workshop 6 - tutorial 13

*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: Tue, 16 Nov 2010 16:07:59 +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/16/t1289923586kcxw6qec3wb1w07.htm/, Retrieved Tue, 16 Nov 2010 17:06:26 +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/16/t1289923586kcxw6qec3wb1w07.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?

No (this computation is public)

User-defined keywords:

Dataseries X:

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13 12 15 12 10 12 15 9 12 11 11 11 15 7 11 11 10 14 10 6 11 15 11 12 14 15 9 13 13 16 13 12 14 11 9 16 12 10 13 16 14 15 5 8 11 16 17 9 9 13 10 6 12 8 14 12 11 16 8 15 7 16 14 16 9 14 11 13 15 5 15 13 11 11 12 12 12 12 14 6 7 14 14 10 13 12 9 12 16 10 14 10 16 15 12 10 8 8 11 13 16 16 14 11 4 14 9 14 8 8 11 12 11 14 15 16 16 11 14 14 12 14 8 13 16 12 16 12 11 4 16 15 10 13 15 12 14 7 19 12 12 13 15 8 12 10 8 10 15 16 13 16 9 14 14 12

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 12.0448717948718 0.235118355131195 51.2289726939898 Geometric Mean 11.6231650748094 Harmonic Mean 11.1068291141763 Quadratic Mean 12.3954602938913 Winsorized Mean ( 1 / 52 ) 12.0320512820513 0.233011689890686 51.637114376948 Winsorized Mean ( 2 / 52 ) 12.0320512820513 0.228712343268093 52.6077915608931 Winsorized Mean ( 3 / 52 ) 12.0320512820513 0.228712343268093 52.6077915608931 Winsorized Mean ( 4 / 52 ) 12.0576923076923 0.223928453770887 53.8461821382876 Winsorized Mean ( 5 / 52 ) 12.0576923076923 0.223928453770887 53.8461821382876 Winsorized Mean ( 6 / 52 ) 12.0576923076923 0.223928453770887 53.8461821382876 Winsorized Mean ( 7 / 52 ) 12.1025641025641 0.216594341910975 55.8766401549793 Winsorized Mean ( 8 / 52 ) 12.1025641025641 0.216594341910975 55.8766401549793 Winsorized Mean ( 9 / 52 ) 12.1025641025641 0.216594341910975 55.8766401549793 Winsorized Mean ( 10 / 52 ) 12.1025641025641 0.216594341910975 55.8766401549793 Winsorized Mean ( 11 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 12 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 13 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 14 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 15 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 16 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 17 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 18 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 19 / 52 ) 12.1730769230769 0.206623863908187 58.9141868360664 Winsorized Mean ( 20 / 52 ) 12.0448717948718 0.192571503637128 62.547529449469 Winsorized Mean ( 21 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 22 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 23 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 24 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 25 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 26 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 27 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 28 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 29 / 52 ) 12.1794871794872 0.175526427751788 69.3883384712314 Winsorized Mean ( 30 / 52 ) 12.3717948717949 0.154667644080959 79.9895475573355 Winsorized Mean ( 31 / 52 ) 12.3717948717949 0.154667644080959 79.9895475573355 Winsorized Mean ( 32 / 52 ) 12.3717948717949 0.154667644080959 79.9895475573355 Winsorized Mean ( 33 / 52 ) 12.3717948717949 0.154667644080959 79.9895475573355 Winsorized Mean ( 34 / 52 ) 12.3717948717949 0.154667644080959 79.9895475573355 Winsorized Mean ( 35 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 36 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 37 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 38 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 39 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 40 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 41 / 52 ) 12.1474358974359 0.132046463731185 91.993647949294 Winsorized Mean ( 42 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 43 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 44 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 45 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 46 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 47 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 48 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 49 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 50 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 51 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Winsorized Mean ( 52 / 52 ) 12.4166666666667 0.106044894800559 117.088773486163 Trimmed Mean ( 1 / 52 ) 12.0519480519481 0.227882456628179 52.8866865412656 Trimmed Mean ( 2 / 52 ) 12.0723684210526 0.222297874182759 54.3071698973041 Trimmed Mean ( 3 / 52 ) 12.0933333333333 0.218669285737575 