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Central tendency: Goudprijs

*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: Fri, 12 Dec 2008 05:54:43 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229086536i8z3svtial3qkly.htm/, Retrieved Fri, 12 Dec 2008 13:55:36 +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/2008/Dec/12/t1229086536i8z3svtial3qkly.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},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10070 10137 9984 9732 9103 9155 9308 9394 9948 10177 10002 9728 10002 10063 10018 9960 10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	12765.7777777778	330.004784844266	38.6836141900249
Geometric Mean	12387.9539316305
Harmonic Mean	12056.236229819
Quadratic Mean	13177.1617489342
Winsorized Mean ( 1 / 33 )	12765.898989899	329.853705163252	38.7016995415615
Winsorized Mean ( 2 / 33 )	12759.6161616162	327.444571136842	38.9672551825078
Winsorized Mean ( 3 / 33 )	12754.6464646465	325.566211599193	39.1768126120802
Winsorized Mean ( 4 / 33 )	12759.8181818182	322.580065172092	39.5555074831143
Winsorized Mean ( 5 / 33 )	12759.3131313131	322.371504093504	39.579531594121
Winsorized Mean ( 6 / 33 )	12723.5555555556	315.27414496212	40.3571170007749
Winsorized Mean ( 7 / 33 )	12723.2020202020	313.278247496574	40.6131039160042
Winsorized Mean ( 8 / 33 )	12725.3838383838	312.122087040514	40.7705329636991
Winsorized Mean ( 9 / 33 )	12723.2929292929	311.048647036169	40.9045114020812
Winsorized Mean ( 10 / 33 )	12694.2020202020	305.05701315991	41.612555924252
Winsorized Mean ( 11 / 33 )	12658.4242424242	298.362790214881	42.4262832282391
Winsorized Mean ( 12 / 33 )	12655.3939393939	297.064277689173	42.6015340445465
Winsorized Mean ( 13 / 33 )	12574.7676767677	282.931961998357	44.4444932553810
Winsorized Mean ( 14 / 33 )	12570.2424242424	282.200591419194	44.5436430909885
Winsorized Mean ( 15 / 33 )	12482.6666666667	267.922922562721	46.5905139704666
Winsorized Mean ( 16 / 33 )	12475.3939393939	265.063977457471	47.0655954802293
Winsorized Mean ( 17 / 33 )	12446.2020202020	260.468619349038	47.7838829541443
Winsorized Mean ( 18 / 33 )	12436.3838383838	256.154850235013	48.5502571080496
Winsorized Mean ( 19 / 33 )	12433.3131313131	254.406643767423	48.8718098992713
Winsorized Mean ( 20 / 33 )	12420.5858585859	252.354102962124	49.2188782064307
Winsorized Mean ( 21 / 33 )	12419.9494949495	251.967078100397	49.2919534908474
Winsorized Mean ( 22 / 33 )	12402.1717171717	248.987613739297	49.8103963121532
Winsorized Mean ( 23 / 33 )	12384.5151515152	243.837379768450	50.7900600116176
Winsorized Mean ( 24 / 33 )	12379.1818181818	242.651398870195	51.016321668947
Winsorized Mean ( 25 / 33 )	12383.4747474747	240.253016472266	51.5434724995608
Winsorized Mean ( 26 / 33 )	12369.5555555556	238.2673478472	51.914606291283
Winsorized Mean ( 27 / 33 )	12384.8282828283	235.998679737512	52.4783795256958
Winsorized Mean ( 28 / 33 )	12308.1818181818	225.312063929250	54.6272649743543
Winsorized Mean ( 29 / 33 )	12271.5656565657	219.579131717662	55.8867573642863
Winsorized Mean ( 30 / 33 )	12269.4444444444	217.678917102180	56.3648726655742
Winsorized Mean ( 31 / 33 )	12214.0202020202	209.845210978384	58.2049032478438
Winsorized Mean ( 32 / 33 )	12212.4040404040	208.346432201289	58.6158539475507
Winsorized Mean ( 33 / 33 )	12206.0707070707	205.595992349552	59.369205438198
Trimmed Mean ( 1 / 33 )	12727.4329896907	325.815569307914	39.0633050984209
