R version 2.7.1 (2008-06-23)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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.

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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(8
+ ,10
+ ,10
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+ ,9
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+ ,9
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+ ,9
+ ,12
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+ ,12
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+ ,12
+ ,12
+ ,12
+ ,8
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+ ,8
+ ,12
+ ,12
+ ,10
+ ,10
+ ,12
+ ,8
+ ,8
+ ,10
+ ,10
+ ,9
+ ,9
+ ,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] 10.83049
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.0971422
> (armose <- arm / armse)
[1] 111.4911
> (geo <- geomean(x))
[1] 10.61856
> (har <- harmean(x))
[1] 10.43728
> (qua <- quamean(x))
[1] 11.18159
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.76707 0.06553710
  [2,] 10.76463 0.06523038
  [3,] 10.75732 0.06450883
  [4,] 10.75732 0.06450883
  [5,] 10.75732 0.06450883
  [6,] 10.75732 0.06450883
  [7,] 10.75732 0.06450883
  [8,] 10.75732 0.06450883
  [9,] 10.75732 0.06450883
 [10,] 10.75732 0.06450883
 [11,] 10.75732 0.06450883
 [12,] 10.75732 0.06450883
 [13,] 10.75732 0.06450883
 [14,] 10.75732 0.06450883
 [15,] 10.75732 0.06450883
 [16,] 10.75732 0.06450883
 [17,] 10.75732 0.06450883
 [18,] 10.75732 0.06450883
 [19,] 10.75732 0.06450883
 [20,] 10.75732 0.06450883
 [21,] 10.75732 0.06450883
 [22,] 10.75732 0.06450883
 [23,] 10.75732 0.06067885
 [24,] 10.75732 0.06067885
 [25,] 10.75732 0.06067885
 [26,] 10.75732 0.06067885
 [27,] 10.75732 0.06067885
 [28,] 10.75732 0.06067885
 [29,] 10.75732 0.06067885
 [30,] 10.75732 0.06067885
 [31,] 10.75732 0.06067885
 [32,] 10.75732 0.06067885
 [33,] 10.75732 0.06067885
 [34,] 10.75732 0.06067885
 [35,] 10.75732 0.06067885
 [36,] 10.75732 0.06067885
 [37,] 10.75732 0.06067885
 [38,] 10.75732 0.06067885
 [39,] 10.75732 0.06067885
 [40,] 10.75732 0.06067885
 [41,] 10.75732 0.06067885
 [42,] 10.75732 0.06067885
 [43,] 10.75732 0.06067885
 [44,] 10.75732 0.06067885
 [45,] 10.75732 0.06067885
 [46,] 10.75732 0.06067885
 [47,] 10.75732 0.06067885
 [48,] 10.75732 0.06067885
 [49,] 10.75732 0.06067885
 [50,] 10.75732 0.06067885
 [51,] 10.75732 0.06067885
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 [55,] 10.75732 0.06067885
 [56,] 10.75732 0.06067885
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 [58,] 10.75732 0.06067885
 [59,] 10.75732 0.06067885
 [60,] 10.75732 0.06067885
 [61,] 10.68293 0.05636424
 [62,] 10.68293 0.05636424
 [63,] 10.68293 0.05636424
