R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(10
+ ,10
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+ ,9
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+ ,12
+ ,12
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+ ,8
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+ ,10
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+ ,5
+ ,9
+ ,9
+ ,99
+ ,9
+ ,10
+ ,12)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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] 12.32555
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.3981922
> (armose <- arm / armse)
[1] 30.95378
> (geo <- geomean(x))
[1] 10.91575
> (har <- harmean(x))
[1] 10.15565
> (qua <- quamean(x))
[1] 16.96007
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 12.32555 0.39819221
  [2,] 12.32555 0.39819221
  [3,] 12.32905 0.39808099
  [4,] 12.33839 0.39782522
  [5,] 12.34422 0.39769085
  [6,] 12.34422 0.39769085
  [7,] 12.35239 0.39752650
  [8,] 12.35239 0.39752650
  [9,] 12.35239 0.39752650
 [10,] 12.35239 0.39752650
 [11,] 12.35239 0.39752650
 [12,] 12.35239 0.39752650
 [13,] 12.18553 0.35546925
 [14,] 11.90782 0.28310371
 [15,] 11.68028 0.22947601
 [16,] 11.54959 0.19967415
 [17,] 11.11319 0.10797099
 [18,] 10.94516 0.08102798
 [19,] 10.90082 0.07568854
 [20,] 10.90082 0.07568854
 [21,] 10.87631 0.07314530
 [22,] 10.87631 0.07314530
 [23,] 10.84947 0.07068776
 [24,] 10.84947 0.07068776
 [25,] 10.84947 0.07068776
 [26,] 10.84947 0.07068776
 [27,] 10.81797 0.06821490
 [28,] 10.81797 0.06821490
 [29,] 10.81797 0.06821490
 [30,] 10.81797 0.06821490
 [31,] 10.81797 0.06821490
 [32,] 10.81797 0.06821490
 [33,] 10.81797 0.06821490
 [34,] 10.81797 0.06821490
 [35,] 10.81797 0.06821490
 [36,] 10.81797 0.06821490
 [37,] 10.86114 0.06569931
 [38,] 10.86114 0.06569931
 [39,] 10.86114 0.06569931
 [40,] 10.86114 0.06569931
 [41,] 10.86114 0.06569931
 [42,] 10.86114 0.06569931
 [43,] 10.86114 0.06569931
 [44,] 10.86114 0.06569931
 [45,] 10.86114 0.06569931
 [46,] 10.86114 0.06569931
 [47,] 10.80630 0.06202108
 [48,] 10.80630 0.06202108
 [49,] 10.80630 0.06202108
 [50,] 10.80630 0.06202108
 [51,] 10.80630 0.06202108
 [52,] 10.80630 0.06202108
 [53,] 10.80630 0.06202108
 [54,] 10.80630 0.06202108
 [55,] 10.80630 0.06202108
 [56,] 10.80630 0.06202108
 [57,] 10.80630 0.06202108
 [58,] 10.80630 0.06202108
 [59,] 10.80630 0.06202108
 [60,] 10.80630 0.06202108
 [61,] 10.80630 0.06202108
 [62,] 10.80630 0.06202108
 [63,] 10.80630 0.06202108
 [64,] 10.80630 0.06202108
 [65,] 10.80630 0.06202108
 [66,] 10.80630 0.06202108
 [67,] 10.80630 0.06202108
 [68,] 10.80630 0.06202108
 [69,] 10.80630 0.06202108
 [70,] 10.80630 0.06202108
 [71,] 10.80630 0.06202108
 [72,] 10.80630 0.06202108
 [73,] 10.80630 0.06202108
 [74,] 10.80630 0.06202108
 [75,] 10.80630 0.06202108
 [76,] 10.80630 0.06202108