Trimmed Mean ( 2 / 33 )	12687.3473684211	321.170691281219	39.5034407336749
Trimmed Mean ( 3 / 33 )	12648.8817204301	317.257703466668	39.8694234441467
Trimmed Mean ( 4 / 33 )	12610.5274725275	313.505062573180	40.2243184496706
Trimmed Mean ( 5 / 33 )	12569.0112359551	310.091500423551	40.5332336384170
Trimmed Mean ( 6 / 33 )	12525.7011494253	306.13138876835	40.9160955360363
Trimmed Mean ( 7 / 33 )	12487.2941176471	303.239552171198	41.1796351374282
Trimmed Mean ( 8 / 33 )	12447.0963855422	300.210212184708	41.4612690719659
Trimmed Mean ( 9 / 33 )	12404.5802469136	296.79939647548	41.7944928265324
Trimmed Mean ( 10 / 33 )	12360.2025316456	292.909930391948	42.1979634323294
Trimmed Mean ( 11 / 33 )	12317.2597402597	289.368166677081	42.566049616664
Trimmed Mean ( 12 / 33 )	12276.32	286.283501621908	42.8816887122375
Trimmed Mean ( 13 / 33 )	12233.4794520548	282.717101227230	43.2710982071874
Trimmed Mean ( 14 / 33 )	12196.8732394366	280.735610261764	43.4461208111930
Trimmed Mean ( 15 / 33 )	12158.6086956522	278.300580706175	43.688765092765
Trimmed Mean ( 16 / 33 )	12126.6865671642	277.465683340226	43.7051761543229
Trimmed Mean ( 17 / 33 )	12093.4923076923	276.606979689627	43.7208501436301
Trimmed Mean ( 18 / 33 )	12060.8888888889	275.979823233711	43.7020675916415
Trimmed Mean ( 19 / 33 )	12027.0327868852	275.510295511626	43.6536600730325
Trimmed Mean ( 20 / 33 )	11991.1525423729	274.821048851100	43.6325841579543
Trimmed Mean ( 21 / 33 )	11953.8596491228	273.912817293783	43.6411109462680
Trimmed Mean ( 22 / 33 )	11913.9090909091	272.444545709187	43.7296663799842
Trimmed Mean ( 23 / 33 )	11872.4528301887	270.708509152296	43.8569621153263
Trimmed Mean ( 24 / 33 )	11829.2352941176	268.945055381768	43.9838363167749
Trimmed Mean ( 25 / 33 )	11782.9387755102	266.445231842432	44.2227421148909
Trimmed Mean ( 26 / 33 )	11732.3404255319	263.142668690689	44.5854732868226
Trimmed Mean ( 27 / 33 )	11732.3404255319	258.787213180923	45.3358582957869
Trimmed Mean ( 28 / 33 )	11618.1860465116	252.906134798308	45.9387276460379
Trimmed Mean ( 29 / 33 )	11558.6829268293	247.205425681992	46.7573998221968
Trimmed Mean ( 30 / 33 )	11496.2820512821	240.416861175066	47.8181188918805
Trimmed Mean ( 31 / 33 )	11427.3243243243	230.944483448981	49.4808282651566
Trimmed Mean ( 32 / 33 )	11355.5428571429	219.617805307683	51.7059299505968
Trimmed Mean ( 33 / 33 )	11275.2121212121	203.064667065839	55.5252289043292
Median	10812
Midrange	14625.5
Midmean - Weighted Average at Xnp	11752.16
Midmean - Weighted Average at X(n+1)p	11829.2352941176
Midmean - Empirical Distribution Function	11829.2352941176
Midmean - Empirical Distribution Function - Averaging	11829.2352941176
Midmean - Empirical Distribution Function - Interpolation	11782.9387755102
Midmean - Closest Observation	11752.16
Midmean - True Basic - Statistics Graphics Toolkit	11829.2352941176
Midmean - MS Excel (old versions)	11829.2352941176
Number of observations	99

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229086536i8z3svtial3qkly/1pt701229086477.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229086536i8z3svtial3qkly/1pt701229086477.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229086536i8z3svtial3qkly/282eb1229086477.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229086536i8z3svtial3qkly/282eb1229086477.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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