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

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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
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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> x <- c(8
+ ,10
+ ,10
+ ,13
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+ ,9
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+ ,10
+ ,12
+ ,12
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+ ,10
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+ ,10
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+ ,12
+ ,12
+ ,12
+ ,9
+ ,12
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+ ,9
+ ,12
+ ,12
+ ,12
+ ,15
+ ,12
+ ,12
+ ,12
+ ,8
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+ ,12
+ ,8
+ ,12
+ ,12
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+ ,12
+ ,8
+ ,8
+ ,10
+ ,10
+ ,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] 10.73716
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.07056414
> (armose <- arm / armse)
[1] 152.1616
> (geo <- geomean(x))
[1] 10.5244
> (har <- harmean(x))
[1] 10.23462
> (qua <- quamean(x))
[1] 10.92928
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.73835 0.06972396
  [2,] 10.74074 0.06946771
  [3,] 10.73716 0.06904918
  [4,] 10.74194 0.06861403
  [5,] 10.73596 0.06801142
  [6,] 10.73596 0.06801142
  [7,] 10.73596 0.06801142
  [8,] 10.73596 0.06801142
  [9,] 10.72521 0.06710338
 [10,] 10.72521 0.06710338
 [11,] 10.73835 0.06610457
 [12,] 10.73835 0.06610457
 [13,] 10.73835 0.06610457
 [14,] 10.73835 0.06610457
 [15,] 10.73835 0.06610457
 [16,] 10.73835 0.06610457
 [17,] 10.73835 0.06610457
 [18,] 10.73835 0.06610457
 [19,] 10.73835 0.06610457
 [20,] 10.73835 0.06610457
 [21,] 10.73835 0.06610457
 [22,] 10.73835 0.06610457
 [23,] 10.73835 0.06610457
 [24,] 10.73835 0.06610457
 [25,] 10.73835 0.06610457
 [26,] 10.73835 0.06610457
 [27,] 10.73835 0.06610457
 [28,] 10.73835 0.06610457
 [29,] 10.70370 0.06369128
 [30,] 10.70370 0.06369128
 [31,] 10.70370 0.06369128
 [32,] 10.70370 0.06369128
 [33,] 10.70370 0.06369128
 [34,] 10.74432 0.06118227
 [35,] 10.74432 0.06118227
 [36,] 10.74432 0.06118227
 [37,] 10.74432 0.06118227
 [38,] 10.74432 0.06118227
 [39,] 10.74432 0.06118227
 [40,] 10.74432 0.06118227
 [41,] 10.74432 0.06118227
 [42,] 10.74432 0.06118227
 [43,] 10.74432 0.06118227
 [44,] 10.74432 0.06118227
 [45,] 10.74432 0.06118227
 [46,] 10.74432 0.06118227
 [47,] 10.74432 0.06118227
 [48,] 10.74432 0.06118227
 [49,] 10.74432 0.06118227
 [50,] 10.74432 0.06118227
 [51,] 10.74432 0.06118227
 [52,] 10.74432 0.06118227
 [53,] 10.74432 0.06118227
 [54,] 10.74432 0.06118227
 [55,] 10.74432 0.06118227
 [56,] 10.74432 0.06118227
 [57,] 10.74432 0.06118227
 [58,] 10.74432 0.06118227
 [59,] 10.74432 0.06118227
