R version 2.8.0 (2008-10-20)
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(10
+ ,10
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+ ,8
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+ ,5
+ ,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] 10.69570
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.07219099
> (armose <- arm / armse)
[1] 148.1584
> (geo <- geomean(x))
[1] 10.44014
> (har <- harmean(x))
[1] 9.963584
> (qua <- quamean(x))
[1] 10.89771
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.69570 0.07219099
  [2,] 10.69332 0.07192168
  [3,] 10.69690 0.07137276
  [4,] 10.70167 0.06965830
  [5,] 10.70764 0.06902042
  [6,] 10.70764 0.06902042
  [7,] 10.71599 0.06826267
  [8,] 10.70644 0.06745779
  [9,] 10.70644 0.06745779
 [10,] 10.70644 0.06745779
 [11,] 10.70644 0.06745779
 [12,] 10.70644 0.06745779
 [13,] 10.70644 0.06745779
 [14,] 10.72315 0.06619894
 [15,] 10.72315 0.06619894
 [16,] 10.72315 0.06619894
 [17,] 10.72315 0.06619894
 [18,] 10.72315 0.06619894
 [19,] 10.72315 0.06619894
 [20,] 10.72315 0.06619894
 [21,] 10.72315 0.06619894
 [22,] 10.72315 0.06619894
 [23,] 10.72315 0.06619894
 [24,] 10.72315 0.06619894
 [25,] 10.72315 0.06619894
 [26,] 10.72315 0.06619894
 [27,] 10.72315 0.06619894
 [28,] 10.68974 0.06387036
 [29,] 10.68974 0.06387036
 [30,] 10.68974 0.06387036
 [31,] 10.68974 0.06387036
 [32,] 10.68974 0.06387036
 [33,] 10.68974 0.06387036
 [34,] 10.68974 0.06387036
 [35,] 10.68974 0.06387036
 [36,] 10.68974 0.06387036
 [37,] 10.73389 0.06116019
 [38,] 10.73389 0.06116019
 [39,] 10.73389 0.06116019
 [40,] 10.73389 0.06116019
 [41,] 10.73389 0.06116019
 [42,] 10.73389 0.06116019
 [43,] 10.73389 0.06116019
 [44,] 10.73389 0.06116019
 [45,] 10.73389 0.06116019
 [46,] 10.73389 0.06116019
 [47,] 10.73389 0.06116019
 [48,] 10.73389 0.06116019
 [49,] 10.73389 0.06116019
 [50,] 10.73389 0.06116019
 [51,] 10.73389 0.06116019
 [52,] 10.73389 0.06116019
 [53,] 10.73389 0.06116019
 [54,] 10.73389 0.06116019
 [55,] 10.73389 0.06116019
 [56,] 10.73389 0.06116019
 [57,] 10.73389 0.06116019
 [58,] 10.73389 0.06116019
 [59,] 10.73389 0.06116019
 [60,] 10.73389 0.06116019
 [61,] 10.73389 0.06116019
 [62,] 10.73389 0.06116019
 [63,] 10.73389 0.06116019
 [64,] 10.73389 0.06116019
 [65,] 10.73389 0.06116019
 [66,] 10.65513 0.05667975
 [67,] 10.65513 0.05667975
 [68,] 10.65513 0.05667975
 [69,] 10.65513 0.05667975
 [70,] 10.65513 0.05667975
 [71,] 10.65513 0.05667975
 [72,] 10.65513 0.05667975
 [73,] 10.65513 0.05667975
 [74,] 10.65513 0.05667975
 [75,] 10.65513 0.05667975
 [76,] 10.65513 0.05667975
 [77,] 10.65513 0.05667975
 [78,] 10.65513 0.05667975
 [79,] 10.65513 0.05667975
 [80,] 10.65513 0.05667975
