Central tendency paper

*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: Thu, 17 Dec 2009 07:38:34 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t12610610351xtrjq6rxn67xas.htm/, Retrieved Thu, 17 Dec 2009 15:43:57 +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/2009/Dec/17/t12610610351xtrjq6rxn67xas.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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91,02 91,19 91,53 91,88 92,06 92,32 92,67 92,85 92,82 93,46 93,23 93,54 93,29 93,20 93,60 93,81 94,62 95,22 95,38 95,31 95,30 95,57 95,42 95,53 95,33 95,90 96,06 96,31 96,34 96,49 96,22 96,53 96,50 96,77 96,66 96,58 96,63 97,06 97,73 98,01 97,76 97,49 97,77 97,96 98,23 98,51 98,19 98,37 98,31 98,60 98,97 99,11 99,64 100,03 99,98 100,32 100,44 100,51 101,00 100,88 100,55 100,83 101,51 102,16 102,39 102,54 102,85 103,47 103,57 103,69 103,50 103,47 103,45 103,48 103,93 103,89 104,40 104,79 104,77 105,13 105,26 104,96 104,75 105,01 105,15 105,20 105,77 105,78 106,26 106,13 106,12 106,57 106,44 106,54 107,10 108,10 108,40 108,84 109,62 110,42 110,67 111,66 112,28 112,87 112,18 112,36 112,16 111,49 111,25 111,36 111,74 111,10 111,33 111,25 111,04 110,97 111,31 111,02 111,07 111,36

