*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 15:35:05 +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/t1292945574iw845vwrm15xbmy.htm/, Retrieved Tue, 21 Dec 2010 16:32:54 +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/t1292945574iw845vwrm15xbmy.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 «

320 324 343 295 301 367 196 182 342 361 333 330 345 323 365 323 316 358 235 169 430 409 407 341 326 374 364 349 300 385 304 196 443 414 325 388 356 386 444 387 327 448 225 182 460 411 342 361 377 331 428 340 352 461 221 198 422 329 320 375 364 351 380 319 322 386 221 187 343 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 422 544 420 396 482 261 211 448 468 464 425

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 347.287037037037 7.2961752229765 47.5985055763724 Geometric Mean 337.968537415124 Harmonic Mean 327.305171349205 Quadratic Mean 355.393222491078 Winsorized Mean ( 1 / 36 ) 346.833333333333 7.14615868415188 48.5342333780678 Winsorized Mean ( 2 / 36 ) 346.574074074074 7.1025252031676 48.7958950035838 Winsorized Mean ( 3 / 36 ) 346.601851851852 7.0552870303373 49.1265416079439 Winsorized Mean ( 4 / 36 ) 346.824074074074 6.96918536134954 49.7653679865553 Winsorized Mean ( 5 / 36 ) 346.777777777778 6.96212287708129 49.809201000939 Winsorized Mean ( 6 / 36 ) 346.222222222222 6.84259475889802 50.5980895291219 Winsorized Mean ( 7 / 36 ) 347 6.68938237968711 51.8732493232403 Winsorized Mean ( 8 / 36 ) 346.777777777778 6.63401053402446 52.2727204003109 Winsorized Mean ( 9 / 36 ) 347.277777777778 6.51266616554416 53.3234421894802 Winsorized Mean ( 10 / 36 ) 347.37037037037 6.46574958694762 53.724686627457 Winsorized Mean ( 11 / 36 ) 347.268518518519 6.41932934844018 54.0973207119994 Winsorized Mean ( 12 / 36 ) 346.268518518519 6.2888199942124 55.0609683274747 Winsorized Mean ( 13 / 36 ) 346.62962962963 6.184589774083 56.0473115100063 Winsorized Mean ( 14 / 36 ) 347.796296296296 5.93377784366486 58.6129621734352 Winsorized Mean ( 15 / 36 ) 351.268518518519 5.30580262044526 66.2045959201249 Winsorized Mean ( 16 / 36 ) 351.564814814815 5.17238776720062 67.9695395314662 Winsorized Mean ( 17 / 36 ) 356.12962962963 4.47488457983797 79.5840927907294 Winsorized Mean ( 18 / 36 ) 356.62962962963 4.41191220402817 80.8333468884578 Winsorized Mean ( 19 / 36 ) 356.453703703704 4.2925508068954 83.040066323993 Winsorized Mean ( 20 / 36 ) 356.638888888889 4.26989384891708 83.5240644165752 Winsorized Mean ( 21 / 36 ) 356.25 4.21458684788594 84.5278583305733 Winsorized Mean ( 22 / 36 ) 355.638888888889 3.96956355412023 89.591433425912 Winsorized Mean ( 23 / 36 ) 356.916666666667 3.65709893498711 97.595573161032 Winsorized Mean ( 24 / 36 ) 357.138888888889 3.52198402416622 101.402756638976 Winsorized Mean ( 25 / 36 ) 357.37037037037 3.38366959110943 105.616213624805 Winsorized Mean ( 26 / 36 ) 354.962962962963 3.00671125186329 118.056884492313 Winsorized Mean ( 27 / 36 ) 354.212962962963 2.91218097208586 121.631507917331 Winsorized Mean ( 28 / 36 ) 354.212962962963 2.79153553344083 126.888215722034 Winsorized Mean ( 29 / 36 ) 353.944444444444 2.69696037166598 131.238281497553 Winsorized Mean ( 30 / 36 ) 353.666666666667 2.66335464103548 132.789926364881 Winsorized Mean ( 31 / 36 ) 353.666666666667 2.5980928649941 136.125490905988 Winsorized Mean ( 32 / 36 ) 353.666666666667 2.53114897355752 139.725741298265 Winsorized Mean ( 33 / 36 ) 353.666666666667 2.53114897355752 139.725741298265 Winsorized Mean ( 34 / 36 ) 353.666666666667 2.46041699364635 143.742571921734 Winsorized Mean ( 35 / 36 ) 352.046296296296 2.27064522630194 155.042404783618 Winsorized Mean ( 36 / 36 ) 351.37962962963 