R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(28.23472222
+ ,28.05861111
+ ,1.993333333
+ ,26.82222222
+ ,48.84
+ ,94.88055556
+ ,28.77694444
+ ,31.28083333
+ ,23.77055556
+ ,61.33361111
+ ,25.73916667
+ ,37.03555556
+ ,17.04472222
+ ,34.98055556
+ ,22.86555556
+ ,28.33611111
+ ,28.20083333
+ ,11.54611111
+ ,27.75638889
+ ,6.291111111
+ ,12.97166667
+ ,36.58277778
+ ,25.48194444
+ ,22.18416667
+ ,30.01194444
+ ,27.46277778
+ ,33.45694444
+ ,32.23555556
+ ,69.4575
+ ,37.80111111
+ ,25.69416667
+ ,37.71694444
+ ,20.66888889
+ ,22.56666667
+ ,37.04666667
+ ,27.26277778
+ ,22.11638889
+ ,16.44277778
+ ,38.87277778
+ ,32.94777778
+ ,20.24444444
+ ,18.1875
+ ,27.67861111
+ ,19.99027778
+ ,21.46444444
+ ,13.69138889
+ ,37.53638889
+ ,30.12388889
+ ,24.92944444
+ ,12.30444444
+ ,21.56888889
+ ,50.42444444
+ ,37.2275
+ ,34.46222222
+ ,25.73055556
+ ,33.84666667
+ ,14.69861111
+ ,22.74222222
+ ,16.38361111
+ ,14.86527778
+ ,16.89222222
+ ,15.65972222
+ ,18.19166667
+ ,22.48583333
+ ,21.195
+ ,28.89194444
+ ,27.25111111
+ ,18.88583333
+ ,8.608055556
+ ,37.62722222
+ ,20.41777778
+ ,17.53416667
+ ,17.015
+ ,20.80944444
+ ,8.826111111
+ ,22.62138889
+ ,24.21833333
+ ,13.91388889
+ ,18.2625
+ ,15.73694444
+ ,43.99972222
+ ,12.90416667
+ ,20.45111111
+ ,10.66527778
+ ,25.5275
+ ,38.75722222
+ ,14.49
+ ,14.32416667
+ ,19.5975
+ ,23.57111111
+ ,28.48277778
+ ,24.07722222
+ ,23.80805556
+ ,9.628333333
+ ,41.82777778
+ ,27.66972222
+ ,5.374722222
+ ,27.60361111
+ ,23.95277778
+ ,8.565833333
+ ,8.807222222
+ ,24.94611111
+ ,17.24666667
+ ,11.15305556
+ ,7.676111111
+ ,21.38611111
+ ,10.40555556
+ ,15.04361111
+ ,13.85055556
+ ,23.42694444
+ ,17.82638889
+ ,16.495
+ ,33.14111111
+ ,21.30611111
+ ,28.72916667
+ ,19.54
+ ,12.05833333
+ ,29.12166667
+ ,17.28194444
+ ,19.25111111
+ ,14.75472222
+ ,5.49
+ ,24.07777778
+ ,23.3625
+ ,21.65138889
+ ,24.75361111
+ ,25.27916667
+ ,11.18
+ ,17.82972222
+ ,14.12694444
+ ,15.72583333
+ ,17.44222222
+ ,20.14861111)
> 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] 23.80232
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 1.060803
> (armose <- arm / armse)
[1] 22.43803
> (geo <- geomean(x))
[1] 21.08132
> (har <- harmean(x))
[1] 17.89194
> (qua <- quamean(x))
[1] 26.74117
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 23.63659 0.9738075
 [2,] 23.51616 0.9329623
 [3,] 23.28816 0.8628667
 [4,] 23.28216 0.8457114
 [5,] 23.13365 0.8022377
 [6,] 23.03757 0.7834095
 [7,] 22.89253 0.7553134
 [8,] 22.88671 0.7540418
 [9,] 22.87630 0.7363790
[10,] 22.92841 0.7276128
[11,] 22.94247 0.7236904
[12,] 22.97828 0.7168516
[13,] 22.95072 0.7119059
