verbetering task 2- Q7 - Carl Heselmans - Jeroen Michel

*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: Mon, 03 Nov 2008 00:02:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/03/t1225696290mpt0qxyer9725k9.htm/, Retrieved Mon, 03 Nov 2008 07:11:30 +0000

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/2008/Nov/03/t1225696290mpt0qxyer9725k9.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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7.4 7.2 7.1 6.9 6.8 6.8 6.8 6.9 6.7 6.6 6.5 6.4 6.3 6.3 6.3 6.5 6.6 6.5 6.4 6.5 6.7 7.1 7.1 7.2 7.2 7.3 7.3 7.3 7.3 7.4 7.6 7.6 7.6 7.7 7.8 7.9 8.1 8.1 8.1 8.2 8.2 8.2 8.2 8.2 8.2 8.3 8.3 8.4 8.4 8.4 8.3 8.0 8.0 8.2 8.6 8.7 8.7 8.5 8.4 8.4 8.4 8.5 8.5 8.5 8.5 8.5 8.4 8.4 8.4 8.5 8.6 8.6 8.6 8.6 8.5 8.4 8.4 8.3 8.2 8.1 8.2 8.1 8.0 7.9 7.8 7.7 7.7 7.9 7.8 7.6 7.4 7.3 7.1 7.1 7.0 7.0 7.0 6.9 6.8 6.7 6.6 6.6

