*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: Tue, 21 Dec 2010 15:40:09 +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/21/t1292945876xaiylw7p0ls979j.htm/, Retrieved Tue, 21 Dec 2010 16:37:58 +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/21/t1292945876xaiylw7p0ls979j.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:

» Textbox « » Textfile « » CSV «

196 178 201 181 193 181 115 104 200 244 172 182 192 183 214 120 181 199 99 74 202 185 148 193 184 183 213 189 204 206 97 86 220 205 174 216 182 213 227 209 219 221 114 97 205 215 224 189 182 201 198 173 238 258 122 101 259 243 188 173 224 215 196 159 187 208 131 93 210 228 176 195 188 188 190 188 176 225 93 79 235 247 195 197 211 156 209 180 185 303 129 85 249 231 212 240 234 217 287 221 208 241 156 96 320 242 227 200

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 189.138888888889 4.63773217930187 40.7826242604118 Geometric Mean 181.775976318340 Harmonic Mean 172.772650026599 Quadratic Mean 195.127996928132 Winsorized Mean ( 1 / 36 ) 189.027777777778 4.58813273371984 41.1992827471064 Winsorized Mean ( 2 / 36 ) 188.842592592593 4.49905112947164 41.9738711915394 Winsorized Mean ( 3 / 36 ) 188.092592592593 4.35420202700517 43.1979479652126 Winsorized Mean ( 4 / 36 ) 188.314814814815 4.29326164593158 43.8628787027847 Winsorized Mean ( 5 / 36 ) 187.898148148148 4.23353283261892 44.3832977272345 Winsorized Mean ( 6 / 36 ) 187.953703703704 4.18413543214289 44.9205592772708 Winsorized Mean ( 7 / 36 ) 187.824074074074 4.14570696522979 45.3056802251973 Winsorized Mean ( 8 / 36 ) 187.75 4.13639313687205 45.3897861705614 Winsorized Mean ( 9 / 36 ) 187.833333333333 4.09204201982386 45.9021027700538 Winsorized Mean ( 10 / 36 ) 187.925925925926 4.04324374180468 46.4790000125113 Winsorized Mean ( 11 / 36 ) 188.129629629630 3.96981716890721 47.3899984873653 Winsorized Mean ( 12 / 36 ) 189.018518518519 3.72791712983857 50.7035194011149 Winsorized Mean ( 13 / 36 ) 188.777777777778 3.66178598355529 51.5534710727388 Winsorized Mean ( 14 / 36 ) 189.296296296296 3.52588360344708 53.6876192144377 Winsorized Mean ( 15 / 36 ) 189.157407407407 3.4264552695559 55.2049837300003 Winsorized Mean ( 16 / 36 ) 189.75 3.18876871736549 59.5057267611332 Winsorized Mean ( 17 / 36 ) 189.907407407407 3.11534175994314 60.9587717948717 Winsorized Mean ( 18 / 36 ) 192.740740740741 2.63832847644049 73.0541107606045 Winsorized Mean ( 19 / 36 ) 193.796296296296 2.37904923471708 81.4595568129733 Winsorized Mean ( 20 / 36 ) 193.611111111111 2.35653915669701 82.1590893412022 Winsorized Mean ( 21 / 36 ) 194.194444444444 2.27076237738499 85.519491770019 Winsorized Mean ( 22 / 36 ) 196.231481481481 1.83682790146834 106.83171859738 Winsorized Mean ( 23 / 36 ) 196.444444444444 1.81081389428409 108.484060711335 Winsorized Mean ( 24 / 36 ) 196.222222222222 1.7828814332832 110.059041817984 Winsorized Mean ( 25 / 36 ) 196.222222222222 1.72616204298395 113.675435640457 Winsorized Mean ( 26 / 36 ) 196.222222222222 1.61017088617371 121.864221932686 Winsorized Mean ( 27 / 36 ) 195.972222222222 1.58028801160032 124.010446693046 Winsorized Mean ( 28 / 36 ) 196.231481481481 1.48935338309522 131.756159222378 Winsorized Mean ( 29 / 36 ) 196.768518518519 1.42916310448145 137.680939216461 Winsorized Mean ( 30 / 36 ) 196.768518518519 1.36600714030062 144.046478757948 Winsorized Mean ( 31 / 36 ) 196.481481481481 1.33245567437522 147.458174602026 Winsorized Mean ( 32 / 36 ) 196.481481481481 1.33245567437522 147.458174602026 Winsorized Mean ( 33 / 36 ) 196.481481481481 1.26427340457527 155.410594552124 Winsorized Mean ( 34 / 36 ) 196.166666666667 1.22844869204730 159.686495607513 Winsorized Mean ( 35 / 36 ) 195.842592592593 1.19217493369172 164.273368830312 Winsorized Mean ( 36 / 36 ) 195.842592592593 