 [64,] 10.68293 0.05636424
 [65,] 10.68293 0.05636424
 [66,] 10.68293 0.05636424
 [67,] 10.68293 0.05636424
 [68,] 10.68293 0.05636424
 [69,] 10.68293 0.05636424
 [70,] 10.68293 0.05636424
 [71,] 10.68293 0.05636424
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 [73,] 10.68293 0.05636424
 [74,] 10.68293 0.05636424
 [75,] 10.68293 0.05636424
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 [77,] 10.68293 0.05636424
 [78,] 10.68293 0.05636424
 [79,] 10.68293 0.05636424
 [80,] 10.68293 0.05636424
 [81,] 10.68293 0.05636424
 [82,] 10.68293 0.05636424
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 [84,] 10.68293 0.05636424
 [85,] 10.68293 0.05636424
 [86,] 10.68293 0.05636424
 [87,] 10.57683 0.05188831
 [88,] 10.57683 0.05188831
 [89,] 10.57683 0.05188831
 [90,] 10.57683 0.05188831
 [91,] 10.57683 0.05188831
 [92,] 10.57683 0.05188831
 [93,] 10.57683 0.05188831
 [94,] 10.57683 0.05188831
 [95,] 10.57683 0.05188831
 [96,] 10.57683 0.05188831
 [97,] 10.57683 0.05188831
 [98,] 10.57683 0.05188831
 [99,] 10.57683 0.05188831
[100,] 10.57683 0.05188831
[101,] 10.57683 0.05188831
[102,] 10.57683 0.05188831
[103,] 10.57683 0.05188831
[104,] 10.57683 0.05188831
[105,] 10.57683 0.05188831
[106,] 10.57683 0.05188831
[107,] 10.57683 0.05188831
[108,] 10.57683 0.05188831
[109,] 10.57683 0.05188831
[110,] 10.57683 0.05188831
[111,] 10.57683 0.05188831
[112,] 10.57683 0.05188831
[113,] 10.57683 0.05188831
[114,] 10.57683 0.05188831
[115,] 10.57683 0.05188831
[116,] 10.57683 0.05188831
[117,] 10.57683 0.05188831
[118,] 10.57683 0.05188831
[119,] 10.57683 0.05188831
[120,] 10.57683 0.05188831
[121,] 10.72439 0.04378855
[122,] 10.72439 0.04378855
[123,] 10.72439 0.04378855
[124,] 10.72439 0.04378855
[125,] 10.72439 0.04378855
[126,] 10.72439 0.04378855
[127,] 10.72439 0.04378855
[128,] 10.72439 0.04378855
[129,] 10.72439 0.04378855
[130,] 10.72439 0.04378855
[131,] 10.72439 0.04378855
[132,] 10.72439 0.04378855
[133,] 10.72439 0.04378855
[134,] 10.72439 0.04378855
[135,] 10.72439 0.04378855
[136,] 10.72439 0.04378855
[137,] 10.72439 0.04378855
[138,] 10.72439 0.04378855
[139,] 10.72439 0.04378855
[140,] 10.72439 0.04378855
[141,] 10.72439 0.04378855
[142,] 10.72439 0.04378855
[143,] 10.72439 0.04378855
[144,] 10.72439 0.04378855
[145,] 10.72439 0.04378855
[146,] 10.72439 0.04378855
[147,] 10.72439 0.04378855
[148,] 10.72439 0.04378855
[149,] 10.72439 0.04378855
[150,] 10.72439 0.04378855
[151,] 10.72439 0.04378855
[152,] 10.72439 0.04378855
[153,] 10.72439 0.04378855
[154,] 10.72439 0.04378855
[155,] 10.72439 0.04378855
[156,] 10.72439 0.04378855
[157,] 10.72439 0.04378855
[158,] 10.72439 0.04378855
[159,] 10.72439 0.04378855
[160,] 10.72439 0.04378855
[161,] 10.72439 0.04378855
