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Earthquakes

*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 17 Mar 2010 03:51:13 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/17/t1268819898haefgsgp9q9t3ol.htm/, Retrieved Wed, 17 Mar 2010 10:58:21 +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/Mar/17/t1268819898haefgsgp9q9t3ol.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

13 14 8 10 16 26 32 27 18 32 36 24 22 23 22 18 25 21 21 14 8 11 14 23 18 17 19 20 22 19 13 26 13 14 22 24 21 22 26 21 23 24 27 41 31 27 35 26 28 36 39 21 17 22 17 19 15 34 10 15 22 18 15 20 15 22 19 16 30 27 29 23 20 16 21 21 25 16 18 15 18 14 10 15 8 15 6 11 8 7 13 10 23 16 15 25 22 20 16

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	20.0202020202020	0.729983324527194	27.4255607594447
Geometric Mean	18.6627092290924
Harmonic Mean	17.2068905040705
Quadratic Mean	21.2845085221694
Winsorized Mean ( 1 / 33 )	20.010101010101	0.722391945955743	27.6997841990433
Winsorized Mean ( 2 / 33 )	19.9696969696970	0.703593061607274	28.3824529538119
Winsorized Mean ( 3 / 33 )	19.9696969696970	0.703593061607274	28.3824529538119
Winsorized Mean ( 4 / 33 )	19.9292929292929	0.69442111240578	28.6991460559848
Winsorized Mean ( 5 / 33 )	19.8787878787879	0.68350303747777	29.083686229316
Winsorized Mean ( 6 / 33 )	19.8787878787879	0.638597839030945	31.1288054293347
Winsorized Mean ( 7 / 33 )	19.8787878787879	0.638597839030945	31.1288054293347
Winsorized Mean ( 8 / 33 )	19.7979797979798	0.623358251559752	31.7601952784643
Winsorized Mean ( 9 / 33 )	19.7070707070707	0.607153896046413	32.4581145495346
Winsorized Mean ( 10 / 33 )	19.7070707070707	0.573993616218868	34.3332576360157
Winsorized Mean ( 11 / 33 )	19.5959595959596	0.55624102686412	35.2292597085733
Winsorized Mean ( 12 / 33 )	19.7171717171717	0.502116814507679	39.2680968800143
Winsorized Mean ( 13 / 33 )	19.7171717171717	0.502116814507679	39.2680968800143
Winsorized Mean ( 14 / 33 )	19.7171717171717	0.502116814507679	39.2680968800143
Winsorized Mean ( 15 / 33 )	19.7171717171717	0.502116814507679	39.2680968800143
Winsorized Mean ( 16 / 33 )	19.7171717171717	0.457431457431457	43.1041009463722
Winsorized Mean ( 17 / 33 )	19.7171717171717	0.457431457431457	43.1041009463722
Winsorized Mean ( 18 / 33 )	19.7171717171717	0.457431457431457	43.1041009463722
Winsorized Mean ( 19 / 33 )	19.7171717171717	0.457431457431457	43.1041009463722
Winsorized Mean ( 20 / 33 )	19.5151515151515	0.430099161684132	45.3736097478925
Winsorized Mean ( 21 / 33 )	19.7272727272727	0.403504076111898	48.889897017551
Winsorized Mean ( 22 / 33 )	19.7272727272727	0.403504076111898	48.889897017551
Winsorized Mean ( 23 / 33 )	19.4949494949495	0.373678869099732	52.1703288760126
Winsorized Mean ( 24 / 33 )	19.4949494949495	0.373678869099732	52.1703288760126
Winsorized Mean ( 25 / 33 )	19.4949494949495	0.373678869099732	52.1703288760126
Winsorized Mean ( 26 / 33 )	19.2323232323232	0.342733347909389	56.1145372915618
Winsorized Mean ( 27 / 33 )	19.2323232323232	0.342733347909389	56.1145372915618
Winsorized Mean ( 28 / 33 )	19.2323232323232	0.342733347909389	56.1145372915618
Winsorized Mean ( 29 / 33 )	19.5252525252525	0.307047515100283	63.5903290696734
Winsorized Mean ( 30 / 33 )	19.5252525252525	0.307047515100283	63.5903290696734
Winsorized Mean ( 31 / 33 )	19.2121212121212	0.272521051697613	70.4977508799534
Winsorized Mean ( 32 / 33 )	19.2121212121212	0.272521051697613	70.4977508799534
Winsorized Mean ( 33 / 33 )	19.2121212121212	0.272521051697613	70.4977508799534
Trimmed Mean ( 1 / 33 )	19.9484536082474	0.697684427024376	28.5923733360763