 [81,] 10.65513 0.05667975
 [82,] 10.65513 0.05667975
 [83,] 10.65513 0.05667975
 [84,] 10.65513 0.05667975
 [85,] 10.65513 0.05667975
 [86,] 10.65513 0.05667975
 [87,] 10.65513 0.05667975
 [88,] 10.65513 0.05667975
 [89,] 10.65513 0.05667975
 [90,] 10.65513 0.05667975
 [91,] 10.65513 0.05667975
 [92,] 10.54535 0.05209827
 [93,] 10.54535 0.05209827
 [94,] 10.54535 0.05209827
 [95,] 10.54535 0.05209827
 [96,] 10.54535 0.05209827
 [97,] 10.54535 0.05209827
 [98,] 10.54535 0.05209827
 [99,] 10.54535 0.05209827
[100,] 10.54535 0.05209827
[101,] 10.54535 0.05209827
[102,] 10.54535 0.05209827
[103,] 10.54535 0.05209827
[104,] 10.54535 0.05209827
[105,] 10.54535 0.05209827
[106,] 10.54535 0.05209827
[107,] 10.54535 0.05209827
[108,] 10.54535 0.05209827
[109,] 10.54535 0.05209827
[110,] 10.54535 0.05209827
[111,] 10.54535 0.05209827
[112,] 10.54535 0.05209827
[113,] 10.54535 0.05209827
[114,] 10.54535 0.05209827
[115,] 10.54535 0.05209827
[116,] 10.54535 0.05209827
[117,] 10.54535 0.05209827
[118,] 10.54535 0.05209827
[119,] 10.54535 0.05209827
[120,] 10.54535 0.05209827
[121,] 10.54535 0.05209827
[122,] 10.54535 0.05209827
[123,] 10.54535 0.05209827
[124,] 10.54535 0.05209827
[125,] 10.54535 0.05209827
[126,] 10.54535 0.05209827
[127,] 10.54535 0.05209827
[128,] 10.54535 0.05209827
[129,] 10.54535 0.05209827
[130,] 10.54535 0.05209827
[131,] 10.54535 0.05209827
[132,] 10.54535 0.05209827
[133,] 10.54535 0.05209827
[134,] 10.70525 0.04361393
[135,] 10.70525 0.04361393
[136,] 10.70525 0.04361393
[137,] 10.70525 0.04361393
[138,] 10.70525 0.04361393
[139,] 10.70525 0.04361393
[140,] 10.70525 0.04361393
[141,] 10.70525 0.04361393
[142,] 10.70525 0.04361393
[143,] 10.70525 0.04361393
[144,] 10.70525 0.04361393
[145,] 10.70525 0.04361393
[146,] 10.70525 0.04361393
[147,] 10.70525 0.04361393
[148,] 10.70525 0.04361393
[149,] 10.70525 0.04361393
[150,] 10.70525 0.04361393
[151,] 10.70525 0.04361393
[152,] 10.70525 0.04361393
[153,] 10.70525 0.04361393
[154,] 10.70525 0.04361393
[155,] 10.70525 0.04361393
[156,] 10.70525 0.04361393
[157,] 10.70525 0.04361393
[158,] 10.70525 0.04361393
[159,] 10.70525 0.04361393
[160,] 10.70525 0.04361393
[161,] 10.70525 0.04361393
[162,] 10.70525 0.04361393
[163,] 10.70525 0.04361393
[164,] 10.70525 0.04361393
[165,] 10.70525 0.04361393
[166,] 10.70525 0.04361393
[167,] 10.70525 0.04361393
[168,] 10.70525 0.04361393
[169,] 10.70525 0.04361393
[170,] 10.70525 0.04361393
[171,] 10.70525 0.04361393
[172,] 10.70525 0.04361393
[173,] 10.70525 0.04361393
[174,] 10.70525 0.04361393
[175,] 10.70525 0.04361393
[176,] 10.70525 0.04361393
[177,] 10.70525 0.04361393
[178,] 10.70525 0.04361393
[179,] 10.70525 0.04361393
[180,] 10.70525 0.04361393