55.304215644837 Trimmed Mean ( 4 / 52 ) 12.1148648648649 0.214719348597917 56.4218592501002 Trimmed Mean ( 5 / 52 ) 12.1301369863014 0.211895576511906 57.2458245045989 Trimmed Mean ( 6 / 52 ) 12.1458333333333 0.208820816610518 58.1639011401203 Trimmed Mean ( 7 / 52 ) 12.1619718309859 0.205468472938447 59.1914256092677 Trimmed Mean ( 8 / 52 ) 12.1714285714286 0.203247745770088 59.8846915881505 Trimmed Mean ( 9 / 52 ) 12.1811594202899 0.200822256431759 60.6564214381742 Trimmed Mean ( 10 / 52 ) 12.1911764705882 0.198171023243600 61.5184615341182 Trimmed Mean ( 11 / 52 ) 12.2014925373134 0.195270028112499 62.4852295831284 Trimmed Mean ( 12 / 52 ) 12.2045454545455 0.193503868119108 63.0713255149667 Trimmed Mean ( 13 / 52 ) 12.2076923076923 0.191562060748483 63.7270880256437 Trimmed Mean ( 14 / 52 ) 12.2109375 0.189426566726636 64.4626448708316 Trimmed Mean ( 15 / 52 ) 12.2142857142857 0.187076808894913 65.2902184211772 Trimmed Mean ( 16 / 52 ) 12.2177419354839 0.184489174275862 66.224709300368 Trimmed Mean ( 17 / 52 ) 12.2213114754098 0.181636382687443 67.2844905551773 Trimmed Mean ( 18 / 52 ) 12.225 0.178486674564795 68.492508081112 Trimmed Mean ( 19 / 52 ) 12.2288135593220 0.175002749072653 69.8778369146943 Trimmed Mean ( 20 / 52 ) 12.2327586206897 0.171140349665010 71.4779340151757 Trimmed Mean ( 21 / 52 ) 12.2456140350877 0.168355703307982 72.7365559614345 Trimmed Mean ( 22 / 52 ) 12.25 0.167068370471015 73.3232745699477 Trimmed Mean ( 23 / 52 ) 12.2545454545455 0.165616780664759 73.9933804132511 Trimmed Mean ( 24 / 52 ) 12.2592592592593 0.163981680106611 74.7599320319749 Trimmed Mean ( 25 / 52 ) 12.2641509433962 0.162140825279642 75.6388831883913 Trimmed Mean ( 26 / 52 ) 12.2692307692308 0.160068348703541 76.6499490286762 Trimmed Mean ( 27 / 52 ) 12.2745098039216 0.157733942606479 77.817808907145 Trimmed Mean ( 28 / 52 ) 12.28 0.155101791274523 79.1738115923173 Trimmed Mean ( 29 / 52 ) 12.2857142857143 0.152129148849682 80.7584501629846 Trimmed Mean ( 30 / 52 ) 12.2916666666667 0.148764404187347 82.6250522348552 Trimmed Mean ( 31 / 52 ) 12.2916666666667 0.147131763258901 83.541897374244 Trimmed Mean ( 32 / 52 ) 12.2826086956522 0.145259613180465 84.5562536394253 Trimmed Mean ( 33 / 52 ) 12.2777777777778 0.143113041914380 85.7907680078746 Trimmed Mean ( 34 / 52 ) 12.2727272727273 0.140650148026338 87.2571230456797 Trimmed Mean ( 35 / 52 ) 12.2674418604651 0.137820060133787 89.0105681898312 Trimmed Mean ( 36 / 52 ) 12.2738095238095 0.136918792466208 89.6429869321168 Trimmed Mean ( 37 / 52 ) 12.2804878048780 0.135832927653201 90.4087691920456 Trimmed Mean ( 38 / 52 ) 12.2875 0.134533594223464 91.3340647064715 Trimmed Mean ( 39 / 52 ) 12.2948717948718 0.132986112608966 92.4522986172532 Trimmed Mean ( 40 / 52 ) 12.3026315789474 0.131148418457474 93.8069381518058 Trimmed Mean ( 41 / 52 ) 12.3108108108108 0.128968906239563 95.4556502785496 Trimmed Mean ( 42 / 52 ) 12.3194444444444 0.126383407162418 97.4767552247776 Trimmed Mean ( 43 / 52 ) 12.3142857142857 0.126332003919963 97.475582846666 Trimmed Mean ( 44 / 52 ) 12.3088235294118 0.126159856753958 97.565294112666 Trimmed Mean ( 45 / 52 ) 12.3088235294118 0.125843905549539 97.810247350964 Trimmed Mean ( 46 / 52 ) 12.296875 0.12535601582838 98.0956112775246 Trimmed Mean ( 47 / 52 ) 12.2903225806452 0.124661565696999 98.5895092198493 Trimmed Mean ( 48 / 52 ) 12.2833333333333 0.123717526508367 99.2853129221158 Trimmed Mean ( 49 / 52 ) 12.2758620689655 0.122469803056851 100.235827629011 Trimmed Mean ( 50 / 52 ) 12.2678571428571 0.120849459397776 101.513545894132 Trimmed Mean ( 51 / 52 ) 12.2592592592593 0.118767209382842 103.220908556856 Trimmed Mean ( 52 / 52 ) 12.25 0.116105091003206 105.507862697095 Median 12 Midrange 11.5 Midmean - Weighted Average at Xnp 12.1428571428571 Midmean - Weighted Average at X(n+1)p 12.1428571428571 Midmean - Empirical Distribution Function 12.1428571428571 Midmean - Empirical Distribution Function - Averaging 12.1428571428571 Midmean - Empirical Distribution Function - Interpolation 12.1428571428571 Midmean - Closest Observation 12.1428571428571 Midmean - True Basic - Statistics Graphics Toolkit 12.1428571428571 Midmean - MS Excel (old versions) 12.1428571428571 Number of observations 156

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289923586kcxw6qec3wb1w07/1mo2q1289923675.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289923586kcxw6qec3wb1w07/1mo2q1289923675.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289923586kcxw6qec3wb1w07/2wf1b1289923675.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289923586kcxw6qec3wb1w07/2wf1b1289923675.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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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