*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: Fri, 17 Dec 2010 11:20:18 +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/Dec/17/t129258505040zsgup91igas22.htm/, Retrieved Fri, 17 Dec 2010 12:24:12 +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/Dec/17/t129258505040zsgup91igas22.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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13.193 15.234 14.718 16.961 13.945 15.876 16.226 18.316 16.748 17.904 17.209 18.950 17.225 18.710 17.236 18.687 17.580 19.568 17.381 19.580 17.260 18.661 15.658 18.674 15.908 17.475 17.725 19.562 16.368 19.555 17.743 19.867 15.703 19.324 18.162 19.074 15.323 19.704 18.375 18.352 13.927 17.795 16.761 18.902 16.239 19.158 18.279 15.698 16.239 18.431 18.414 19.801 14.995 18.706 18.232 19.409 16.263 19.017 20.298 19.891 15.203 17.845 17.502 18.532 15.737 17.770 17.224 17.601 14.940 18.507 17.635 19.392 15.699 17.661 18.243 19.643 15.770 17.344 17.229 17.322 16.152 17.919 16.918 18.114 16.308 17.759 16.021 17.952 15.954 17.762 16.610 17.751 15.458 18.106 15.990 15.349 13.185 15.409 16.007 16.633 14.800 15.974 15.693