 [60,] 10.74432 0.06118227
 [61,] 10.74432 0.06118227
 [62,] 10.74432 0.06118227
 [63,] 10.74432 0.06118227
 [64,] 10.74432 0.06118227
 [65,] 10.74432 0.06118227
 [66,] 10.74432 0.06118227
 [67,] 10.66428 0.05663822
 [68,] 10.66428 0.05663822
 [69,] 10.66428 0.05663822
 [70,] 10.66428 0.05663822
 [71,] 10.66428 0.05663822
 [72,] 10.66428 0.05663822
 [73,] 10.66428 0.05663822
 [74,] 10.66428 0.05663822
 [75,] 10.66428 0.05663822
 [76,] 10.66428 0.05663822
 [77,] 10.66428 0.05663822
 [78,] 10.66428 0.05663822
 [79,] 10.66428 0.05663822
 [80,] 10.66428 0.05663822
 [81,] 10.66428 0.05663822
 [82,] 10.66428 0.05663822
 [83,] 10.66428 0.05663822
 [84,] 10.66428 0.05663822
 [85,] 10.66428 0.05663822
 [86,] 10.66428 0.05663822
 [87,] 10.66428 0.05663822
 [88,] 10.66428 0.05663822
 [89,] 10.66428 0.05663822
 [90,] 10.66428 0.05663822
 [91,] 10.66428 0.05663822
 [92,] 10.66428 0.05663822
 [93,] 10.55317 0.05201111
 [94,] 10.55317 0.05201111
 [95,] 10.55317 0.05201111
 [96,] 10.55317 0.05201111
 [97,] 10.55317 0.05201111
 [98,] 10.55317 0.05201111
 [99,] 10.55317 0.05201111
[100,] 10.55317 0.05201111
[101,] 10.55317 0.05201111
[102,] 10.55317 0.05201111
[103,] 10.55317 0.05201111
[104,] 10.55317 0.05201111
[105,] 10.55317 0.05201111
[106,] 10.55317 0.05201111
[107,] 10.55317 0.05201111
[108,] 10.55317 0.05201111
[109,] 10.55317 0.05201111
[110,] 10.55317 0.05201111
[111,] 10.55317 0.05201111
[112,] 10.55317 0.05201111
[113,] 10.55317 0.05201111
[114,] 10.55317 0.05201111
[115,] 10.55317 0.05201111
[116,] 10.55317 0.05201111
[117,] 10.55317 0.05201111
[118,] 10.55317 0.05201111
[119,] 10.55317 0.05201111
[120,] 10.55317 0.05201111
[121,] 10.55317 0.05201111
[122,] 10.55317 0.05201111
[123,] 10.55317 0.05201111
[124,] 10.55317 0.05201111
[125,] 10.55317 0.05201111
[126,] 10.55317 0.05201111
[127,] 10.55317 0.05201111
[128,] 10.55317 0.05201111
[129,] 10.55317 0.05201111
[130,] 10.55317 0.05201111
[131,] 10.55317 0.05201111
[132,] 10.71087 0.04359785
[133,] 10.71087 0.04359785
[134,] 10.71087 0.04359785
[135,] 10.71087 0.04359785
[136,] 10.71087 0.04359785
[137,] 10.71087 0.04359785
[138,] 10.71087 0.04359785
[139,] 10.71087 0.04359785
[140,] 10.71087 0.04359785
[141,] 10.71087 0.04359785
[142,] 10.71087 0.04359785
[143,] 10.71087 0.04359785
[144,] 10.71087 0.04359785
[145,] 10.71087 0.04359785
[146,] 10.71087 0.04359785
[147,] 10.71087 0.04359785
[148,] 10.71087 0.04359785
[149,] 10.71087 0.04359785
[150,] 10.71087 0.04359785
[151,] 10.71087 0.04359785
[152,] 10.71087 0.04359785
[153,] 10.71087 0.04359785
[154,] 10.71087 0.04359785
[155,] 10.71087 0.04359785
[156,] 10.71087 0.04359785
[157,] 10.71087 0.04359785
[158,] 10.71087 0.04359785
[159,] 10.71087 0.04359785
[160,] 10.71087 0.04359785
[161,] 10.71087 0.04359785
[162,] 10.71087 0.04359785
