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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 18 Nov 2007 15:13:30 -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/18/t1195423599fwsm2zum4to83sz.htm/, Retrieved Sun, 18 Nov 2007 23:06:42 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
105.3 103 103.8 103.4 105.8 101.4 97 94.3 96.6 97.1 95.7 96.9 97.4 95.3 93.6 91.5 93.1 91.7 94.3 93.9 90.9 88.3 91.3 91.7 92.4 92 95.6 95.8 96.4 99 107 109.7 116.2 115.9 113.8 112.6 113.7 115.9 110.3 111.3 113.4 108.2 104.8 106 110.9 115 118.4 121.4 128.8 131.7 141.7 142.9 139.4 134.7 125 113.6 111.5 108.5 112.3 116.6 115.5 120.1 132.9 128.1 129.3 132.5 131 124.9 120.8 122 122.1 127.4 135.2 137.3 135 136 138.4 134.7 138.4 133.9 133.6 141.2 151.8 155.4 156.6 161.6 160.7 156 159.5 168.7 169.9 169.9 185.9
 
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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.1612903225812.3206403737780651.348451776086
Geometric Mean117.203849345169
Harmonic Mean115.369174339074
Quadratic Mean121.222387832562
Winsorized Mean ( 1 / 31 )119.0172043010752.2688087791676152.4580147052942
Winsorized Mean ( 2 / 31 )119.0258064516132.2676577924254752.4884340349714
Winsorized Mean ( 3 / 31 )118.9935483870972.2574497760685152.7114931408714
Winsorized Mean ( 4 / 31 )118.6967741935482.1871407146944254.2702960975844
Winsorized Mean ( 5 / 31 )118.6483870967742.1769021081482054.5033176515701
Winsorized Mean ( 6 / 31 )118.5903225806452.1581997678077954.948723630484
Winsorized Mean ( 7 / 31 )118.4021505376342.1101953021947856.1095697703839
Winsorized Mean ( 8 / 31 )118.4107526881722.0920855683181356.5993831616384
Winsorized Mean ( 9 / 31 )118.4010752688172.0744615182061457.0755708070221
Winsorized Mean ( 10 / 31 )118.0462365591401.9971306902107459.1079177430713
Winsorized Mean ( 11 / 31 )117.0408602150541.8117153145358364.6022359451326
Winsorized Mean ( 12 / 31 )116.8860215053761.7880234982748465.371636121199
Winsorized Mean ( 13 / 31 )116.9559139784951.7585611484058666.5065949424138
Winsorized Mean ( 14 / 31 )116.7301075268821.7127050369477968.1554062192204
Winsorized Mean ( 15 / 31 )116.5849462365591.6876029196440869.0831622056849
Winsorized Mean ( 16 / 31 )116.6021505376341.6852916634431669.1881132903776
Winsorized Mean ( 17 / 31 )116.5107526881721.6426671762715670.9277901033014
Winsorized Mean ( 18 / 31 )116.2978494623661.6033916676426572.5324022878014
Winsorized Mean ( 19 / 31 )116.1956989247311.5735705119560073.8420668421755
Winsorized Mean ( 20 / 31 )116.1741935483871.5650705340627374.2293660380998
Winsorized Mean ( 21 / 31 )116.1290322580651.5532330520833274.7660063647906
Winsorized Mean ( 22 / 31 )116.21.5438108801471175.2682867404895
Winsorized Mean ( 23 / 31 )116.3978494623661.4663691141396979.378274092097
Winsorized Mean ( 24 / 31 )116.9397849462371.3783142638295584.842613919795
Winsorized Mean ( 25 / 31 )117.1817204301081.301758211758590.0180381975933
Winsorized Mean ( 26 / 31 )117.1817204301081.2739147094115091.9855305574118
Winsorized Mean ( 27 / 31 )117.0655913978491.2300815970681295.1689641377231
Winsorized Mean ( 28 / 31 )117.1559139784951.16791037264670100.312418420429
Winsorized Mean ( 29 / 31 )116.7817204301081.08245814207824107.885668637399
Winsorized Mean ( 30 / 31 )116.7817204301081.04370365160850111.891646877089
Winsorized Mean ( 31 / 31 )116.6150537634411.00700439191706115.803917738072
