Central Tendency - Dollar

*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, 20 Oct 2008 17:50:48 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/21/t1224546864pgvw0k3q09zwist.htm/, Retrieved Mon, 20 Oct 2008 23:54:26 +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/Oct/21/t1224546864pgvw0k3q09zwist.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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0,8721 0,8552 0,8564 0,8973 0,9383 0,9217 0,9095 0,892 0,8742 0,8532 0,8607 0,9005 0,9111 0,9059 0,8883 0,8924 0,8833 0,87 0,8758 0,8858 0,917 0,9554 0,9922 0,9778 0,9808 0,9811 1,0014 1,0183 1,0622 1,0773 1,0807 1,0848 1,1582 1,1663 1,1372 1,1139 1,1222 1,1692 1,1702 1,2286 1,2613 1,2646 1,2262 1,1985 1,2007 1,2138 1,2266 1,2176 1,2218 1,249 1,2991 1,3408 1,3119 1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,202 1,2271 1,277 1,265 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,457 1,4718 1,4748 1,5527 1,575 1,5557 1,5553

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 1.16698510638298 0.0201490262798525 57.9176924072938 Geometric Mean 1.1503115799852 Harmonic Mean 1.13326120960729 Quadratic Mean 1.18305142817298 Winsorized Mean ( 1 / 31 ) 1.16680106382979 0.0201017613908596 58.0447176315771 Winsorized Mean ( 2 / 31 ) 1.16681808510638 0.0200957434312778 58.0629469666846 Winsorized Mean ( 3 / 31 ) 1.16687234042553 0.0200558761561857 58.1810702927403 Winsorized Mean ( 4 / 31 ) 1.16395319148936 0.0193610992939658 60.1181355364531 Winsorized Mean ( 5 / 31 ) 1.16390531914894 0.0193154586288563 60.2577107545415 Winsorized Mean ( 6 / 31 ) 1.16382234042553 0.0192566787835354 60.4373346779098 Winsorized Mean ( 7 / 31 ) 1.16309255319149 0.0190949567126644 60.9109814017065 Winsorized Mean ( 8 / 31 ) 1.16081170212766 0.0185282265547516 62.6509881394972 Winsorized Mean ( 9 / 31 ) 1.15788191489362 0.0180294227462678 64.2217962931347 Winsorized Mean ( 10 / 31 ) 1.15623297872340 0.0177287951381196 65.2177979222813 Winsorized Mean ( 11 / 31 ) 1.15556595744681 0.0175169710534439 65.9683659875444 Winsorized Mean ( 12 / 31 ) 1.15426382978723 0.0173400642597245 66.5662948244215 Winsorized Mean ( 13 / 31 ) 1.15487234042553 0.0172220859198964 67.0576343537648 Winsorized Mean ( 14 / 31 ) 1.15397872340426 0.0169800300481319 67.9609352947649 Winsorized Mean ( 15 / 31 ) 1.15466489361702 0.0168214688968786 68.6423344296217 Winsorized Mean ( 16 / 31 ) 1.15245212765957 0.0163966071904903 70.2860118725032 Winsorized Mean ( 17 / 31 ) 1.15221702127660 0.0162917307567608 70.7240402188974 Winsorized Mean ( 18 / 31 ) 1.15311702127660 0.0160870311327614 71.6799148183573 Winsorized Mean ( 19 / 31 ) 1.15240957446809 0.0157545390298735 73.1477812383403 Winsorized Mean ( 20 / 31 ) 1.15498404255319 0.0150997833616413 76.490106837377 Winsorized Mean ( 21 / 31 ) 1.15746382978723 0.0143711844409336 80.5406008491837 Winsorized Mean ( 22 / 31 ) 1.16235531914894 0.0135526406700201 85.7659660172495 Winsorized Mean ( 23 / 31 ) 1.16289361702128 0.0134240064181695 86.6279097905744 Winsorized Mean ( 24 / 31 ) 1.16161702127660 0.0132665034414798 87.5601492435918 Winsorized Mean ( 25 / 31 ) 1.16305319148936 0.0126749144452096 91.7602400013777 Winsorized Mean ( 26 / 31 ) 1.16366170212766 0.0121033221667793 96.1439913845831 Winsorized Mean ( 27 / 31 ) 1.16733829787234 0.0112856516216090 103.435613379842 Winsorized Mean ( 28 / 31 ) 1.17913404255319 0.00933643261854888 126.293852344693 Winsorized Mean ( 29 / 31 ) 1.18277446808511 0.00860555703264311 137.44310375244 