Mini-tutorial Univariate analysis of Y

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Sun, 14 Nov 2010 20:54:36 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm.htm/, Retrieved Sun, 14 Nov 2010 21:53:15 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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5 2 3 5 3 5 3 3 6 6 6 5 4 3 5 3 2 5 1 2 4 7 6 5 1 3 5 5 6 5 4 3 5 3 5 1 2 6 1 5 6 5 4 5 6 2 6 2 4 6 6 3 5 2 7 2 6 5 4 1 5 4 4 2 3 2 3 5 2 7 1 2 2 6 5 1 4 4 3 4 3 3 2 3 3 3 2 5 2 2 5 1 2 5 2 6 2 6 3 2 2 2 5 3 1 3 6 6 3 2 5 3 3 4 5 5 5 4 6 1 5 5 3 1 5 2 4 5 4 2 5 4 3 3 5 2 5 4 4 1 7 4 2 5 3 6 2 1 3 3 5 3 2 2 2 3 2 1 6 6 6 2 2 7

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3.70731707317073 0.130313337365229 28.4492527635928 Geometric Mean 3.27293717459938 Harmonic Mean 2.79398044862694 Quadratic Mean 4.06352004079606 Winsorized Mean ( 1 / 54 ) 3.70731707317073 0.130313337365229 28.4492527635928 Winsorized Mean ( 2 / 54 ) 3.70731707317073 0.130313337365229 28.4492527635928 Winsorized Mean ( 3 / 54 ) 3.70731707317073 0.130313337365229 28.4492527635928 Winsorized Mean ( 4 / 54 ) 3.70731707317073 0.130313337365229 28.4492527635928 Winsorized Mean ( 5 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 6 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 7 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 8 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 9 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 10 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 11 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 12 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 13 / 54 ) 3.67682926829268 0.126218726075184 29.1306162138140 Winsorized Mean ( 14 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 15 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 16 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 17 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 18 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 19 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 20 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 21 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 22 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 23 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 24 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 25 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 26 / 54 ) 3.76219512195122 0.116646366200245 32.2529989103365 Winsorized Mean ( 27 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 28 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 29 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 30 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 31 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 32 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 33 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 34 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 35 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 36 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 37 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 38 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 39 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 40 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 41 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 42 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 43 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 44 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 45 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 46 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 47 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 48 / 54 ) 3.59756097560976 0.0996475579575698 36.1028513828870 Winsorized Mean ( 49 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Winsorized Mean ( 50 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Winsorized Mean ( 51 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Winsorized Mean ( 52 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Winsorized Mean ( 53 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Winsorized Mean ( 54 / 54 ) 3.89634146341463 0.0732003406599902 53.2284608006516 Trimmed Mean ( 1 / 54 ) 3.70370370370370 0.129259387793646 28.6532666363578 Trimmed Mean ( 2 / 54 ) 3.7 0.128121404689547 28.8788591489887 Trimmed Mean ( 3 / 54 ) 3.69620253164557 0.126892307586801 29.1286572207475 Trimmed Mean ( 4 / 54 ) 3.69230769230769 0.125564197235557 29.4057364567144 Trimmed Mean ( 5 / 54 ) 3.68831168831169 0.12412822410302 29.7137231678315 Trimmed Mean ( 6 / 54 ) 3.69078947368421 0.123570090036319 29.8679840129551 