[181,] 10.70525 0.04361393
[182,] 10.70525 0.04361393
[183,] 10.70525 0.04361393
[184,] 10.70525 0.04361393
[185,] 10.70525 0.04361393
[186,] 10.70525 0.04361393
[187,] 10.70525 0.04361393
[188,] 10.70525 0.04361393
[189,] 10.70525 0.04361393
[190,] 10.70525 0.04361393
[191,] 10.70525 0.04361393
[192,] 10.70525 0.04361393
[193,] 10.70525 0.04361393
[194,] 10.70525 0.04361393
[195,] 10.70525 0.04361393
[196,] 10.70525 0.04361393
[197,] 10.70525 0.04361393
[198,] 10.70525 0.04361393
[199,] 10.70525 0.04361393
[200,] 10.70525 0.04361393
[201,] 10.70525 0.04361393
[202,] 10.94630 0.03374236
[203,] 10.94630 0.03374236
[204,] 10.94630 0.03374236
[205,] 10.94630 0.03374236
[206,] 10.94630 0.03374236
[207,] 10.94630 0.03374236
[208,] 10.94630 0.03374236
[209,] 10.94630 0.03374236
[210,] 10.94630 0.03374236
[211,] 10.94630 0.03374236
[212,] 10.94630 0.03374236
[213,] 10.94630 0.03374236
[214,] 10.94630 0.03374236
[215,] 10.94630 0.03374236
[216,] 10.94630 0.03374236
[217,] 10.94630 0.03374236
[218,] 10.94630 0.03374236
[219,] 10.94630 0.03374236
[220,] 10.94630 0.03374236
[221,] 10.94630 0.03374236
[222,] 10.94630 0.03374236
[223,] 10.94630 0.03374236
[224,] 10.94630 0.03374236
[225,] 10.94630 0.03374236
[226,] 10.94630 0.03374236
[227,] 10.94630 0.03374236
[228,] 10.94630 0.03374236
[229,] 10.94630 0.03374236
[230,] 10.94630 0.03374236
[231,] 10.94630 0.03374236
[232,] 10.94630 0.03374236
[233,] 10.94630 0.03374236
[234,] 10.94630 0.03374236
[235,] 10.94630 0.03374236
[236,] 10.94630 0.03374236
[237,] 10.94630 0.03374236
[238,] 10.94630 0.03374236
[239,] 10.94630 0.03374236
[240,] 10.94630 0.03374236
[241,] 10.94630 0.03374236
[242,] 10.94630 0.03374236
[243,] 10.94630 0.03374236
[244,] 10.94630 0.03374236
[245,] 10.94630 0.03374236
[246,] 10.94630 0.03374236
[247,] 10.94630 0.03374236
[248,] 10.94630 0.03374236
[249,] 10.94630 0.03374236
[250,] 10.94630 0.03374236
[251,] 10.94630 0.03374236
[252,] 10.94630 0.03374236
[253,] 10.94630 0.03374236
[254,] 10.94630 0.03374236
[255,] 10.94630 0.03374236
[256,] 10.94630 0.03374236
[257,] 10.94630 0.03374236
[258,] 10.94630 0.03374236
[259,] 10.94630 0.03374236
[260,] 10.94630 0.03374236
[261,] 10.94630 0.03374236
[262,] 10.94630 0.03374236
[263,] 10.94630 0.03374236
[264,] 10.94630 0.03374236
[265,] 10.94630 0.03374236
[266,] 10.94630 0.03374236
[267,] 10.94630 0.03374236
[268,] 10.94630 0.03374236
[269,] 10.94630 0.03374236
[270,] 10.94630 0.03374236
[271,] 10.94630 0.03374236
[272,] 10.94630 0.03374236
[273,] 10.94630 0.03374236
[274,] 10.94630 0.03374236
[275,] 10.94630 0.03374236
[276,] 10.94630 0.03374236
[277,] 10.94630 0.03374236
[278,] 10.94630 0.03374236
[279,] 10.94630 0.03374236
