Central tendency Q9

*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: Mon, 20 Oct 2008 13:49:16 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/20/t1224532259bmy2ynfijmmi3uh.htm/, Retrieved Mon, 20 Oct 2008 19:51:01 +0000

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/2008/Oct/20/t1224532259bmy2ynfijmmi3uh.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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IsPrivate?

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Dataseries X:

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110,089 99,966 94,195 119,588 125,946 118,906 108,717 118,357 115,422 130,937 111,802 120,357 121,12 108,752 98,973 116,721 123,857 114,056 98,309 110,251 108,538 122,526 118,394 116,691 116,014 111,784 95,164 121,028 129,89 116,102 102,055 113,562 113,071 126,486 119,472 117,141 121,925 112,688 90,974 126,398 130,401 116,873 111,917 113,919 117,931 139,332 127,781 118,103 136,984 119,566 107,238 139,389 139,798 138,074 129,739 125,098 129,341 149,083 137,721 130,126 140,499 118,165 115,932 144,662 136,159 147,339 138,807 135,275 135,84 161,702 132,606 147,419 154,865 131,545 126,212 150,316 154,524 154,28 131,059 147,168 141,8 162,022 143,924 151,406 159,601 143,513 132,302 152,021 171,573 161,591 134,057 172,247 173,384 173,706 188,178 165,932 179,795