Trimmed Mean ( 1 / 31 )118.7670329670332.2280436262232953.305523989381
Trimmed Mean ( 2 / 31 )118.5056179775282.1811298153891754.3322167903078
Trimmed Mean ( 3 / 31 )118.2275862068972.1276785496967855.566469955598
Trimmed Mean ( 4 / 31 )117.9482352941182.070287069070556.9719229068426
Trimmed Mean ( 5 / 31 )117.7385542168672.0284697394255658.0430419682817
Trimmed Mean ( 6 / 31 )117.5296296296301.9828488705262159.2731152518143
Trimmed Mean ( 7 / 31 )117.3215189873421.9345277210956160.6460779589643
Trimmed Mean ( 8 / 31 )117.1350649350651.8895553895498661.9908077756692
Trimmed Mean ( 9 / 31 )116.9373333333331.8406322585218163.5310680837704
Trimmed Mean ( 10 / 31 )116.7301369863011.7865477846399165.3383794096663
Trimmed Mean ( 11 / 31 )116.5577464788731.7385806347791667.0418985160725
Trimmed Mean ( 12 / 31 )116.4985507246381.717039489002267.8484982266406
Trimmed Mean ( 13 / 31 )116.4985507246381.6950353563128668.7292747556915
Trimmed Mean ( 14 / 31 )116.3984615384621.6731038238332569.5703756577287
Trimmed Mean ( 15 / 31 )116.3634920634921.6538110986326670.3608121627064
Trimmed Mean ( 16 / 31 )116.3409836065571.633883665035571.205181920972
Trimmed Mean ( 17 / 31 )116.3152542372881.6092656419155072.2784674000988
Trimmed Mean ( 18 / 31 )116.2964912280701.5855984949443273.3454853791056
Trimmed Mean ( 19 / 31 )116.2963636363641.562276168234774.4403364789038
Trimmed Mean ( 20 / 31 )116.3056603773581.5375475144447375.6436203009706
Trimmed Mean ( 21 / 31 )116.3176470588241.5072548892068977.17184922852
Trimmed Mean ( 22 / 31 )116.3346938775511.4704994495496879.1123681910773
Trimmed Mean ( 23 / 31 )116.3468085106381.4249782154682381.6481313522455
Trimmed Mean ( 24 / 31 )116.3422222222221.3818904080598384.1906286805813
Trimmed Mean ( 25 / 31 )116.2883720930231.3435016861755986.556178745149
Trimmed Mean ( 26 / 31 )116.2883720930231.3082822019914588.8863059636605
Trimmed Mean ( 27 / 31 )116.1179487179491.2665203683263891.6826540037337
Trimmed Mean ( 28 / 31 )116.0297297297301.2199595379549495.1094902083677
Trimmed Mean ( 29 / 31 )115.9228571428571.1710089430819598.9939981480947
Trimmed Mean ( 30 / 31 )115.8393939393941.12637911591258102.842277793425
Trimmed Mean ( 31 / 31 )115.7451612903231.07300040294692107.870566471771
Median115
Midrange137.1
Midmean - Weighted Average at Xnp115.965217391304
Midmean - Weighted Average at X(n+1)p116.346808510638
Midmean - Empirical Distribution Function116.346808510638
Midmean - Empirical Distribution Function - Averaging116.346808510638
Midmean - Empirical Distribution Function - Interpolation116.346808510638
Midmean - Closest Observation115.952083333333
Midmean - True Basic - Statistics Graphics Toolkit116.346808510638
Midmean - MS Excel (old versions)116.346808510638
Number of observations93
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423599fwsm2zum4to83sz/174621195424004.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423599fwsm2zum4to83sz/174621195424004.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423599fwsm2zum4to83sz/2ckdv1195424004.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195423599fwsm2zum4to83sz/2ckdv1195424004.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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Creative Commons License

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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