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 101.660583333333 0.578804709810231 175.638832252530 Geometric Mean 101.465623073329 Harmonic Mean 101.272025572635 Quadratic Mean 101.856472429754 Winsorized Mean ( 1 / 40 ) 101.65775 0.577910929895046 175.905567348349 Winsorized Mean ( 2 / 40 ) 101.662083333333 0.576854589154388 176.235199034058 Winsorized Mean ( 3 / 40 ) 101.668333333333 0.575197863086561 176.753670098446 Winsorized Mean ( 4 / 40 ) 101.673666666667 0.574244454691697 177.056418805565 Winsorized Mean ( 5 / 40 ) 101.667 0.57009398458544 178.333753291451 Winsorized Mean ( 6 / 40 ) 101.6805 0.567127397763604 179.290403533605 Winsorized Mean ( 7 / 40 ) 101.679333333333 0.564508942715019 180.119969126271 Winsorized Mean ( 8 / 40 ) 101.672666666667 0.56298592124997 180.595398266671 Winsorized Mean ( 9 / 40 ) 101.698916666667 0.559582174506727 181.740808231275 Winsorized Mean ( 10 / 40 ) 101.698916666667 0.55890110513381 181.962275136884 Winsorized Mean ( 11 / 40 ) 101.702583333333 0.557937107986423 182.283239235287 Winsorized Mean ( 12 / 40 ) 101.713583333333 0.554930356190536 183.290717832725 Winsorized Mean ( 13 / 40 ) 101.72225 0.553850785638245 183.663637639834 Winsorized Mean ( 14 / 40 ) 101.71175 0.550463856631826 184.774620121933 Winsorized Mean ( 15 / 40 ) 101.73425 0.546701986917918 186.087214669798 Winsorized Mean ( 16 / 40 ) 101.83825 0.533401518695868 190.922309799544 Winsorized Mean ( 17 / 40 ) 101.920416666667 0.523583354732948 194.659390420558 Winsorized Mean ( 18 / 40 ) 101.924916666667 0.521202673470119 195.557163949409 Winsorized Mean ( 19 / 40 ) 101.879 0.514156817024726 198.147718024131 Winsorized Mean ( 20 / 40 ) 101.840666666667 0.507847226820214 200.534060812583 Winsorized Mean ( 21 / 40 ) 101.709416666667 0.487406175641721 208.67486246508 Winsorized Mean ( 22 / 40 ) 101.57375 0.467501659885608 217.269282048868 Winsorized Mean ( 23 / 40 ) 101.5105 0.454286275720633 223.450510009298 Winsorized Mean ( 24 / 40 ) 101.4585 0.445820312907073 227.577113609779 Winsorized Mean ( 25 / 40 ) 101.318916666667 0.412886043716308 245.39196276705 Winsorized Mean ( 26 / 40 ) 101.23875 0.395808493618376 255.777103402967 Winsorized Mean ( 27 / 40 ) 101.268 0.391112659018879 258.922838892596 Winsorized Mean ( 28 / 40 ) 101.265666666667 0.386206497161877 262.206015203886 Winsorized Mean ( 29 / 40 ) 101.229416666667 0.380559173132601 266.001777945304 Winsorized Mean ( 30 / 40 ) 101.234416666667 0.372932278752431 271.455227756969 Winsorized Mean ( 31 / 40 ) 101.234416666667 0.372371286878813 271.864185649773 Winsorized Mean ( 32 / 40 ) 101.15175 0.361638983485949 279.703667522144 Winsorized Mean ( 33 / 40 ) 101.16275 0.359869120359771 281.109837651157 Winsorized Mean ( 34 / 40 ) 101.032416666667 0.343086154173177 294.481183334695 Winsorized Mean ( 35 / 40 ) 101.023666666667 0.340334650214052 296.836265725891 Winsorized Mean ( 36 / 40 ) 101.041666666667 0.335244263415689 301.397153338845 Winsorized Mean ( 37 / 40 ) 101.124916666667 0.325121761199568 311.037059757417 Winsorized Mean ( 38 / 40 ) 101.223083333333 0.307071712074247 329.639883301457 Winsorized Mean ( 39 / 40 ) 101.284833333333 0.297484622471329 340.470819943289 Winsorized Mean ( 40 / 40 ) 101.238166666667 0.290628050318822 348.342723820386 Trimmed Mean ( 1 / 40 ) 101.655762711864 0.573772261650562 177.170925655125 Trimmed Mean ( 2 / 40 ) 101.653706896552 0.569135138213949 178.610843139223 Trimmed Mean ( 3 / 40 ) 101.649298245614 0.564543481068323 180.055747084806 Trimmed Mean ( 4 / 40 ) 101.6425 0.560042982182521 181.490534179882 Trimmed Mean ( 5 / 40 ) 101.634 0.555270721941593 183.035042158572 Trimmed Mean ( 6 / 40 ) 101.626666666667 0.55096252979849 184.452954911173 Trimmed Mean ( 7 / 40 ) 101.616509433962 0.546740353586547 185.858806227437 Trimmed Mean ( 8 / 40 ) 101.606153846154 0.542461393533645 187.30577891319 Trimmed Mean ( 9 / 40 ) 101.596372549020 0.537863786392428 188.888664973058 Trimmed Mean ( 10 / 40 ) 101.5827 0.533190906266463 190.518440592522 Trimmed Mean ( 11 / 40 ) 101.568469387755 0.527957976065003 192.379837018031 Trimmed Mean ( 12 / 40 ) 101.553229166667 0.522125180232816 194.49977325626 Trimmed Mean ( 13 / 40 ) 101.536170212766 0.515898132618392 196.814378252212 Trimmed Mean ( 14 / 40 ) 101.5175 0.50892203665514 199.475543773301 Trimmed Mean ( 15 / 40 ) 101.499 0.501411218201017 202.426663615868 Trimmed Mean ( 16 / 40 ) 101.477613636364 0.493300836843043 205.711415950124 Trimmed Mean ( 17 / 40 ) 101.446162790698 0.485705888178582 208.863357969831 Trimmed Mean ( 18 / 40 ) 101.406309523810 0.478143455542457 212.083441377993 Trimmed Mean ( 19 / 40 ) 101.364146341463 0.469652627824682 215.827912665916 Trimmed Mean ( 20 / 40 ) 101.3235 0.460748225406447 219.910776456313 Trimmed Mean ( 21 / 40 ) 101.283717948718 0.451230275510861 224.461263894692 Trimmed Mean ( 22 / 40 ) 101.251710526316 0.442966253047423 228.576578531087 Trimmed Mean ( 23 / 40 ) 101.227972972973 0.435982507815034 232.183565070732 Trimmed Mean ( 24 / 40 ) 101.2075 0.429470219462678 235.656619279967 Trimmed Mean ( 25 / 40 ) 101.189571428571 0.422839334651032 239.309740452796 Trimmed Mean ( 26 / 40 ) 101.180441176471 0.419208535267854 241.360641934023 Trimmed Mean ( 27 / 40 ) 101.176363636364 0.416832580656399 242.726620546403 Trimmed Mean ( 28 / 40 ) 101.17 0.41429330008107 244.198976860603 Trimmed Mean ( 29 / 40 ) 101.163387096774 0.41157659130498 245.794802799685 Trimmed Mean ( 30 / 40 ) 101.158833333333 0.408736242475965 247.491714266766 Trimmed Mean ( 31 / 40 ) 101.153620689655 0.405981867036849 249.157977000174 Trimmed Mean ( 32 / 40 ) 101.148035714286 0.402337441533753 251.401001429792 Trimmed Mean ( 33 / 40 ) 101.147777777778 0.399070781861409 253.458239428074 Trimmed Mean ( 34 / 40 ) 101.146730769231 0.394898341267962 256.133592368262 Trimmed Mean ( 35 / 40 ) 101.1548 0.391877869354466 258.128381086257 Trimmed Mean ( 36 / 40 ) 101.164166666667 0.388025077027106 260.715537876434 Trimmed Mean ( 37 / 40 ) 101.173043478261 0.383520416800618 263.800932222229 Trimmed Mean ( 38 / 40 ) 101.176590909091 0.379089253435071 266.893851493524 Trimmed Mean ( 39 / 40 ) 101.173095238095 0.376124174533407 268.988547103104 Trimmed Mean ( 40 / 40 ) 101.1645 0.373318271788674 270.987271839903 Median 100.855 Midrange 101.945 Midmean - Weighted Average at Xnp 101.079836065574 Midmean - Weighted Average at X(n+1)p 101.158833333333 Midmean - Empirical Distribution Function 101.079836065574 Midmean - Empirical Distribution Function - Averaging 101.158833333333 Midmean - Empirical Distribution Function - Interpolation 101.158833333333 Midmean - Closest Observation 101.079836065574 Midmean - True Basic - Statistics Graphics Toolkit 101.158833333333 Midmean - MS Excel (old versions) 101.163387096774 Number of observations 120

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610610351xtrjq6rxn67xas/1ks0h1261060712.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t12610610351xtrjq6rxn67xas/1ks0h1261060712.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t12610610351xtrjq6rxn67xas/2mvg71261060712.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t12610610351xtrjq6rxn67xas/2mvg71261060712.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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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