*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: Wed, 21 Oct 2009 09:49:56 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402303nupb9b4nqvw7hw.htm/, Retrieved Wed, 21 Oct 2009 17:50:31 +0200

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/Oct/21/t12561402303nupb9b4nqvw7hw.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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208152.89004464300000 205007.89004464300000 200287.89004464300000 198085.89004464300000 195183.89004464300000 191392.89004464300000 213765.89004464300000 225777.89004464300000 230576.89004464300000 229258.89004464300000 216225.89004464300000 216710.89004464300000 220203.89004464300000 220112.89004464300000 218441.89004464300000 214909.89004464300000 210702.89004464300000 209670.89004464300000 237038.89004464300000 242078.89004464300000 241875.89004464300000 242618.89004464300000 238542.89004464300000 240334.89004464300000 244749.89004464300000 244573.89004464300000 241569.89004464300000 240538.89004464300000 236086.89004464300000 236994.89004464300000 264576.89004464300000 270346.89004464300000 269642.89004464300000 267034.89004464300000 258110.89004464300000 262810.89004464300000 267410.89004464300000 267363.89004464300000 264774.89004464300000 258860.89004464300000 254841.89004464300000 254865.89004464300000 277264.89004464300000 285348.89004464300000 286599.89004 etc...

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 253589.132763090 2483.86831420206 102.094435245676 Geometric Mean 252292.904156377 Harmonic Mean 250939.912167493 Quadratic Mean 254826.897401688 Winsorized Mean ( 1 / 34 ) 253621.958005808 2474.47691104556 102.495180647551 Winsorized Mean ( 2 / 34 ) 253678.307520371 2461.71490480022 103.049425839569 Winsorized Mean ( 3 / 34 ) 253709.996840760 2442.80332777998 103.860181438074 Winsorized Mean ( 4 / 34 ) 253875.433733963 2402.17608362824 105.685605424274 Winsorized Mean ( 5 / 34 ) 253983.249267944 2365.74621737430 107.358620042447 Winsorized Mean ( 6 / 34 ) 253977.54053008 2335.37750668821 108.752242326015 Winsorized Mean ( 7 / 34 ) 253984.67645241 2313.45709561010 109.785773392711 Winsorized Mean ( 8 / 34 ) 254171.550238818 2263.63063323890 112.284904836766 Winsorized Mean ( 9 / 34 ) 254162.200724255 2231.09466234689 113.918160898158 Winsorized Mean ( 10 / 34 ) 254065.792957264 2179.21900073682 116.585709316669 Winsorized Mean ( 11 / 34 ) 254076.365772798 2165.07420028864 117.352267067302 Winsorized Mean ( 12 / 34 ) 254140.67645241 2113.71540352321 120.234103431711 Winsorized Mean ( 13 / 34 ) 254216.657034934 2062.19898902178 123.274552256242 Winsorized Mean ( 14 / 34 ) 254199.394899012 2056.51380076347 123.606948226967 Winsorized Mean ( 15 / 34 ) 254732.987132022 1904.52537328593 133.751427366139 Winsorized Mean ( 16 / 34 ) 254676.288102895 1888.09888764995 134.885036884843 Winsorized Mean ( 17 / 34 ) 254744.123054352 1849.21527165501 137.757959800083 Winsorized Mean ( 18 / 34 ) 255143.093928138 1784.87649966266 142.947197734051 Winsorized Mean ( 19 / 34 ) 255381.608491245 1750.13902998996 145.920754931515 Winsorized Mean ( 20 / 34 ) 256260.443442701 1620.04697857161 158.180871809436 Winsorized Mean ( 21 / 34 ) 256376.249267944 1597.92303895604 160.443427510402 Winsorized Mean ( 22 / 34 ) 256255.996840760 1535.31856942948 166.907378014703 Winsorized Mean ( 23 / 34 ) 256225.851209692 1529.28080722437 167.546633685110 Winsorized Mean ( 24 / 34 ) 256075.326937847 1509.06219194461 169.691698794642 Winsorized Mean ( 25 / 34 ) 255982.123054352 1497.75147908136 170.910946595330 Winsorized Mean ( 26 / 34 ) 256119.191015517 1425.57293339637 179.660531576819 Winsorized Mean ( 27 / 34 ) 256312.909462119 1337.72189104905 191.604033078293 Winsorized Mean ( 28 / 34 ) 256182.967714546 1310.08290737406 195.547141537814 Winsorized Mean ( 29 / 34 ) 256202.394899012 1245.96447801023 205.625761745759 Winsorized Mean ( 30 / 34 ) 256233.559947556 1229.28919481873 