R version 2.7.0 (2008-04-22)
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
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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
+ ,13
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+ ,9
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+ ,12
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+ ,12
+ ,12
+ ,8
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+ ,12
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+ ,12
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+ ,10
+ ,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] 10.72189
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.0666889
> (armose <- arm / armse)
[1] 160.7747
> (geo <- geomean(x))
[1] 10.54389
> (har <- harmean(x))
[1] 10.35743
> (qua <- quamean(x))
[1] 10.89185
> (win <- winmean(x))
           [,1]       [,2]
  [1,] 10.72068 0.06653993
  [2,] 10.72068 0.06605414
  [3,] 10.71705 0.06573549
  [4,] 10.71705 0.06573549
  [5,] 10.71705 0.06573549
  [6,] 10.71705 0.06573549
  [7,] 10.72551 0.06507412
  [8,] 10.72551 0.06507412
  [9,] 10.72551 0.06507412
 [10,] 10.72551 0.06507412
 [11,] 10.72551 0.06507412
 [12,] 10.72551 0.06507412
 [13,] 10.72551 0.06507412
 [14,] 10.72551 0.06507412
 [15,] 10.72551 0.06507412
 [16,] 10.72551 0.06507412
 [17,] 10.72551 0.06507412
 [18,] 10.72551 0.06507412
 [19,] 10.72551 0.06507412
 [20,] 10.72551 0.06507412
 [21,] 10.72551 0.06507412
 [22,] 10.72551 0.06507412
 [23,] 10.69770 0.06308352
 [24,] 10.69770 0.06308352
 [25,] 10.69770 0.06308352
 [26,] 10.69770 0.06308352
 [27,] 10.69770 0.06308352
 [28,] 10.69770 0.06308352
 [29,] 10.69770 0.06308352
 [30,] 10.73398 0.06080353
 [31,] 10.73398 0.06080353
 [32,] 10.73398 0.06080353
 [33,] 10.73398 0.06080353
 [34,] 10.73398 0.06080353
 [35,] 10.73398 0.06080353
 [36,] 10.73398 0.06080353
 [37,] 10.73398 0.06080353
 [38,] 10.73398 0.06080353
 [39,] 10.73398 0.06080353
 [40,] 10.73398 0.06080353
 [41,] 10.73398 0.06080353
 [42,] 10.73398 0.06080353
 [43,] 10.73398 0.06080353
 [44,] 10.73398 0.06080353
 [45,] 10.73398 0.06080353
 [46,] 10.73398 0.06080353
 [47,] 10.73398 0.06080353
 [48,] 10.73398 0.06080353
 [49,] 10.73398 0.06080353
 [50,] 10.73398 0.06080353
 [51,] 10.73398 0.06080353
 [52,] 10.73398 0.06080353
 [53,] 10.73398 0.06080353
 [54,] 10.73398 0.06080353
 [55,] 10.73398 0.06080353
 [56,] 10.73398 0.06080353
 [57,] 10.73398 0.06080353
 [58,] 10.73398 0.06080353
 [59,] 10.73398 0.06080353
 [60,] 10.73398 0.06080353
 [61,] 10.66022 0.05653741
 [62,] 10.66022 0.05653741
 [63,] 10.66022 0.05653741
 [64,] 10.66022 0.05653741
 [65,] 10.66022 0.05653741
 [66,] 10.66022 0.05653741
 [67,] 10.66022 0.05653741
 [68,] 10.66022 0.05653741