[162,] 10.72439 0.04378855
[163,] 10.72439 0.04378855
[164,] 10.72439 0.04378855
[165,] 10.72439 0.04378855
[166,] 10.72439 0.04378855
[167,] 10.72439 0.04378855
[168,] 10.72439 0.04378855
[169,] 10.72439 0.04378855
[170,] 10.72439 0.04378855
[171,] 10.72439 0.04378855
[172,] 10.72439 0.04378855
[173,] 10.72439 0.04378855
[174,] 10.72439 0.04378855
[175,] 10.72439 0.04378855
[176,] 10.72439 0.04378855
[177,] 10.72439 0.04378855
[178,] 10.72439 0.04378855
[179,] 10.72439 0.04378855
[180,] 10.72439 0.04378855
[181,] 10.72439 0.04378855
[182,] 10.72439 0.04378855
[183,] 10.72439 0.04378855
[184,] 10.72439 0.04378855
[185,] 10.72439 0.04378855
[186,] 10.72439 0.04378855
[187,] 10.72439 0.04378855
[188,] 10.72439 0.04378855
[189,] 10.95488 0.03410896
[190,] 10.95488 0.03410896
[191,] 10.95488 0.03410896
[192,] 10.95488 0.03410896
[193,] 10.95488 0.03410896
[194,] 10.95488 0.03410896
[195,] 10.95488 0.03410896
[196,] 10.95488 0.03410896
[197,] 10.95488 0.03410896
[198,] 10.95488 0.03410896
[199,] 10.95488 0.03410896
[200,] 10.95488 0.03410896
[201,] 10.95488 0.03410896
[202,] 10.95488 0.03410896
[203,] 10.95488 0.03410896
[204,] 10.95488 0.03410896
[205,] 10.95488 0.03410896
[206,] 10.95488 0.03410896
[207,] 10.95488 0.03410896
[208,] 10.95488 0.03410896
[209,] 10.95488 0.03410896
[210,] 10.95488 0.03410896
[211,] 10.95488 0.03410896
[212,] 10.95488 0.03410896
[213,] 10.95488 0.03410896
[214,] 10.95488 0.03410896
[215,] 10.95488 0.03410896
[216,] 10.95488 0.03410896
[217,] 10.95488 0.03410896
[218,] 10.95488 0.03410896
[219,] 10.95488 0.03410896
[220,] 10.95488 0.03410896
[221,] 10.95488 0.03410896
[222,] 10.95488 0.03410896
[223,] 10.95488 0.03410896
[224,] 10.95488 0.03410896
[225,] 10.95488 0.03410896
[226,] 10.95488 0.03410896
[227,] 10.95488 0.03410896
[228,] 10.95488 0.03410896
[229,] 10.95488 0.03410896
[230,] 10.95488 0.03410896
[231,] 10.95488 0.03410896
[232,] 10.95488 0.03410896
[233,] 10.95488 0.03410896
[234,] 10.95488 0.03410896
[235,] 10.95488 0.03410896
[236,] 10.95488 0.03410896
[237,] 10.95488 0.03410896
[238,] 10.95488 0.03410896
[239,] 10.95488 0.03410896
[240,] 10.95488 0.03410896
[241,] 10.95488 0.03410896
[242,] 10.95488 0.03410896
[243,] 10.95488 0.03410896
[244,] 10.95488 0.03410896
[245,] 10.95488 0.03410896
[246,] 10.95488 0.03410896
[247,] 10.95488 0.03410896
[248,] 10.95488 0.03410896
[249,] 10.95488 0.03410896
[250,] 10.95488 0.03410896
[251,] 10.95488 0.03410896
[252,] 10.95488 0.03410896
[253,] 10.95488 0.03410896
[254,] 10.95488 0.03410896
[255,] 10.95488 0.03410896
[256,] 10.95488 0.03410896
[257,] 10.95488 0.03410896
[258,] 10.95488 0.03410896
[259,] 10.95488 0.03410896
[260,] 10.95488 0.03410896
[261,] 10.95488 0.03410896
[262,] 10.95488 0.03410896