 [77,] 10.80630 0.06202108
 [78,] 10.80630 0.06202108
 [79,] 10.80630 0.06202108
 [80,] 10.80630 0.06202108
 [81,] 10.80630 0.06202108
 [82,] 10.80630 0.06202108
 [83,] 10.80630 0.06202108
 [84,] 10.80630 0.06202108
 [85,] 10.70712 0.05666476
 [86,] 10.70712 0.05666476
 [87,] 10.70712 0.05666476
 [88,] 10.70712 0.05666476
 [89,] 10.70712 0.05666476
 [90,] 10.70712 0.05666476
 [91,] 10.70712 0.05666476
 [92,] 10.70712 0.05666476
 [93,] 10.70712 0.05666476
 [94,] 10.70712 0.05666476
 [95,] 10.70712 0.05666476
 [96,] 10.70712 0.05666476
 [97,] 10.70712 0.05666476
 [98,] 10.70712 0.05666476
 [99,] 10.70712 0.05666476
[100,] 10.70712 0.05666476
[101,] 10.70712 0.05666476
[102,] 10.70712 0.05666476
[103,] 10.70712 0.05666476
[104,] 10.70712 0.05666476
[105,] 10.70712 0.05666476
[106,] 10.70712 0.05666476
[107,] 10.70712 0.05666476
[108,] 10.70712 0.05666476
[109,] 10.70712 0.05666476
[110,] 10.70712 0.05666476
[111,] 10.57760 0.05146585
[112,] 10.57760 0.05146585
[113,] 10.57760 0.05146585
[114,] 10.57760 0.05146585
[115,] 10.57760 0.05146585
[116,] 10.57760 0.05146585
[117,] 10.57760 0.05146585
[118,] 10.57760 0.05146585
[119,] 10.57760 0.05146585
[120,] 10.57760 0.05146585
[121,] 10.57760 0.05146585
[122,] 10.57760 0.05146585
[123,] 10.57760 0.05146585
[124,] 10.57760 0.05146585
[125,] 10.57760 0.05146585
[126,] 10.57760 0.05146585
[127,] 10.57760 0.05146585
[128,] 10.57760 0.05146585
[129,] 10.57760 0.05146585
[130,] 10.57760 0.05146585
[131,] 10.57760 0.05146585
[132,] 10.57760 0.05146585
[133,] 10.57760 0.05146585
[134,] 10.73396 0.04314132
[135,] 10.73396 0.04314132
[136,] 10.73396 0.04314132
[137,] 10.73396 0.04314132
[138,] 10.73396 0.04314132
[139,] 10.73396 0.04314132
[140,] 10.73396 0.04314132
[141,] 10.73396 0.04314132
[142,] 10.73396 0.04314132
[143,] 10.73396 0.04314132
[144,] 10.73396 0.04314132
[145,] 10.73396 0.04314132
[146,] 10.73396 0.04314132
[147,] 10.73396 0.04314132
[148,] 10.73396 0.04314132
[149,] 10.73396 0.04314132
[150,] 10.73396 0.04314132
[151,] 10.73396 0.04314132
[152,] 10.73396 0.04314132
[153,] 10.73396 0.04314132
[154,] 10.73396 0.04314132
[155,] 10.73396 0.04314132
[156,] 10.73396 0.04314132
[157,] 10.73396 0.04314132
[158,] 10.73396 0.04314132
[159,] 10.73396 0.04314132
[160,] 10.73396 0.04314132
[161,] 10.73396 0.04314132
[162,] 10.73396 0.04314132
[163,] 10.73396 0.04314132
[164,] 10.73396 0.04314132
[165,] 10.73396 0.04314132
[166,] 10.73396 0.04314132
[167,] 10.73396 0.04314132
[168,] 10.73396 0.04314132
[169,] 10.73396 0.04314132
[170,] 10.73396 0.04314132
[171,] 10.73396 0.04314132
[172,] 10.73396 0.04314132
[173,] 10.73396 0.04314132
[174,] 10.73396 0.04314132
[175,] 10.73396 0.04314132
[176,] 10.73396 0.04314132
[177,] 10.73396 0.04314132
[178,] 10.73396 0.04314132
[179,] 10.73396 0.04314132
[180,] 10.73396 0.04314132