 [69,] 10.66022 0.05653741
 [70,] 10.66022 0.05653741
 [71,] 10.66022 0.05653741
 [72,] 10.66022 0.05653741
 [73,] 10.66022 0.05653741
 [74,] 10.66022 0.05653741
 [75,] 10.66022 0.05653741
 [76,] 10.66022 0.05653741
 [77,] 10.66022 0.05653741
 [78,] 10.66022 0.05653741
 [79,] 10.66022 0.05653741
 [80,] 10.66022 0.05653741
 [81,] 10.66022 0.05653741
 [82,] 10.66022 0.05653741
 [83,] 10.66022 0.05653741
 [84,] 10.66022 0.05653741
 [85,] 10.66022 0.05653741
 [86,] 10.66022 0.05653741
 [87,] 10.55502 0.05210039
 [88,] 10.55502 0.05210039
 [89,] 10.55502 0.05210039
 [90,] 10.55502 0.05210039
 [91,] 10.55502 0.05210039
 [92,] 10.55502 0.05210039
 [93,] 10.55502 0.05210039
 [94,] 10.55502 0.05210039
 [95,] 10.55502 0.05210039
 [96,] 10.55502 0.05210039
 [97,] 10.55502 0.05210039
 [98,] 10.55502 0.05210039
 [99,] 10.55502 0.05210039
[100,] 10.55502 0.05210039
[101,] 10.55502 0.05210039
[102,] 10.55502 0.05210039
[103,] 10.55502 0.05210039
[104,] 10.55502 0.05210039
[105,] 10.55502 0.05210039
[106,] 10.55502 0.05210039
[107,] 10.55502 0.05210039
[108,] 10.55502 0.05210039
[109,] 10.55502 0.05210039
[110,] 10.55502 0.05210039
[111,] 10.55502 0.05210039
[112,] 10.55502 0.05210039
[113,] 10.55502 0.05210039
[114,] 10.55502 0.05210039
[115,] 10.55502 0.05210039
[116,] 10.55502 0.05210039
[117,] 10.55502 0.05210039
[118,] 10.55502 0.05210039
[119,] 10.55502 0.05210039
[120,] 10.55502 0.05210039
[121,] 10.55502 0.05210039
[122,] 10.55502 0.05210039
[123,] 10.55502 0.05210039
[124,] 10.55502 0.05210039
[125,] 10.55502 0.05210039
[126,] 10.55502 0.05210039
[127,] 10.55502 0.05210039
[128,] 10.70979 0.04376423
[129,] 10.70979 0.04376423
[130,] 10.70979 0.04376423
[131,] 10.70979 0.04376423
[132,] 10.70979 0.04376423
[133,] 10.70979 0.04376423
[134,] 10.70979 0.04376423
[135,] 10.70979 0.04376423
[136,] 10.70979 0.04376423
[137,] 10.70979 0.04376423
[138,] 10.70979 0.04376423
[139,] 10.70979 0.04376423
[140,] 10.70979 0.04376423
[141,] 10.70979 0.04376423
[142,] 10.70979 0.04376423
[143,] 10.70979 0.04376423
[144,] 10.70979 0.04376423
[145,] 10.70979 0.04376423
[146,] 10.70979 0.04376423
[147,] 10.70979 0.04376423
[148,] 10.70979 0.04376423
[149,] 10.70979 0.04376423
[150,] 10.70979 0.04376423
[151,] 10.70979 0.04376423
[152,] 10.70979 0.04376423
[153,] 10.70979 0.04376423
[154,] 10.70979 0.04376423
[155,] 10.70979 0.04376423
[156,] 10.70979 0.04376423
[157,] 10.70979 0.04376423
[158,] 10.70979 0.04376423
[159,] 10.70979 0.04376423
[160,] 10.70979 0.04376423
[161,] 10.70979 0.04376423
[162,] 10.70979 0.04376423
[163,] 10.70979 0.04376423
[164,] 10.70979 0.04376423
[165,] 10.70979 0.04376423
[166,] 10.70979 0.04376423
[167,] 10.70979 0.04376423
[168,] 10.70979 0.04376423
