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Type 'q()' to quit R. > x <- c(23100 + ,22650 + ,22440 + ,22910 + ,22980 + ,22535 + ,22300 + ,22780 + ,22780 + ,23300 + ,23800 + ,24510 + ,24660 + ,24730 + ,25070 + ,24690 + ,24880 + ,23920 + ,23880 + ,23990 + ,24590 + ,23610 + ,23580 + ,23360 + ,23910 + ,23940 + ,23060 + ,22800 + ,23020 + ,22890 + ,22780 + ,22530 + ,22290 + ,22820 + ,22480 + ,22110 + ,22000 + ,22230 + ,22260 + ,22590 + ,22820 + ,22420 + ,22230 + ,21600 + ,21000 + ,21360 + ,21640 + ,21450 + ,21710 + ,21620 + ,21800 + ,21490 + ,21670 + ,22130 + ,22050 + ,22050 + ,22140 + ,22390 + ,22220 + ,21790 + ,21510 + ,21670 + ,21745 + ,21850 + ,22105 + ,22050 + ,21670 + ,21680 + ,21800 + ,21920 + ,21980 + ,22270 + ,21740 + ,21950 + ,22010 + ,21890 + ,21920 + ,22110 + ,22340 + ,22210 + ,22240 + ,21960 + ,22220 + ,22060 + ,22090 + ,21960 + ,21940 + ,21790 + ,21710 + ,21690 + ,21710 + ,21670 + ,21640 + ,21500 + ,21290 + ,21250 + ,21580 + ,21670 + ,21620 + ,21510 + ,21360 + ,21420 + ,21470 + ,21370 + ,21370 + ,21340 + ,21130 + ,21130 + ,20990 + ,21240 + ,21320 + ,21430 + ,21390 + ,21530 + ,21510 + ,21630 + ,21560 + ,21610 + ,21560 + ,21310 + ,21340 + ,21410 + ,21550 + ,21380 + ,21600 + ,21530 + ,21560 + ,21670 + ,21540 + ,21540 + ,21550 + ,21590 + ,21420 + ,21420 + ,21370 + ,21380 + ,21210 + ,21505 + ,21365 + ,21385 + ,21350 + ,21360 + ,21530 + ,21380 + ,21630 + ,22145 + ,22315 + ,22340 + ,22440 + ,22135 + ,21955 + ,22060 + ,22050 + ,22035 + ,22280 + ,22315 + ,22205 + ,21970 + ,22075 + ,22115 + ,22105 + ,21885 + ,21805 + ,21910 + ,21995 + ,22245 + ,22100 + ,22130 + ,22300 + ,22915 + ,23040 + ,22880 + ,23000 + ,23160 + ,23020 + ,22770 + ,22660 + ,22740 + ,22905 + ,22720 + ,22705 + ,22735 + ,22600 + ,22510 + ,22560 + ,22575 + ,22685 + ,22980 + ,23275 + ,23845 + ,23640 + ,23640 + ,23835 + ,23625 + ,24055 + ,24005 + ,24325 + ,24445 + ,24670 + ,24615 + ,24700 + ,25065 + ,25185 + ,25220 + ,25235 + ,24975 + ,25055 + ,25520 + ,25880 + ,25960 + ,25740 + ,24965 + ,25235 + ,24895 + ,24635 + ,24835 + ,24635 + ,24695 + ,25090 + ,25220 + ,24740 + ,25005 + ,24650 + ,24460 + ,24680 + ,24840 + ,24630 + ,24490 + ,24695) > ylimmax = '' > ylimmin = '' > main = 'Centrummaten Goudkoers 2009' > #'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] 22633.47 > sqrtn <- sqrt(length(x)) > (armse <- sd(x) / sqrtn) [1] 82.34465 > (armose <- arm / armse) [1] 274.8627 > (geo <- geomean(x)) [1] 22600.37 > (har <- harmean(x)) [1] 22568.32 > (qua <- quamean(x)) [1] 22667.6 > (win <- winmean(x)) [,1] [,2] [1,] 22633.17 82.27966 [2,] 22633.08 81.97714 [3,] 22630.20 81.51348 [4,] 22626.62 80.66302 [5,] 22627.27 80.61308 [6,] 22627.14 80.53774 [7,] 22628.36 80.44728 [8,] 22627.84 80.22476 [9,] 22624.50 79.68214 [10,] 22624.50 79.50167 [11,] 22624.26 79.46929 [12,] 22624.26 79.36177 [13,] 22621.99 78.94333 [14,] 22620.15 78.70157 [15,] 22619.50 78.61573 [16,] 22614.96 77.95746 [17,] 22614.21 77.78884 [18,] 22611.07 77.38941 [19,] 22610.66 77.33705 [20,] 22603.23 76.24224 [21,] 22602.31 76.12968 [22,] 22599.43 75.77783 [23,] 22599.43 75.68141 [24,] 22599.96 75.64459 [25,] 22601.59 75.42606 [26,] 22601.59 75.20986 [27,] 22600.41 75.06712 [28,] 22599.19 74.91944 [29,] 22599.19 74.67960 [30,] 22599.85 74.26424 [31,] 22602.55 74.08154 [32,] 22604.65 73.81120 [33,] 22603.93 73.45614 [34,] 22600.96 72.96246 [35,] 22589.50 71.46027 [36,] 22586.35 71.09033 [37,] 22581.51 70.52254 [38,] 22582.34 70.01194 [39,] 22561.90 67.65115 [40,] 22514.74 62.39696 [41,] 22507.58 61.30890 [42,] 22504.83 61.01469 [43,] 22497.31 59.88723 [44,] 22493.47 59.48211 [45,] 22493.47 59.13917 [46,] 22487.45 58.50808 [47,] 22480.26 57.76092 [48,] 22482.36 57.25234 [49,] 22477.01 56.33073 [50,] 22444.26 52.63695 [51,] 22444.26 52.63695 [52,] 22443.12 52.13850 [53,] 22441.97 51.63179 [54,] 22434.89 50.93202 [55,] 22384.45 45.67366 [56,] 22369.78 44.31073 [57,] 22366.05 43.55735 [58,] 22336.92 40.93872 [59,] 22329.19 39.01205 [60,] 22318.71 38.11081 [61,] 22313.38 37.65813 [62,] 22307.97 37.20172 [63,] 22307.97 37.20172 [64,] 22302.38 36.73431 [65,] 22299.54 36.04875 [66,] 22302.42 35.83210 [67,] 22289.26 33.83261 [68,] 22287.77 33.71229 [69,] 22286.27 33.59046 [70,] 22290.85 32.53450 [71,] 22289.30 32.16935 [72,] 22284.59 29.61799 [73,] 22284.59 29.61799 [74,] 22281.35 28.87066 [75,] 22274.80 28.35667 [76,] 22276.46 28.23498 > (tri <- trimean(x)) [,1] [,2] [1,] 22626.06 81.43909 [2,] 22618.82 80.54965 [3,] 22611.50 79.77229 [4,] 22605.05 79.12181 [5,] 22599.41 78.67404 [6,] 22593.53 78.20938 [7,] 22587.56 77.73013 [8,] 22581.29 77.23540 [9,] 22574.98 76.74334 [10,] 22568.95 76.29655 [11,] 22562.80 75.84309 [12,] 22556.56 75.36298 [13,] 22550.20 74.86250 [14,] 22543.91 74.37354 [15,] 22537.64 73.87612 [16,] 22531.29 73.35274 [17,] 22525.15 72.85609 [18,] 22518.94 72.33963 [19,] 22512.80 71.82237 [20,] 22506.56 71.27249 [21,] 22500.64 70.77578 [22,] 22494.65 70.25174 [23,] 22488.69 69.71761 [24,] 22482.60 69.15092 [25,] 22476.34 68.54413 [26,] 22469.86 67.90683 [27,] 22463.23 67.23675 [28,] 22456.50 66.52609 [29,] 22456.50 65.77161 [30,] 22442.69 64.97519 [31,] 22435.51 64.14499 [32,] 22428.03 63.25875 [33,] 22420.28 62.31746 [34,] 22412.36 61.32371 [35,] 22404.37 60.28402 [36,] 22396.66 59.27543 [37,] 22388.87 58.20844 [38,] 22381.08 57.09303 [39,] 22373.05 55.91374 [40,] 22365.60 54.82466 [41,] 22359.80 54.06131 [42,] 22354.10 53.31085 [43,] 22348.36 52.51401 [44,] 22342.73 51.72952 [45,] 22337.09 50.90286 [46,] 22331.28 50.02144 [47,] 22325.52 49.10592 [48,] 22319.85 48.16226 [49,] 22313.93 47.15967 [50,] 22308.02 46.13077 [51,] 22303.11 45.31535 [52,] 22298.04 44.41370 [53,] 22292.85 43.45578 [54,] 22287.52 42.43481 [55,] 22282.27 41.36520 [56,] 22278.63 40.66070 [57,] 22275.39 39.99748 [58,] 22275.39 39.32229 [59,] 22269.86 38.79931 [60,] 22267.75 38.36991 [61,] 22265.93 37.96304 [62,] 22264.24 37.54288 [63,] 22264.24 37.10805 [64,] 22261.04 36.61651 [65,] 22259.55 36.10344 [66,] 22258.09 35.58396 [67,] 22256.47 35.01223 [68,] 22255.27 34.55194 [69,] 22254.07 34.03716 [70,] 22252.87 33.46002 [71,] 22251.44 32.90153 [72,] 22250.00 32.29677 [73,] 22248.67 31.86567 [74,] 22247.28 31.36307 [75,] 22245.95 30.85997 [76,] 22244.81 30.33230 > (midr <- midrange(x)) [1] 23475 > midm <- array(NA,dim=8) > for (j in 1:8) midm[j] <- midmean(x,j) > midm [1] 22266.62 22275.39 22275.39 22275.39 22275.39 22264.36 22275.39 22275.39 > postscript(file="/var/www/html/rcomp/tmp/19dvw1275584126.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/2kndz1275584126.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/3mrpq1275584127.tab") > > try(system("convert tmp/19dvw1275584126.ps tmp/19dvw1275584126.png",intern=TRUE)) character(0) > try(system("convert tmp/2kndz1275584126.ps tmp/2kndz1275584126.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 1.120 0.348 1.900