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 130.268701030928 2.07557079680569 62.7628319069683 Geometric Mean 128.737937677714 Harmonic Mean 127.259430264763 Quadratic Mean 131.846508884423 Winsorized Mean ( 1 / 32 ) 130.215484536082 2.04577062507285 63.6510676906633 Winsorized Mean ( 2 / 32 ) 130.109917525773 2.01210221302269 64.6636719962229 Winsorized Mean ( 3 / 32 ) 130.197226804124 1.99294650505620 65.3290123311425 Winsorized Mean ( 4 / 32 ) 130.177721649485 1.97792845103630 65.8151823344672 Winsorized Mean ( 5 / 32 ) 130.194164948454 1.96194959918504 66.3595869142274 Winsorized Mean ( 6 / 32 ) 129.974453608247 1.86812403243544 69.5748522857993 Winsorized Mean ( 7 / 32 ) 130.066319587629 1.75856600441096 73.9615796401086 Winsorized Mean ( 8 / 32 ) 130.147144329897 1.73938638049971 74.8235962917605 Winsorized Mean ( 9 / 32 ) 130.153453608247 1.73529827347997 75.0035055052739 Winsorized Mean ( 10 / 32 ) 129.951907216495 1.69679513914283 76.586680512382 Winsorized Mean ( 11 / 32 ) 129.566453608247 1.58349767516302 81.8229515840043 Winsorized Mean ( 12 / 32 ) 129.544309278351 1.57393680775937 82.3059151039027 Winsorized Mean ( 13 / 32 ) 129.71706185567 1.54296188341497 84.070166120094 Winsorized Mean ( 14 / 32 ) 129.393618556701 1.4897984020918 86.8531060142243 Winsorized Mean ( 15 / 32 ) 129.316298969072 1.47265681382850 87.8115646189732 Winsorized Mean ( 16 / 32 ) 129.263680412371 1.42930450583221 90.438167573751 Winsorized Mean ( 17 / 32 ) 129.114711340206 1.38844074528582 92.9925974720853 Winsorized Mean ( 18 / 32 ) 128.897041237113 1.33198442609719 96.7706819326645 Winsorized Mean ( 19 / 32 ) 128.951298969072 1.32137720359015 97.5885603434919 Winsorized Mean ( 20 / 32 ) 128.944288659794 1.31293090430695 98.2110240811635 Winsorized Mean ( 21 / 32 ) 128.697484536082 1.20158892747301 107.106083947310 Winsorized Mean ( 22 / 32 ) 128.645773195876 1.16534461929663 110.392901005990 Winsorized Mean ( 23 / 32 ) 128.567762886598 1.14988235799864 111.809492503537 Winsorized Mean ( 24 / 32 ) 128.165701030928 1.09108611771599 117.466164173386 Winsorized Mean ( 25 / 32 ) 127.982195876289 1.03062955475385 124.178658845908 Winsorized Mean ( 26 / 32 ) 127.802340206186 1.00615408326944 127.020644582487 Winsorized Mean ( 27 / 32 ) 127.730804123711 0.987231549338924 129.382822306726 Winsorized Mean ( 28 / 32 ) 127.791711340206 0.976379864394977 130.883190037305 Winsorized Mean ( 29 / 32 ) 127.87093814433 0.930543182582552 137.415372588564 Winsorized Mean ( 30 / 32 ) 127.697432989691 0.897082517110799 142.347477020243 Winsorized Mean ( 31 / 32 ) 127.604432989691 0.881331908273046 144.785899377828 Winsorized Mean ( 32 / 32 ) 127.424639175258 0.84540104088425 150.726853898805 Trimmed Mean ( 1 / 32 ) 130.072757894737 1.98580724285098 65.5012002615088 Trimmed Mean ( 2 / 32 ) 129.923892473118 1.91733247639168 67.7628392951587 Trimmed Mean ( 3 / 32 ) 129.824747252747 1.85977403911862 69.8067316362118 Trimmed Mean ( 4 / 32 ) 129.689426966292 1.802101243394 71.9656719852436 Trimmed Mean ( 5 / 32 ) 129.553321839080 1.74100590990375 74.412913306103 Trimmed Mean ( 6 / 32 ) 129.407058823529 1.67515293205042 77.2508923499495 Trimmed Mean ( 7 / 32 ) 129.407058823529 1.62411848838869 79.6783361243035 Trimmed Mean ( 8 / 32 ) 129.164851851852 1.59056151472776 81.2070772842507 Trimmed Mean ( 9 / 32 ) 129.014088607595 1.55541020482933 82.9453787862679 Trimmed Mean ( 10 / 32 ) 128.854610389610 1.51505020074737 85.0497299205314 Trimmed Mean ( 11 / 32 ) 128.712693333333 1.47541906704970 87.2380574494754 Trimmed Mean ( 12 / 32 ) 128.609561643836 1.44995272084605 88.6991415615207 Trimmed Mean ( 13 / 32 ) 128.503140845070 1.42135342029724 90.4089996267062 Trimmed Mean ( 14 / 32 ) 128.503140845070 1.39230126557246 92.2954995607468 Trimmed Mean ( 15 / 32 ) 128.266208955224 1.36679505886697 93.8445073554428 Trimmed Mean ( 16 / 32 ) 128.161738461538 1.33889747971636 95.721846073449 Trimmed Mean ( 17 / 32 ) 128.055698412698 1.31228128787715 97.5825073447871 Trimmed Mean ( 18 / 32 ) 127.956639344262 1.28666615165328 99.4482050995484 Trimmed Mean ( 19 / 32 ) 127.870745762712 1.264627033306 101.113405292651 Trimmed Mean ( 20 / 32 ) 127.773964912281 1.23880239962488 103.143136428353 Trimmed Mean ( 21 / 32 ) 127.670763636364 1.20794876442833 105.692201023762 Trimmed Mean ( 22 / 32 ) 127.581283018868 1.18873641045416 107.325124305837 Trimmed Mean ( 23 / 32 ) 127.489254901961 1.17009562902074 108.956269675716 Trimmed Mean ( 24 / 32 ) 127.396428571429 1.14849826896235 110.924354014507 Trimmed Mean ( 25 / 32 ) 127.396428571429 1.13133178120718 112.607486758209 Trimmed Mean ( 26 / 32 ) 127.274066666667 1.11925688162759 113.713007939329 Trimmed Mean ( 27 / 32 ) 127.228232558140 1.10673733571872 114.957929449012 Trimmed Mean ( 28 / 32 ) 127.228232558140 1.09235596316755 116.471403872059 Trimmed Mean ( 29 / 32 ) 127.130230769231 1.07365948711874 118.408333642537 Trimmed Mean ( 30 / 32 ) 127.063270270270 1.05666373706407 120.249485066380 Trimmed Mean ( 31 / 32 ) 127.063270270270 1.03938662242514 122.248321778282 Trimmed Mean ( 32 / 32 ) 126.947818181818 1.01713541459260 124.809161455327 Median 126.486 Midrange 139.576 Midmean - Weighted Average at Xnp 127.096354166667 Midmean - Weighted Average at X(n+1)p 127.396428571429 Midmean - Empirical Distribution Function 127.396428571429 Midmean - Empirical Distribution Function - Averaging 127.396428571429 Midmean - Empirical Distribution Function - Interpolation 127.396428571429 Midmean - Closest Observation 127.16878 Midmean - True Basic - Statistics Graphics Toolkit 127.396428571429 Midmean - MS Excel (old versions) 127.396428571429 Number of observations 97

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224532259bmy2ynfijmmi3uh/1ghpc1224532153.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224532259bmy2ynfijmmi3uh/1ghpc1224532153.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224532259bmy2ynfijmmi3uh/2h1nv1224532153.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/20/t1224532259bmy2ynfijmmi3uh/2h1nv1224532153.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')

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Software written by Ed van Stee & Patrick Wessa

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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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