[181,] 10.73396 0.04314132
[182,] 10.73396 0.04314132
[183,] 10.73396 0.04314132
[184,] 10.73396 0.04314132
[185,] 10.73396 0.04314132
[186,] 10.73396 0.04314132
[187,] 10.73396 0.04314132
[188,] 10.73396 0.04314132
[189,] 10.73396 0.04314132
[190,] 10.73396 0.04314132
[191,] 10.73396 0.04314132
[192,] 10.73396 0.04314132
[193,] 10.73396 0.04314132
[194,] 10.73396 0.04314132
[195,] 10.73396 0.04314132
[196,] 10.73396 0.04314132
[197,] 10.73396 0.04314132
[198,] 10.73396 0.04314132
[199,] 10.73396 0.04314132
[200,] 10.73396 0.04314132
[201,] 10.73396 0.04314132
[202,] 10.96966 0.03341725
[203,] 10.96966 0.03341725
[204,] 10.96966 0.03341725
[205,] 10.96966 0.03341725
[206,] 10.96966 0.03341725
[207,] 10.96966 0.03341725
[208,] 10.96966 0.03341725
[209,] 10.96966 0.03341725
[210,] 10.96966 0.03341725
[211,] 10.96966 0.03341725
[212,] 10.96966 0.03341725
[213,] 10.96966 0.03341725
[214,] 10.96966 0.03341725
[215,] 10.96966 0.03341725
[216,] 10.96966 0.03341725
[217,] 10.96966 0.03341725
[218,] 10.96966 0.03341725
[219,] 10.96966 0.03341725
[220,] 10.96966 0.03341725
[221,] 10.96966 0.03341725
[222,] 10.96966 0.03341725
[223,] 10.96966 0.03341725
[224,] 10.96966 0.03341725
[225,] 10.96966 0.03341725
[226,] 10.96966 0.03341725
[227,] 10.96966 0.03341725
[228,] 10.96966 0.03341725
[229,] 10.96966 0.03341725
[230,] 10.96966 0.03341725
[231,] 10.96966 0.03341725
[232,] 10.96966 0.03341725
[233,] 10.96966 0.03341725
[234,] 10.96966 0.03341725
[235,] 10.96966 0.03341725
[236,] 10.96966 0.03341725
[237,] 10.96966 0.03341725
[238,] 10.96966 0.03341725
[239,] 10.96966 0.03341725
[240,] 10.96966 0.03341725
[241,] 10.96966 0.03341725
[242,] 10.96966 0.03341725
[243,] 10.96966 0.03341725
[244,] 10.96966 0.03341725
[245,] 10.96966 0.03341725
[246,] 10.96966 0.03341725
[247,] 10.96966 0.03341725
[248,] 10.96966 0.03341725
[249,] 10.96966 0.03341725
[250,] 10.96966 0.03341725
[251,] 10.96966 0.03341725
[252,] 10.96966 0.03341725
[253,] 10.96966 0.03341725
[254,] 10.96966 0.03341725
[255,] 10.96966 0.03341725
[256,] 10.96966 0.03341725
[257,] 10.96966 0.03341725
[258,] 10.96966 0.03341725
[259,] 10.96966 0.03341725
[260,] 10.96966 0.03341725
[261,] 10.96966 0.03341725
[262,] 10.96966 0.03341725
[263,] 10.96966 0.03341725
[264,] 10.96966 0.03341725
[265,] 10.96966 0.03341725
[266,] 10.96966 0.03341725
[267,] 10.96966 0.03341725
[268,] 10.96966 0.03341725
[269,] 10.96966 0.03341725
[270,] 10.96966 0.03341725
[271,] 10.96966 0.03341725
[272,] 10.96966 0.03341725
[273,] 10.96966 0.03341725
[274,] 10.96966 0.03341725
[275,] 10.96966 0.03341725
[276,] 10.96966 0.03341725
[277,] 10.96966 0.03341725
[278,] 10.96966 0.03341725
[279,] 10.96966 0.03341725
[280,] 10.96966 0.03341725
[281,] 10.96966 0.03341725
[282,] 10.96966 0.03341725
[283,] 10.96966 0.03341725
[284,] 10.96966 0.03341725
