R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(1.56,1.56,1.54,1.54,1.54,1.54,1.57,1.58,1.57,1.57,1.57,1.57,1.56,1.58,1.58,1.58,1.58,1.53,1.48,1.48,1.48,1.48,1.48,1.57,1.57,1.57,1.60,1.60,1.65,1.71,1.71,1.71,1.74,1.78,1.84,1.84,1.76,1.72,1.66,1.65,1.66,1.66,1.66,1.61,1.55,1.56,1.55,1.55,1.61,1.54,1.48,1.42,1.42,1.42,1.43,1.46,1.50,1.47,1.43,1.42,1.39,1.37,1.38,1.51,1.47,1.47,1.53,1.55,1.50,1.52,1.53,1.53,1.52,1.60,1.52,1.64,1.63,1.69,1.73,1.69,1.61,1.52,1.55,1.56,1.56,1.56,1.54,1.53,1.54,1.48,1.38,1.34,1.28,1.28,1.30,1.31,1.31,1.31,1.32,1.31,1.27,1.24,1.24,1.24,1.24,1.24,1.24,1.24,1.23,1.26,1.28,1.32,1.40,1.41,1.37,1.33,1.33,1.34,1.34,1.38,1.43,1.39,1.33,1.33,1.34,1.38,1.37,1.38,1.31,1.38,1.30,1.30,1.29,1.31,1.31,1.32,1.31,1.30,1.31,1.33,1.34,1.42,1.42,1.36,1.36,1.34,1.34,1.33,1.31,1.25,1.23,1.17,1.19,1.19,1.19,1.19)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.2.291 ()
> #Author: root
> #To cite this work: Wessa, P., (2012), Central Tendency (v1.0.4) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #
> 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] 1.456731
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.01211544
> (armose <- arm / armse)
[1] 120.2376
> (geo <- geomean(x))
[1] 1.448956
> (har <- harmean(x))
[1] 1.441231
> (qua <- quamean(x))
[1] 1.464519
> (win <- winmean(x))
          [,1]        [,2]
 [1,] 1.456859 0.012096525
 [2,] 1.456090 0.011950606
 [3,] 1.455705 0.011885208
 [4,] 1.455192 0.011802928
 [5,] 1.456154 0.011579717
 [6,] 1.455769 0.011521921
 [7,] 1.455769 0.011400680
 [8,] 1.455769 0.011400680
 [9,] 1.455769 0.011400680
[10,] 1.454487 0.011221617
[11,] 1.454487 0.011221617
[12,] 1.452179 0.010923561
[13,] 1.452179 0.010923561
[14,] 1.453077 0.010812950
[15,] 1.454038 0.010698430
[16,] 1.454038 0.010454430
[17,] 1.455128 0.010332955
[18,] 1.453974 0.010194826
[19,] 1.452756 0.010053856
[20,] 1.451474 0.009631251
[21,] 1.452821 0.009488487
[22,] 1.452821 0.009488487
[23,] 1.451346 0.009333933
[24,] 1.451346 0.009333933
[25,] 1.452949 0.009169490
[26,] 1.449615 0.008838167
[27,] 1.449615 0.008838167
[28,] 1.449615 0.008838167
[29,] 1.449615 0.008838167
[30,] 1.449615 0.008838167
[31,] 1.447628 0.008652903
[32,] 1.447628 0.008652903
[33,] 1.447628 0.008652903
[34,] 1.447628 0.008652903
[35,] 1.449872 0.008426193
[36,] 1.449872 0.008426193
[37,] 1.449872 0.008426193
[38,] 1.452308 0.008187649
[39,] 1.449808 0.007960028
[40,] 1.449808 0.007960028
[41,] 1.449808 0.007960028
[42,] 1.449808 0.007960028
[43,] 1.449808 0.007960028
[44,] 1.452628 0.007689762
[45,] 1.452628 0.007689762
[46,] 1.449679 0.007428412
[47,] 1.449679 0.007428412
[48,] 1.449679 0.007428412
[49,] 1.449679 0.007428412
[50,] 1.449679 0.007428412
[51,] 1.452949 0.006533124
[52,] 1.452949 0.006533124
> (tri <- trimean(x))
          [,1]        [,2]
 [1,] 1.456104 0.011870446
 [2,] 1.455329 0.011625067
 [3,] 1.454933 0.011441808
 [4,] 1.454662 0.011268757
 [5,] 1.454521 0.011106085
 [6,] 1.454167 0.010985130
 [7,] 1.453873 0.010865938
 [8,] 1.453571 0.010759002
 [9,] 1.453261 0.010642217
[10,] 1.452941 0.010514601
[11,] 1.452761 0.010401756
[12,] 1.452576 0.010278125
[13,] 1.452615 0.010181744
[14,] 1.452656 0.010075676
[15,] 1.452619 0.009972138
[16,] 1.452500 0.009871071
[17,] 1.452377 0.009786401
[18,] 1.452167 0.009705166
[19,] 1.452034 0.009629196
[20,] 1.451983 0.009558641
[21,] 1.452018 0.009520551
[22,] 1.451964 0.009489749
[23,] 1.451909 0.009453363
[24,] 1.451944 0.009424839
[25,] 1.451981 0.009390615
[26,] 1.451923 0.009364693
[27,] 1.452059 0.009361626
[28,] 1.452200 0.009354500
[29,] 1.452347 0.009342807
[30,] 1.452500 0.009325968
[31,] 1.452500 0.009303318
[32,] 1.452935 0.009289805
[33,] 1.453222 0.009270290
[34,] 1.453523 0.009243936
[35,] 1.453837 0.009209774
[36,] 1.454048 0.009188407
[37,] 1.454268 0.009159220
[38,] 1.454500 0.009121022
[39,] 1.454615 0.009096172
[40,] 1.454868 0.009083421
[41,] 1.455135 0.009062380
[42,] 1.455417 0.009031629
[43,] 1.455714 0.008989461
[44,] 1.456029 0.008933811
[45,] 1.456029 0.008894002
[46,] 1.456406 0.008839865
[47,] 1.456774 0.008798148
[48,] 1.457167 0.008740101
[49,] 1.457586 0.008662211
[50,] 1.458036 0.008560024
[51,] 1.458519 0.008427798
[52,] 1.458846 0.008395637
> (midr <- midrange(x))
[1] 1.505
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 1.453038 1.453038 1.453038 1.453038 1.453038 1.453038 1.453038 1.463793
> postscript(file="/var/wessaorg/rcomp/tmp/1baga1483719446.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=13.888888888889,height=8.3333333333333) 
> 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/2zin31483719446.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=13.888888888889,height=8.3333333333333) 
> 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/3fwiz1483719446.tab") 
> 
> try(system("convert tmp/1baga1483719446.ps tmp/1baga1483719446.png",intern=TRUE))
character(0)
> try(system("convert tmp/2zin31483719446.ps tmp/2zin31483719446.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.645   0.062   1.719