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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> x <- c(6.9,6.8,6.7,6.6,6.5,6.5,7,7.5,7.6,7.6,7.6,7.8,8,8,8,7.9,7.9,8,8.5,9.2,9.4,9.5,9.5,9.6,9.7,9.7,9.6,9.5,9.4,9.3,9.6,10.2,10.2,10.1,9.9,9.8,9.8,9.7,9.5,9.3,9.1,9,9.5,10,10.2,10.1,10,9.9,10,9.9,9.7,9.5,9.2,9,9.3,9.8,9.8,9.6,9.4,9.3,9.2,9.2,9,8.8,8.7,8.7,9.1,9.7,9.8,9.6,9.4,9.4,9.5,9.4,9.3,9.2,9,8.9,9.2,9.8,9.9,9.6,9.2,9.1,9.1,9,8.9,8.7,8.5,8.3,8.5,8.7,8.4,8.1,7.8,7.7,7.5,7.2,6.8,6.7,6.4,6.3,6.8,7.3,7.1,7,6.8,6.6,6.3,6.1,6.1,6.3,6.3,6,6.2,6.4,6.8,7.5,7.5,7.6,7.6,7.4,7.3,7.1,6.9,6.8,7.5,7.6,7.8,8,8.1,8.2,8.3,8.2,8,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8,8.2,8.1,8.1,8,7.9,7.9)
> 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] 8.397222
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.08024803
> (armose <- arm / armse)
[1] 104.6409
> (geo <- geomean(x))
[1] 8.325469
> (har <- harmean(x))
[1] 8.250673
> (qua <- quamean(x))
[1] 8.46558
> (win <- winmean(x))
          [,1]       [,2]
 [1,] 8.397778 0.08015718
 [2,] 8.397778 0.08015718
 [3,] 8.397778 0.07969119
 [4,] 8.400000 0.07935572
 [5,] 8.397222 0.07903213
 [6,] 8.397222 0.07903213
 [7,] 8.397222 0.07903213
 [8,] 8.397222 0.07789292
 [9,] 8.397222 0.07789292
[10,] 8.402778 0.07711202
[11,] 8.402778 0.07711202
[12,] 8.402778 0.07550135
[13,] 8.402778 0.07550135
[14,] 8.410556 0.07448352
[15,] 8.410556 0.07448352
[16,] 8.419444 0.07336506
[17,] 8.419444 0.07336506
[18,] 8.409444 0.07234091
[19,] 8.409444 0.07234091
[20,] 8.409444 0.07234091
[21,] 8.409444 0.07234091
[22,] 8.421667 0.07084782
[23,] 8.408889 0.06959263
[24,] 8.422222 0.06800589
[25,] 8.422222 0.06800589
[26,] 8.436667 0.06634887
[27,] 8.436667 0.06634887
[28,] 8.452222 0.06463120
[29,] 8.436111 0.06307240
[30,] 8.452778 0.06128376
[31,] 8.452778 0.06128376
[32,] 8.470556 0.05945489
[33,] 8.470556 0.05945489
[34,] 8.489444 0.05759777
[35,] 8.489444 0.05759777
[36,] 8.469444 0.05568320
[37,] 8.469444 0.05568320
[38,] 8.469444 0.05568320
[39,] 8.469444 0.05568320
[40,] 8.491667 0.05356835
[41,] 8.491667 0.05356835
[42,] 8.468333 0.05140771
[43,] 8.468333 0.05140771
[44,] 8.468333 0.05140771
[45,] 8.468333 0.05140771
[46,] 8.468333 0.05140771
[47,] 8.468333 0.05140771
[48,] 8.495000 0.04893829
[49,] 8.495000 0.04403088
[50,] 8.495000 0.04403088
[51,] 8.495000 0.04403088
[52,] 8.523889 0.04154350
[53,] 8.523889 0.04154350
[54,] 8.523889 0.04154350
[55,] 8.523889 0.04154350
[56,] 8.492778 0.03876612
[57,] 8.492778 0.03876612
[58,] 8.525000 0.03607767
[59,] 8.525000 0.03607767
[60,] 8.491667 0.03316414
> (tri <- trimean(x))
          [,1]       [,2]
 [1,] 8.400562 0.07937297
 [2,] 8.403409 0.07853322
 [3,] 8.406322 0.07763339
 [4,] 8.409302 0.07684560
 [5,] 8.411765 0.07609886
 [6,] 8.414881 0.07537398
 [7,] 8.418072 0.07459414
 [8,] 8.421341 0.07375464
 [9,] 8.424691 0.07303945
[10,] 8.428125 0.07226769
[11,] 8.431013 0.07154610
[12,] 8.433974 0.07076620
[13,] 8.433974 0.07012274
[14,] 8.440132 0.06942514
[15,] 8.442667 0.06878522
[16,] 8.445270 0.06809016
[17,] 8.447260 0.06745383
[18,] 8.449306 0.06676127
[19,] 8.452113 0.06610531
[20,] 8.455000 0.06538938
[21,] 8.457971 0.06460756
[22,] 8.461029 0.06375310
[23,] 8.463433 0.06296227
[24,] 8.466667 0.06220621
[25,] 8.469231 0.06152355
[26,] 8.469231 0.06077276
[27,] 8.473810 0.06009705
[28,] 8.475806 0.05935190
[29,] 8.477049 0.05868295
[30,] 8.479167 0.05807240
[31,] 8.480508 0.05754979
[32,] 8.481897 0.05696732
[33,] 8.482456 0.05647413
[34,] 8.483036 0.05592167
[35,] 8.482727 0.05545865
[36,] 8.482407 0.05493677
[37,] 8.483019 0.05450870
[38,] 8.483654 0.05402249
[39,] 8.484314 0.05347096
[40,] 8.485000 0.05284578
[41,] 8.484694 0.05232551
[42,] 8.484375 0.05173160
[43,] 8.485106 0.05124748
[44,] 8.485870 0.05068997
[45,] 8.486667 0.05004867
[46,] 8.487500 0.04931115
[47,] 8.488372 0.04846251
[48,] 8.489286 0.04748457
[49,] 8.489286 0.04662684
[50,] 8.488750 0.04614897
[51,] 8.488462 0.04558353
[52,] 8.488462 0.04491579
[53,] 8.486486 0.04439416
[54,] 8.484722 0.04376901
[55,] 8.482857 0.04302108
[56,] 8.480882 0.04212618
[57,] 8.480303 0.04143238
[58,] 8.479688 0.04059208
[59,] 8.477419 0.03992453
[60,] 8.475000 0.03910185
> (midr <- midrange(x))
[1] 8.1
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 8.466327 8.466327 8.466327 8.466327 8.466327 8.466327 8.466327 8.466327
> postscript(file="/var/www/html/rcomp/tmp/14xlp1257511267.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/218ig1257511267.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/36dk91257511268.tab") 
> 
> system("convert tmp/14xlp1257511267.ps tmp/14xlp1257511267.png")
> system("convert tmp/218ig1257511267.ps tmp/218ig1257511267.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.024   0.364   1.554