[14,] 22.97023 0.7042368
[15,] 23.02674 0.6970530
[16,] 23.00188 0.6853017
[17,] 22.87374 0.6463610
[18,] 22.81273 0.6354419
[19,] 22.82761 0.6114762
[20,] 22.79294 0.6008313
[21,] 22.75307 0.5930413
[22,] 22.75633 0.5848489
[23,] 22.66727 0.5650004
[24,] 22.52491 0.5399968
[25,] 22.34666 0.5096070
[26,] 22.33574 0.5058377
[27,] 22.17745 0.4830335
[28,] 22.16663 0.4735054
[29,] 22.27590 0.4557544
[30,] 22.28003 0.4529536
[31,] 22.22519 0.4465230
[32,] 22.34549 0.4259499
[33,] 22.33502 0.4217214
[34,] 22.33971 0.4193924
[35,] 22.40681 0.4045122
[36,] 22.35824 0.3924901
[37,] 22.34487 0.3893875
[38,] 22.40003 0.3832092
[39,] 22.39099 0.3801389
[40,] 22.39684 0.3708535
[41,] 22.36353 0.3616310
[42,] 22.45212 0.3519890
[43,] 22.31454 0.3377061
[44,] 22.07459 0.2904401
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 23.42622 0.9134451
 [2,] 23.20932 0.8438790
 [3,] 23.04865 0.7900458
 [4,] 22.96371 0.7601721
 [5,] 22.87762 0.7325495
 [6,] 22.82134 0.7139546
 [7,] 22.78106 0.6978226
 [8,] 22.76296 0.6858208
 [9,] 22.74507 0.6727508
[10,] 22.72790 0.6613026
[11,] 22.70388 0.6499644
[12,] 22.67741 0.6379153
[13,] 22.64625 0.6254426
[14,] 22.61658 0.6121904
[15,] 22.58396 0.5983728
[16,] 22.54509 0.5837641
[17,] 22.50674 0.5688806
[18,] 22.47714 0.5572777
[19,] 22.45104 0.5455572
[20,] 22.42269 0.5352459
[21,] 22.39564 0.5248280
[22,] 22.37020 0.5139061
[23,] 22.34337 0.5024037
[24,] 22.32134 0.4917134
[25,] 22.30774 0.4825345
[26,] 22.30519 0.4755949
[27,] 22.30321 0.4679453
[28,] 22.31126 0.4617072
[29,] 22.32041 0.4554695
[30,] 22.32321 0.4502048
[31,] 22.32591 0.4442222
[32,] 22.33217 0.4378273
[33,] 22.33134 0.4327162
[34,] 22.33112 0.4269933
[35,] 22.33058 0.4202841
[36,] 22.32583 0.4140838
[37,] 22.32380 0.4080814
[38,] 22.32248 0.4010186
[39,] 22.31754 0.3931082
[40,] 22.31281 0.3836581
[41,] 22.30734 0.3733363
[42,] 22.30362 0.3619197
[43,] 22.29361 0.3491438
[44,] 22.29217 0.3356857
> (midr <- midrange(x))
[1] 48.43694
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 22.24190 22.33134 22.33134 22.33134 22.33134 22.24388 22.33134 22.33134
> postscript(file="/var/www/rcomp/tmp/1ontr1323786644.ps",horizontal=F,onefile=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/rcomp/tmp/22d8t1323786644.ps",horizontal=F,onefile=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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/35kx41323786645.tab") 
> 
> try(system("convert tmp/1ontr1323786644.ps tmp/1ontr1323786644.png",intern=TRUE))
character(0)
> try(system("convert tmp/22d8t1323786644.ps tmp/22d8t1323786644.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.070   0.080   1.122