2.12086004977767 165.677895468145 Trimmed Mean ( 1 / 36 ) 347.11320754717 6.99562590529093 49.6186062900592 Trimmed Mean ( 2 / 36 ) 347.403846153846 6.82671901156056 50.8888450755836 Trimmed Mean ( 3 / 36 ) 347.843137254902 6.66255083245432 52.2087029430986 Trimmed Mean ( 4 / 36 ) 348.29 6.4972301013508 53.6059204564094 Trimmed Mean ( 5 / 36 ) 348.69387755102 6.33923207325751 55.0056968291175 Trimmed Mean ( 6 / 36 ) 349.125 6.16196329643943 56.6580784734202 Trimmed Mean ( 7 / 36 ) 349.68085106383 5.98977647958938 58.3796160433355 Trimmed Mean ( 8 / 36 ) 350.130434782609 5.82886652751063 60.0683568803799 Trimmed Mean ( 9 / 36 ) 350.633333333333 5.65611376930184 61.9919166471458 Trimmed Mean ( 10 / 36 ) 351.090909090909 5.48236548749379 64.040040725451 Trimmed Mean ( 11 / 36 ) 351.558139534884 5.29102703383961 66.4442153265212 Trimmed Mean ( 12 / 36 ) 352.059523809524 5.07763455636884 69.3353410729289 Trimmed Mean ( 13 / 36 ) 352.69512195122 4.85119395754569 72.7027459709433 Trimmed Mean ( 14 / 36 ) 353.325 4.60461295257679 76.7328337123917 Trimmed Mean ( 15 / 36 ) 353.871794871795 4.36147114640142 81.1358789255706 Trimmed Mean ( 16 / 36 ) 354.118421052632 4.1911337956542 84.4922730502706 Trimmed Mean ( 17 / 36 ) 354.351351351351 4.01337233623181 88.2926680269228 Trimmed Mean ( 18 / 36 ) 354.194444444444 3.91855857257905 90.388962646366 Trimmed Mean ( 19 / 36 ) 353.985714285714 3.81565332450588 92.7719800989925 Trimmed Mean ( 20 / 36 ) 353.779411764706 3.7120243116131 95.3063293949622 Trimmed Mean ( 21 / 36 ) 353.545454545455 3.59144164119221 98.4410968816666 Trimmed Mean ( 22 / 36 ) 353.328125 3.45586218995238 102.240224169607 Trimmed Mean ( 23 / 36 ) 353.145161290323 3.33394689371436 105.924051146742 Trimmed Mean ( 24 / 36 ) 352.85 3.23616787047207 109.033280757629 Trimmed Mean ( 25 / 36 ) 352.51724137931 3.13810387563048 112.334471818109 Trimmed Mean ( 26 / 36 ) 352.142857142857 3.03961170745483 115.851263593704 Trimmed Mean ( 27 / 36 ) 351.925925925926 2.98480332848744 117.905901057898 Trimmed Mean ( 28 / 36 ) 351.75 2.93145357465061 119.991666605849 Trimmed Mean ( 29 / 36 ) 351.56 2.88290669644513 121.946367682833 Trimmed Mean ( 30 / 36 ) 351.375 2.83588094684542 123.903297277293 Trimmed Mean ( 31 / 36 ) 351.195652173913 2.77977852751722 126.339436288684 Trimmed Mean ( 32 / 36 ) 351 2.71749480453689 129.163080427606 Trimmed Mean ( 33 / 36 ) 350.785714285714 2.64740482008331 132.50172834341 Trimmed Mean ( 34 / 36 ) 350.55 2.55226144067148 137.348781913099 Trimmed Mean ( 35 / 36 ) 350.289473684211 2.4398621485722 143.569370871711 Trimmed Mean ( 36 / 36 ) 350.138888888889 2.3394995997916 149.664008884669 Median 350 Midrange 356.5 Midmean - Weighted Average at Xnp 351.345454545455 Midmean - Weighted Average at X(n+1)p 351.345454545455 Midmean - Empirical Distribution Function 351.345454545455 Midmean - Empirical Distribution Function - Averaging 351.345454545455 Midmean - Empirical Distribution Function - Interpolation 351.345454545455 Midmean - Closest Observation 351.345454545455 Midmean - True Basic - Statistics Graphics Toolkit 351.345454545455 Midmean - MS Excel (old versions) 352.142857142857 Number of observations 108

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945574iw845vwrm15xbmy/1zeo41292945701.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945574iw845vwrm15xbmy/1zeo41292945701.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945574iw845vwrm15xbmy/2m2zj1292945701.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292945574iw845vwrm15xbmy/2m2zj1292945701.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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