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

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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(2430.47
+ ,2516.3
+ ,2633.63
+ ,2799.84
+ ,3001.93
+ ,3229.29
+ ,3173.02
+ ,3322.08
+ ,3417.88
+ ,3486.95
+ ,3016.22
+ ,2709.61
+ ,2914.87
+ ,3203.08
+ ,3320.25
+ ,3446.25
+ ,3456.85
+ ,3566.53
+ ,3763.67
+ ,3607.75
+ ,3747.38
+ ,3623.91
+ ,3699.76
+ ,3629.61
+ ,3911.52
+ ,4281.47
+ ,4742.42
+ ,4522.42
+ ,4879.79
+ ,5059.11
+ ,5093.19
+ ,4941.81
+ ,4832.67
+ ,4876.18
+ ,5018.07
+ ,4780.34
+ ,4953.59
+ ,4622.32
+ ,4557.13
+ ,4560.03
+ ,4105.66
+ ,4004.89
+ ,4277.26
+ ,4245.98
+ ,4057.64
+ ,3931.42
+ ,3637.15
+ ,3339.91
+ ,3465.74
+ ,3571.25
+ ,3706.93
+ ,3584.17
+ ,3552.11
+ ,3695.24
+ ,3510
+ ,3357.7
+ ,3060.91
+ ,2736.98
+ ,2709.45
+ ,2314.96
+ ,2561.29
+ ,2663.49
+ ,2407.87
+ ,2237.74
+ ,2165.44
+ ,2098.89
+ ,2318.54
+ ,2315.49
+ ,2395.47
+ ,2474.07
+ ,2479.57
+ ,2386.92
+ ,2537.84
+ ,2567.13
+ ,2660.37
+ ,2696.28
+ ,2748.5
+ ,2663.32
+ ,2707.69
+ ,2669.36
+ ,2687.68
+ ,2650.24
+ ,2620.03
+ ,2668.47
+ ,2692.06
+ ,2737.67
+ ,2774.77
+ ,2819.19
+ ,2892.56
+ ,2866.08
+ ,2817.41
+ ,2934.75
+ ,3036.54
+ ,3139.5
+ ,3114.31
+ ,3261.3
+ ,3201.79
+ ,3264.53
+ ,3349.1
+ ,3446.17
+ ,3469.48
+ ,3507.13
+ ,3536.2
+ ,3359.05
+ ,3378.85
+ ,3449.15
+ ,3522.89
+ ,3551.04
+ ,3669.15
+ ,3602
+ ,3697.22
+ ,3760.9
+ ,3665.08
+ ,3708.8
+ ,3858.21
+ ,3933.16
+ ,3946.98
+ ,3794.29
+ ,3765.56
+ ,3820.33
+ ,3885.12
+ ,3752.67
+ ,3683.79
+ ,3240.75
+ ,3188.82
+ ,3017.98
+ ,3237.2
+ ,3182.53
+ ,2906.42
+ ,2881.35
+ ,2915.64
+ ,2635.13
+ ,2331.43
+ ,2159.04
+ ,2065.46
+ ,1983.48
+ ,1770.41
+ ,1815.99
+ ,2026.97
+ ,2124.81
+ ,2098.28
+ ,2291.39
+ ,2401.57
+ ,2453.89
+ ,2409.53)
> 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] 3257.925
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 63.50177
> (armose <- arm / armse)
[1] 51.30447
> (geo <- geomean(x))
[1] 3170.117
> (har <- harmean(x))
[1] 3083.630
> (qua <- quamean(x))
[1] 3345.856
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 3258.004 63.40461
 [2,] 3259.748 62.94873
 [3,] 3259.314 62.56901
 [4,] 3260.051 62.36479
 [5,] 3259.044 61.82078
 [6,] 3258.920 61.79031
 [7,] 3258.070 61.24995
 [8,] 3257.072 60.49943
 [9,] 3255.115 60.04114
[10,] 3251.819 58.03201
[11,] 3251.163 56.78029
[12,] 3252.874 56.51495
[13,] 3249.810 56.01459
[14,] 3226.840 52.51557
[15,] 3227.738 52.29542
[16,] 3230.409 51.10121
[17,] 3214.960 48.80548
[18,] 3209.757 47.97337
[19,] 3203.670 47.04350
[20,] 3195.911 46.09199
[21,] 3196.943 45.50929
[22,] 3200.232 45.06744
[23,] 3200.276 44.34774
[24,] 3196.817 43.76217
[25,] 3198.510 42.54587
[26,] 3195.580 41.39596
[27,] 3195.098 40.41347
[28,] 3190.678 39.72616
[29,] 3200.880 38.55764
[30,] 3203.121 38.20673
[31,] 3201.682 37.99574
[32,] 3203.849 37.53483
[33,] 3197.374 36.42907
[34,] 3197.627 36.31560
[35,] 3195.938 36.14336
[36,] 3196.543 35.95605
[37,] 3196.265 35.88407
[38,] 3198.066 35.10787
[39,] 3195.306 34.61259
[40,] 3195.348 34.38853
[41,] 3190.676 33.32147
[42,] 3189.002 33.06749
[43,] 3187.359 32.90664
[44,] 3190.761 31.62362
[45,] 3189.191 31.43922
[46,] 3186.970 30.58385
[47,] 3191.297 29.36345
[48,] 3198.034 28.41016
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 3255.493 62.22203
 [2,] 3252.910 60.93254
 [3,] 3249.344 59.78499
 [4,] 3245.827 58.68204
 [5,] 3242.007 57.53804
 [6,] 3238.293 56.42626
 [7,] 3234.487 55.21225
 [8,] 3230.701 53.98751
 [9,] 3226.937 52.77873
[10,] 3223.305 51.52510
[11,] 3219.944 50.46762
[12,] 3216.543 49.48811
[13,] 3212.854 48.44021
[14,] 3209.330 47.34883
[15,] 3207.753 46.61211
[16,] 3206.044 45.82078
[17,] 3204.055 45.08520
[18,] 3203.201 44.53881
[19,] 3202.708 44.02140
[20,] 3202.638 43.54297
[21,] 3203.111 43.10560
[22,] 3203.533 42.67208
[23,] 3203.753 42.22644
[24,] 3203.979 41.79447
[25,] 3204.434 41.36156
[26,] 3204.803 40.99095
[27,] 3205.369 40.67883
[28,] 3205.988 40.41228
[29,] 3206.900 40.16391
[30,] 3207.254 39.98440
[31,] 3207.495 39.79731
[32,] 3207.830 39.58639
[33,] 3208.059 39.37327
[34,] 3208.668 39.22074
[35,] 3209.296 39.03391
[36,] 3210.054 38.81261
[37,] 3210.821 38.55292
[38,] 3211.647 38.23460
[39,] 3212.421 37.92939
[40,] 3213.400 37.60313
[41,] 3214.439 37.21874
[42,] 3215.816 36.86903
[43,] 3217.385 36.45351
[44,] 3219.162 35.94445
[45,] 3220.863 35.48802
[46,] 3222.789 34.92413
[47,] 3225.003 34.33219
[48,] 3227.125 33.77386
> (midr <- midrange(x))
[1] 3431.8
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 3203.288 3210.054 3210.054 3210.054 3210.054 3202.668 3210.054 3210.054
> postscript(file="/var/www/html/rcomp/tmp/1udx11260381224.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/2i3371260381224.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/3gcj11260381224.tab") 
> 
> system("convert tmp/1udx11260381224.ps tmp/1udx11260381224.png")
> system("convert tmp/2i3371260381224.ps tmp/2i3371260381224.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.844   0.358   1.124