R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> x <- c(250785
+ ,250140
+ ,255755
+ ,254671
+ ,253919
+ ,253741
+ ,252729
+ ,253810
+ ,256653
+ ,255231
+ ,258405
+ ,251061
+ ,254811
+ ,254895
+ ,258325
+ ,257608
+ ,258759
+ ,258621
+ ,257852
+ ,260560
+ ,262358
+ ,260812
+ ,261165
+ ,257164
+ ,260720
+ ,259581
+ ,264743
+ ,261845
+ ,262262
+ ,261631
+ ,258953
+ ,259966
+ ,262850
+ ,262204
+ ,263418
+ ,262752
+ ,266433
+ ,267722
+ ,266003
+ ,262971
+ ,265521
+ ,264676
+ ,270223
+ ,269508
+ ,268457
+ ,265814
+ ,266680
+ ,263018
+ ,269285
+ ,269829
+ ,270911
+ ,266844
+ ,271244
+ ,269907
+ ,271296
+ ,270157
+ ,271322
+ ,267179
+ ,264101
+ ,265518
+ ,269419
+ ,268714
+ ,272482
+ ,268351
+ ,268175
+ ,270674
+ ,272764
+ ,272599
+ ,270333
+ ,270846
+ ,270491
+ ,269160
+ ,274027
+ ,273784
+ ,276663
+ ,274525
+ ,271344
+ ,271115
+ ,270798
+ ,273911
+ ,273985
+ ,271917
+ ,273338
+ ,270601
+ ,273547
+ ,275363
+ ,281229
+ ,277793
+ ,279913
+ ,282500
+ ,280041
+ ,282166
+ ,290304
+ ,283519
+ ,287816
+ ,285226
+ ,287595
+ ,289741
+ ,289148
+ ,288301
+ ,290155
+ ,289648
+ ,288225
+ ,289351
+ ,294735
+ ,305333
+ ,309030
+ ,310215
+ ,321935
+ ,325734
+ ,320846
+ ,323023
+ ,319753
+ ,321753
+ ,320757
+ ,324479
+ ,324641
+ ,322767
+ ,324181
+ ,321389
+ ,327897
+ ,334287
+ ,332653
+ ,334819
+ ,335264
+ ,339622
+ ,342440
+ ,346585
+ ,335378
+ ,337010
+ ,339130
+ ,341193
+ ,343507
+ ,348915
+ ,346431
+ ,348322
+ ,348288
+ ,346597
+ ,351076
+ ,355215
+ ,350562
+ ,355266
+ ,361565
+ ,363462
+ ,366183
+ ,365423
+ ,369208
+ ,366713
+ ,369354
+ ,371970
+ ,371824
+ ,373187
+ ,367270
+ ,368140
+ ,373742
+ ,364815
+ ,368558
+ ,371503
+ ,372611
+ ,370197
+ ,375441
+ ,375888
+ ,375132
+ ,381142
+ ,372024
+ ,376070
+ ,376864
+ ,371401
+ ,375687
+ ,384304
+ ,380738
+ ,379908
+ ,384007
+ ,384499
+ ,385106
+ ,387935
+ ,380435
+ ,379281
+ ,384153
+ ,380599)
> 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] 304357.4
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 3388.88
> (armose <- arm / armse)
[1] 89.81063
> (geo <- geomean(x))
[1] 301120.8
> (har <- harmean(x))
[1] 298054.1
> (qua <- quamean(x))
[1] 307716.1
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 304345.3 3386.432
 [2,] 304341.6 3385.266
 [3,] 304366.2 3382.429
 [4,] 304385.3 3380.086
 [5,] 304383.2 3379.391
 [6,] 304291.3 3366.713
 [7,] 304304.8 3362.285
 [8,] 304304.9 3360.989
 [9,] 304300.9 3359.604
[10,] 304290.3 3354.378
[11,] 304284.0 3346.962
[12,] 304182.7 3322.211
[13,] 304162.3 3312.292
[14,] 304182.6 3307.849
[15,] 304186.2 3304.227
[16,] 304206.4 3298.305
[17,] 304184.8 3294.202
[18,] 304067.4 3275.906
[19,] 304023.4 3267.834
[20,] 303980.9 3258.619
[21,] 303985.7 3244.951
[22,] 304026.2 3240.592
[23,] 304083.4 3232.670
[24,] 304061.9 3226.063
[25,] 304060.5 3223.451
[26,] 303937.6 3199.426
[27,] 303881.1 3179.633
[28,] 303891.7 3174.555