[169,] 10.70979 0.04376423
[170,] 10.70979 0.04376423
[171,] 10.70979 0.04376423
[172,] 10.70979 0.04376423
[173,] 10.70979 0.04376423
[174,] 10.70979 0.04376423
[175,] 10.70979 0.04376423
[176,] 10.70979 0.04376423
[177,] 10.70979 0.04376423
[178,] 10.70979 0.04376423
[179,] 10.70979 0.04376423
[180,] 10.70979 0.04376423
[181,] 10.70979 0.04376423
[182,] 10.70979 0.04376423
[183,] 10.70979 0.04376423
[184,] 10.70979 0.04376423
[185,] 10.70979 0.04376423
[186,] 10.70979 0.04376423
[187,] 10.70979 0.04376423
[188,] 10.70979 0.04376423
[189,] 10.70979 0.04376423
[190,] 10.70979 0.04376423
[191,] 10.70979 0.04376423
[192,] 10.70979 0.04376423
[193,] 10.70979 0.04376423
[194,] 10.70979 0.04376423
[195,] 10.70979 0.04376423
[196,] 10.94680 0.03395677
[197,] 10.94680 0.03395677
[198,] 10.94680 0.03395677
[199,] 10.94680 0.03395677
[200,] 10.94680 0.03395677
[201,] 10.94680 0.03395677
[202,] 10.94680 0.03395677
[203,] 10.94680 0.03395677
[204,] 10.94680 0.03395677
[205,] 10.94680 0.03395677
[206,] 10.94680 0.03395677
[207,] 10.94680 0.03395677
[208,] 10.94680 0.03395677
[209,] 10.94680 0.03395677
[210,] 10.94680 0.03395677
[211,] 10.94680 0.03395677
[212,] 10.94680 0.03395677
[213,] 10.94680 0.03395677
[214,] 10.94680 0.03395677
[215,] 10.94680 0.03395677
[216,] 10.94680 0.03395677
[217,] 10.94680 0.03395677
[218,] 10.94680 0.03395677
[219,] 10.94680 0.03395677
[220,] 10.94680 0.03395677
[221,] 10.94680 0.03395677
[222,] 10.94680 0.03395677
[223,] 10.94680 0.03395677
[224,] 10.94680 0.03395677
[225,] 10.94680 0.03395677
[226,] 10.94680 0.03395677
[227,] 10.94680 0.03395677
[228,] 10.94680 0.03395677
[229,] 10.94680 0.03395677
[230,] 10.94680 0.03395677
[231,] 10.94680 0.03395677
[232,] 10.94680 0.03395677
[233,] 10.94680 0.03395677
[234,] 10.94680 0.03395677
[235,] 10.94680 0.03395677
[236,] 10.94680 0.03395677
[237,] 10.94680 0.03395677
[238,] 10.94680 0.03395677
[239,] 10.94680 0.03395677
[240,] 10.94680 0.03395677
[241,] 10.94680 0.03395677
[242,] 10.94680 0.03395677
[243,] 10.94680 0.03395677
[244,] 10.94680 0.03395677
[245,] 10.94680 0.03395677
[246,] 10.94680 0.03395677
[247,] 10.94680 0.03395677
[248,] 10.94680 0.03395677
[249,] 10.94680 0.03395677
[250,] 10.94680 0.03395677
[251,] 10.94680 0.03395677
[252,] 10.94680 0.03395677
[253,] 10.94680 0.03395677
[254,] 10.94680 0.03395677
[255,] 10.94680 0.03395677
[256,] 10.94680 0.03395677
[257,] 10.94680 0.03395677
[258,] 10.94680 0.03395677
[259,] 10.94680 0.03395677
[260,] 10.94680 0.03395677
[261,] 10.94680 0.03395677
[262,] 10.94680 0.03395677
[263,] 10.94680 0.03395677
[264,] 10.94680 0.03395677
[265,] 10.94680 0.03395677
[266,] 10.94680 0.03395677
[267,] 10.94680 0.03395677
[268,] 10.94680 0.03395677
