R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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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(426.113
+ ,383.703
+ ,232.444
+ ,70.939
+ ,226.731
+ ,947.293
+ ,611.281
+ ,158.047
+ ,33.999
+ ,37.028
+ ,388.3
+ ,506.652
+ ,392.25
+ ,180.818
+ ,198.296
+ ,217.465
+ ,275.562
+ ,1030.944
+ ,57.47
+ ,136.452
+ ,556.277
+ ,213.361
+ ,274.482
+ ,220.553
+ ,236.71
+ ,260.642
+ ,2763.544
+ ,213.923
+ ,169.861
+ ,403.064
+ ,449.594
+ ,406.167
+ ,206.893
+ ,156.187
+ ,257.102
+ ,62.156
+ ,662.883
+ ,251.422
+ ,171.328
+ ,350.089
+ ,221.588
+ ,4.813
+ ,183.186
+ ,190.379
+ ,223.166
+ ,232.669
+ ,356.725
+ ,109.215
+ ,475.834
+ ,315.955
+ ,694.87
+ ,8.95
+ ,278.741
+ ,308.16
+ ,207.533
+ ,192.797
+ ,601.162
+ ,289.714
+ ,293.671
+ ,386.688
+ ,699.645
+ ,85.094
+ ,131.812
+ ,645.285
+ ,197.549
+ ,308.174
+ ,86.58
+ ,242.205
+ ,238.502
+ ,187.881
+ ,140.321
+ ,440.31
+ ,421.403
+ ,218.761
+ ,1305.923
+ ,137.55
+ ,262.517
+ ,348.821
+ ,150.034
+ ,64.016
+ ,261.596
+ ,259.7
+ ,171.26
+ ,203.077
+ ,249.148
+ ,211.655
+ ,252.64
+ ,438.555
+ ,239.89
+ ,401.915
+ ,216.886
+ ,184.641
+ ,380.155
+ ,653.641
+ ,313.906
+ ,366.936
+ ,236.302
+ ,229.641
+ ,235.577
+ ,103.898
+ ,263.906
+ ,241.171
+ ,216.548
+ ,295.281
+ ,193.299
+ ,204.386
+ ,257.567
+ ,136.813
+ ,240.755
+ ,59.609
+ ,213.511
+ ,380.531
+ ,242.344
+ ,250.407
+ ,183.613
+ ,191.835
+ ,266.793
+ ,246.542
+ ,330.563
+ ,403.556
+ ,208.108
+ ,324.04
+ ,308.532
+ ,199.297
+ ,200.156
+ ,262.875
+ ,287.069
+ ,190.157
+ ,199.746
+ ,265.777
+ ,435.956
+ ,72.844
+ ,756.46
+ ,206.771
+ ,4202.361
+ ,401.422
+ ,216.046
+ ,39.047
+ ,441.437)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> x <- x[x<800]
> 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] 269.2859
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 12.67569
> (armose <- arm / armse)
[1] 21.24428
> (geo <- geomean(x))
[1] 223.577
> (har <- harmean(x))
[1] 133.0801
> (qua <- quamean(x))
[1] 306.4056
> (win <- winmean(x))
          [,1]      [,2]
 [1,] 268.8928 12.554885
 [2,] 269.1954 12.480961
 [3,] 268.5471 12.293134
 [4,] 268.3314 12.218638
 [5,] 268.7071 12.051230
 [6,] 267.2803 11.691081
 [7,] 266.8847 11.557380
 [8,] 264.3161 10.982592
 [9,] 261.4480 10.285403
[10,] 259.2903  9.869245
[11,] 258.1419  9.384888
[12,] 257.5445  9.255830
[13,] 259.1153  9.013868
[14,] 259.4874  8.914999
[15,] 261.7260  8.565952
[16,] 261.1048  8.325704
[17,] 260.5530  8.232121
[18,] 258.6054  7.927150
[19,] 258.6281  7.830608
[20,] 260.0043  7.659712
[21,] 260.7886  7.531981
[22,] 261.0130  7.488847
[23,] 261.4665  7.064435
[24,] 261.0096  6.942032
[25,] 260.7215  6.899424
[26,] 261.9837  6.645457
[27,] 261.8217  6.514095
[28,] 261.8323  6.495243
[29,] 259.1940  6.088513
[30,] 257.6333  5.720824
[31,] 256.6246  5.474113
[32,] 256.3749  5.430455
[33,] 252.2371  4.834845
[34,] 250.8261  4.612219
[35,] 248.8454  4.351156
[36,] 249.4367  4.179193
[37,] 248.1591  3.989362
[38,] 248.3415  3.951221
[39,] 248.4681  3.938582
[40,] 244.7460  3.498622
[41,] 245.1471  3.360226
[42,] 244.3171  3.187840
[43,] 244.2337  3.025541
[44,] 241.5392  2.736158
> (tri <- trimean(x))
          [,1]      [,2]
 [1,] 267.5988 12.157538
 [2,] 266.2649 11.716341
 [3,] 264.7310 11.268334
 [4,] 263.3783 10.848179
 [5,] 262.0401 10.403149
 [6,] 260.5756  9.950658
 [7,] 259.3277  9.534323
 [8,] 258.1018  9.095700
 [9,] 257.2045  8.725033
[10,] 256.6502  8.444315
[11,] 256.3344  8.203945
[12,] 256.1342  8.014037
[13,] 255.9884  7.821605
[14,] 255.6843  7.641163
[15,] 255.3343  7.452512
[16,] 254.7745  7.286933
[17,] 254.2443  7.132545
[18,] 253.7369  6.970583
[19,] 253.3594  6.827602
[20,] 252.9641  6.677421
[21,] 252.4513  6.526794
[22,] 251.8602  6.369809
[23,] 251.2267  6.194730
[24,] 250.5330  6.046414
[25,] 249.8367  5.890842
[26,] 249.1252  5.715965
[27,] 248.2968  5.542944
[28,] 247.4363  5.357578
[29,] 247.4363  5.140892
[30,] 245.7390  4.948266
[31,] 245.0011  4.775171
[32,] 244.2833  4.606183
[33,] 243.5387  4.410017
[34,] 243.0035  4.273320
[35,] 242.5218  4.143938
[36,] 242.1313  4.029689
[37,] 241.6781  3.915134
[38,] 241.2734  3.806462
[39,] 240.8284  3.677430
[40,] 240.3423  3.517863
[41,] 240.0586  3.406857
[42,] 239.7259  3.290892
[43,] 239.4208  3.177746
[44,] 239.0947  3.064523
> (midr <- midrange(x))
[1] 380.6365
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 242.2398 243.5387 243.5387 243.5387 243.0035 243.5387 243.5387 243.5387
> postscript(file="/var/wessaorg/rcomp/tmp/1fo2q1317752752.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/wessaorg/rcomp/tmp/2wrrd1317752752.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/398j71317752752.tab") 
> 
> try(system("convert tmp/1fo2q1317752752.ps tmp/1fo2q1317752752.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wrrd1317752752.ps tmp/2wrrd1317752752.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.955   0.120   1.081