[285,] 10.96966 0.03341725
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 12.32555 0.38578066
  [2,] 12.23743 0.37280675
  [3,] 12.05993 0.35920764
  [4,] 12.05993 0.34494950
  [5,] 11.87603 0.32997543
  [6,] 11.78107 0.31413349
  [7,] 11.68565 0.29724756
  [8,] 11.68565 0.27915636
  [9,] 11.49106 0.25957115
 [10,] 11.39307 0.23812024
 [11,] 11.29461 0.21424025
 [12,] 11.19568 0.18699857
 [13,] 11.09627 0.15462322
 [14,] 11.00965 0.12393920
 [15,] 11.00965 0.10154932
 [16,] 10.94317 0.08494671
 [17,] 10.84933 0.07046763
 [18,] 10.83313 0.06731027
 [19,] 10.82662 0.06637338
 [20,] 10.82252 0.06578650
 [21,] 10.81840 0.06518776
 [22,] 10.81550 0.06473338
 [23,] 10.81258 0.06427068
 [24,] 10.81088 0.06393571
 [25,] 10.80917 0.06359517
 [26,] 10.80745 0.06324892
 [27,] 10.80573 0.06289681
 [28,] 10.80524 0.06265577
 [29,] 10.80476 0.06241097
 [30,] 10.80476 0.06216232
 [31,] 10.80427 0.06190974
 [32,] 10.80377 0.06165316
 [33,] 10.80278 0.06139249
 [34,] 10.80228 0.06112763
 [35,] 10.80178 0.06085850
 [36,] 10.80127 0.06058500
 [37,] 10.80077 0.06030704
 [38,] 10.79898 0.06011468
 [39,] 10.79718 0.05991924
 [40,] 10.79537 0.05972067
 [41,] 10.79355 0.05951889
 [42,] 10.79172 0.05931385
 [43,] 10.78988 0.05910548
 [44,] 10.78804 0.05889371
 [45,] 10.78618 0.05867846
 [46,] 10.78431 0.05845968
 [47,] 10.78244 0.05823727
 [48,] 10.78187 0.05812190
 [49,] 10.78129 0.05800466
 [50,] 10.78071 0.05788553
 [51,] 10.78013 0.05776446
 [52,] 10.77955 0.05764143
 [53,] 10.77896 0.05751640
 [54,] 10.77837 0.05738933
 [55,] 10.77778 0.05726019
 [56,] 10.77718 0.05712894
 [57,] 10.77658 0.05699553
 [58,] 10.77598 0.05685994
 [59,] 10.77537 0.05672213
 [60,] 10.77537 0.05658204
 [61,] 10.77476 0.05643963
 [62,] 10.77415 0.05629487
 [63,] 10.77353 0.05614771
 [64,] 10.77291 0.05599811
 [65,] 10.77166 0.05584600
 [66,] 10.77103 0.05569136
 [67,] 10.77040 0.05553412
 [68,] 10.76976 0.05537424
 [69,] 10.76912 0.05521166
 [70,] 10.76848 0.05504633
 [71,] 10.76783 0.05487819
 [72,] 10.76718 0.05470719
 [73,] 10.76653 0.05453327
 [74,] 10.76587 0.05435637
 [75,] 10.76521 0.05417642
 [76,] 10.76454 0.05399336
 [77,] 10.76387 0.05380713
 [78,] 10.76320 0.05361766
 [79,] 10.76252 0.05342487
 [80,] 10.76184 0.05322869
 [81,] 10.76115 0.05302906
 [82,] 10.76046 0.05282589
 [83,] 10.75977 0.05261910
 [84,] 10.75907 0.05240861
 [85,] 10.75837 0.05219434
 [86,] 10.75912 0.05208865
 [87,] 10.75988 0.05198103
 [88,] 10.76065 0.05187146
 [89,] 10.76141 0.05175988
 [90,] 10.76219 0.05164626
 [91,] 10.76296 0.05153057
 [92,] 10.76374 0.05141276
 [93,] 10.76453 0.05129278
 [94,] 10.76532 0.05117060
 [95,] 10.76612 0.05104617
 [96,] 10.76692 0.05091944
 [97,] 10.76772 0.05079038
 [98,] 10.76853 0.05065892
 [99,] 10.76935 0.05052503
[100,] 10.77017 0.05038864
[101,] 10.77099 0.05024972
[102,] 10.77182 0.05010820
