TDEown

*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: Thu, 05 Aug 2010 13:28:20 +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/Aug/05/t12810148997qcf2e4vp5y208j.htm/, Retrieved Thu, 05 Aug 2010 15:28:20 +0200

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/Aug/05/t12810148997qcf2e4vp5y208j.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 «

3552000 2368000 1184000 1184000 0 0 3552000 4736000 1184000 4736000 3552000 0 0 4736000 7104000 5920000 2368000 2368000 5920000 0 1184000 5920000 0 3552000 3552000 4736000 3552000 1184000 1184000 3552000 1184000 3552000 4736000 2368000 3552000 4736000 3552000 4736000 5920000 2368000 2368000 3552000 0 1184000 1184000 0 1184000 3552000 3552000 7104000 2368000 2368000 2368000 4736000 5920000 2368000 3552000 2368000 2368000 5920000 3552000 0 3552000 4736000 2368000 3552000 4736000 2368000 2368000 7104000 3552000 3552000 3552000 4736000 1184000 2368000 3552000 0 1184000 1184000 2368000 3552000 2368000 2368000 1184000 2368000 1184000 3552000 5920000 1184000 2368000 2368000 3552000 2368000 5920000 0 2368000 4736000 1184000 4736000

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2924480 182383.210994119 16.0348092571651 Geometric Mean 0 Harmonic Mean 0 Quadratic Mean 3441755.83096768 Winsorized Mean ( 1 / 33 ) 2924480 182383.210994119 16.0348092571651 Winsorized Mean ( 2 / 33 ) 2924480 182383.210994119 16.0348092571651 Winsorized Mean ( 3 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 4 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 5 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 6 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 7 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 8 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 9 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 10 / 33 ) 2888960 175147.292657502 16.4944599266477 Winsorized Mean ( 11 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 12 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 13 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 14 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 15 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 16 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 17 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 18 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 19 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 20 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 21 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 22 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 23 / 33 ) 2888960 134965.298884677 21.4052058112249 Winsorized Mean ( 24 / 33 ) 2604800 100971.859266017 25.7972866790289 Winsorized Mean ( 25 / 33 ) 2604800 100971.859266017 25.7972866790289 Winsorized Mean ( 26 / 33 ) 2604800 100971.859266017 25.7972866790289 Winsorized Mean ( 27 / 33 ) 2604800 100971.859266017 25.7972866790289 Winsorized Mean ( 28 / 33 ) 2936320 59450.6210177315 49.3909054225729 Winsorized Mean ( 29 / 33 ) 2936320 59450.6210177315 49.3909054225729 Winsorized Mean ( 30 / 33 ) 2936320 59450.6210177315 49.3909054225729 Winsorized Mean ( 31 / 33 ) 2936320 59450.6210177315 49.3909054225729 Winsorized Mean ( 32 / 33 ) 2936320 59450.6210177315 49.3909054225729 Winsorized Mean ( 33 / 33 ) 2936320 59450.6210177315 49.3909054225729 Trimmed Mean ( 1 / 33 ) 2911673.46938776 178615.001915341 16.301393713658 Trimmed Mean ( 2 / 33 ) 2898333.33333333 174341.62537725 16.6244482754005 Trimmed Mean ( 3 / 33 ) 2884425.53191489 169478.546404723 17.0194139205487 Trimmed Mean ( 4 / 33 ) 2882782.60869565 167026.709247436 17.2594109150834 Trimmed Mean ( 5 / 33 ) 2881066.66666667 164224.052062739 17.5435122351384 Trimmed Mean ( 6 / 33 ) 2879272.72727273 161015.774397497 17.8819295068862 Trimmed Mean ( 7 / 33 ) 2877395.34883721 157334.817102878 18.288357286841 Trimmed Mean ( 8 / 33 ) 2875428.57142857 153097.843205891 18.7816399709929 Trimmed Mean ( 9 / 33 ) 2873365.85365854 148199.320837974 19.3885224130006 Trimmed Mean ( 10 / 33 ) 2871200 142502.452121918 20.1484252182801 Trimmed Mean ( 11 / 33 ) 2868923.07692308 135824.550853159 21.1222717756283 Trimmed Mean ( 12 / 33 ) 2866526.31578947 135384.548437695 21.1732162116614 Trimmed Mean ( 13 / 33 ) 2864000 134792.382208231 21.247491535357 Trimmed Mean ( 14 / 33 ) 2861333.33333333 134022.257745514 21.3496875926872 Trimmed Mean ( 15 / 33 ) 2858514.28571429 133043.050587664 21.4856339589926 Trimmed Mean ( 16 / 33 ) 2855529.41176471 131816.871650434 21.6628522283347 Trimmed Mean ( 17 / 33 ) 2852363.63636364 130297.124385051 21.891224766668 Trimmed Mean ( 18 / 33 ) 2849000 128425.817015857 22.1840130450423 Trimmed Mean ( 19 / 33 ) 2845419.35483871 126129.749342346 22.5594625350089 Trimmed Mean ( 20 / 33 ) 2841600 123314.936481036 23.0434372436058 Trimmed Mean ( 21 / 33 ) 2837517.24137931 119858.146751221 23.6739622486313 Trimmed Mean ( 22 / 33 ) 2833142.85714286 115593.453024768 24.5095442951757 Trimmed Mean ( 23 / 33 ) 2828444.44444444 110289.558115883 25.6456231465952 Trimmed Mean ( 24 / 33 ) 2823384.61538462 103608.46268454 27.2505212627375 Trimmed Mean ( 25 / 33 ) 2841600 101485.714285714 28 Trimmed Mean ( 26 / 33 ) 2861333.33333333 98666.6666666667 29 Trimmed Mean ( 27 / 33 ) 2882782.60869565 94921.2229342155 30.3702640946119 Trimmed Mean ( 28 / 33 ) 2906181.81818182 89905.3253080105 32.3249129929223 Trimmed Mean ( 29 / 33 ) 2906181.81818182 92034.6154667504 31.5770517803896 Trimmed Mean ( 30 / 33 ) 2900800 94320.6968069779 30.7546498085815 Trimmed Mean ( 31 / 33 ) 2897684.21052632 96783.5062984016 29.9398556773942 Trimmed Mean ( 32 / 33 ) 2894222.22222222 99446.6524539833 29.1032644217105 Trimmed Mean ( 33 / 33 ) 2890352.94117647 102338.311081763 28.2431174662169 Median 2368000 Midrange 3552000 Midmean - Weighted Average at Xnp 2495507.69230769 Midmean - Weighted Average at X(n+1)p 2495507.69230769 Midmean - Empirical Distribution Function 2495507.69230769 Midmean - Empirical Distribution Function - Averaging 2495507.69230769 Midmean - Empirical Distribution Function - Interpolation 2495507.69230769 Midmean - Closest Observation 2495507.69230769 Midmean - True Basic - Statistics Graphics Toolkit 2495507.69230769 Midmean - MS Excel (old versions) 2495507.69230769 Number of observations 100

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t12810148997qcf2e4vp5y208j/1t45m1281014895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810148997qcf2e4vp5y208j/1t45m1281014895.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810148997qcf2e4vp5y208j/23v5p1281014895.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810148997qcf2e4vp5y208j/23v5p1281014895.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = TRUE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = TRUE ;

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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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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