[163,] 10.71087 0.04359785
[164,] 10.71087 0.04359785
[165,] 10.71087 0.04359785
[166,] 10.71087 0.04359785
[167,] 10.71087 0.04359785
[168,] 10.71087 0.04359785
[169,] 10.71087 0.04359785
[170,] 10.71087 0.04359785
[171,] 10.71087 0.04359785
[172,] 10.71087 0.04359785
[173,] 10.71087 0.04359785
[174,] 10.71087 0.04359785
[175,] 10.71087 0.04359785
[176,] 10.71087 0.04359785
[177,] 10.71087 0.04359785
[178,] 10.71087 0.04359785
[179,] 10.71087 0.04359785
[180,] 10.71087 0.04359785
[181,] 10.71087 0.04359785
[182,] 10.71087 0.04359785
[183,] 10.71087 0.04359785
[184,] 10.71087 0.04359785
[185,] 10.71087 0.04359785
[186,] 10.71087 0.04359785
[187,] 10.71087 0.04359785
[188,] 10.71087 0.04359785
[189,] 10.71087 0.04359785
[190,] 10.71087 0.04359785
[191,] 10.71087 0.04359785
[192,] 10.71087 0.04359785
[193,] 10.71087 0.04359785
[194,] 10.71087 0.04359785
[195,] 10.71087 0.04359785
[196,] 10.71087 0.04359785
[197,] 10.71087 0.04359785
[198,] 10.71087 0.04359785
[199,] 10.71087 0.04359785
[200,] 10.94982 0.03376808
[201,] 10.94982 0.03376808
[202,] 10.94982 0.03376808
[203,] 10.94982 0.03376808
[204,] 10.94982 0.03376808
[205,] 10.94982 0.03376808
[206,] 10.94982 0.03376808
[207,] 10.94982 0.03376808
[208,] 10.94982 0.03376808
[209,] 10.94982 0.03376808
[210,] 10.94982 0.03376808
[211,] 10.94982 0.03376808
[212,] 10.94982 0.03376808
[213,] 10.94982 0.03376808
[214,] 10.94982 0.03376808
[215,] 10.94982 0.03376808
[216,] 10.94982 0.03376808
[217,] 10.94982 0.03376808
[218,] 10.94982 0.03376808
[219,] 10.94982 0.03376808
[220,] 10.94982 0.03376808
[221,] 10.94982 0.03376808
[222,] 10.94982 0.03376808
[223,] 10.94982 0.03376808
[224,] 10.94982 0.03376808
[225,] 10.94982 0.03376808
[226,] 10.94982 0.03376808
[227,] 10.94982 0.03376808
[228,] 10.94982 0.03376808
[229,] 10.94982 0.03376808
[230,] 10.94982 0.03376808
[231,] 10.94982 0.03376808
[232,] 10.94982 0.03376808
[233,] 10.94982 0.03376808
[234,] 10.94982 0.03376808
[235,] 10.94982 0.03376808
[236,] 10.94982 0.03376808
[237,] 10.94982 0.03376808
[238,] 10.94982 0.03376808
[239,] 10.94982 0.03376808
[240,] 10.94982 0.03376808
[241,] 10.94982 0.03376808
[242,] 10.94982 0.03376808
[243,] 10.94982 0.03376808
[244,] 10.94982 0.03376808
[245,] 10.94982 0.03376808
[246,] 10.94982 0.03376808
[247,] 10.94982 0.03376808
[248,] 10.94982 0.03376808
[249,] 10.94982 0.03376808
[250,] 10.94982 0.03376808
[251,] 10.94982 0.03376808
[252,] 10.94982 0.03376808
[253,] 10.94982 0.03376808
[254,] 10.94982 0.03376808
[255,] 10.94982 0.03376808
[256,] 10.94982 0.03376808
[257,] 10.94982 0.03376808
[258,] 10.94982 0.03376808
[259,] 10.94982 0.03376808
[260,] 10.94982 0.03376808
[261,] 10.94982 0.03376808
[262,] 10.94982 0.03376808
[263,] 10.94982 0.03376808
[264,] 10.94982 0.03376808
[265,] 10.94982 0.03376808
[266,] 10.94982 0.03376808