[103,] 10.77266 0.04996403
[104,] 10.77350 0.04981715
[105,] 10.77434 0.04966750
[106,] 10.77519 0.04951503
[107,] 10.77605 0.04935967
[108,] 10.77691 0.04920136
[109,] 10.77778 0.04904003
[110,] 10.77865 0.04887561
[111,] 10.77953 0.04870804
[112,] 10.78199 0.04862567
[113,] 10.78447 0.04854142
[114,] 10.78696 0.04845525
[115,] 10.78947 0.04836712
[116,] 10.79200 0.04827698
[117,] 10.79454 0.04818479
[118,] 10.79710 0.04809051
[119,] 10.79968 0.04799410
[120,] 10.79968 0.04789549
[121,] 10.80488 0.04779465
[122,] 10.80488 0.04769153
[123,] 10.81015 0.04758607
[124,] 10.81015 0.04747822
[125,] 10.81549 0.04736792
[126,] 10.81549 0.04725513
[127,] 10.82090 0.04713977
[128,] 10.82090 0.04702180
[129,] 10.82638 0.04690115
[130,] 10.82915 0.04677775
[131,] 10.83193 0.04665155
[132,] 10.83474 0.04652246
[133,] 10.83756 0.04639043
[134,] 10.84041 0.04625538
[135,] 10.84157 0.04626467
[136,] 10.84274 0.04627348
[137,] 10.84391 0.04628182
[138,] 10.84509 0.04628968
[139,] 10.84629 0.04629703
[140,] 10.84749 0.04630387
[141,] 10.84870 0.04631020
[142,] 10.84991 0.04631599
[143,] 10.85114 0.04632123
[144,] 10.85237 0.04632592
[145,] 10.85362 0.04633003
[146,] 10.85487 0.04633357
[147,] 10.85613 0.04633650
[148,] 10.85740 0.04633883
[149,] 10.85868 0.04634054
[150,] 10.85996 0.04634160
[151,] 10.86126 0.04634201
[152,] 10.86257 0.04634176
[153,] 10.86388 0.04634082
[154,] 10.86521 0.04633918
[155,] 10.86654 0.04633683
[156,] 10.86789 0.04633375
[157,] 10.86924 0.04632992
[158,] 10.87061 0.04632532
[159,] 10.87199 0.04631994
[160,] 10.87337 0.04631375
[161,] 10.87477 0.04630675
[162,] 10.87617 0.04629890
[163,] 10.87759 0.04629020
[164,] 10.87902 0.04628062
[165,] 10.88046 0.04627013
[166,] 10.88190 0.04625872
[167,] 10.88337 0.04624637
[168,] 10.88484 0.04623305
[169,] 10.88632 0.04621875
[170,] 10.88781 0.04620342
[171,] 10.88932 0.04618706
[172,] 10.89084 0.04616964
[173,] 10.89237 0.04615113
[174,] 10.89391 0.04613150
[175,] 10.89546 0.04611073
[176,] 10.89703 0.04608880
[177,] 10.89861 0.04606566
[178,] 10.90020 0.04604129
[179,] 10.90180 0.04601566
[180,] 10.90342 0.04598875
[181,] 10.90505 0.04596051
[182,] 10.90669 0.04593091
[183,] 10.90835 0.04589993
[184,] 10.91002 0.04586751
[185,] 10.91170 0.04583364
[186,] 10.91340 0.04579827
[187,] 10.91511 0.04576137
[188,] 10.91684 0.04572288
[189,] 10.91858 0.04568278
[190,] 10.92034 0.04564103
[191,] 10.92211 0.04559756
[192,] 10.92389 0.04555236
[193,] 10.92569 0.04550536
[194,] 10.92751 0.04545652
[195,] 10.92934 0.04540579
[196,] 10.93118 0.04535312
[197,] 10.93305 0.04529845
[198,] 10.93492 0.04524175
[199,] 10.93682 0.04518294
[200,] 10.93873 0.04512197
[201,] 10.94066 0.04505878
[202,] 10.94260 0.04499332
[203,] 10.94235 0.04508354
[204,] 10.94209 0.04517430
[205,] 10.94183 0.04526560
[206,] 10.94157 0.04535744