[269,] 10.94680 0.03395677
[270,] 10.94680 0.03395677
[271,] 10.94680 0.03395677
[272,] 10.94680 0.03395677
[273,] 10.94680 0.03395677
[274,] 10.94680 0.03395677
[275,] 10.94680 0.03395677
> (tri <- trimean(x))
           [,1]       [,2]
  [1,] 10.72000 0.06590087
  [2,] 10.71932 0.06524882
  [3,] 10.71864 0.06483583
  [4,] 10.71917 0.06452641
  [5,] 10.71971 0.06421204
  [6,] 10.72025 0.06389261
  [7,] 10.72079 0.06356801
  [8,] 10.72010 0.06333962
  [9,] 10.71941 0.06310774
 [10,] 10.71871 0.06287228
 [11,] 10.71801 0.06263318
 [12,] 10.71731 0.06239035
 [13,] 10.71660 0.06214373
 [14,] 10.71589 0.06189323
 [15,] 10.71518 0.06163878
 [16,] 10.71447 0.06138028
 [17,] 10.71375 0.06111766
 [18,] 10.71302 0.06085081
 [19,] 10.71229 0.06057965
 [20,] 10.71156 0.06030409
 [21,] 10.71083 0.06002402
 [22,] 10.71009 0.05973933
 [23,] 10.70935 0.05944994
 [24,] 10.70988 0.05926135
 [25,] 10.71042 0.05906981
 [26,] 10.71097 0.05887525
 [27,] 10.71151 0.05867761
 [28,] 10.71206 0.05847683
 [29,] 10.71261 0.05827284
 [30,] 10.71317 0.05806559
 [31,] 10.71242 0.05794996
 [32,] 10.71166 0.05783245
 [33,] 10.71091 0.05771305
 [34,] 10.71014 0.05759172
 [35,] 10.70938 0.05746843
 [36,] 10.70861 0.05734314
 [37,] 10.70784 0.05721582
 [38,] 10.70706 0.05708642
 [39,] 10.70628 0.05695492
 [40,] 10.70549 0.05682127
 [41,] 10.70470 0.05668543
 [42,] 10.70390 0.05654737
 [43,] 10.70310 0.05640704
 [44,] 10.70230 0.05626440
 [45,] 10.70149 0.05611940
 [46,] 10.70068 0.05597201
 [47,] 10.69986 0.05582217
 [48,] 10.69904 0.05566984
 [49,] 10.69822 0.05551497
 [50,] 10.69739 0.05535751
 [51,] 10.69655 0.05519741
 [52,] 10.69571 0.05503462
 [53,] 10.69487 0.05486908
 [54,] 10.69402 0.05470074
 [55,] 10.69317 0.05452954
 [56,] 10.69231 0.05435542
 [57,] 10.69144 0.05417832
 [58,] 10.69058 0.05399818
 [59,] 10.68970 0.05381494
 [60,] 10.68883 0.05362853
 [61,] 10.68794 0.05343887
 [62,] 10.68848 0.05335283
 [63,] 10.68902 0.05326521
 [64,] 10.68956 0.05317599
 [65,] 10.69010 0.05308515
 [66,] 10.69065 0.05299265
 [67,] 10.69120 0.05289846
 [68,] 10.69175 0.05280256
 [69,] 10.69231 0.05270490
 [70,] 10.69287 0.05260546
 [71,] 10.69343 0.05250421
 [72,] 10.69400 0.05240110
 [73,] 10.69457 0.05229611
 [74,] 10.69514 0.05218920
 [75,] 10.69572 0.05208034
 [76,] 10.69630 0.05196947
 [77,] 10.69688 0.05185657
 [78,] 10.69747 0.05174160
 [79,] 10.69806 0.05162451
 [80,] 10.69865 0.05150527
 [81,] 10.69925 0.05138382
 [82,] 10.69985 0.05126013
 [83,] 10.70045 0.05113416
 [84,] 10.70106 0.05100584
 [85,] 10.70167 0.05087515
 [86,] 10.70229 0.05074202
 [87,] 10.70291 0.05060640
 [88,] 10.70507 0.05055227
 [89,] 10.70724 0.05049678
 [90,] 10.70943 0.05043991
 [91,] 10.71163 0.05038163