1.11940018467813 174.953153727507 Trimmed Mean ( 1 / 36 ) 188.990566037736 4.42740171487038 42.6865638604626 Trimmed Mean ( 2 / 36 ) 188.951923076923 4.24546456165039 44.5067719522948 Trimmed Mean ( 3 / 36 ) 189.009803921569 4.09379677371372 46.169806262783 Trimmed Mean ( 4 / 36 ) 189.34 3.98396330760759 47.5255381088588 Trimmed Mean ( 5 / 36 ) 189.622448979592 3.88029692823056 48.8680254338322 Trimmed Mean ( 6 / 36 ) 190.010416666667 3.77917002142059 50.2783456657612 Trimmed Mean ( 7 / 36 ) 190.404255319149 3.67634542794128 51.7917206234273 Trimmed Mean ( 8 / 36 ) 190.836956521739 3.56729306776466 53.4962933789237 Trimmed Mean ( 9 / 36 ) 191.3 3.44373175341999 55.5502035865653 Trimmed Mean ( 10 / 36 ) 191.772727272727 3.31007010096995 57.9361528375281 Trimmed Mean ( 11 / 36 ) 192.255813953488 3.16444794434657 60.7549301915243 Trimmed Mean ( 12 / 36 ) 192.738095238095 3.00869456501447 64.060372720874 Trimmed Mean ( 13 / 36 ) 193.146341463415 2.87368953159604 67.2119723929055 Trimmed Mean ( 14 / 36 ) 193.6 2.72631341010651 71.0116449863468 Trimmed Mean ( 15 / 36 ) 194.025641025641 2.57785688254499 75.2662579289853 Trimmed Mean ( 16 / 36 ) 194.486842105263 2.41853177304154 80.4152520438783 Trimmed Mean ( 17 / 36 ) 194.918918918919 2.27324121116317 85.7449345725977 Trimmed Mean ( 18 / 36 ) 195.361111111111 2.11127326203729 92.5323664273549 Trimmed Mean ( 19 / 36 ) 195.585714285714 2.01130272639452 97.2432999364166 Trimmed Mean ( 20 / 36 ) 195.735294117647 1.93763811392052 101.017466941547 Trimmed Mean ( 21 / 36 ) 195.909090909091 1.85270259001609 105.742331211071 Trimmed Mean ( 22 / 36 ) 196.046875 1.76586202580961 111.020494316432 Trimmed Mean ( 23 / 36 ) 196.032258064516 1.73402929927779 113.050141739913 Trimmed Mean ( 24 / 36 ) 196 1.69895281805178 115.365181373757 Trimmed Mean ( 25 / 36 ) 195.982758620690 1.66027049365622 118.042667968579 Trimmed Mean ( 26 / 36 ) 195.964285714286 1.62168028253892 120.840271553084 Trimmed Mean ( 27 / 36 ) 195.944444444444 1.59257024670264 123.036610064856 Trimmed Mean ( 28 / 36 ) 195.942307692308 1.56059446980932 125.556197643228 Trimmed Mean ( 29 / 36 ) 195.92 1.53512347439307 127.624913088805 Trimmed Mean ( 30 / 36 ) 195.854166666667 1.51177106675390 129.552794714618 Trimmed Mean ( 31 / 36 ) 195.782608695652 1.49165570993572 131.251874941094 Trimmed Mean ( 32 / 36 ) 195.727272727273 1.47041423035859 133.110295511449 Trimmed Mean ( 33 / 36 ) 195.666666666667 1.44092605831673 135.792302136059 Trimmed Mean ( 34 / 36 ) 195.6 1.41457613475756 138.274635909592 Trimmed Mean ( 35 / 36 ) 195.552631578947 1.38560849742561 141.131230028016 Trimmed Mean ( 36 / 36 ) 195.527777777778 1.35311874390129 144.501566221776 Median 195.5 Midrange 197 Midmean - Weighted Average at Xnp 195.581818181818 Midmean - Weighted Average at X(n+1)p 195.581818181818 Midmean - Empirical Distribution Function 195.581818181818 Midmean - Empirical Distribution Function - Averaging 195.581818181818 Midmean - Empirical Distribution Function - Interpolation 195.581818181818 Midmean - Closest Observation 195.581818181818 Midmean - True Basic - Statistics Graphics Toolkit 195.581818181818 Midmean - MS Excel (old versions) 195.964285714286 Number of observations 108

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945876xaiylw7p0ls979j/11jau1292946007.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945876xaiylw7p0ls979j/11jau1292946007.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945876xaiylw7p0ls979j/2usrf1292946007.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945876xaiylw7p0ls979j/2usrf1292946007.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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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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