[267,] 10.94982 0.03376808
[268,] 10.94982 0.03376808
[269,] 10.94982 0.03376808
[270,] 10.94982 0.03376808
[271,] 10.94982 0.03376808
[272,] 10.94982 0.03376808
[273,] 10.94982 0.03376808
[274,] 10.94982 0.03376808
[275,] 10.94982 0.03376808
[276,] 10.94982 0.03376808
[277,] 10.94982 0.03376808
[278,] 10.94982 0.03376808
[279,] 10.94982 0.03376808
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.73716 0.06887553
  [2,] 10.73772 0.06800777
  [3,] 10.73526 0.06725442
  [4,] 10.73526 0.06663275
  [5,] 10.73277 0.06611468
  [6,] 10.73212 0.06571622
  [7,] 10.73147 0.06531101
  [8,] 10.73147 0.06489887
  [9,] 10.73016 0.06447962
 [10,] 10.73072 0.06416467
 [11,] 10.73129 0.06384466
 [12,] 10.73063 0.06362027
 [13,] 10.72996 0.06339247
 [14,] 10.72930 0.06316117
 [15,] 10.72862 0.06292631
 [16,] 10.72862 0.06268782
 [17,] 10.72727 0.06244562
 [18,] 10.72659 0.06219964
 [19,] 10.72591 0.06194979
 [20,] 10.72522 0.06169599
 [21,] 10.72453 0.06143817
 [22,] 10.72383 0.06117624
 [23,] 10.72314 0.06091009
 [24,] 10.72243 0.06063966
 [25,] 10.72173 0.06036483
 [26,] 10.72102 0.06008550
 [27,] 10.72031 0.05980159
 [28,] 10.71959 0.05951298
 [29,] 10.71887 0.05921956
 [30,] 10.71943 0.05902755
 [31,] 10.72000 0.05883252
 [32,] 10.72000 0.05863440
 [33,] 10.72114 0.05843313
 [34,] 10.72172 0.05822866
 [35,] 10.72099 0.05811533
 [36,] 10.72026 0.05800018
 [37,] 10.71953 0.05788318
 [38,] 10.71879 0.05776429
 [39,] 10.71805 0.05764347
 [40,] 10.71731 0.05752070
 [41,] 10.71656 0.05739595
 [42,] 10.71580 0.05726916
 [43,] 10.71505 0.05714031
 [44,] 10.71429 0.05700937
 [45,] 10.71352 0.05687629
 [46,] 10.71275 0.05674103
 [47,] 10.71198 0.05660355
 [48,] 10.71120 0.05646382
 [49,] 10.71042 0.05632178
 [50,] 10.70963 0.05617741
 [51,] 10.70884 0.05603064
 [52,] 10.70805 0.05588144
 [53,] 10.70725 0.05572976
 [54,] 10.70645 0.05557556
 [55,] 10.70564 0.05541877
 [56,] 10.70483 0.05525936
 [57,] 10.70401 0.05509727
 [58,] 10.70319 0.05493244
 [59,] 10.70236 0.05476483
 [60,] 10.70153 0.05459437
 [61,] 10.70070 0.05442100
 [62,] 10.69986 0.05424467
 [63,] 10.69902 0.05406532
 [64,] 10.69902 0.05388288
 [65,] 10.69731 0.05369728
 [66,] 10.69645 0.05350846
 [67,] 10.69559 0.05331635
 [68,] 10.69615 0.05322836
 [69,] 10.69671 0.05313876
 [70,] 10.69727 0.05304753
 [71,] 10.69784 0.05295464
 [72,] 10.69841 0.05286005
 [73,] 10.69899 0.05276374
 [74,] 10.69956 0.05266567
 [75,] 10.70015 0.05256582
 [76,] 10.70073 0.05246414
 [77,] 10.70132 0.05236060
 [78,] 10.70191 0.05225517
 [79,] 10.70250 0.05214781
 [80,] 10.70310 0.05203849
 [81,] 10.70370 0.05192716
 [82,] 10.70431 0.05181379
 [83,] 10.70492 0.05169834
 [84,] 10.70553 0.05158076
 [85,] 10.70615 0.05146102
 [86,] 10.70677 0.05133907
 [87,] 10.70739 0.05121486
 [88,] 10.70802 0.05108836
 [89,] 10.70865 0.05095951