 [92,] 10.71384 0.05032192
 [93,] 10.71607 0.05026074
 [94,] 10.71831 0.05019807
 [95,] 10.72057 0.05013387
 [96,] 10.72283 0.05006811
 [97,] 10.72512 0.05000077
 [98,] 10.72742 0.04993180
 [99,] 10.72973 0.04986118
[100,] 10.73206 0.04978887
[101,] 10.73440 0.04971484
[102,] 10.73676 0.04963904
[103,] 10.73913 0.04956145
[104,] 10.74152 0.04948203
[105,] 10.74392 0.04940072
[106,] 10.74634 0.04931751
[107,] 10.74878 0.04923233
[108,] 10.75123 0.04914516
[109,] 10.75123 0.04905594
[110,] 10.75618 0.04896464
[111,] 10.75868 0.04887120
[112,] 10.76119 0.04877558
[113,] 10.76373 0.04867773
[114,] 10.76628 0.04857759
[115,] 10.76628 0.04847513
[116,] 10.77143 0.04837027
[117,] 10.77403 0.04826298
[118,] 10.77665 0.04815319
[119,] 10.77929 0.04804084
[120,] 10.78194 0.04792587
[121,] 10.78194 0.04780823
[122,] 10.78731 0.04768784
[123,] 10.79002 0.04756465
[124,] 10.79275 0.04743858
[125,] 10.79549 0.04730956
[126,] 10.79826 0.04717752
[127,] 10.79826 0.04704238
[128,] 10.80385 0.04690408
[129,] 10.80492 0.04691484
[130,] 10.80600 0.04692512
[131,] 10.80708 0.04693491
[132,] 10.80817 0.04694421
[133,] 10.80927 0.04695299
[134,] 10.81038 0.04696124
[135,] 10.81149 0.04696896
[136,] 10.81261 0.04697614
[137,] 10.81374 0.04698275
[138,] 10.81488 0.04698878
[139,] 10.81603 0.04699423
[140,] 10.81718 0.04699908
[141,] 10.81835 0.04700331
[142,] 10.81952 0.04700691
[143,] 10.82070 0.04700986
[144,] 10.82189 0.04701216
[145,] 10.82309 0.04701378
[146,] 10.82430 0.04701470
[147,] 10.82552 0.04701492
[148,] 10.82674 0.04701441
[149,] 10.82798 0.04701317
[150,] 10.82922 0.04701116
[151,] 10.83048 0.04700837
[152,] 10.83174 0.04700479
[153,] 10.83301 0.04700039
[154,] 10.83430 0.04699515
[155,] 10.83559 0.04698906
[156,] 10.83689 0.04698210
[157,] 10.83821 0.04697424
[158,] 10.83953 0.04696545
[159,] 10.84086 0.04695573
[160,] 10.84221 0.04694504
[161,] 10.84356 0.04693337
[162,] 10.84493 0.04692068
[163,] 10.84631 0.04690695
[164,] 10.84770 0.04689216
[165,] 10.84909 0.04687629
[166,] 10.85051 0.04685929
[167,] 10.85193 0.04684116
[168,] 10.85336 0.04682185
[169,] 10.85481 0.04680134
[170,] 10.85626 0.04677959
[171,] 10.85773 0.04675659
[172,] 10.85921 0.04673228
[173,] 10.86071 0.04670665
[174,] 10.86221 0.04667966
[175,] 10.86373 0.04665127
[176,] 10.86526 0.04662145
[177,] 10.86681 0.04659015
[178,] 10.86837 0.04655735
[179,] 10.86994 0.04652300
[180,] 10.87152 0.04648706
[181,] 10.87312 0.04644948
[182,] 10.87473 0.04641024
[183,] 10.87636 0.04636928
[184,] 10.87800 0.04632655
[185,] 10.87965 0.04628201
[186,] 10.88132 0.04623561
[187,] 10.88300 0.04618730
[188,] 10.88470 0.04613702
[189,] 10.88641 0.04608473
[190,] 10.88814 0.04603037
[191,] 10.88989 0.04597387
[192,] 10.89165 0.04591519
