12658660 [349,] 33.72594 0.12648187 [350,] 33.72802 0.12637561 [351,] 33.73010 0.12627031 [352,] 33.73219 0.12616377 [353,] 33.73429 0.12605626 [354,] 33.73641 0.12594819 [355,] 33.73856 0.12583933 [356,] 33.74073 0.12572948 [357,] 33.74290 0.12561800 [358,] 33.74507 0.12550528 [359,] 33.74725 0.12539194 [360,] 33.74944 0.12527691 [361,] 33.75163 0.12516018 [362,] 33.75383 0.12504129 [363,] 33.75604 0.12492213 [364,] 33.75825 0.12480163 [365,] 33.76046 0.12467934 [366,] 33.76267 0.12455674 [367,] 33.76489 0.12443276 [368,] 33.76710 0.12430693 [369,] 33.76934 0.12418031 [370,] 33.77154 0.12405403 [371,] 33.77377 0.12392717 [372,] 33.77603 0.12379862 [373,] 33.77829 0.12366858 [374,] 33.78055 0.12353704 [375,] 33.78281 0.12340510 [376,] 33.78505 0.12327300 [377,] 33.78731 0.12313911 [378,] 33.78958 0.12300481 [379,] 33.78958 0.12286939 [380,] 33.79414 0.12273213 [381,] 33.79642 0.12259535 [382,] 33.79869 0.12245906 [383,] 33.80097 0.12232020 [384,] 33.80327 0.12217921 [385,] 33.80556 0.12203606 [386,] 33.80786 0.12189155 [387,] 33.81018 0.12174468 [388,] 33.81251 0.12159556 [389,] 33.81487 0.12144436 [390,] 33.81487 0.12129300 [391,] 33.81967 0.12113930 [392,] 33.82209 0.12098322 [393,] 33.82209 0.12082508 [394,] 33.82696 0.12066611 [395,] 33.82941 0.12050466 [396,] 33.83189 0.12034092 [397,] 33.83438 0.12017463 [398,] 33.83685 0.12000731 [399,] 33.83934 0.11983828 [400,] 33.84186 0.11966849 [401,] 33.84440 0.11949733 [402,] 33.84693 0.11932400 [403,] 33.84948 0.11914794 [404,] 33.84948 0.11896987 [405,] 33.85463 0.11878976 [406,] 33.85726 0.11861023 [407,] 33.85726 0.11842729 [408,] 33.86251 0.11824421 [409,] 33.86510 0.11805986 [410,] 33.86771 0.11787257 [411,] 33.87034 0.11768251 [412,] 33.87292 0.11749643 [413,] 33.87550 0.11730790 [414,] 33.87809 0.11711576 [415,] 33.88070 0.11691994 [416,] 33.88332 0.11672234 [417,] 33.88596 0.11652195 [418,] 33.88596 0.11632106 [419,] 33.89122 0.11611689 [420,] 33.89380 0.11591412 [421,] 33.89380 0.11570861 [422,] 33.89898 0.11550427 [423,] 33.90156 0.11529895 [424,] 33.90411 0.11509368 [425,] 33.90667 0.11488708 [426,] 33.90927 0.11468089 [427,] 33.91188 0.11447126 [428,] 33.91444 0.11426243 [429,] 33.91702 0.11405222 [430,] 33.91959 0.11384124 [431,] 33.92220 0.11362802 [432,] 33.92220 0.11341410 [433,] 33.92750 0.11319871 [434,] 33.93009 0.11298538 [435,] 33.93009 0.11277286 [436,] 33.93518 0.11255671 [437,] 33.93773 0.11233860 [438,] 33.94028 0.11211850 [439,] 33.94280 0.11190009 [440,] 33.94532 0.11167856 [441,] 33.94785 0.11145612 [442,] 33.95037 0.11123046 [443,] 33.95290 0.11100250 [444,] 33.95547 0.11077152 [445,] 33.95802 0.11053785 [446,] 33.95802 0.11030006 [447,] 33.96313 0.11006014 [448,] 33.96563 0.10982248 [449,] 33.96563 0.10958200 [450,] 33.97052 0.10934761 [451,] 33.97292 0.10911006 [452,] 33.97526 0.10887693 [453,] 33.97764 0.10864169 [454,] 33.98004 0.10840150 [455,] 33.98246 0.10816171 [456,] 33.98487 0.10792271 [457,] 33.98730 0.10767865 [458,] 33.98978 0.10743403 [459,] 33.99225 0.10718640 [460,] 33.99225 0.10693529 [461,] 33.99723 0.10668614 [462,] 33.99972 0.10643313 [463,] 33.99972 0.10618059 [464,] 34.00473 0.10592261 [465,] 34.00727 0.10566278 [466,] 34.00978 0.10540267 [467,] 34.01231 0.10513802 [468,] 34.01487 0.10487029 [469,] 34.01744 0.10459941 [470,] 34.01997 0.10432811 [471,] 34.02249 0.10405401 [472,] 34.02500 0.10377548 [473,] 34.02757 0.10349315 [474,] 34.02757 0.10320900 [475,] 34.03271 0.10291936 [476,] 34.03529 0.10262493 [477,] 34.03529 0.10232931 [478,] 34.04045 0.10202768 [479,] 34.04307 0.10172367 [480,] 34.04570 0.10141870 [481,] 34.04838 0.10111607 [482,] 34.05108 0.10080658 [483,] 34.05374 0.10049528 [484,] 34.05636 0.10018602 [485,] 34.05900 0.09986969 [486,] 34.06162 0.09954966 [487,] 34.06428 0.09922356 [488,] 34.06428 0.09890068 [489,] 34.06958 0.09857253 [490,] 34.07220 0.09824226 [491,] 34.07220 0.09791023 [492,] 34.07745 0.09757456 [493,] 34.08010 0.09723101 [494,] 34.08271 0.09688830 [495,] 34.08534 0.09654405 [496,] 34.08800 0.09619397 [497,] 34.09065 0.09584180 [498,] 34.09319 0.09549384 [499,] 34.09566 0.09514726 [500,] 34.09815 0.09479234 [501,] 34.10064 0.09443767 [502,] 34.10064 0.09407640 [503,] 34.10565 0.09371130 > (midr <- midrange(x)) [1] 31.0075 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 33.78731 33.78731 33.78731 33.78731 33.79588 33.78731 33.78731 33.78731 > postscript(file="/var/wessaorg/rcomp/tmp/1pz171413132270.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > 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() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/25p8z1413132270.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > 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() null device 1 > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/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="/var/wessaorg/rcomp/tmp/32nds1413132270.tab") > > try(system("convert tmp/1pz171413132270.ps tmp/1pz171413132270.png",intern=TRUE)) character(0) > try(system("convert tmp/25p8z1413132270.ps tmp/25p8z1413132270.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 21.839 0.222 22.065