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 7.66470588235294 0.0727292906346356 105.386781796863 Geometric Mean 7.62889533005202 Harmonic Mean 7.59224755133191 Quadratic Mean 7.69947795531059 Winsorized Mean ( 1 / 34 ) 7.66470588235294 0.0727292906346356 105.386781796863 Winsorized Mean ( 2 / 34 ) 7.66274509803922 0.0724655451185538 105.743289248745 Winsorized Mean ( 3 / 34 ) 7.6656862745098 0.0719354838599548 106.563351814433 Winsorized Mean ( 4 / 34 ) 7.6656862745098 0.0719354838599548 106.563351814433 Winsorized Mean ( 5 / 34 ) 7.67058823529412 0.0711088675555192 107.871050390518 Winsorized Mean ( 6 / 34 ) 7.67058823529412 0.0711088675555192 107.871050390518 Winsorized Mean ( 7 / 34 ) 7.66372549019608 0.0702602038481258 109.076334403498 Winsorized Mean ( 8 / 34 ) 7.66372549019608 0.0702602038481258 109.076334403498 Winsorized Mean ( 9 / 34 ) 7.67254901960784 0.0688558752221016 111.429111820295 Winsorized Mean ( 10 / 34 ) 7.67254901960784 0.0688558752221016 111.429111820295 Winsorized Mean ( 11 / 34 ) 7.67254901960784 0.0688558752221016 111.429111820295 Winsorized Mean ( 12 / 34 ) 7.67254901960784 0.0688558752221016 111.429111820295 Winsorized Mean ( 13 / 34 ) 7.68529411764706 0.0669436643812049 114.802411679824 Winsorized Mean ( 14 / 34 ) 7.68529411764706 0.0669436643812049 114.802411679824 Winsorized Mean ( 15 / 34 ) 7.67058823529412 0.0652428260782516 117.569834054921 Winsorized Mean ( 16 / 34 ) 7.68627450980392 0.0629939493460701 122.016075981803 Winsorized Mean ( 17 / 34 ) 7.68627450980392 0.0629939493460701 122.016075981803 Winsorized Mean ( 18 / 34 ) 7.68627450980392 0.0629939493460701 122.016075981803 Winsorized Mean ( 19 / 34 ) 7.68627450980392 0.0629939493460701 122.016075981803 Winsorized Mean ( 20 / 34 ) 7.70588235294118 0.0603301524490761 127.728541038341 Winsorized Mean ( 21 / 34 ) 7.70588235294118 0.0603301524490761 127.728541038341 Winsorized Mean ( 22 / 34 ) 7.70588235294118 0.0603301524490761 127.728541038341 Winsorized Mean ( 23 / 34 ) 7.72843137254902 0.0574210768274783 134.592240333094 Winsorized Mean ( 24 / 34 ) 7.72843137254902 0.0574210768274783 134.592240333094 Winsorized Mean ( 25 / 34 ) 7.72843137254902 0.0574210768274783 134.592240333094 Winsorized Mean ( 26 / 34 ) 7.72843137254902 0.0513906294828328 150.386003252416 Winsorized Mean ( 27 / 34 ) 7.72843137254902 0.0513906294828328 150.386003252416 Winsorized Mean ( 28 / 34 ) 7.72843137254902 0.0513906294828328 150.386003252416 Winsorized Mean ( 29 / 34 ) 7.72843137254902 0.0513906294828328 150.386003252416 Winsorized Mean ( 30 / 34 ) 7.69901960784314 0.0482562382221448 159.544545772531 Winsorized Mean ( 31 / 34 ) 7.72941176470588 0.0445993888404646 173.307571374007 Winsorized Mean ( 32 / 34 ) 7.72941176470588 0.0445993888404646 173.307571374007 Winsorized Mean ( 33 / 34 ) 7.72941176470588 0.0445993888404646 173.307571374006 Winsorized Mean ( 34 / 34 ) 7.76274509803922 0.0407634760022518 190.433835858610 Trimmed Mean ( 1 / 34 ) 7.668 0.0721653544565422 106.255973628144 Trimmed Mean ( 2 / 34 ) 7.67142857142857 0.0715168820801775 107.267380068781 Trimmed Mean ( 3 / 34 ) 7.67604166666667 0.07092349460502 108.229885024917 Trimmed Mean ( 4 / 34 ) 7.67978723404255 0.0704526624181618 109.006345118092 Trimmed Mean ( 5 / 34 ) 7.68369565217391 0.0698998870119504 109.924292879905 Trimmed Mean ( 6 / 34 ) 7.68666666666667 0.0694763721860521 110.637133529114 Trimmed Mean ( 7 / 34 ) 7.68977272727273 0.0689721479369215 111.490985235162 Trimmed Mean ( 8 / 34 ) 7.69418604651163 0.0685466610158621 112.247422886596 Trimmed Mean ( 9 / 34 ) 7.69880952380952 0.0680330580021343 113.162773361856 Trimmed Mean ( 10 / 34 ) 7.70243902439024 0.0676747542070834 113.815544875434 Trimmed Mean ( 11 / 34 ) 7.70625 0.0672315042091715 114.622602761114 Trimmed Mean ( 12 / 34 ) 7.71025641025641 0.0666897165511456 115.613872857643 Trimmed Mean ( 13 / 34 ) 7.71447368421053 0.0660330578393012 116.827448805787 Trimmed Mean ( 14 / 34 ) 7.71756756756757 0.0655441187281125 117.746148965421 Trimmed Mean ( 15 / 34 ) 7.72083333333333 0.0649406102823939 118.890680265543 Trimmed Mean ( 16 / 34 ) 7.72571428571429 0.0644352987081583 119.898789027203 Trimmed Mean ( 17 / 34 ) 7.72941176470588 0.0641366936132857 120.514659070370 Trimmed Mean ( 18 / 34 ) 7.73333333333333 0.063735077172308 121.335592211275 Trimmed Mean ( 19 / 34 ) 7.7375 0.0632102500729566 122.408944610557 Trimmed Mean ( 20 / 34 ) 7.74193548387097 0.0625370704276008 123.797540097978 Trimmed Mean ( 21 / 34 ) 7.745 0.0620927409169242 124.732776901607 Trimmed Mean ( 22 / 34 ) 7.74827586206897 0.0615017437528082 125.984653267903 Trimmed Mean ( 23 / 34 ) 7.75178571428571 0.0607309946450339 127.641342935252 Trimmed Mean ( 24 / 34 ) 7.7537037037037 0.0602065489148476 128.785054839633 Trimmed Mean ( 25 / 34 ) 7.75576923076923 0.0594984987540474 130.35235162537 Trimmed Mean ( 26 / 34 ) 7.758 0.058560277684186 132.478879998464 Trimmed Mean ( 27 / 34 ) 7.76041666666667 0.0583262090381031 133.051964025246 Trimmed Mean ( 28 / 34 ) 7.76304347826087 0.0579320521240705 134.002563237965 Trimmed Mean ( 29 / 34 ) 7.76590909090909 0.0573317173302136 135.455720717029 Trimmed Mean ( 30 / 34 ) 7.76904761904762 0.0564625100700964 137.596568225582 Trimmed Mean ( 31 / 34 ) 7.76904761904762 0.0557869114325169 139.262909875294 Trimmed Mean ( 32 / 34 ) 7.77894736842105 0.0555789258157637 139.962175487291 Trimmed Mean ( 33 / 34 ) 7.78333333333333 0.05513331605919 141.172958379237 Trimmed Mean ( 34 / 34 ) 7.78823529411765 0.0543581419061192 143.276333977135 Median 7.8 Midrange 7.5 Midmean - Weighted Average at Xnp 7.71509433962264 Midmean - Weighted Average at X(n+1)p 7.8328125 Midmean - Empirical Distribution Function 7.8328125 Midmean - Empirical Distribution Function - Averaging 7.8328125 Midmean - Empirical Distribution Function - Interpolation 7.758 Midmean - Closest Observation 7.8328125 Midmean - True Basic - Statistics Graphics Toolkit 7.8328125 Midmean - MS Excel (old versions) 7.8328125 Number of observations 102

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/03/t1225696290mpt0qxyer9725k9/1mgy71225695734.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/03/t1225696290mpt0qxyer9725k9/1mgy71225695734.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/03/t1225696290mpt0qxyer9725k9/2mot61225695734.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/03/t1225696290mpt0qxyer9725k9/2mot61225695734.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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Software written by Ed van Stee & Patrick Wessa

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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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