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Paper_Cen-ten.a

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 30 Nov 2007 05:28:07 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/30/t1196425062nkg9s17mforeb7j.htm/, Retrieved Fri, 30 Nov 2007 13:17:42 +0100
 
User-defined keywords:
 
Dataseries X:
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48527 44446 46380 48950 38883 42928 37107 30186 32602 39892 32194 21629 59968 45694 55756 48554 41052 49822 39191 31994 35735 38930 33658 23849 58972 59249 63955 53785 52760 44795 37348 32370 32717 40974 33591 21124 58608 46865 51378 46235 47206 45382 41227 33795 31295 42625 33625 21538 56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean40724.13541666671045.0058406220338.9702467044833
Geometric Mean39373.8834760349
Harmonic Mean37935.1008938386
Quadratic Mean41978.5509527634
Winsorized Mean ( 1 / 32 )40725.1251033.4901300730139.4054319581387
Winsorized Mean ( 2 / 32 )40697.10416666671026.4774034308839.6473454073527
Winsorized Mean ( 3 / 32 )40687.57291666671019.5266550623539.9082973599923
Winsorized Mean ( 4 / 32 )40679.82291666671016.5788438838340.0163973128239
Winsorized Mean ( 5 / 32 )40776.4895833333991.17821735119341.1394125390524
Winsorized Mean ( 6 / 32 )40717.6145833333952.63938444283442.7418971420625
Winsorized Mean ( 7 / 32 )40765.375928.16252077268543.9205140130667
Winsorized Mean ( 8 / 32 )40604.2083333333901.0292001368645.0642535526772
Winsorized Mean ( 9 / 32 )40700.2083333333883.81567597804746.0505617172876
Winsorized Mean ( 10 / 32 )40835.9375857.2541915105447.6357396725518
Winsorized Mean ( 11 / 32 )40891.5104166667836.31448037599948.8948970467213
Winsorized Mean ( 12 / 32 )40878.7604166667823.82890987816849.6204490113269
Winsorized Mean ( 13 / 32 )40862.2395833333816.66403294573450.0355567710529
Winsorized Mean ( 14 / 32 )40990.4270833333795.17159901109351.5491588662254
Winsorized Mean ( 15 / 32 )40868.5520833333769.10357278665753.137904346558
Winsorized Mean ( 16 / 32 )40930.5520833333758.34348034513553.9736321919787
Winsorized Mean ( 17 / 32 )40798.625735.91358504928355.439423634594
Winsorized Mean ( 18 / 32 )40751.375719.49096730154256.6391752669786
Winsorized Mean ( 19 / 32 )40730.3958333333707.55076478949857.5653336272641
Winsorized Mean ( 20 / 32 )40729.3541666667694.9185084085558.6102595827271
Winsorized Mean ( 21 / 32 )40615.6041666667673.4487627652160.3098652968003
Winsorized Mean ( 22 / 32 )40535.8541666667661.41561086993561.2865095720245
Winsorized Mean ( 23 / 32 )40685.3541666667642.72068501239363.3017656276025
Winsorized Mean ( 24 / 32 )40735.8541666667636.09319475035464.0407011155876
Winsorized Mean ( 25 / 32 )40737.6770833333634.13765653292464.2410629043258
Winsorized Mean ( 26 / 32 )40457.6354166667596.51243500365567.8236245258136
Winsorized Mean ( 27 / 32 )40398.5729166667586.24604602429668.910610469162
Winsorized Mean ( 28 / 32 )40326.2395833333570.90718700337270.6353685876705
Winsorized Mean ( 29 / 32 )40193.9270833333551.71113509586772.8532098166717
Winsorized Mean ( 30 / 32 )40349.5520833333522.29102802355577.2549209509178
Winsorized Mean ( 31 / 32 )40439.96875470.75460290049385.9045636534075
Winsorized Mean ( 32 / 32 )40467.6354166667459.86334452781287.9992630380637
Trimmed Mean ( 1 / 32 )40714.62765957451010.1719073066840.3046524706156
