Mini-tutorial Univariate analysis of X

*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 20:27:58 +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/t1289766550dugw5v6ra74j9w8.htm/, Retrieved Sun, 14 Nov 2010 21:29:12 +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/t1289766550dugw5v6ra74j9w8.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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Dataseries X:

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1 6 6 5 6 6 7 4 7 1 4 3 3 3 7 4 7 5 7 3 5 6 7 4 5 6 7 6 1 5 7 5 6 4 7 5 6 6 6 6 7 5 5 6 3 6 2 5 3 6 3 6 6 6 2 6 3 7 6 5 2 3 6 6 6 3 6 5 7 7 6 7 2 7 5 6 5 5 7 6 6 7 6 4 3 6 7 5 6 6 6 7 6 4 7 6 6 6 4 6 6 2 3 1 5 2 6 4 6 4 7 1 3 6 6 5 5 6 5 5 1 5 6 6 4 6 4 6 6 5 6 5 5 6 6 5 4 5 4 6 2 7 5 5 6 3 7 2 4 7 6 6 6 2 4 5 6 3 7 5 4 5 5 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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 5.07317073170732 0.124615516908804 40.7105861095932 Geometric Mean 4.70319438729971 Harmonic Mean 4.12776412776413 Quadratic Mean 5.31679345874248 Winsorized Mean ( 1 / 54 ) 5.07317073170732 0.124615516908804 40.7105861095932 Winsorized Mean ( 2 / 54 ) 5.07317073170732 0.124615516908804 40.7105861095932 Winsorized Mean ( 3 / 54 ) 5.07317073170732 0.124615516908804 40.7105861095932 Winsorized Mean ( 4 / 54 ) 5.07317073170732 0.124615516908804 40.7105861095932 Winsorized Mean ( 5 / 54 ) 5.07317073170732 0.124615516908804 40.7105861095932 Winsorized Mean ( 6 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 7 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 8 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 9 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 10 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 11 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 12 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 13 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 14 / 54 ) 5.10975609756098 0.117969565689610 43.3141892800152 Winsorized Mean ( 15 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 16 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 17 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 18 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 19 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 20 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 21 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 22 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 23 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 24 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 25 / 54 ) 5.20121951219512 0.104578659145088 49.7349990400926 Winsorized Mean ( 26 / 54 ) 5.04268292682927 0.0908629097278696 55.4977046402309 Winsorized Mean ( 27 / 54 ) 5.04268292682927 0.0908629097278696 55.4977046402309 Winsorized Mean ( 28 / 54 ) 5.04268292682927 0.0908629097278696 55.4977046402309 Winsorized Mean ( 29 / 54 ) 5.04268292682927 0.0908629097278696 55.4977046402309 Winsorized Mean ( 30 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 31 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 32 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 33 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 34 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 35 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 36 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 37 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 38 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 39 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 40 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 41 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 42 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 43 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 44 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 45 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 46 / 54 ) 5.22560975609756 0.067736440055569 77.1462118737067 Winsorized Mean ( 47 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 48 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 49 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 50 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 51 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 52 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 53 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Winsorized Mean ( 54 / 54 ) 5.51219512195122 0.0391513720387803 140.791876118448 Trimmed Mean ( 1 / 54 ) 5.08641975308642 0.123030473191280 41.3427634727403 Trimmed Mean ( 2 / 54 ) 5.1 0.121313565325876 42.0398162917746 Trimmed Mean ( 3 / 54 ) 5.11392405063291 0.119451663002008 42.8116605672283 Trimmed Mean ( 4 / 54 ) 5.12820512820513 0.11742972088893 43.6704191186455 Trimmed Mean ( 5 / 54 ) 5.14285714285714 