[263,] 10.95488 0.03410896
[264,] 10.95488 0.03410896
[265,] 10.95488 0.03410896
[266,] 10.95488 0.03410896
[267,] 10.95488 0.03410896
[268,] 10.95488 0.03410896
[269,] 10.95488 0.03410896
[270,] 10.95488 0.03410896
[271,] 10.95488 0.03410896
[272,] 10.95488 0.03410896
[273,] 10.95488 0.03410896
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.76284 0.06493548
  [2,] 10.75858 0.06432150
  [3,] 10.75553 0.06385452
  [4,] 10.75493 0.06362978
  [5,] 10.75432 0.06340159
  [6,] 10.75371 0.06316991
  [7,] 10.75310 0.06293466
  [8,] 10.75249 0.06269576
  [9,] 10.75187 0.06245315
 [10,] 10.75125 0.06220674
 [11,] 10.75063 0.06195646
 [12,] 10.75000 0.06170223
 [13,] 10.74937 0.06144395
 [14,] 10.74874 0.06118155
 [15,] 10.74874 0.06091493
 [16,] 10.74746 0.06064401
 [17,] 10.74682 0.06036868
 [18,] 10.74617 0.06008884
 [19,] 10.74552 0.05980440
 [20,] 10.74487 0.05951525
 [21,] 10.74422 0.05922128
 [22,] 10.74356 0.05892237
 [23,] 10.74289 0.05861841
 [24,] 10.74223 0.05851061
 [25,] 10.74156 0.05840109
 [26,] 10.74089 0.05828980
 [27,] 10.74021 0.05817673
 [28,] 10.73953 0.05806183
 [29,] 10.73953 0.05794507
 [30,] 10.73885 0.05782644
 [31,] 10.73747 0.05770588
 [32,] 10.73677 0.05758337
 [33,] 10.73607 0.05745887
 [34,] 10.73537 0.05733235
 [35,] 10.73467 0.05720377
 [36,] 10.73396 0.05707310
 [37,] 10.73324 0.05694029
 [38,] 10.73253 0.05680531
 [39,] 10.73181 0.05666811
 [40,] 10.73108 0.05652866
 [41,] 10.73035 0.05638691
 [42,] 10.72962 0.05624282
 [43,] 10.72888 0.05609635
 [44,] 10.72814 0.05594744
 [45,] 10.72740 0.05579606
 [46,] 10.72665 0.05564216
 [47,] 10.72590 0.05548568
 [48,] 10.72514 0.05532658
 [49,] 10.72438 0.05516480
 [50,] 10.72361 0.05500029
 [51,] 10.72284 0.05483300
 [52,] 10.72207 0.05466286
 [53,] 10.72129 0.05448983
 [54,] 10.72051 0.05431383
 [55,] 10.71972 0.05413482
 [56,] 10.71893 0.05395272
 [57,] 10.71813 0.05376747
 [58,] 10.71813 0.05357900
 [59,] 10.71733 0.05338725
 [60,] 10.71652 0.05319214
 [61,] 10.71490 0.05299359
 [62,] 10.71552 0.05290050
 [63,] 10.71614 0.05280571
 [64,] 10.71676 0.05270919
 [65,] 10.71739 0.05261091
 [66,] 10.71802 0.05251085
 [67,] 10.71866 0.05240896
 [68,] 10.71930 0.05230521
 [69,] 10.71994 0.05219956
 [70,] 10.72059 0.05209198
 [71,] 10.72124 0.05198244
 [72,] 10.72189 0.05187089
 [73,] 10.72255 0.05175730
 [74,] 10.72321 0.05164162
 [75,] 10.72388 0.05152382
 [76,] 10.72455 0.05140385
 [77,] 10.72523 0.05128167
 [78,] 10.72590 0.05115723
 [79,] 10.72659 0.05103049
 [80,] 10.72727 0.05090140
 [81,] 10.72796 0.05076992
 [82,] 10.72866 0.05063599
 [83,] 10.72936 0.05049957
 [84,] 10.73006 0.05036060
 [85,] 10.73077 0.05021902
 [86,] 10.73148 0.05007479
 [87,] 10.73220 0.04992784
 [88,] 10.73447 0.04986373