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.69856 0.07089013
  [2,] 10.70144 0.06955152
  [3,] 10.70553 0.06831680
  [4,] 10.70843 0.06724569
  [5,] 10.71014 0.06661270
  [6,] 10.71065 0.06610497
  [7,] 10.71117 0.06558792
  [8,] 10.71046 0.06517982
  [9,] 10.71098 0.06487475
 [10,] 10.71149 0.06456483
 [11,] 10.71201 0.06424995
 [12,] 10.71253 0.06392999
 [13,] 10.71305 0.06360485
 [14,] 10.71358 0.06327439
 [15,] 10.71287 0.06304108
 [16,] 10.71216 0.06280416
 [17,] 10.71144 0.06256357
 [18,] 10.71072 0.06231923
 [19,] 10.71000 0.06207106
 [20,] 10.70927 0.06181897
 [21,] 10.70854 0.06156290
 [22,] 10.70781 0.06130275
 [23,] 10.70707 0.06103843
 [24,] 10.70633 0.06076985
 [25,] 10.70558 0.06049693
 [26,] 10.70483 0.06021955
 [27,] 10.70408 0.05993763
 [28,] 10.70332 0.05965105
 [29,] 10.70332 0.05946489
 [30,] 10.70437 0.05927581
 [31,] 10.70437 0.05908376
 [32,] 10.70543 0.05888868
 [33,] 10.70596 0.05869050
 [34,] 10.70649 0.05848918
 [35,] 10.70703 0.05828464
 [36,] 10.70757 0.05807683
 [37,] 10.70812 0.05786566
 [38,] 10.70735 0.05774696
 [39,] 10.70658 0.05762634
 [40,] 10.70580 0.05750376
 [41,] 10.70503 0.05737921
 [42,] 10.70424 0.05725263
 [43,] 10.70346 0.05712400
 [44,] 10.70267 0.05699327
 [45,] 10.70187 0.05686041
 [46,] 10.70107 0.05672538
 [47,] 10.70027 0.05658813
 [48,] 10.69946 0.05644864
 [49,] 10.69865 0.05630685
 [50,] 10.69783 0.05616273
 [51,] 10.69701 0.05601622
 [52,] 10.69619 0.05586729
 [53,] 10.69619 0.05571588
 [54,] 10.69452 0.05556195
 [55,] 10.69368 0.05540545
 [56,] 10.69284 0.05524633
 [57,] 10.69199 0.05508453
 [58,] 10.69199 0.05492001
 [59,] 10.69028 0.05475271
 [60,] 10.68942 0.05458257
 [61,] 10.68855 0.05440954
 [62,] 10.68855 0.05423355
 [63,] 10.68680 0.05405454
 [64,] 10.68592 0.05387245
 [65,] 10.68503 0.05368722
 [66,] 10.68414 0.05349877
 [67,] 10.68466 0.05341368
 [68,] 10.68519 0.05332703
 [69,] 10.68571 0.05323880
 [70,] 10.68625 0.05314896
 [71,] 10.68678 0.05305748
 [72,] 10.68732 0.05296433
 [73,] 10.68786 0.05286949
 [74,] 10.68841 0.05277291
 [75,] 10.68895 0.05267457
 [76,] 10.68950 0.05257443
 [77,] 10.69006 0.05247246
 [78,] 10.69062 0.05236863
 [79,] 10.69118 0.05226290
 [80,] 10.69174 0.05215524
 [81,] 10.69231 0.05204560
 [82,] 10.69288 0.05193395
 [83,] 10.69345 0.05182025
 [84,] 10.69403 0.05170446
 [85,] 10.69461 0.05158654
 [86,] 10.69520 0.05146644
 [87,] 10.69578 0.05134413
 [88,] 10.69637 0.05121955
 [89,] 10.69697 0.05109267
 [90,] 10.69757 0.05096343
 [91,] 10.69817 0.05083179
 [92,] 10.69878 0.05069770
 [93,] 10.70092 0.05064490
 [94,] 10.70308 0.05059077
 [95,] 10.70525 0.05053528
 [96,] 10.70743 0.05047841
 [97,] 10.70963 0.05042013
 [98,] 10.71184 0.05036041