[29,] 303844.8 3158.272
[30,] 303784.8 3149.597
[31,] 303651.5 3131.324
[32,] 303622.5 3114.955
[33,] 303543.3 3102.661
[34,] 303422.6 3084.831
[35,] 303313.5 3070.911
[36,] 303122.9 3034.889
[37,] 302873.4 2981.560
[38,] 301665.0 2829.152
[39,] 301668.4 2826.922
[40,] 300920.9 2718.278
[41,] 300804.5 2706.181
[42,] 300488.5 2661.936
[43,] 300392.0 2644.282
[44,] 300488.8 2635.828
[45,] 300127.8 2588.758
[46,] 300166.7 2585.429
[47,] 300213.9 2575.113
[48,] 299579.0 2487.174
[49,] 299411.9 2449.789
[50,] 299114.4 2412.434
[51,] 298699.3 2367.109
[52,] 298631.4 2348.106
[53,] 298138.5 2278.949
[54,] 297686.4 2229.837
[55,] 297692.5 2223.637
[56,] 297581.7 2208.616
[57,] 297514.9 2185.559
[58,] 297013.5 2134.475
[59,] 295536.6 1984.879
[60,] 294837.6 1918.021
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 304192.5 3380.770
 [2,] 304036.2 3374.357
 [3,] 303878.2 3367.767
 [4,] 303708.0 3361.382
 [5,] 303528.7 3354.813
 [6,] 303345.6 3347.534
 [7,] 303174.7 3341.875
 [8,] 302997.5 3336.132
 [9,] 302816.0 3329.719
[10,] 302630.4 3322.577
[11,] 302441.3 3315.136
[12,] 302248.0 3307.580
[13,] 302248.0 3301.859
[14,] 301868.0 3296.257
[15,] 301669.6 3290.124
[16,] 301465.5 3283.308
[17,] 301254.3 3275.942
[18,] 301038.8 3267.796
[19,] 300825.6 3260.109
[20,] 300609.2 3251.908
[21,] 300389.3 3243.213
[22,] 300162.6 3234.294
[23,] 299926.7 3224.288
[24,] 299680.3 3213.355
[25,] 299427.5 3201.319
[26,] 299427.5 3187.721
[27,] 298904.7 3174.185
[28,] 298637.2 3160.276
[29,] 298360.3 3144.703
[30,] 298076.7 3128.203
[31,] 297786.4 3110.053
[32,] 297492.8 3090.883
[33,] 297190.4 3070.305
[34,] 296881.0 3047.850
[35,] 296566.1 3023.772
[36,] 296244.8 2997.524
[37,] 295920.4 2970.739
[38,] 295595.2 2944.799
[39,] 295313.3 2928.781
[40,] 295020.0 2910.044
[41,] 294749.0 2897.667
[42,] 294472.1 2883.714
[43,] 294197.8 2870.813
[44,] 293915.9 2856.583
[45,] 293617.2 2839.801
[46,] 293321.2 2823.996
[47,] 293009.8 2804.867
[48,] 292681.3 2782.509
[49,] 292681.3 2764.611
[50,] 292042.3 2746.238
[51,] 291715.9 2727.462
[52,] 291715.9 2709.146
[53,] 291052.9 2688.067
[54,] 290718.7 2669.668
[55,] 290386.9 2652.094
[56,] 290035.3 2629.871
[57,] 289667.8 2603.316
[58,] 289280.6 2572.384
[59,] 288893.5 2540.762
[60,] 288555.8 2523.081
> (midr <- midrange(x))
[1] 319037.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 293318.4 293617.2 293318.4 293617.2 293617.2 293318.4 293617.2 293915.9
> postscript(file="/var/wessaorg/rcomp/tmp/1lppn1457477295.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/2c9rs1457477295.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/3q18y1457477295.tab") 
> 
> try(system("convert tmp/1lppn1457477295.ps tmp/1lppn1457477295.png",intern=TRUE))
character(0)
> try(system("convert tmp/2c9rs1457477295.ps tmp/2c9rs1457477295.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.239   0.129   1.375