 [89,] 10.73676 0.04979808
 [90,] 10.73906 0.04973087
 [91,] 10.74138 0.04966207
 [92,] 10.74371 0.04959163
 [93,] 10.74606 0.04951953
 [94,] 10.74842 0.04944572
 [95,] 10.75079 0.04937019
 [96,] 10.75318 0.04929288
 [97,] 10.75559 0.04921377
 [98,] 10.75801 0.04913280
 [99,] 10.76045 0.04904996
[100,] 10.76290 0.04896518
[101,] 10.76537 0.04887844
[102,] 10.76786 0.04878969
[103,] 10.77036 0.04869888
[104,] 10.77288 0.04860598
[105,] 10.77541 0.04851093
[106,] 10.77796 0.04841368
[107,] 10.78053 0.04831419
[108,] 10.78311 0.04821241
[109,] 10.78571 0.04810829
[110,] 10.78833 0.04800176
[111,] 10.79097 0.04789278
[112,] 10.79362 0.04778129
[113,] 10.79630 0.04766723
[114,] 10.79899 0.04755054
[115,] 10.80169 0.04743116
[116,] 10.80169 0.04730902
[117,] 10.80442 0.04718405
[118,] 10.80717 0.04705620
[119,] 10.80993 0.04692539
[120,] 10.81271 0.04679154
[121,] 10.81834 0.04665457
[122,] 10.81944 0.04666480
[123,] 10.82056 0.04667455
[124,] 10.82168 0.04668381
[125,] 10.82281 0.04669259
[126,] 10.82394 0.04670085
[127,] 10.82509 0.04670860
[128,] 10.82624 0.04671582
[129,] 10.82740 0.04672250
[130,] 10.82857 0.04672862
[131,] 10.82975 0.04673418
[132,] 10.83094 0.04673915
[133,] 10.83213 0.04674353
[134,] 10.83333 0.04674731
[135,] 10.83455 0.04675046
[136,] 10.83577 0.04675298
[137,] 10.83700 0.04675485
[138,] 10.83824 0.04675605
[139,] 10.83948 0.04675657
[140,] 10.84074 0.04675639
[141,] 10.84201 0.04675550
[142,] 10.84328 0.04675388
[143,] 10.84457 0.04675151
[144,] 10.84586 0.04674837
[145,] 10.84717 0.04674445
[146,] 10.84848 0.04673973
[147,] 10.84981 0.04673419
[148,] 10.85115 0.04672781
[149,] 10.85249 0.04672057
[150,] 10.85385 0.04671244
[151,] 10.85521 0.04670342
[152,] 10.85659 0.04669347
[153,] 10.85798 0.04668257
[154,] 10.85938 0.04667071
[155,] 10.86078 0.04665785
[156,] 10.86220 0.04664397
[157,] 10.86364 0.04662906
[158,] 10.86508 0.04661307
[159,] 10.86653 0.04659599
[160,] 10.86800 0.04657779
[161,] 10.86948 0.04655845
[162,] 10.87097 0.04653793
[163,] 10.87247 0.04651620
[164,] 10.87398 0.04649323
[165,] 10.87551 0.04646900
[166,] 10.87705 0.04644347
[167,] 10.87860 0.04641660
[168,] 10.88017 0.04638837
[169,] 10.88174 0.04635874
[170,] 10.88333 0.04632768
[171,] 10.88494 0.04629514
[172,] 10.88655 0.04626109
[173,] 10.88819 0.04622549
[174,] 10.88983 0.04618829
[175,] 10.89149 0.04614947
[176,] 10.89316 0.04610897
[177,] 10.89485 0.04606675
[178,] 10.89655 0.04602276
[179,] 10.89827 0.04597696
[180,] 10.90000 0.04592930
[181,] 10.90175 0.04587973
[182,] 10.90351 0.04582820
[183,] 10.90529 0.04577464
[184,] 10.90708 0.04571902
[185,] 10.90889 0.04566127
[186,] 10.91071 0.04560133
[187,] 10.91256 0.04553914
[188,] 10.91441 0.04547464
[189,] 10.91629 0.04540776