Winsorized Mean ( 30 / 31 ) 1.18354042553192 0.00842831810879845 140.424270922617 Winsorized Mean ( 31 / 31 ) 1.18377127659574 0.00813018581279569 145.601995311431 Trimmed Mean ( 1 / 31 ) 1.16596086956522 0.0198057694131321 58.8697588689554 Trimmed Mean ( 2 / 31 ) 1.16508333333333 0.0194671004678206 59.8488375430761 Trimmed Mean ( 3 / 31 ) 1.16508333333333 0.0190826164550835 61.0546953074121 Trimmed Mean ( 4 / 31 ) 1.16316744186047 0.0186580125448954 62.3414438735971 Trimmed Mean ( 5 / 31 ) 1.16294761904762 0.0184049153176287 63.1867954281603 Trimmed Mean ( 6 / 31 ) 1.16294761904762 0.0181238152090219 64.166821700362 Trimmed Mean ( 7 / 31 ) 1.16251375 0.0178115489969316 65.2674144287095 Trimmed Mean ( 8 / 31 ) 1.16241410256410 0.0174845937345748 66.4821911341007 Trimmed Mean ( 9 / 31 ) 1.16266184210526 0.0172211736225268 67.513507940272 Trimmed Mean ( 10 / 31 ) 1.16333648648649 0.0170058638725239 68.4079618187509 Trimmed Mean ( 11 / 31 ) 1.16426388888889 0.0168021168865227 69.2926907217726 Trimmed Mean ( 12 / 31 ) 1.16426388888889 0.0165927299161172 70.1671090154968 Trimmed Mean ( 13 / 31 ) 1.1666 0.0163672479120414 71.2764910918061 Trimmed Mean ( 14 / 31 ) 1.16788484848485 0.0161130952321402 72.4804782482332 Trimmed Mean ( 15 / 31 ) 1.16934375 0.0158420123260491 73.812829199561 Trimmed Mean ( 16 / 31 ) 1.17082741935484 0.0155370295419555 75.3572242488944 Trimmed Mean ( 17 / 31 ) 1.17262666666667 0.0152286035629779 77.0015886103588 Trimmed Mean ( 18 / 31 ) 1.17457241379310 0.0148621733664851 79.0309993585338 Trimmed Mean ( 19 / 31 ) 1.17657321428571 0.0144430942225426 81.4626835605168 Trimmed Mean ( 20 / 31 ) 1.17878703703704 0.0139751051611365 84.3490638134973 Trimmed Mean ( 21 / 31 ) 1.18093846153846 0.0135141789552468 87.3851430744869 Trimmed Mean ( 22 / 31 ) 1.18304 0.0130734721275332 90.4916451008049 Trimmed Mean ( 23 / 31 ) 1.18488125 0.0126813258502952 93.4351237392435 Trimmed Mean ( 24 / 31 ) 1.18488125 0.0121966639207634 97.1479789635655 Trimmed Mean ( 25 / 31 ) 1.18907954545455 0.0115852445792641 102.637414110603 Trimmed Mean ( 26 / 31 ) 1.19140952380952 0.0109147694849541 109.155720187391 Trimmed Mean ( 27 / 31 ) 1.1939175 0.0101509768934337 117.616019870196 Trimmed Mean ( 28 / 31 ) 1.19635263157895 0.00934469120541919 128.024843762109 Trimmed Mean ( 29 / 31 ) 1.19795833333333 0.00885768554725038 135.245073551432 Trimmed Mean ( 30 / 31 ) 1.19940588235294 0.00839766110080241 142.826183142630 Trimmed Mean ( 31 / 31 ) 1.19940588235294 0.00778981300680238 153.971074954633 Median 1.207 Midrange 1.2141 Midmean - Weighted Average at Xnp 1.18245106382979 Midmean - Weighted Average at X(n+1)p 1.18488125 Midmean - Empirical Distribution Function 1.18488125 Midmean - Empirical Distribution Function - Averaging 1.18488125 Midmean - Empirical Distribution Function - Interpolation 1.18683478260870 Midmean - Closest Observation 1.18488125 Midmean - True Basic - Statistics Graphics Toolkit 1.18488125 Midmean - MS Excel (old versions) 1.18488125 Number of observations 94

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224546864pgvw0k3q09zwist/1858v1224546646.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224546864pgvw0k3q09zwist/1858v1224546646.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224546864pgvw0k3q09zwist/2dmzr1224546646.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t1224546864pgvw0k3q09zwist/2dmzr1224546646.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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