Trimmed Mean ( 2 / 33 )	19.8842105263158	0.669418888219295	29.7036890895166
Trimmed Mean ( 3 / 33 )	19.8387096774194	0.648710434126586	30.5817644264191
Trimmed Mean ( 4 / 33 )	19.7912087912088	0.624981852438166	31.6668535478266
Trimmed Mean ( 5 / 33 )	19.7528089887640	0.600961287071669	32.8686879066944
Trimmed Mean ( 6 / 33 )	19.7241379310345	0.576583429344819	34.2086451451568
Trimmed Mean ( 7 / 33 )	19.6941176470588	0.560367908710464	35.1449776850704
Trimmed Mean ( 8 / 33 )	19.6626506024096	0.541619861323201	36.3034150084026
Trimmed Mean ( 9 / 33 )	19.6419753086420	0.523317009056354	37.5336076770377
Trimmed Mean ( 10 / 33 )	19.6329113924051	0.505464207734026	38.8413483922404
Trimmed Mean ( 11 / 33 )	19.6233766233766	0.491221280300172	39.9481402991851
Trimmed Mean ( 12 / 33 )	19.6266666666667	0.477898301719923	41.0687097987828
Trimmed Mean ( 13 / 33 )	19.6164383561644	0.471658775361283	41.5903177909465
Trimmed Mean ( 14 / 33 )	19.6056338028169	0.464203033199877	42.2350402746616
Trimmed Mean ( 15 / 33 )	19.5942028985507	0.455298839769209	43.035916604758
Trimmed Mean ( 16 / 33 )	19.5820895522388	0.444652255252365	44.0391099357516
Trimmed Mean ( 17 / 33 )	19.5692307692308	0.439059982962526	44.5707455213495
Trimmed Mean ( 18 / 33 )	19.5555555555556	0.432178407634495	45.2488028325890
Trimmed Mean ( 19 / 33 )	19.5409836065574	0.423731646759439	46.1164129608926
Trimmed Mean ( 20 / 33 )	19.5254237288136	0.413362381368266	47.2356087754833
Trimmed Mean ( 21 / 33 )	19.5263157894737	0.405248510622913	48.1835596618468
Trimmed Mean ( 22 / 33 )	19.5090909090909	0.399387348392145	48.8475435880247
Trimmed Mean ( 23 / 33 )	19.4905660377358	0.391883029471407	49.7356725654228
Trimmed Mean ( 24 / 33 )	19.4901960784314	0.387422401105207	50.3073545123652
Trimmed Mean ( 25 / 33 )	19.4897959183673	0.381460727398342	51.0925359244520
Trimmed Mean ( 26 / 33 )	19.4893617021277	0.373587181856258	52.1681755923479
Trimmed Mean ( 27 / 33 )	19.4893617021277	0.368757430635247	52.8514413080542
Trimmed Mean ( 28 / 33 )	19.5348837209302	0.362024633452267	53.9600952969569
Trimmed Mean ( 29 / 33 )	19.5609756097561	0.352774336229552	55.4489757356603
Trimmed Mean ( 30 / 33 )	19.5641025641026	0.348110131554348	56.2008996312369
Trimmed Mean ( 31 / 33 )	19.5675675675676	0.341214357917218	57.3468469703576
Trimmed Mean ( 32 / 33 )	19.6	0.338558486438452	57.8925083408392
Trimmed Mean ( 33 / 33 )	19.6363636363636	0.333763496544101	58.8331673166332
Median	20
Midrange	23.5
Midmean - Weighted Average at Xnp	19.3272727272727
Midmean - Weighted Average at X(n+1)p	19.3272727272727
Midmean - Empirical Distribution Function	19.3272727272727
Midmean - Empirical Distribution Function - Averaging	19.3272727272727
Midmean - Empirical Distribution Function - Interpolation	19.3272727272727
Midmean - Closest Observation	19.3272727272727
Midmean - True Basic - Statistics Graphics Toolkit	19.3272727272727
Midmean - MS Excel (old versions)	19.3272727272727
Number of observations	99

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/17/t1268819898haefgsgp9q9t3ol/1j7ds1268819471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/17/t1268819898haefgsgp9q9t3ol/1j7ds1268819471.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/17/t1268819898haefgsgp9q9t3ol/2gi3g1268819471.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/17/t1268819898haefgsgp9q9t3ol/2gi3g1268819471.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')

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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