[190,] 10.91591 0.04549995
[191,] 10.91553 0.04559269
[192,] 10.91514 0.04568598
[193,] 10.91475 0.04577983
[194,] 10.91435 0.04587424
[195,] 10.91395 0.04596922
[196,] 10.91355 0.04606477
[197,] 10.91315 0.04616089
[198,] 10.91274 0.04625760
[199,] 10.91232 0.04635490
[200,] 10.91190 0.04645279
[201,] 10.91148 0.04655128
[202,] 10.91106 0.04665038
[203,] 10.91063 0.04675009
[204,] 10.91019 0.04685041
[205,] 10.90976 0.04695136
[206,] 10.90931 0.04705295
[207,] 10.90887 0.04715516
[208,] 10.90842 0.04725802
[209,] 10.90796 0.04736153
[210,] 10.90750 0.04746569
[211,] 10.90704 0.04757052
[212,] 10.90657 0.04767601
[213,] 10.90609 0.04778217
[214,] 10.90561 0.04788902
[215,] 10.90513 0.04799656
[216,] 10.90464 0.04810479
[217,] 10.90415 0.04821373
[218,] 10.90365 0.04832337
[219,] 10.90314 0.04843373
[220,] 10.90263 0.04854481
[221,] 10.90212 0.04865663
[222,] 10.90160 0.04876918
[223,] 10.90107 0.04888248
[224,] 10.90054 0.04899653
[225,] 10.90000 0.04911134
[226,] 10.89946 0.04922693
[227,] 10.89891 0.04934329
[228,] 10.89835 0.04946043
[229,] 10.89779 0.04957837
[230,] 10.89722 0.04969710
[231,] 10.89722 0.04981665
[232,] 10.89665 0.04993701
[233,] 10.89607 0.05005821
[234,] 10.89548 0.05018023
[235,] 10.89489 0.05030310
[236,] 10.89429 0.05042682
[237,] 10.89368 0.05055140
[238,] 10.89306 0.05067685
[239,] 10.89244 0.05080318
[240,] 10.89181 0.05093040
[241,] 10.89053 0.05105851
[242,] 10.88988 0.05118753
[243,] 10.88922 0.05131747
[244,] 10.88855 0.05144833
[245,] 10.88788 0.05158013
[246,] 10.88720 0.05171287
[247,] 10.88650 0.05184656
[248,] 10.88580 0.05198122
[249,] 10.88509 0.05211686
[250,] 10.88438 0.05225348
[251,] 10.88365 0.05239109
[252,] 10.88291 0.05252971
[253,] 10.88217 0.05266934
[254,] 10.88141 0.05281000
[255,] 10.88065 0.05295170
[256,] 10.87987 0.05309444
[257,] 10.87908 0.05323824
[258,] 10.87829 0.05338310
[259,] 10.87748 0.05352905
[260,] 10.87667 0.05367609
[261,] 10.87584 0.05382422
[262,] 10.87500 0.05397347
[263,] 10.87415 0.05412384
[264,] 10.87329 0.05427535
[265,] 10.87241 0.05442800
[266,] 10.87153 0.05458180
[267,] 10.87063 0.05473677
[268,] 10.86972 0.05489292
[269,] 10.86879 0.05505026
[270,] 10.86786 0.05520881
[271,] 10.86691 0.05536856
[272,] 10.86594 0.05552953
[273,] 10.86496 0.05569174
> (midr <- midrange(x))
[1] 38.5
> 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/1qita1218456962.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/221nm1218456962.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/3hm4g1218456963.tab") 
> 
> system("convert tmp/1qita1218456962.ps tmp/1qita1218456962.png")
> system("convert tmp/221nm1218456962.ps tmp/221nm1218456962.png")
> 
> 
> proc.time()
   user  system elapsed 
  9.409   0.450  10.061