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Data:
14.15 13.95 13.96 13.99 14.08 14.03 13.93 13.95 13.94 14.01 13.98 13.84 14.16 13.92 13.97 14 14 13.87 13.94 13.98 13.95 14.01 13.96 13.88 13.76 13.79 13.97 13.84 13.94 13.97 13.92 13.87 13.9 13.85 13.7 13.87 13.74 13.64 13.83 13.88 14.01 13.98 14.02 14.1 14.11 14.14 14.04 14.19 14.17 14.14 13.94 14.09 14.06 14.07 14.07 14.07 14.05 13.99 13.85 13.95 14.13 14.2 14.2 14.18 14.13 14.07 14.06 14.07 14.1 14.1 14 14.16 13.85 13.97 13.91 13.9 13.83 13.9 13.79 13.88 13.94 13.95 14.08 13.87 14.16 13.9 13.74 13.82 13.82 13.88 13.9 14.04 13.92 13.96 13.8 13.74 13.84 13.71 13.78 13.78 13.76 13.81 13.87 13.76 13.82 13.82 13.83 13.91 13.92 14 13.99 14.01 14.09 14.13 14.03 14.1 14.05 14.02 14.11 14.21 14.38 14.23 14.1 14.04 14.12 14 14.11 14.03 14.03 14.04 14.06 14.1 14.11 14.12 14.24 14.17 14.08 14.07 14.09 14.02 14.01 13.98 13.92 14.03 14.01 14.19 13.73 13.92 13.94 14.03 14.04 14.03 14.07 14.04 13.93 14.17 14.06 14.2 14.16 14.11 14.16 14.13 14.01 14.05 14.04 14.1 14.05 14.02 14.11 14.21 14.38 14.23 14.1 14.04 14.12 14 14.11 14.03 14.03 14.04 14.06 14.1 14.11 14.12 14.24 14.17 14.08 14.07 14.09 14.02 14.01 13.98 13.92 14.03 14.01 14.19 13.73 13.92 13.94 14.03 14.04 14.03 14.07 14.04 13.93 14.17 14.06 14.2 14.16 14.11 14.16 14.13 14.01 14.05 14.04 14.03 14.04 13.9 14.09 14.16 14.09 14.08 13.95 14.01 14 13.99 14 14.02 14.06 14.02 13.97 14.19 13.97 13.98 14.03 14.04 14.13 14.22 14.21 14.15 14.17 14.03 14.02 13.91 13.81 13.78 13.83 13.96 13.9 14.1 13.99 13.9 13.88 13.89 14.03 14.19 14.16 14.1 14.03 14.06 14.07 14.11 14.17 14.23 14.11 14.25 14.03 14.07 13.99 14.01 13.98 13.93 14.06 13.98 14 13.86 13.98 13.8 13.8 13.89 13.88 13.78 13.89 13.93 13.95 13.92 13.96 13.91 13.76 13.79 13.99 13.99 13.99 14.04 14.01 14.13 14.01 14.07 14.04 14.18 14.26 14.31 14.26 14.2 14.18 14.14 14.08 14 14.04 14.08 14 13.94 13.83 13.75 13.92 13.91 13.91 13.9 13.95 14.02 13.89 13.89 13.89 13.87 14.03 13.96 14.06 13.98 14.08 13.95 13.95 13.84 13.94 13.88 13.83 13.8 13.92 13.9 13.73 13.87 13.76 13.86 13.9 13.85 13.9 13.75 13.87 13.97 13.97 14.14 14.18 14.17 14.2 14.17 14.15 14.1 14.04 14.01 14.15 14.03 14.04 14.05 14.12 14.09 13.98 13.94 14.04 13.86 14.03 13.99 14.08 14.01 14.04 13.9 14.09 14.04 13.97 14.08 13.99 14.11 14.16 14.18 14.18 14.38 14.18 14.22 14.13 14.2 14.25 14.14 14.15 14.13 14.1 14.09 14.23 14.11 14.4 14.3 14.37 14.24 14.14 14.17 14.19 14.24 14.11 14.07 14.15 14.28 14.03 14.06 13.94 14.05 14.12 14 14.12 13.99 14.04 14.05 14.06 14.33 14.45 14.39 14.39 14.23 14.25 14.15 14.12 14.26 14.28 14.12 14.29 14.12 14.22 14.09 14.17 14.01 14.22 13.98 14.12 14.09 14.11 14.05 13.96 13.81 14.09 13.87 14.1 14.08 14.09 14.08 13.95 14.08 14 14.05 13.98 14.04 14.24 14.28 14.23 14.16 14.11 14.07 14.07 14.08 14.02 14.08 14.01 14.08 14.23 14.39 14.13 14.21 14.21 14.26 14.36 14.18 14.34 14.26 14.22 14.46 14.51 14.32 14.44 14.35 14.3 14.32 14.24 14.27 14.26 14.26 14.05 14.22 14.11 14.25 14.26 14.16 14.07 14.06 14.22 14.24 14.25 14.23 14.14 14.29 14.33 14.34 14.65 14.43 14.32 14.31 14.34 14.28 14.23 14.4 14.45 14.39 14.35 14.43 14.29 14.41 14.31 14.42 14.43 14.3 14.36 14.22 14.16 14.2 14.38 14.37 14.34 14.19 14.22 14.15 14 14.01 13.94 14 13.93 14.13 14.28 14.26 14.3 14.18 14.18 14.1 14.09 14.03 14.02 14.16 14 14.14 14.28 13.94 14.25 14.26 14.22 14.29 14.2 14.19 14.25 14.38 14.37 14.29 14.44 14.7 14.44 14.34 14.11 14.33 14.46 14.37 14.24 14.42 14.37 14.26 14.23 14.43 14.25 14.2 14.21 14.18 14.3 14.32 14.16 14.15 14.28 14.31 14.27 14.31 14.46 14.33 14.31 14.43 14.28 14.36 14.45 14.5 14.55 14.53 14.55 14.83 14.56 14.58 14.59 14.59 14.67 14.6 14.43 14.42 14.4 14.51 14.45 14.64 14.27 14.28 14.23 14.28 14.26 14.27 14.25 14.3 14.32 14.37 14.21 14.49 14.46 14.5 14.3 14.31 14.28 14.37 14.29 14.21 14.21 14.19 14.38 14.4 14.56 14.42 14.47 14.45 14.46 14.45 14.45 14.43 14.68 14.47 14.74 14.75 14.81 14.54 14.51 14.43 14.53 14.43 14.46 14.48 14.51 14.33
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R Code
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)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') 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() bitmap(file='test2.png') 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() load(file='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='mytable.tab')
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Big Analytics Cloud Computing Center
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