208.440423154733 Winsorized Mean ( 31 / 34 ) 256197.142471828 1211.51357379342 211.468652117233 Winsorized Mean ( 32 / 34 ) 256308.67645241 1186.23922650679 216.068285995888 Winsorized Mean ( 33 / 34 ) 256369.550238818 1135.89022271053 225.699231416089 Winsorized Mean ( 34 / 34 ) 256523.705578624 1069.02856824123 239.959635504089 Trimmed Mean ( 1 / 34 ) 253589.132763090 2425.40011564454 104.555586984335 Trimmed Mean ( 2 / 34 ) 253817.622717910 2369.91305632685 107.099972313459 Trimmed Mean ( 3 / 34 ) 254203.240560107 2314.74448038202 109.819136718777 Trimmed Mean ( 4 / 34 ) 254203.240560107 2260.14287061388 112.472199817644 Trimmed Mean ( 5 / 34 ) 254521.621227439 2211.79544140055 115.074665795618 Trimmed Mean ( 6 / 34 ) 254643.494440247 2167.02784281171 117.508178441237 Trimmed Mean ( 7 / 34 ) 254771.946224418 2123.34648275843 119.986044808592 Trimmed Mean ( 8 / 34 ) 254771.946224418 2078.14655222521 122.595755314570 Trimmed Mean ( 9 / 34 ) 255016.207691702 2036.58478915577 125.217574563843 Trimmed Mean ( 10 / 34 ) 255133.962333800 1994.87585068552 127.894656825950 Trimmed Mean ( 11 / 34 ) 255269.791279211 1955.94241609084 130.509870423177 Trimmed Mean ( 12 / 34 ) 255411.244475023 1913.08834885426 133.507291823709 Trimmed Mean ( 13 / 34 ) 255552.87705763 1871.86766068804 136.522940389759 Trimmed Mean ( 14 / 34 ) 255694.036711310 1832.12554860071 139.561416468755 Trimmed Mean ( 15 / 34 ) 255694.036711310 1786.15300944605 143.153489851695 Trimmed Mean ( 16 / 34 ) 255844.670866561 1756.65031630097 145.643483220553 Trimmed Mean ( 17 / 34 ) 256071.223377976 1723.83550259628 148.547366029012 Trimmed Mean ( 18 / 34 ) 256191.233328225 1690.55735252237 151.542467900292 Trimmed Mean ( 19 / 34 ) 256283.505429258 1660.76337719869 154.316688908174 Trimmed Mean ( 20 / 34 ) 256361.112266865 1630.11128989155 157.266018496149 Trimmed Mean ( 21 / 34 ) 256369.611356118 1612.74789412885 158.964468215661 Trimmed Mean ( 22 / 34 ) 256369.059536168 1594.06031199859 160.827703698827 Trimmed Mean ( 23 / 34 ) 256378.346184994 1579.64295283458 162.301452821941 Trimmed Mean ( 24 / 34 ) 256390.762771916 1561.62072635004 164.182479423909 Trimmed Mean ( 25 / 34 ) 256416.305138983 1541.31140994737 166.362425843418 Trimmed Mean ( 26 / 34 ) 256451.380240721 1516.65396349928 169.090238388345 Trimmed Mean ( 27 / 34 ) 256478.236983419 1496.81483381448 171.349342075807 Trimmed Mean ( 28 / 34 ) 256491.65600209 1485.09256018446 172.710888788125 Trimmed Mean ( 29 / 34 ) 256516.890044643 1472.68410726740 174.183240505403 Trimmed Mean ( 30 / 34 ) 256516.890044643 1465.64766240331 175.019478845289 Trimmed Mean ( 31 / 34 ) 256542.866788829 1456.53822268432 176.131915244925 Trimmed Mean ( 32 / 34 ) 256568.768093423 1444.79427057032 177.581523764034 Trimmed Mean ( 33 / 34 ) 256625.808963562 1431.08951826112 179.321982090527 Trimmed Mean ( 34 / 34 ) 256648.661473214 1420.03476764498 180.734068855826 Median 255762.890044643 Midrange 242050.390044643 Midmean - Weighted Average at Xnp 256078.909275412 Midmean - Weighted Average at X(n+1)p 256416.305138982 Midmean - Empirical Distribution Function 256416.305138982 Midmean - Empirical Distribution Function - Averaging 256416.305138982 Midmean - Empirical Distribution Function - Interpolation 256451.380240721 Midmean - Closest Observation 256078.909275412 Midmean - True Basic - Statistics Graphics Toolkit 256416.305138982 Midmean - MS Excel (old versions) 256416.305138982 Number of observations 103

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402303nupb9b4nqvw7hw/16qta1256140191.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402303nupb9b4nqvw7hw/16qta1256140191.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402303nupb9b4nqvw7hw/227o11256140191.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402303nupb9b4nqvw7hw/227o11256140191.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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