Trimmed Mean ( 7 / 54 ) 3.69333333333333 0.122956374164986 30.0377541092543 Trimmed Mean ( 8 / 54 ) 3.69594594594595 0.122282478616344 30.2246567763956 Trimmed Mean ( 9 / 54 ) 3.6986301369863 0.121543320445013 30.4305503868441 Trimmed Mean ( 10 / 54 ) 3.70138888888889 0.120733264210564 30.6575732304688 Trimmed Mean ( 11 / 54 ) 3.70422535211268 0.119846042313431 30.9081992246778 Trimmed Mean ( 12 / 54 ) 3.70714285714286 0.118874660243636 31.1853076975782 Trimmed Mean ( 13 / 54 ) 3.71014492753623 0.117811283069866 31.4922716301798 Trimmed Mean ( 14 / 54 ) 3.71323529411765 0.1166470983754 31.8330703963807 Trimmed Mean ( 15 / 54 ) 3.7089552238806 0.116443301243168 31.8520274183503 Trimmed Mean ( 16 / 54 ) 3.70454545454545 0.116198278082092 31.8812422670176 Trimmed Mean ( 17 / 54 ) 3.7 0.115908174129583 31.9218211121459 Trimmed Mean ( 18 / 54 ) 3.6953125 0.115568707700472 31.9750265753375 Trimmed Mean ( 19 / 54 ) 3.69047619047619 0.115175110689979 32.0423064355455 Trimmed Mean ( 20 / 54 ) 3.68548387096774 0.114722058612173 32.1253289520092 Trimmed Mean ( 21 / 54 ) 3.68032786885246 0.114203587871880 32.2260266724829 Trimmed Mean ( 22 / 54 ) 3.675 0.113612997343025 32.3466512278019 Trimmed Mean ( 23 / 54 ) 3.66949152542373 0.112942730495097 32.4898425010455 Trimmed Mean ( 24 / 54 ) 3.66379310344828 0.112184233190310 32.6587168201523 Trimmed Mean ( 25 / 54 ) 3.65789473684211 0.111327780747195 32.8569806412338 Trimmed Mean ( 26 / 54 ) 3.65178571428571 0.110362265753069 33.0890788565035 Trimmed Mean ( 27 / 54 ) 3.64545454545455 0.109274935135807 33.3603908428222 Trimmed Mean ( 28 / 54 ) 3.64814814814815 0.109527774899126 33.3079728087973 Trimmed Mean ( 29 / 54 ) 3.65094339622642 0.109759561474908 33.2631011564404 Trimmed Mean ( 30 / 54 ) 3.65384615384615 0.10996743252125 33.2266205555003 Trimmed Mean ( 31 / 54 ) 3.65686274509804 0.110148148625148 33.1994935070852 Trimmed Mean ( 32 / 54 ) 3.66 0.110298035184932 33.1828213790339 Trimmed Mean ( 33 / 54 ) 3.66326530612245 0.110412913543555 33.1778701290894 Trimmed Mean ( 34 / 54 ) 3.66666666666667 0.110488018984781 33.1861019896803 Trimmed Mean ( 35 / 54 ) 3.67021276595745 0.110517902569927 33.2092148024184 Trimmed Mean ( 36 / 54 ) 3.67391304347826 0.110496312957940 33.2491912637548 Trimmed Mean ( 37 / 54 ) 3.67777777777778 0.110416053241490 33.3083611468536 Trimmed Mean ( 38 / 54 ) 3.68181818181818 0.110268806338750 33.3894807068783 Trimmed Mean ( 39 / 54 ) 3.68604651162791 0.110044920447391 33.4958351248032 Trimmed Mean ( 40 / 54 ) 3.69047619047619 0.109733143260507 33.6313722620247 Trimmed Mean ( 41 / 54 ) 3.69512195121951 0.109320289710189 33.8008796081255 Trimmed Mean ( 42 / 54 ) 3.7 0.108790822397731 34.0102218041249 Trimmed Mean ( 43 / 54 ) 3.70512820512821 0.108126315727665 34.2666646892902 Trimmed Mean ( 44 / 54 ) 3.71052631578947 0.107304762690337 34.5793254908676 Trimmed Mean ( 45 / 54 ) 3.71621621621622 0.106299664909249 34.9598112034393 Trimmed Mean ( 46 / 54 ) 3.72222222222222 0.105078817988759 35.4231451539587 Trimmed Mean ( 47 / 54 ) 3.72222222222222 0.103602658245928 35.9278640649021 Trimmed Mean ( 48 / 54 ) 3.73529411764706 0.101821960376609 36.6845629747387 Trimmed Mean ( 49 / 54 ) 3.74242424242424 0.0996745427903686 37.5464400202482 Trimmed Mean ( 50 / 54 ) 3.734375 0.100203630718288 37.2678611865753 Trimmed Mean ( 51 / 54 ) 3.7258064516129 0.100683425721796 37.0051617225249 Trimmed Mean ( 52 / 54 ) 3.71666666666667 0.101100349171685 36.7621546029992 Trimmed Mean ( 53 / 54 ) 3.70689655172414 0.101437402848782 36.5436855402361 Trimmed Mean ( 54 / 54 ) 3.69642857142857 0.101673154897033 36.3559936265578 Median 4 Midrange 4 Midmean - Weighted Average at Xnp 3.47154471544715 Midmean - Weighted Average at X(n+1)p 3.47154471544715 Midmean - Empirical Distribution Function 3.47154471544715 Midmean - Empirical Distribution Function - Averaging 3.47154471544715 Midmean - Empirical Distribution Function - Interpolation 3.47154471544715 Midmean - Closest Observation 3.47154471544715 Midmean - True Basic - Statistics Graphics Toolkit 3.47154471544715 Midmean - MS Excel (old versions) 3.47154471544715 Number of observations 164

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm/1a3af1289768074.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm/1a3af1289768074.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm/23ds01289768074.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289767993lge3wlwx6ks8lgm/23ds01289768074.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

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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