 [99,] 10.71406 0.05029922
[100,] 10.71630 0.05023653
[101,] 10.71855 0.05017231
[102,] 10.72082 0.05010654
[103,] 10.72310 0.05003917
[104,] 10.72540 0.04997018
[105,] 10.72771 0.04989953
[106,] 10.72771 0.04982719
[107,] 10.73003 0.04975312
[108,] 10.73473 0.04967728
[109,] 10.73710 0.04959965
[110,] 10.73948 0.04952017
[111,] 10.74188 0.04943882
[112,] 10.74430 0.04935554
[113,] 10.74673 0.04927030
[114,] 10.74918 0.04918306
[115,] 10.74918 0.04909378
[116,] 10.75164 0.04900240
[117,] 10.75662 0.04890887
[118,] 10.75914 0.04881317
[119,] 10.76167 0.04871522
[120,] 10.76421 0.04861499
[121,] 10.76678 0.04851242
[122,] 10.76936 0.04840746
[123,] 10.77196 0.04830005
[124,] 10.77196 0.04819013
[125,] 10.77458 0.04807766
[126,] 10.77986 0.04796255
[127,] 10.78253 0.04784477
[128,] 10.78522 0.04772423
[129,] 10.78793 0.04760088
[130,] 10.79066 0.04747464
[131,] 10.79340 0.04734544
[132,] 10.79617 0.04721322
[133,] 10.79895 0.04707789
[134,] 10.80175 0.04693939
[135,] 10.80282 0.04695022
[136,] 10.80389 0.04696057
[137,] 10.80496 0.04697044
[138,] 10.80605 0.04697980
[139,] 10.80714 0.04698865
[140,] 10.80824 0.04699697
[141,] 10.80935 0.04700476
[142,] 10.81047 0.04701200
[143,] 10.81159 0.04701867
[144,] 10.81273 0.04702477
[145,] 10.81387 0.04703028
[146,] 10.81502 0.04703519
[147,] 10.81618 0.04703948
[148,] 10.81734 0.04704314
[149,] 10.81852 0.04704615
[150,] 10.81970 0.04704850
[151,] 10.82090 0.04705017
[152,] 10.82210 0.04705115
[153,] 10.82331 0.04705142
[154,] 10.82453 0.04705096
[155,] 10.82576 0.04704976
[156,] 10.82700 0.04704780
[157,] 10.82824 0.04704505
[158,] 10.82950 0.04704151
[159,] 10.83077 0.04703715
[160,] 10.83205 0.04703195
[161,] 10.83333 0.04702589
[162,] 10.83463 0.04701896
[163,] 10.83594 0.04701113
[164,] 10.83725 0.04700237
[165,] 10.83858 0.04699267
[166,] 10.83992 0.04698200
[167,] 10.84127 0.04697035
[168,] 10.84263 0.04695767
[169,] 10.84400 0.04694396
[170,] 10.84538 0.04692918
[171,] 10.84677 0.04691331
[172,] 10.84818 0.04689632
[173,] 10.84959 0.04687818
[174,] 10.85102 0.04685887
[175,] 10.85246 0.04683835
[176,] 10.85391 0.04681659
[177,] 10.85537 0.04679357
[178,] 10.85685 0.04676924
[179,] 10.85833 0.04674359
[180,] 10.85983 0.04671656
[181,] 10.86134 0.04668814
[182,] 10.86287 0.04665827
[183,] 10.86441 0.04662693
[184,] 10.86596 0.04659408
[185,] 10.86752 0.04655967
[186,] 10.86910 0.04652367
[187,] 10.87069 0.04648603
[188,] 10.87229 0.04644671
[189,] 10.87391 0.04640566
[190,] 10.87555 0.04636285
[191,] 10.87719 0.04631821
[192,] 10.87885 0.04627171
[193,] 10.88053 0.04622329
[194,] 10.88222 0.04617290
[195,] 10.88393 0.04612048
[196,] 10.88565 0.04606598
[197,] 10.88739 0.04600934
[198,] 10.88914 0.04595051