 [90,] 10.70928 0.05082827
 [91,] 10.70992 0.05069458
 [92,] 10.71057 0.05055840
 [93,] 10.71121 0.05041968
 [94,] 10.71341 0.05036281
 [95,] 10.71561 0.05030454
 [96,] 10.71783 0.05024484
 [97,] 10.72006 0.05018368
 [98,] 10.72231 0.05012103
 [99,] 10.72457 0.05005686
[100,] 10.72684 0.04999114
[101,] 10.72913 0.04992384
[102,] 10.73144 0.04985492
[103,] 10.73376 0.04978436
[104,] 10.73609 0.04971211
[105,] 10.73609 0.04963815
[106,] 10.74080 0.04956243
[107,] 10.74318 0.04948493
[108,] 10.74557 0.04940560
[109,] 10.74557 0.04932440
[110,] 10.75041 0.04924129
[111,] 10.75285 0.04915624
[112,] 10.75530 0.04906919
[113,] 10.75530 0.04898012
[114,] 10.76026 0.04888896
[115,] 10.76277 0.04879568
[116,] 10.76529 0.04870023
[117,] 10.76529 0.04860256
[118,] 10.77038 0.04850261
[119,] 10.77295 0.04840035
[120,] 10.77554 0.04829571
[121,] 10.77815 0.04818865
[122,] 10.78078 0.04807910
[123,] 10.78342 0.04796700
[124,] 10.78608 0.04785230
[125,] 10.78876 0.04773494
[126,] 10.79145 0.04761485
[127,] 10.79417 0.04749196
[128,] 10.79417 0.04736622
[129,] 10.79965 0.04723754
[130,] 10.80243 0.04710586
[131,] 10.80522 0.04697111
[132,] 10.80803 0.04683320
[133,] 10.80911 0.04684381
[134,] 10.81019 0.04685395
[135,] 10.81129 0.04686359
[136,] 10.81239 0.04687274
[137,] 10.81350 0.04688138
[138,] 10.81462 0.04688950
[139,] 10.81574 0.04689709
[140,] 10.81688 0.04690412
[141,] 10.81802 0.04691060
[142,] 10.81917 0.04691650
[143,] 10.82033 0.04692182
[144,] 10.82149 0.04692654
[145,] 10.82267 0.04693065
[146,] 10.82385 0.04693413
[147,] 10.82505 0.04693697
[148,] 10.82625 0.04693915
[149,] 10.82746 0.04694066
[150,] 10.82868 0.04694147
[151,] 10.82991 0.04694159
[152,] 10.83114 0.04694098
[153,] 10.83239 0.04693963
[154,] 10.83365 0.04693753
[155,] 10.83491 0.04693465
[156,] 10.83619 0.04693098
[157,] 10.83748 0.04692650
[158,] 10.83877 0.04692118
[159,] 10.84008 0.04691502
[160,] 10.84139 0.04690799
[161,] 10.84272 0.04690006
[162,] 10.84405 0.04689122
[163,] 10.84540 0.04688144
[164,] 10.84676 0.04687070
[165,] 10.84813 0.04685898
[166,] 10.84950 0.04684626
[167,] 10.85089 0.04683250
[168,] 10.85230 0.04681769
[169,] 10.85371 0.04680179
[170,] 10.85513 0.04678478
[171,] 10.85657 0.04676664
[172,] 10.85801 0.04674733
[173,] 10.85947 0.04672683
[174,] 10.86094 0.04670511
[175,] 10.86242 0.04668213
[176,] 10.86392 0.04665786
[177,] 10.86542 0.04663227
[178,] 10.86694 0.04660533
[179,] 10.86848 0.04657700
[180,] 10.87002 0.04654724
[181,] 10.87158 0.04651603
[182,] 10.87315 0.04648332
[183,] 10.87473 0.04644907
[184,] 10.87633 0.04641324
[185,] 10.87794 0.04637580
[186,] 10.87957 0.04633669
[187,] 10.88121 0.04629588
[188,] 10.88286 0.04625331
[189,] 10.88453 0.04620895
[190,] 10.88621 0.04616275
[191,] 10.88791 0.04611464
[192,] 10.88962 0.04606459