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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17.2893009708738 0.156728944024702 110.313389007131 Geometric Mean 17.2147097273669 Harmonic Mean 17.1378901107552 Quadratic Mean 17.3616085710615 Winsorized Mean ( 1 / 34 ) 17.285427184466 0.156013540271775 110.794403834147 Winsorized Mean ( 2 / 34 ) 17.299213592233 0.152556732916432 113.395280965471 Winsorized Mean ( 3 / 34 ) 17.2978155339806 0.152129619847755 113.704455130378 Winsorized Mean ( 4 / 34 ) 17.3240679611650 0.145634248496267 118.956002039651 Winsorized Mean ( 5 / 34 ) 17.3250873786408 0.144473894157563 119.918463329756 Winsorized Mean ( 6 / 34 ) 17.329572815534 0.142532071864487 121.583672985615 Winsorized Mean ( 7 / 34 ) 17.3324951456311 0.141796677360934 122.234846882289 Winsorized Mean ( 8 / 34 ) 17.3481844660194 0.139197619585338 124.629893224458 Winsorized Mean ( 9 / 34 ) 17.3502815533981 0.138695034744433 125.096630786882 Winsorized Mean ( 10 / 34 ) 17.3447475728155 0.135249822585866 128.242294453317 Winsorized Mean ( 11 / 34 ) 17.3457087378641 0.134573239935482 128.894189856617 Winsorized Mean ( 12 / 34 ) 17.3447766990291 0.132392573199646 131.010193999882 Winsorized Mean ( 13 / 34 ) 17.3300097087379 0.128510285535869 134.853094726810 Winsorized Mean ( 14 / 34 ) 17.3457766990291 0.123158803145843 140.840737778918 Winsorized Mean ( 15 / 34 ) 17.342572815534 0.121344154716512 142.920545748992 Winsorized Mean ( 16 / 34 ) 17.3329417475728 0.119847988007471 144.624386572867 Winsorized Mean ( 17 / 34 ) 17.3251844660194 0.118786343740664 145.851651969724 Winsorized Mean ( 18 / 34 ) 17.2923300970874 0.114468808863452 151.065869111254 Winsorized Mean ( 19 / 34 ) 17.2978640776699 0.113529578401425 152.364382227397 Winsorized Mean ( 20 / 34 ) 17.3005825242718 0.112221558483722 154.164518458201 Winsorized Mean ( 21 / 34 ) 17.3195436893204 0.109051829418249 158.819377737300 Winsorized Mean ( 22 / 34 ) 17.3236019417476 0.107830575256632 160.65575000892 Winsorized Mean ( 23 / 34 ) 17.3050679611650 0.103075819886971 167.886784506211 Winsorized Mean ( 24 / 34 ) 17.3039029126214 0.101800572030544 169.978444791348 Winsorized Mean ( 25 / 34 ) 17.2893398058252 0.0991927665743886 174.300409222474 Winsorized Mean ( 26 / 34 ) 17.2893398058252 0.0981592775830823 176.13556488526 Winsorized Mean ( 27 / 34 ) 17.282786407767 0.0965479866962588 179.007217023995 Winsorized Mean ( 28 / 34 ) 17.3121456310680 0.0913523025260281 189.509680132423 Winsorized Mean ( 29 / 34 ) 17.3228446601942 0.0876481430725303 197.640749169771 Winsorized Mean ( 30 / 34 ) 17.3158543689320 0.0859931093177615 201.363277898774 Winsorized Mean ( 31 / 34 ) 17.3050194174757 0.0848107757950262 204.04269687733 Winsorized Mean ( 32 / 34 ) 17.3090582524272 0.0835231880622272 207.236560936005 Winsorized Mean ( 33 / 34 ) 17.3010485436893 0.0793452412552243 218.047714897460 Winsorized Mean ( 34 / 34 ) 17.3050097087379 0.0752428753460289 229.988681707805 Trimmed Mean ( 1 / 34 ) 17.2893009708738 0.151611653060673 114.036755235133 Trimmed Mean ( 2 / 34 ) 17.3001485148515 0.146615475207151 117.996742774992 Trimmed Mean ( 3 / 34 ) 17.3240927835052 0.143050607801169 121.104642963730 Trimmed Mean ( 4 / 34 ) 17.3240927835052 0.139184147755782 124.468864183461 Trimmed Mean ( 5 / 34 ) 17.3362258064516 0.136976802744807 126.563224276373 Trimmed Mean ( 6 / 34 ) 17.3387472527473 0.134781041258179 128.643814373968 Trimmed Mean ( 7 / 34 ) 17.3405168539326 0.132741135940122 130.634085139626 Trimmed Mean ( 8 / 34 ) 17.3405168539326 0.130560338871470 132.816114019155 Trimmed Mean ( 9 / 34 ) 17.3409176470588 0.128574585937322 134.870491867750 Trimmed Mean ( 10 / 34 ) 17.3396265060241 0.126373132388683 137.209754781522 Trimmed Mean ( 11 / 34 ) 17.3389753086420 0.124439387267418 139.336713956819 Trimmed Mean ( 12 / 34 ) 17.3381772151899 0.122301367099934 141.766013138861 Trimmed Mean ( 13 / 34 ) 17.3374415584416 0.120167079364196 144.277797631215 Trimmed Mean ( 14 / 34 ) 17.3382266666667 0.118288731459892 146.575472174588 Trimmed Mean ( 15 / 34 ) 17.3382266666667 0.116895348418182 148.322639876489 Trimmed Mean ( 16 / 34 ) 17.3374657534247 0.115495267999664 150.114078729832 Trimmed Mean ( 17 / 34 ) 17.3373478260870 0.114028301152851 152.044252618014 Trimmed Mean ( 18 / 34 ) 17.3384477611940 0.112408674995276 154.244748120398 Trimmed Mean ( 19 / 34 ) 17.3425076923077 0.111068016935996 156.143128964853 Trimmed Mean ( 20 / 34 ) 17.3463492063492 0.109554441756212 158.335426006273 Trimmed Mean ( 21 / 34 ) 17.3502131147541 0.107882457577083 160.825156419497 Trimmed Mean ( 22 / 34 ) 17.3527627118644 0.106305123463939 163.235431618222 Trimmed Mean ( 23 / 34 ) 17.3551578947368 0.104521998828087 166.043111395926 Trimmed Mean ( 24 / 34 ) 17.3592363636364 0.103023321094388 168.498124300731 Trimmed Mean ( 25 / 34 ) 17.3637169811321 0.101308017932232 171.395288700123 Trimmed Mean ( 26 / 34 ) 17.3697254901961 0.0995236934187577 174.528545852000 Trimmed Mean ( 27 / 34 ) 17.3762244897959 0.097389529538322 178.419842175729 Trimmed Mean ( 28 / 34 ) 17.3838085106383 0.0949004378146267 183.179434267678 Trimmed Mean ( 29 / 34 ) 17.3896666666667 0.0927004571049935 187.589869669908 Trimmed Mean ( 30 / 34 ) 17.3896666666667 0.0905298740229013 192.087604830507 Trimmed Mean ( 31 / 34 ) 17.3951860465116 0.0879358684166702 197.816731212425 Trimmed Mean ( 32 / 34 ) 17.4018292682927 0.0846492436243503 205.575720741430 Trimmed Mean ( 33 / 34 ) 17.4188648648649 0.0804690748999795 216.466572860642 Trimmed Mean ( 34 / 34 ) 17.4293714285714 0.0757867872313344 229.979024910627 Median 17.502 Midrange 16.7415 Midmean - Weighted Average at Xnp 17.3431923076923 Midmean - Weighted Average at X(n+1)p 17.3637169811321 Midmean - Empirical Distribution Function 17.3637169811321 Midmean - Empirical Distribution Function - Averaging 17.3637169811321 Midmean - Empirical Distribution Function - Interpolation 17.3697254901961 Midmean - Closest Observation 17.3431923076923 Midmean - True Basic - Statistics Graphics Toolkit 17.3637169811321 Midmean - MS Excel (old versions) 17.3637169811321 Number of observations 103

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t129258505040zsgup91igas22/1lpdo1292584806.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t129258505040zsgup91igas22/1lpdo1292584806.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t129258505040zsgup91igas22/2lpdo1292584806.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t129258505040zsgup91igas22/2lpdo1292584806.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

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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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