[193,] 10.89342 0.04585425
[194,] 10.89522 0.04579100
[195,] 10.89703 0.04572537
[196,] 10.89885 0.04565729
[197,] 10.89838 0.04575052
[198,] 10.89791 0.04584431
[199,] 10.89744 0.04593864
[200,] 10.89696 0.04603353
[201,] 10.89647 0.04612899
[202,] 10.89598 0.04622502
[203,] 10.89549 0.04632162
[204,] 10.89499 0.04641881
[205,] 10.89448 0.04651658
[206,] 10.89398 0.04661494
[207,] 10.89346 0.04671389
[208,] 10.89294 0.04681345
[209,] 10.89242 0.04691362
[210,] 10.89189 0.04701440
[211,] 10.89136 0.04711580
[212,] 10.89082 0.04721782
[213,] 10.89027 0.04732048
[214,] 10.88972 0.04742377
[215,] 10.88917 0.04752770
[216,] 10.88861 0.04763229
[217,] 10.88861 0.04773752
[218,] 10.88804 0.04784343
[219,] 10.88689 0.04794999
[220,] 10.88630 0.04805724
[221,] 10.88571 0.04816516
[222,] 10.88512 0.04827377
[223,] 10.88451 0.04838307
[224,] 10.88391 0.04849308
[225,] 10.88329 0.04860379
[226,] 10.88267 0.04871521
[227,] 10.88204 0.04882736
[228,] 10.88140 0.04894023
[229,] 10.88140 0.04905383
[230,] 10.88076 0.04916818
[231,] 10.87945 0.04928328
[232,] 10.87879 0.04939913
[233,] 10.87812 0.04951575
[234,] 10.87744 0.04963313
[235,] 10.87675 0.04975130
[236,] 10.87606 0.04987024
[237,] 10.87535 0.04998999
[238,] 10.87464 0.05011053
[239,] 10.87393 0.05023188
[240,] 10.87320 0.05035404
[241,] 10.87320 0.05047703
[242,] 10.87246 0.05060085
[243,] 10.87172 0.05072551
[244,] 10.87021 0.05085102
[245,] 10.86944 0.05097738
[246,] 10.86866 0.05110460
[247,] 10.86787 0.05123270
[248,] 10.86707 0.05136167
[249,] 10.86626 0.05149153
[250,] 10.86544 0.05162229
[251,] 10.86462 0.05175395
[252,] 10.86378 0.05188653
[253,] 10.86293 0.05202003
[254,] 10.86293 0.05215445
[255,] 10.86207 0.05228981
[256,] 10.86032 0.05242612
[257,] 10.85942 0.05256339
[258,] 10.85852 0.05270161
[259,] 10.85761 0.05284081
[260,] 10.85668 0.05298099
[261,] 10.85574 0.05312216
[262,] 10.85479 0.05326432
[263,] 10.85382 0.05340749
[264,] 10.85284 0.05355167
[265,] 10.85185 0.05369688
[266,] 10.85085 0.05384311
[267,] 10.84983 0.05399039
[268,] 10.84880 0.05413871
[269,] 10.84775 0.05428809
[270,] 10.84669 0.05443852
[271,] 10.84561 0.05459003
[272,] 10.84452 0.05474262
[273,] 10.84342 0.05489630
[274,] 10.84229 0.05505107
[275,] 10.84116 0.05520693
> (midr <- midrange(x))
[1] 11.5
> 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/10gyc1219000886.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/2g05k1219000886.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/3xoix1219000886.tab") 
> 
> system("convert tmp/10gyc1219000886.ps tmp/10gyc1219000886.png")
> system("convert tmp/2g05k1219000886.ps tmp/2g05k1219000886.png")
> 
> 
> proc.time()
   user  system elapsed 
 12.817   0.675  12.962