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Data:
8.6658 8.756 8.8178 8.8595 8.8762 8.968 9.0638 9.0789 9.0529 8.9548 9.0355 9.053 9.1 9.0772 9.1346 9.2651 9.2939 9.3752 9.4915 9.3559 9.3608 9.3325 9.2437 9.2667 9.2212 9.2691 9.342 9.2787 9.3212 9.2202 9.2089 9.2326 9.3568 9.3783 9.3018 9.2313 9.2922 9.2548 9.3298 9.2713 9.2205 9.1703 9.1843 9.1321 9.1014 9.0055 9.0192 8.9966 8.9369 8.9644 8.8008 8.7783 8.7809 8.7947 8.7574 8.669 8.6558 8.6138 8.6248 8.6267 8.655 8.7381 8.732 8.727 8.7187 8.6318 8.6398 8.6426 8.631 8.5751 8.5719 8.6391 8.631 8.7159 8.7477 8.7346 8.7281 8.6978 8.6781 8.8183 8.8937 8.9684 8.9179 8.9281 8.9434 8.9546 8.8559 8.8265 8.8557 8.806 8.8345 8.7666 8.7446 8.7123 8.686 8.7058 8.7823 8.8075 8.6955 8.6056 8.5117 8.5126 8.5597 8.5785 8.5169 8.5287 8.4908 8.4964 8.3596 8.3215 8.2918 8.3864 8.3476 8.3378 8.3595 8.3521 8.4229 8.4454 8.4428 8.388 8.376 8.3689 8.2855 8.2277 8.2005 8.1558 8.1706 8.2355 8.3768 8.3448 8.3021 8.4031 8.4599 8.372 8.4059 8.3495 8.44 8.5326 8.4215 8.3772 8.4851 8.4315 8.528 8.5943 8.6611 8.6715 8.8533 8.7 8.6882 8.8223 8.9352 9.0352 9.0878 9.0484 9.0401 9.0715 9.0937 9.0881 9.1056 9.1304 9.2047 9.1698 9.2383 9.2451 9.2932 9.2712 9.2727 9.1331 9.0739 9.1054 9.1438 9.1937 9.2006 9.2025 9.1958 9.1161 9.1183 9.1054 9.2285 9.1961 9.2486 9.3245 9.3898 9.3672 9.355 9.3953 9.3231 9.29 9.2544 9.3269 9.2718 9.3303 9.3111 9.2485 9.2326 9.2629 9.2087 9.2485 9.2686 9.3017 9.2375 9.2703 9.379 9.3264 9.2977 9.2737 9.3757 9.3847 9.3935 9.3355 9.347 9.4532 9.5463 9.5147 9.499 9.5343 9.557 9.6067 9.6157 9.6607 9.6498 9.6012 9.6481 9.7488 9.8097 9.813 9.89 9.9419 9.8863 9.9174 9.7449 9.7663 9.7973 9.8598 9.8238 9.835 9.7861 9.8569 9.8386 9.831 9.7482 9.7498 9.8105 9.7893 9.7943 9.9416 9.9286 10.0013 10.0755 10.0556 10.083 10.0869 10.0982 10.2869 10.3224 10.3009 10.2895 10.2564 10.1866 10.2882 10.2975 10.2229 10.2233 10.1154 10.1491 10.2111 10.1544 10.2166 10.1493 10.1867 10.2641 10.217 10.2292 10.1467 10.1506 10.0773 10.0085 10.0862 10.1047 10.0972 10.0955 10.1583 10.2547 10.2564 10.2438 10.187 10.22 10.1841 10.1508 10.1502 10.1585 10.1469 10.0748 10.0678 10.0777 10.0306 10.0497 9.9773 9.9234 9.9248 9.9958 9.9341 10.0023 10.017 10.0824 10.091 10.0902 10.0098 10.0404 10.0431 10.0141 9.9777 9.9436 9.9662 9.9334 9.9168 9.8814 9.786 9.7409 9.7915 9.7137 9.777 9.7486 9.8108 9.7479 9.748 9.7859 9.7845 9.7891 9.7305 9.6443 9.6365 9.6203 9.7688 9.7674 9.6853 9.6825 9.7062 9.8084 9.8164 9.8433 9.8246 9.7701 9.6592 9.6014 9.635 9.7197 9.7472 9.7185 9.7198 9.6933 9.7153 9.7118 9.6259 9.6526 9.625 9.5599 9.5487 9.4983 9.5575 9.4984 9.5788 9.4979 9.5714 9.5974 9.6319 9.6545 9.607 9.6329 9.5276 9.5857 9.5537 9.4728 9.5242 9.5139 9.463 9.4926 9.4684 9.5701 9.5475 9.6365 9.5415 9.4803 9.6871 9.6313 9.7044 9.7261 9.7073 9.6263 9.461 9.4917 9.5 9.5601 9.5334 9.3983 9.3434 9.2896 9.2124 9.2271 9.2567 9.2942 9.334 9.2615 9.1583 9.116 9.0877 9.1407 9.0221 9.0575 9.0547 8.8692 8.961 9.0339 8.913 8.8428 8.8354 8.8604 8.922 9.0163 9.0001 9.0702 9.0717 9.0446 9.0622 9.2242 9.1757 9.1533 9.0527 9.0942 9.0893 9.0838 9.2191 9.2176 9.2247 9.2623 9.2509 9.3352 8.974 8.8487 8.9183 8.8244 8.7414 8.7461 8.7451 8.5945 8.6581 8.5885 8.5915 8.6303 8.623 8.6482 8.7429 8.7485 8.7264 8.7487 8.6087 8.6844 8.6131 8.641 8.7236 8.7626 8.7703 8.8409 8.8598 8.8894 8.7453 8.7708 8.7598 8.7891 8.7389 8.7636 8.9653 9.0672 9.0084 8.8826 8.7492 8.8773 8.8276 8.8422 9.0111 9.0732 8.9453 9.004 9.0634 9.1575 9.3538 9.3068 9.2908 9.1138 9.2781 9.4608
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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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