0.115230371378914 44.6310905824106 Trimmed Mean ( 6 / 54 ) 5.15789473684211 0.112833396291803 45.7124832394753 Trimmed Mean ( 7 / 54 ) 5.16666666666667 0.111694961188762 46.2569359591354 Trimmed Mean ( 8 / 54 ) 5.17567567567568 0.110455531154336 46.857550921953 Trimmed Mean ( 9 / 54 ) 5.18493150684932 0.109105273755314 47.5222812645828 Trimmed Mean ( 10 / 54 ) 5.19444444444444 0.107633014226734 48.2606984647116 Trimmed Mean ( 11 / 54 ) 5.20422535211268 0.106025975973331 49.084437132856 Trimmed Mean ( 12 / 54 ) 5.21428571428571 0.104269452053923 50.0077981764894 Trimmed Mean ( 13 / 54 ) 5.22463768115942 0.102346383323579 51.0485814104555 Trimmed Mean ( 14 / 54 ) 5.23529411764706 0.100236807909442 52.2292581620998 Trimmed Mean ( 15 / 54 ) 5.24626865671642 0.0979171294637314 53.5786607047099 Trimmed Mean ( 16 / 54 ) 5.25 0.0970147759838418 54.1154679455675 Trimmed Mean ( 17 / 54 ) 5.25384615384615 0.0960219727770547 54.7150407547303 Trimmed Mean ( 18 / 54 ) 5.2578125 0.0949293236825833 55.386600220398 Trimmed Mean ( 19 / 54 ) 5.26190476190476 0.0937260929457012 56.1413006402942 Trimmed Mean ( 20 / 54 ) 5.26612903225806 0.092399938413948 56.9927764309325 Trimmed Mean ( 21 / 54 ) 5.27049180327869 0.0909365720355287 57.9578896070496 Trimmed Mean ( 22 / 54 ) 5.275 0.0893193214062366 59.0577706698932 Trimmed Mean ( 23 / 54 ) 5.27966101694915 0.087528553914152 60.319299027006 Trimmed Mean ( 24 / 54 ) 5.28448275862069 0.0855409057067975 61.7772598379299 Trimmed Mean ( 25 / 54 ) 5.28947368421053 0.0833282260914639 63.4775745544448 Trimmed Mean ( 26 / 54 ) 5.29464285714286 0.0808560943194812 65.4822979233018 Trimmed Mean ( 27 / 54 ) 5.30909090909091 0.0793483200041563 66.9086744220018 Trimmed Mean ( 28 / 54 ) 5.32407407407407 0.0776389917041178 68.5747452048852 Trimmed Mean ( 29 / 54 ) 5.33962264150943 0.0756959830002715 70.5403699095933 Trimmed Mean ( 30 / 54 ) 5.35576923076923 0.0734794444626891 72.8879929609259 Trimmed Mean ( 31 / 54 ) 5.36274509803922 0.0734500963532056 73.0120907160004 Trimmed Mean ( 32 / 54 ) 5.37 0.0733815268637038 73.1791805037533 Trimmed Mean ( 33 / 54 ) 5.37755102040816 0.0732683623310376 73.3952670609938 Trimmed Mean ( 34 / 54 ) 5.38541666666667 0.073104394932723 73.6674815737521 Trimmed Mean ( 35 / 54 ) 5.39361702127660 0.0728824219388911 74.0043604176453 Trimmed Mean ( 36 / 54 ) 5.40217391304348 0.072594045974283 74.4162119708446 Trimmed Mean ( 37 / 54 ) 5.41111111111111 0.0722294243984054 74.9156061560775 Trimmed Mean ( 38 / 54 ) 5.42045454545455 0.0717769513806576 75.5180380496802 Trimmed Mean ( 39 / 54 ) 5.43023255813953 0.0712228495790958 76.2428432761461 Trimmed Mean ( 40 / 54 ) 5.44047619047619 0.070550638292301 77.114485739102 Trimmed Mean ( 41 / 54 ) 5.45121951219512 0.0697404294442155 78.1644098787129 Trimmed Mean ( 42 / 54 ) 5.4625 0.0687679780866544 79.4337735670622 Trimmed Mean ( 43 / 54 ) 5.47435897435897 0.0676033735007185 80.9776005379494 Trimmed Mean ( 44 / 54 ) 5.48684210526316 0.0662091875021533 82.8713100441644 Trimmed Mean ( 45 / 54 ) 5.5 0.0645377721039217 85.2214109768718 Trimmed Mean ( 46 / 54 ) 5.51388888888889 0.0625271632852148 88.183896392957 Trimmed Mean ( 47 / 54 ) 5.51388888888889 0.060094572022046 91.7535262064284 Trimmed Mean ( 48 / 54 ) 5.52941176470588 0.060978947688096 90.6773890718568 Trimmed Mean ( 49 / 54 ) 5.53030303030303 0.0619033646847995 89.3376807296713 Trimmed Mean ( 50 / 54 ) 5.53125 0.062870923137731 87.9778715493444 Trimmed Mean ( 51 / 54 ) 5.53225806451613 0.0638850680716491 86.597044215583 Trimmed Mean ( 52 / 54 ) 5.53333333333333 0.0649496400596606 85.1942109032566 Trimmed Mean ( 53 / 54 ) 5.53448275862069 0.0660689352060522 83.768305654693 Trimmed Mean ( 54 / 54 ) 5.53571428571429 0.0672477765493766 82.3181757042881 Median 6 Midrange 4 Midmean - Weighted Average at Xnp 5.37962962962963 Midmean - Weighted Average at X(n+1)p 5.37962962962963 Midmean - Empirical Distribution Function 5.37962962962963 Midmean - Empirical Distribution Function - Averaging 5.37962962962963 Midmean - Empirical Distribution Function - Interpolation 5.37962962962963 Midmean - Closest Observation 5.37962962962963 Midmean - True Basic - Statistics Graphics Toolkit 5.37962962962963 Midmean - MS Excel (old versions) 5.37962962962963 Number of observations 164

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/14/t1289766550dugw5v6ra74j9w8/1gg6y1289766476.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289766550dugw5v6ra74j9w8/1gg6y1289766476.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289766550dugw5v6ra74j9w8/2gg6y1289766476.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/14/t1289766550dugw5v6ra74j9w8/2gg6y1289766476.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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