Trimmed Mean ( 2 / 32 )40703.6739130435983.64491082146841.3804549438992
Trimmed Mean ( 3 / 32 )40707.1777777778957.64945858989742.5073887032919
Trimmed Mean ( 4 / 32 )40714.3068181818930.91073685344143.7359944475447
Trimmed Mean ( 5 / 32 )40723.9302325581901.21133920857445.1879913853737
Trimmed Mean ( 6 / 32 )40711.9166666667874.54882904922846.5519080403171
Trimmed Mean ( 7 / 32 )40710.8048780488853.79040985969847.6824340118071
Trimmed Mean ( 8 / 32 )40701.45835.4275731813348.7193041103585
Trimmed Mean ( 9 / 32 )40716.4102564103819.82429008417449.6648010419766
Trimmed Mean ( 10 / 32 )40718.6842105263804.99298377906250.5826572790378
Trimmed Mean ( 11 / 32 )40703.472972973792.49089757600851.361439099771
Trimmed Mean ( 12 / 32 )40680.6805555556781.34514765238952.0649301755873
Trimmed Mean ( 13 / 32 )40658.0428571429770.14599928963352.7926430763063
Trimmed Mean ( 14 / 32 )40635.8676470588757.88744873158453.6172854096843
Trimmed Mean ( 15 / 32 )40599.0303030303746.55569520731654.3817836548097
Trimmed Mean ( 16 / 32 )40572.078125737.03355450657455.0478032878191
Trimmed Mean ( 17 / 32 )40537.3870967742726.928568360155.7652964282636
Trimmed Mean ( 18 / 32 )40512.8718.02962373774856.4221846295256
Trimmed Mean ( 19 / 32 )40490.8620689655709.43091481603757.0751305353887
Trimmed Mean ( 20 / 32 )40469.25700.38009080135157.7818395061693
Trimmed Mean ( 21 / 32 )40446.1296296296690.81525736533458.5484023382534
Trimmed Mean ( 22 / 32 )40431.2307692308682.06755017228959.2774583089577
Trimmed Mean ( 23 / 32 )40422.1672.62189290590860.0963192342218
Trimmed Mean ( 24 / 32 )40399.2083333333663.28104298580660.9081305135354
Trimmed Mean ( 25 / 32 )40369.9347826087651.87089457231261.9293407923898
Trimmed Mean ( 26 / 32 )40337.8409090909636.92726786409363.3319421923355
Trimmed Mean ( 27 / 32 )40327.3095238095624.78314982618664.5460901674901
Trimmed Mean ( 28 / 32 )40320.975610.26310371282166.0714612348158
Trimmed Mean ( 29 / 32 )40320.5593.68669116702367.9154520387532
Trimmed Mean ( 30 / 32 )40332.1388888889575.19551286521970.1190082098913
Trimmed Mean ( 31 / 32 )40330.5556.7908049219572.433847045397
Trimmed Mean ( 32 / 32 )40319.90625544.23446967516774.0855430823141
Median40124.5
Midrange41171
Midmean - Weighted Average at Xnp40255.9387755102
Midmean - Weighted Average at X(n+1)p40399.2083333333
Midmean - Empirical Distribution Function40255.9387755102
Midmean - Empirical Distribution Function - Averaging40399.2083333333
Midmean - Empirical Distribution Function - Interpolation40399.2083333333
Midmean - Closest Observation40255.9387755102
Midmean - True Basic - Statistics Graphics Toolkit40399.2083333333
Midmean - MS Excel (old versions)40422.1
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196425062nkg9s17mforeb7j/19d171196425681.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196425062nkg9s17mforeb7j/19d171196425681.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196425062nkg9s17mforeb7j/2t88o1196425682.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196425062nkg9s17mforeb7j/2t88o1196425682.ps (open in new window)


 
Parameters:
 
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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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:

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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