mini tutorial CLT

*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 14:26:54 +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/t1289918351809fo1e328dlts4.htm/, Retrieved Tue, 16 Nov 2010 15:39:11 +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/t1289918351809fo1e328dlts4.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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53 86 66 67 76 78 53 80 74 76 79 54 67 54 87 58 75 88 64 57 66 68 54 56 86 80 76 69 78 67 80 54 71 84 74 71 63 71 76 69 74 75 54 52 69 68 65 75 74 75 72 67 63 62 63 76 74 67 73 70 53 77 77 52 54 80 66 73 63 69 67 54 81 69 84 80 70 69 77 54 79 30 71 73 72 77 75 69 54 70 73 54 77 82 80 80 69 78 81 76 76 73 85 66 79 68 76 71 54 46 82 74 88 38 76 86 54 70 69 90 54 76 89 76 73 79 90 74 81 72 71 66 77 65 74 82 54 63 54 64 69 54 84 86 77 89 76 60 75 73 85 79 71 72 69 78 54 69 81 84 84 69

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 70.7098765432099 0.842504495852812 83.9281889785465 Geometric Mean 69.7989903669057 Harmonic Mean 68.7449096442281 Quadratic Mean 71.5134020073627 Winsorized Mean ( 1 / 54 ) 70.7592592592593 0.829022924253379 85.3525966401777 Winsorized Mean ( 2 / 54 ) 70.8456790123457 0.805651144356196 87.9359255040334 Winsorized Mean ( 3 / 54 ) 70.9567901234568 0.786666587000972 90.199318613451 Winsorized Mean ( 4 / 54 ) 70.9320987654321 0.783236613228698 90.5627974578872 Winsorized Mean ( 5 / 54 ) 70.962962962963 0.778708350381272 91.1290638250097 Winsorized Mean ( 6 / 54 ) 70.9259259259259 0.773802101423509 91.6589988518363 Winsorized Mean ( 7 / 54 ) 70.8827160493827 0.768373880709042 92.250293547164 Winsorized Mean ( 8 / 54 ) 70.9320987654321 0.761393359845809 93.1609106491245 Winsorized Mean ( 9 / 54 ) 70.9320987654321 0.761393359845809 93.1609106491245 Winsorized Mean ( 10 / 54 ) 70.9320987654321 0.761393359845809 93.1609106491245 Winsorized Mean ( 11 / 54 ) 70.8641975308642 0.753261760528307 94.076456876243 Winsorized Mean ( 12 / 54 ) 70.8641975308642 0.753261760528307 94.076456876243 Winsorized Mean ( 13 / 54 ) 70.783950617284 0.744157476688488 95.1195853494258 Winsorized Mean ( 14 / 54 ) 70.783950617284 0.744157476688488 95.1195853494258 Winsorized Mean ( 15 / 54 ) 70.783950617284 0.744157476688488 95.1195853494258 Winsorized Mean ( 16 / 54 ) 70.783950617284 0.744157476688488 95.1195853494258 Winsorized Mean ( 17 / 54 ) 70.783950617284 0.744157476688488 95.1195853494258 Winsorized Mean ( 18 / 54 ) 70.5617283950617 0.72093059413302 97.8758967496978 Winsorized Mean ( 19 / 54 ) 70.5617283950617 0.72093059413302 97.8758967496978 Winsorized Mean ( 20 / 54 ) 70.5617283950617 0.72093059413302 97.8758967496978 Winsorized Mean ( 21 / 54 ) 70.4320987654321 0.708535522001133 99.4051767037863 Winsorized Mean ( 22 / 54 ) 70.4320987654321 0.708535522001133 99.4051767037863 Winsorized Mean ( 23 / 54 ) 70.4320987654321 0.708535522001133 99.4051767037863 Winsorized Mean ( 24 / 54 ) 70.4320987654321 0.708535522001133 99.4051767037863 Winsorized Mean ( 25 / 54 ) 70.5864197530864 0.650696986812771 108.478172150191 Winsorized Mean ( 26 / 54 ) 70.7469135802469 0.628619370803847 112.543324094164 Winsorized Mean ( 27 / 54 ) 70.9135802469136 0.606270120042448 116.966972150877 Winsorized Mean ( 28 / 54 ) 71.2592592592593 0.561838560870117 126.832268594915 Winsorized Mean ( 29 / 54 ) 71.6172839506173 0.518881714318068 138.022369982221 Winsorized Mean ( 30 / 54 ) 71.8024691358025 0.498047680371451 144.167861764262 Winsorized