[199,] 10.89091 0.04588941
[200,] 10.89269 0.04582599
[201,] 10.89450 0.04576017
[202,] 10.89631 0.04569190
[203,] 10.89583 0.04578526
[204,] 10.89535 0.04587918
[205,] 10.89486 0.04597364
[206,] 10.89437 0.04606867
[207,] 10.89387 0.04616426
[208,] 10.89336 0.04626042
[209,] 10.89286 0.04635716
[210,] 10.89234 0.04645447
[211,] 10.89183 0.04655237
[212,] 10.89183 0.04665087
[213,] 10.89078 0.04674995
[214,] 10.89078 0.04684964
[215,] 10.88971 0.04694994
[216,] 10.88916 0.04705085
[217,] 10.88861 0.04715238
[218,] 10.88806 0.04725454
[219,] 10.88750 0.04735732
[220,] 10.88693 0.04746075
[221,] 10.88693 0.04756481
[222,] 10.88579 0.04766952
[223,] 10.88579 0.04777489
[224,] 10.88462 0.04788092
[225,] 10.88402 0.04798762
[226,] 10.88342 0.04809498
[227,] 10.88281 0.04820303
[228,] 10.88220 0.04831177
[229,] 10.88158 0.04842120
[230,] 10.88158 0.04853132
[231,] 10.88032 0.04864216
[232,] 10.88032 0.04875370
[233,] 10.87903 0.04886597
[234,] 10.87838 0.04897896
[235,] 10.87772 0.04909268
[236,] 10.87705 0.04920714
[237,] 10.87637 0.04932235
[238,] 10.87569 0.04943832
[239,] 10.87569 0.04955505
[240,] 10.87430 0.04967254
[241,] 10.87430 0.04979081
[242,] 10.87288 0.04990986
[243,] 10.87216 0.05002971
[244,] 10.87143 0.05015035
[245,] 10.87069 0.05027180
[246,] 10.86994 0.05039406
[247,] 10.86919 0.05051714
[248,] 10.86919 0.05064105
[249,] 10.86765 0.05076579
[250,] 10.86765 0.05089138
[251,] 10.86607 0.05101782
[252,] 10.86527 0.05114512
[253,] 10.86446 0.05127329
[254,] 10.86364 0.05140233
[255,] 10.86280 0.05153226
[256,] 10.86196 0.05166308
[257,] 10.86111 0.05179479
[258,] 10.86025 0.05192742
[259,] 10.85938 0.05206096
[260,] 10.85849 0.05219543
[261,] 10.85759 0.05233082
[262,] 10.85669 0.05246716
[263,] 10.85577 0.05260444
[264,] 10.85484 0.05274268
[265,] 10.85390 0.05288189
[266,] 10.85294 0.05302207
[267,] 10.85197 0.05316323
[268,] 10.85099 0.05330538
[269,] 10.85000 0.05344852
[270,] 10.84899 0.05359267
[271,] 10.84797 0.05373784
[272,] 10.84694 0.05388402
[273,] 10.84589 0.05403123
[274,] 10.84483 0.05417948
[275,] 10.84375 0.05432877
[276,] 10.84266 0.05447912
[277,] 10.84155 0.05463052
[278,] 10.84043 0.05478299
[279,] 10.83929 0.05493652
> (midr <- midrange(x))
[1] 9.5
> 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/freestat/rcomp/tmp/1qtrj1250083297.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/freestat/rcomp/tmp/2717o1250083297.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3ve991250083298.tab") 
> 
> system("convert tmp/1qtrj1250083297.ps tmp/1qtrj1250083297.png")
> system("convert tmp/2717o1250083297.ps tmp/2717o1250083297.png")
> 
> 
> proc.time()
   user  system elapsed 
  8.410   0.635   8.568