[193,] 10.89135 0.04601253
[194,] 10.89310 0.04595843
[195,] 10.89485 0.04590220
[196,] 10.89663 0.04584381
[197,] 10.89842 0.04578318
[198,] 10.90023 0.04572026
[199,] 10.90205 0.04565498
[200,] 10.90389 0.04558727
[201,] 10.90345 0.04568022
[202,] 10.90300 0.04577373
[203,] 10.90255 0.04586778
[204,] 10.90210 0.04596240
[205,] 10.90164 0.04605758
[206,] 10.90118 0.04615333
[207,] 10.90071 0.04624965
[208,] 10.90024 0.04634656
[209,] 10.89976 0.04644405
[210,] 10.89976 0.04654213
[211,] 10.89928 0.04664080
[212,] 10.89831 0.04674008
[213,] 10.89781 0.04683997
[214,] 10.89731 0.04694047
[215,] 10.89681 0.04704159
[216,] 10.89630 0.04714333
[217,] 10.89578 0.04724571
[218,] 10.89578 0.04734872
[219,] 10.89474 0.04745238
[220,] 10.89421 0.04755668
[221,] 10.89367 0.04766165
[222,] 10.89313 0.04776727
[223,] 10.89258 0.04787356
[224,] 10.89203 0.04798053
[225,] 10.89147 0.04808818
[226,] 10.89147 0.04819652
[227,] 10.89034 0.04830555
[228,] 10.88976 0.04841528
[229,] 10.88918 0.04852573
[230,] 10.88859 0.04863688
[231,] 10.88800 0.04874876
[232,] 10.88740 0.04886137
[233,] 10.88740 0.04897472
[234,] 10.88679 0.04908881
[235,] 10.88556 0.04920365
[236,] 10.88493 0.04931925
[237,] 10.88430 0.04943561
[238,] 10.88366 0.04955275
[239,] 10.88301 0.04967067
[240,] 10.88235 0.04978938
[241,] 10.88235 0.04990888
[242,] 10.88102 0.05002919
[243,] 10.88034 0.05015031
[244,] 10.87966 0.05027225
[245,] 10.87896 0.05039502
[246,] 10.87826 0.05051862
[247,] 10.87755 0.05064307
[248,] 10.87683 0.05076837
[249,] 10.87683 0.05089454
[250,] 10.87537 0.05102157
[251,] 10.87463 0.05114948
[252,] 10.87387 0.05127827
[253,] 10.87311 0.05140796
[254,] 10.87234 0.05153855
[255,] 10.87156 0.05167006
[256,] 10.87156 0.05180249
[257,] 10.86997 0.05193584
[258,] 10.86916 0.05207014
[259,] 10.86834 0.05220538
[260,] 10.86751 0.05234158
[261,] 10.86667 0.05247875
[262,] 10.86581 0.05261689
[263,] 10.86495 0.05275601
[264,] 10.86408 0.05289613
[265,] 10.86319 0.05303724
[266,] 10.86230 0.05317937
[267,] 10.86139 0.05332252
[268,] 10.86047 0.05346670
[269,] 10.85953 0.05361192
[270,] 10.85859 0.05375818
[271,] 10.85763 0.05390551
[272,] 10.85666 0.05405389
[273,] 10.85567 0.05420336
[274,] 10.85467 0.05435390
[275,] 10.85366 0.05450554
[276,] 10.85263 0.05465829
[277,] 10.85159 0.05481214
[278,] 10.85053 0.05496711
[279,] 10.84946 0.05512321
> (midr <- midrange(x))
[1] 10.5
> 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/1puuv1218486895.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/2kyc31218486895.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/3prp01218486896.tab") 
> 
> system("convert tmp/1puuv1218486895.ps tmp/1puuv1218486895.png")
> system("convert tmp/2kyc31218486895.ps tmp/2kyc31218486895.png")
> 
> 
> proc.time()
   user  system elapsed 
 10.358   0.611  10.478