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Data:
4738.4 4687.2 5930.8 5532 5429.8 6107.4 5960.8 5541.8 5362.2 5237 4827 4781.6 4983.2 4718.4 5523.8 5286.6 5389 5810.4 5057.4 5604.4 5285 5215.2 4625.4 4270.4 4685.4 4233.8 5278.4 4978.8 5333.4 5451 5224 5790.2 5079.4 4705.8 4139.6 3720.8 4594 4638.8 4969.4 4764.4 5010.8 5267.8 5312.2 5723.2 4579.6 5015.2 4282.4 3834.2 4523.4 3884.2 3897.8 4845.6 4929 4955.4 5198.4 5122.2 4643.2 4789.8 3950.8 3824.4 4511.8 4262.4 4616.6 5139.6 4972.8 5222 5242 4979.8 4691.8 4821.6 4123.6 4027.4 4365.2 4333.6 4930 5053 5031.4 5342 5191.4 4852.2 4675.6 4689.2 3809.4 4054.2 4409.6 4210.2 4566.4 4907 5021.8 5215.2 4933.6 5197.8 4734.6 4681.8 4172 4037.8 4462.6 4282.6 4962.4 4969.2 5214.6 5416.8 4764.2 5326.2 4545.4 4797.2 4259 4117 4469.2 4203.2 5033.8 4883 5361.6 5044.6 5005.6 5382 4565.4 4825 4290.2 3933.6 4177.6 3949.4 4492.6 4894.2 5224.4 5071 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
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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,'Arithmetic Mean',header=TRUE) a<-table.element(a,signif(arm,6)) a<-table.element(a, signif(armse,6)) a<-table.element(a,signif(armose,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Geometric Mean',header=TRUE) a<-table.element(a,signif(geo,6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Harmonic Mean',header=TRUE) a<-table.element(a,signif(har,6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Quadratic Mean',header=TRUE) a<-table.element(a,signif(qua,6)) 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, mylabel,header=TRUE) a<-table.element(a,signif(win[j,1],6)) a<-table.element(a,signif(win[j,2],6)) a<-table.element(a,signif(win[j,1]/win[j,2],6)) 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, mylabel,header=TRUE) a<-table.element(a,signif(tri[j,1],6)) a<-table.element(a,signif(tri[j,2],6)) a<-table.element(a,signif(tri[j,1]/tri[j,2],6)) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a, 'Median',header=TRUE) a<-table.element(a,signif(median(x),6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Midrange',header=TRUE) a<-table.element(a,signif(midr,6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[1],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[2],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[3],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[4],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[5],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'Closest Observation',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[6],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[7],6)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- 'Midmean' mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[8],6)) 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,signif(length(x),6)) 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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