Mean ( 31 / 54 ) 71.8024691358025 0.498047680371451 144.167861764262 Winsorized Mean ( 32 / 54 ) 71.604938271605 0.478456835606874 149.658094404235 Winsorized Mean ( 33 / 54 ) 71.604938271605 0.478456835606874 149.658094404235 Winsorized Mean ( 34 / 54 ) 71.604938271605 0.478456835606874 149.658094404235 Winsorized Mean ( 35 / 54 ) 71.820987654321 0.454839134438739 157.904151635823 Winsorized Mean ( 36 / 54 ) 71.820987654321 0.454839134438739 157.904151635823 Winsorized Mean ( 37 / 54 ) 71.820987654321 0.408849309546183 175.666158600197 Winsorized Mean ( 38 / 54 ) 71.820987654321 0.408849309546183 175.666158600197 Winsorized Mean ( 39 / 54 ) 72.0617283950617 0.384570458292969 187.382381670525 Winsorized Mean ( 40 / 54 ) 72.0617283950617 0.384570458292969 187.382381670525 Winsorized Mean ( 41 / 54 ) 71.8086419753086 0.36110807989568 198.856370081925 Winsorized Mean ( 42 / 54 ) 71.8086419753086 0.36110807989568 198.856370081925 Winsorized Mean ( 43 / 54 ) 71.8086419753086 0.36110807989568 198.856370081925 Winsorized Mean ( 44 / 54 ) 72.0802469135803 0.334708274846854 215.352449671466 Winsorized Mean ( 45 / 54 ) 72.0802469135803 0.334708274846854 215.352449671466 Winsorized Mean ( 46 / 54 ) 72.0802469135803 0.334708274846854 215.352449671466 Winsorized Mean ( 47 / 54 ) 72.0802469135803 0.334708274846854 215.352449671466 Winsorized Mean ( 48 / 54 ) 71.783950617284 0.308571804000709 232.632890259536 Winsorized Mean ( 49 / 54 ) 71.783950617284 0.308571804000709 232.632890259536 Winsorized Mean ( 50 / 54 ) 72.0925925925926 0.279642540725125 257.802666238310 Winsorized Mean ( 51 / 54 ) 72.0925925925926 0.279642540725125 257.802666238310 Winsorized Mean ( 52 / 54 ) 72.0925925925926 0.279642540725125 257.802666238310 Winsorized Mean ( 53 / 54 ) 72.4197530864197 0.250867430801519 288.677381735203 Winsorized Mean ( 54 / 54 ) 72.4197530864197 0.250867430801519 288.677381735203 Trimmed Mean ( 1 / 54 ) 70.84375 0.80488616304169 88.0171050925751 Trimmed Mean ( 2 / 54 ) 70.9303797468354 0.778506576470594 91.1108292346129 Trimmed Mean ( 3 / 54 ) 70.974358974359 0.763245254341832 92.9902394683897 Trimmed Mean ( 4 / 54 ) 70.9805194805195 0.754156677558551 94.1190625140473 Trimmed Mean ( 5 / 54 ) 70.9934210526316 0.745352552752915 95.2481088183325 Trimmed Mean ( 6 / 54 ) 71 0.736944535444933 96.3437498822534 Trimmed Mean ( 7 / 54 ) 71.0135135135135 0.728872076061517 97.429323808421 Trimmed Mean ( 8 / 54 ) 71.0342465753425 0.72112429824889 98.504857966699 Trimmed Mean ( 9 / 54 ) 71.0486111111111 0.713895946485088 99.5223624127907 Trimmed Mean ( 10 / 54 ) 71.0633802816901 0.706026315656152 100.652594253016 Trimmed Mean ( 11 / 54 ) 71.0785714285714 0.697452997833792 101.911629384823 Trimmed Mean ( 12 / 54 ) 71.1014492753623 0.689211252170727 103.163506183949 Trimmed Mean ( 13 / 54 ) 71.125 0.68020866175712 104.563502346867 Trimmed Mean ( 14 / 54 ) 71.1567164179104 0.67148123369267 105.969776737615 Trimmed Mean ( 15 / 54 ) 71.189393939394 0.661919185800527 107.549978103894 Trimmed Mean ( 16 / 54 ) 71.2230769230769 0.651429819042079 109.333461320223 Trimmed Mean ( 17 / 54 ) 71.2578125 0.639905536919217 111.356768130287 Trimmed Mean ( 18 / 54 ) 71.2936507936508 0.627220369396868 113.666032342359 Trimmed Mean ( 19 / 54 ) 71.3467741935484 0.61571392667499 115.876498975488 Trimmed Mean ( 20 / 54 ) 71.4016393442623 0.602984475096246 118.413727538948 Trimmed Mean ( 21 / 54 ) 71.4583333333333 0.58886681203443 121.348888870910 Trimmed Mean ( 22 / 54 ) 71.5254237288136 0.574421193909131 124.517382866845 Trimmed Mean ( 23 / 54 ) 71.5948275862069 0.558292863809389 128.238837046376 Trimmed Mean ( 24 / 54 ) 71.6666666666667 0.540211431789988 132.664106031965 Trimmed Mean ( 25 / 54 ) 71.7410714285714 0.519835871489616 138.007158342101 Trimmed Mean ( 26 / 54 ) 71.8090909090909 0.503779784049132 142.540636172268 Trimmed Mean ( 27 / 54 ) 71.8703703703704 0.488371633390549 147.163277832920 Trimmed Mean ( 28 / 54 ) 71.9245283018868 0.473692101712785 151.838141361911 Trimmed Mean ( 29 / 54 ) 71.9615384615385 0.46234681513863 155.644066543341 Trimmed Mean ( 30 / 54 ) 71.9803921568627 0.454272923454672 158.451865476515 Trimmed Mean ( 31 / 54 ) 71.99 0.447325384926901 160.934305151862 Trimmed Mean ( 32 / 54 ) 72 0.439478297524885 163.830615540061 Trimmed Mean ( 33 / 54 ) 72.0208333333333 0.432500676063427 166.521897697037 Trimmed Mean ( 34 / 54 ) 72.0425531914894 0.424569949056646 169.683590069342 Trimmed Mean ( 35 / 54 ) 72.0652173913043 0.415538020056288 173.426290527020 Trimmed Mean ( 36 / 54 ) 72.0777777777778 0.407859054311921 176.722269656062 Trimmed Mean ( 37 / 54 ) 72.0909090909091 0.399070355057052 180.647116924039 Trimmed Mean ( 38 / 54 ) 72.1046511627907 0.3938755036621 183.064573684806 Trimmed Mean ( 39 / 54 ) 72.1190476190476 0.387855203145733 185.943225807260 Trimmed Mean ( 40 / 54 ) 72.1219512195122 0.383485592440298 188.069519797515 Trimmed Mean ( 41 / 54 ) 72.125 0.378360470410983 190.625093371029 Trimmed Mean ( 42 / 54 ) 72.1410256410256 0.374745716416897 192.50660509424 Trimmed Mean ( 43 / 54 ) 72.1578947368421 0.370420638837557 194.799876603220 Trimmed Mean ( 44 / 54 ) 72.1756756756757 0.365262306333448 197.599572756863 Trimmed Mean ( 45 / 54 ) 72.1805555555556 0.362204166096623 199.281406211933 Trimmed Mean ( 46 / 54 ) 72.1857142857143 0.358448957498300 201.383524141109 Trimmed Mean ( 47 / 54 ) 72.1911764705882 0.353868222064367 204.005819029031 Trimmed Mean ( 48 / 54 ) 72.1969696969697 0.34830237444183 207.282450522103 Trimmed Mean ( 49 / 54 ) 72.21875 0.344650695897367 209.541866184149 Trimmed Mean ( 50 / 54 ) 72.241935483871 0.340066783398968 212.434554065565 Trimmed Mean ( 51 / 54 ) 72.25 0.338345091777527 213.539376677309 Trimmed Mean ( 52 / 54 ) 72.2586206896552 0.335948913693689 215.088121271733 Trimmed Mean ( 53 / 54 ) 72.2678571428571 0.33272885047833 217.19744782866 Trimmed Mean ( 54 / 54 ) 72.2592592592593 0.332478132701682 217.335373824703 Median 72.5 Midrange 60 Midmean - Weighted Average at Xnp 71.9756097560976 Midmean - Weighted Average at X(n+1)p 72.2558139534884 Midmean - Empirical Distribution Function 72.2558139534884 Midmean - Empirical Distribution Function - Averaging 72.2558139534884 Midmean - Empirical Distribution Function - Interpolation 71.9756097560976 Midmean - Closest Observation 72.2558139534884 Midmean - True Basic - Statistics Graphics Toolkit 72.2558139534884 Midmean - MS Excel (old versions) 72.2558139534884 Number of observations 162

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918351809fo1e328dlts4/1pmp31289917610.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918351809fo1e328dlts4/1pmp31289917610.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918351809fo1e328dlts4/20wo61289917610.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289918351809fo1e328dlts4/20wo61289917610.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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