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

R is free software and comes with ABSOLUTELY NO WARRANTY.
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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(227.86
+ ,198.24
+ ,194.97
+ ,184.88
+ ,196.79
+ ,205.36
+ ,226.72
+ ,226.05
+ ,202.50
+ ,194.79
+ ,192.43
+ ,219.25
+ ,217.47
+ ,192.34
+ ,196.83
+ ,186.07
+ ,197.31
+ ,215.02
+ ,242.67
+ ,225.17
+ ,206.69
+ ,197.75
+ ,196.43
+ ,213.55
+ ,222.75
+ ,194.03
+ ,201.85
+ ,189.50
+ ,206.07
+ ,225.59
+ ,247.91
+ ,247.64
+ ,213.01
+ ,203.01
+ ,200.26
+ ,220.50
+ ,237.90
+ ,216.94
+ ,214.01
+ ,196.00
+ ,208.37
+ ,232.75
+ ,257.46
+ ,267.69
+ ,220.18
+ ,210.61
+ ,209.59
+ ,232.75
+ ,232.75
+ ,219.82
+ ,226.74
+ ,208.04
+ ,220.12
+ ,235.69
+ ,257.05
+ ,258.69
+ ,227.15
+ ,219.91
+ ,219.30
+ ,259.04
+ ,237.29
+ ,212.88
+ ,226.03
+ ,211.07
+ ,222.91
+ ,249.18
+ ,266.38
+ ,268.53
+ ,238.02
+ ,224.69
+ ,213.75
+ ,237.43
+ ,248.46
+ ,210.82
+ ,221.40
+ ,209.00
+ ,234.37
+ ,248.43
+ ,271.98
+ ,268.11
+ ,233.88
+ ,223.43
+ ,221.38
+ ,233.76
+ ,243.97
+ ,217.76
+ ,224.66
+ ,210.84
+ ,220.35
+ ,236.84
+ ,266.15
+ ,255.20
+ ,234.76
+ ,221.29
+ ,221.26
+ ,244.13
+ ,245.78
+ ,224.62
+ ,234.80
+ ,211.37
+ ,222.39
+ ,249.63
+ ,282.29
+ ,279.13
+ ,236.60
+ ,223.62
+ ,225.86
+ ,246.41
+ ,261.70
+ ,225.01
+ ,231.54
+ ,214.82
+ ,227.70
+ ,263.86
+ ,278.15
+ ,274.64
+ ,237.66
+ ,227.97
+ ,224.75
+ ,242.91
+ ,253.08
+ ,228.13
+ ,233.68
+ ,217.38
+ ,236.38
+ ,256.08
+ ,292.83
+ ,304.71
+ ,245.57
+ ,234.41
+ ,234.12
+ ,258.17
+ ,268.66
+ ,245.31
+ ,247.47
+ ,226.25
+ ,251.67
+ ,268.79
+ ,288.94
+ ,290.16
+ ,250.69
+ ,240.80)
> 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] 231.0894
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 2.045293
> (armose <- arm / armse)
[1] 112.9859
> (geo <- geomean(x))
[1] 229.8437
> (har <- harmean(x))
[1] 228.6268
> (qua <- quamean(x))
[1] 232.3621
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 231.0141 2.0242147
 [2,] 231.0248 2.0088705
 [3,] 231.0590 1.9949997
 [4,] 230.8742 1.9579151
 [5,] 230.8193 1.9299414
 [6,] 230.8100 1.9183329
 [7,] 230.6458 1.8876993
 [8,] 230.5540 1.8557259
 [9,] 230.3791 1.8209881
[10,] 230.3953 1.8162800
[11,] 230.3883 1.8143704
[12,] 230.3934 1.8037940
[13,] 230.3952 1.7928858
[14,] 230.3144 1.7677860
[15,] 230.5035 1.7373552
[16,] 230.4246 1.6784664
[17,] 230.2438 1.6331435
[18,] 229.9713 1.5802969
[19,] 230.2389 1.5370842
[20,] 230.2656 1.5160972
[21,] 230.2523 1.4921305
[22,] 230.3980 1.4608466
[23,] 230.2943 1.4348715
[24,] 230.2520 1.4045408
[25,] 229.9827 1.3471731
[26,] 229.9113 1.2962131
[27,] 229.7649 1.2700113
[28,] 229.5598 1.2454337
[29,] 229.5149 1.2299697
[30,] 229.4261 1.2060966
[31,] 229.7492 1.1710099
[32,] 229.6613 1.1548195
[33,] 229.7241 1.1350327
[34,] 229.7313 1.1256489
[35,] 229.5341 1.0902416
[36,] 229.5797 1.0521664
[37,] 229.5771 1.0410214
[38,] 230.0213 0.9836540
[39,] 229.8181 0.9368391
[40,] 229.7984 0.9295750
[41,] 229.5761 0.8888575
[42,] 229.9458 0.8405871
[43,] 229.3946 0.7793894
[44,] 228.6944 0.6775837
[45,] 228.6849 0.6712296
[46,] 228.6751 0.6573832
[47,] 228.6189 0.6481905
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 230.8936 1.9787650
 [2,] 230.7696 1.9289786
 [3,] 230.6363 1.8832426
 [4,] 230.4870 1.8386051
 [5,] 230.3829 1.8014021
 [6,] 230.2875 1.7679044
 [7,] 230.2875 1.7337249
 [8,] 230.1177 1.7023869
 [9,] 230.0552 1.6737677
[10,] 230.0134 1.6481033
[11,] 229.9682 1.6205007
[12,] 229.9222 1.5902562
[13,] 229.8741 1.5582654
[14,] 229.8741 1.5242638
[15,] 229.7798 1.4898756
[16,] 229.7175 1.4555132
[17,] 229.6594 1.4247712
[18,] 229.6134 1.3961154
[19,] 229.5863 1.3705046
[20,] 229.5384 1.3467821
[21,] 229.4868 1.3225012
[22,] 229.4340 1.2978776
[23,] 229.3692 1.2735491
[24,] 229.3084 1.2489847
[25,] 229.2477 1.2245523
[26,] 229.2013 1.2033792
[27,] 229.1573 1.1848929
[28,] 229.1573 1.1666109
[29,] 229.0936 1.1483415
[30,] 229.0684 1.1289575
[31,] 229.0684 1.1092409
[32,] 229.0060 1.0902515
[33,] 228.9678 1.0699793
[34,] 228.9238 1.0485418
[35,] 228.8769 1.0244288
[36,] 228.8389 1.0006494
[37,] 228.7959 0.9774250
[38,] 228.7505 0.9511784
[39,] 228.6763 0.9273296
[40,] 228.6092 0.9054416
[41,] 228.5388 0.8798182
[42,] 228.4769 0.8550952
[43,] 228.3882 0.8316559
[44,] 228.3267 0.8133740
[45,] 228.3038 0.8069932
[46,] 228.2798 0.7991095
[47,] 228.2544 0.7905441
> (midr <- midrange(x))
[1] 244.795
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 228.6300 228.8769 228.8769 228.8769 228.8389 228.8769 228.8769 228.8769
> postscript(file="/var/www/html/rcomp/tmp/18xt61268842330.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/2j6ab1268842330.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/3l3sh1268842330.tab") 
> 
> try(system("convert tmp/18xt61268842330.ps tmp/18xt61268842330.png",intern=TRUE))
character(0)
> try(system("convert tmp/2j6ab1268842330.ps tmp/2j6ab1268842330.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.808   0.336   1.153