[207,] 10.94131 0.04544984
[208,] 10.94104 0.04554278
[209,] 10.94077 0.04563629
[210,] 10.94050 0.04573036
[211,] 10.94023 0.04582500
[212,] 10.93995 0.04592022
[213,] 10.93968 0.04601602
[214,] 10.93939 0.04611241
[215,] 10.93939 0.04620940
[216,] 10.93882 0.04630698
[217,] 10.93853 0.04640517
[218,] 10.93824 0.04650397
[219,] 10.93824 0.04660339
[220,] 10.93765 0.04670343
[221,] 10.93735 0.04680410
[222,] 10.93705 0.04690541
[223,] 10.93705 0.04700736
[224,] 10.93643 0.04710997
[225,] 10.93612 0.04721323
[226,] 10.93580 0.04731715
[227,] 10.93580 0.04742174
[228,] 10.93516 0.04752701
[229,] 10.93484 0.04763297
[230,] 10.93451 0.04773961
[231,] 10.93451 0.04784696
[232,] 10.93384 0.04795501
[233,] 10.93350 0.04806377
[234,] 10.93316 0.04817325
[235,] 10.93282 0.04828347
[236,] 10.93247 0.04839442
[237,] 10.93211 0.04850611
[238,] 10.93176 0.04861855
[239,] 10.93140 0.04873176
[240,] 10.93140 0.04884573
[241,] 10.93067 0.04896048
[242,] 10.93029 0.04907602
[243,] 10.92992 0.04919235
[244,] 10.92992 0.04930948
[245,] 10.92916 0.04942742
[246,] 10.92877 0.04954618
[247,] 10.92837 0.04966577
[248,] 10.92837 0.04978620
[249,] 10.92758 0.04990748
[250,] 10.92717 0.05002961
[251,] 10.92676 0.05015261
[252,] 10.92676 0.05027648
[253,] 10.92593 0.05040125
[254,] 10.92550 0.05052690
[255,] 10.92507 0.05065346
[256,] 10.92507 0.05078094
[257,] 10.92420 0.05090934
[258,] 10.92375 0.05103868
[259,] 10.92330 0.05116897
[260,] 10.92285 0.05130022
[261,] 10.92239 0.05143243
[262,] 10.92192 0.05156563
[263,] 10.92145 0.05169982
[264,] 10.92097 0.05183501
[265,] 10.92049 0.05197121
[266,] 10.92000 0.05210844
[267,] 10.91950 0.05224671
[268,] 10.91900 0.05238603
[269,] 10.91850 0.05252641
[270,] 10.91798 0.05266786
[271,] 10.91746 0.05281041
[272,] 10.91693 0.05295405
[273,] 10.91640 0.05309881
[274,] 10.91586 0.05324469
[275,] 10.91531 0.05339171
[276,] 10.91475 0.05353988
[277,] 10.91419 0.05368922
[278,] 10.91362 0.05383974
[279,] 10.91304 0.05399145
[280,] 10.91246 0.05414437
[281,] 10.91186 0.05429851
[282,] 10.91126 0.05445388
[283,] 10.91065 0.05461051
[284,] 10.91003 0.05476841
[285,] 10.90941 0.05492758
> (midr <- midrange(x))
[1] 50
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949 11.11949
> postscript(file="/var/www/html/rcomp/tmp/1r0tm1250077828.ps",horizontal=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/www/html/rcomp/tmp/22oyv1250077828.ps",horizontal=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/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/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/www/html/rcomp/tmp/30rq81250077829.tab") 
> 
> system("convert tmp/1r0tm1250077828.ps tmp/1r0tm1250077828.png")
> system("convert tmp/22oyv1250077828.ps tmp/22oyv1250077828.png")
> 
> 
> proc.time()
   user  system elapsed 
  8.333   0.479   8.611