WS3.3

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 20 Oct 2009 13:19:42 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t12560664181tldlj4sfjw5rqv.htm/, Retrieved Tue, 20 Oct 2009 21:20:18 +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/2009/Oct/20/t12560664181tldlj4sfjw5rqv.htm/}, year = {2009}, } @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 = {2009}, 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:

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-1,561433447 -1,503623188 -1,484063745 -1,503984064 -1,491935484 -1,5625 -1,556603774 -1,547619048 -1,561032864 -1,556603774 -1,565420561 -1,561032864 -1,561032864 -1,519607843 -1,50990099 -1,458333333 -1,514778325 -1,524390244 -1,538461538 -1,538461538 -1,538461538 -1,538461538 -1,556603774 -1,565420561 -1,561032864 -1,547619048 -1,543062201 -1,547619048 -1,543062201 -1,538461538 -1,533816425 -1,538461538 -1,543062201 -1,552132701 -1,590909091 -1,58677686 -1,585365854 -1,6 -1,554054054 -1,590909091 -1,600719424 -1,589655172 -1,592409241 -1,55483871 -1,57120743 -1,556547619 -1,574074074 -1,560941828 -1,546321526 -1,564171123 -1,544502618 -1,535989717 -1,557788945 -1,544117647 -1,533816425 -1,576212471 -1,624726477 -1,636069114 -1,624726477 -1,6507431 -1,618942731 -1,569767442 -1,582568807 -1,632321041 -1,6507431 -1,645299145 -1,648676171 -1,605263158 -1,609014675 -1,733590734 -1,5 -1,485239852

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -1.56384885566667 0.0053867951106385 -290.311553260711 Geometric Mean NaN Harmonic Mean -1.56255679661621 Quadratic Mean 1.56450742735245 Winsorized Mean ( 1 / 24 ) -1.56305556091667 0.00489048505138667 -319.611560917351 Winsorized Mean ( 2 / 24 ) -1.56308823055556 0.00488310109007704 -320.10155057652 Winsorized Mean ( 3 / 24 ) -1.56328109318056 0.00480088865668186 -325.623276225077 Winsorized Mean ( 4 / 24 ) -1.56354150929167 0.00466429730056363 -335.21480483303 Winsorized Mean ( 5 / 24 ) -1.56315214519444 0.00446353657019421 -350.204847795485 Winsorized Mean ( 6 / 24 ) -1.56286987877778 0.0043871065928052 -356.241601546875 Winsorized Mean ( 7 / 24 ) -1.56270677508333 0.00412001603872615 -379.296284382063 Winsorized Mean ( 8 / 24 ) -1.56324870119444 0.00402511059612745 -388.374099011948 Winsorized Mean ( 9 / 24 ) -1.56312942269444 0.00377160491189599 -414.446756542338 Winsorized Mean ( 10 / 24 ) -1.56241474838889 0.00338720304171858 -461.269882302704 Winsorized Mean ( 11 / 24 ) -1.56328171094444 0.00306417323787390 -510.180590190502 Winsorized Mean ( 12 / 24 ) -1.56252442194444 0.00292129975143705 -534.873020536768 Winsorized Mean ( 13 / 24 ) -1.56278692588889 0.00284416378396889 -549.471494819507 Winsorized Mean ( 14 / 24 ) -1.56179157683333 0.00251790314647303 -620.274683329668 Winsorized Mean ( 15 / 24 ) -1.56147904558333 0.00246485604633692 -633.497054687589 Winsorized Mean ( 16 / 24 ) -1.56147904558333 0.00246485604633692 -633.497054687589 Winsorized Mean ( 17 / 24 ) -1.561182981375 0.00241538148707729 -646.350479097237 Winsorized Mean ( 18 / 24 ) -1.560463403375 0.00229756840913144 -679.180387914939 Winsorized Mean ( 19 / 24 ) -1.56009105456944 0.0022379172809304 -697.11739029105 Winsorized Mean ( 20 / 24 ) -1.56059205901389 0.00194585439454487 -802.008651515215 Winsorized Mean ( 21 / 24 ) -1.55873812768056 0.00166018490295967 -938.894291173074 Winsorized Mean ( 22 / 24 ) -1.55808472859722 0.00156468979158867 -995.778675730515 Winsorized Mean ( 23 / 24 ) -1.55750615145833 0.00138938827887091 -1121.00136091838 Winsorized Mean ( 24 / 24 ) -1.557154479125 0.00130592398478121 -1192.37757884191 Trimmed Mean ( 1 / 24 ) -1.5629313363 0.00473594717595813 -330.014520481598 Trimmed Mean ( 2 / 24 ) -1.56279980435294 0.00455193510549333 -343.326468443484 Trimmed Mean ( 3 / 24 ) -1.56264248096970 0.0043358330451763 -360.401903091764 Trimmed Mean ( 4 / 24 ) -1.56240300139062 0.00411409353891895 -379.768468220383 Trimmed Mean ( 5 / 24 ) -1.56207246683871 0.00389822968231011 -400.713296583648 Trimmed Mean ( 6 / 24 ) -1.56181334403333 0.00370433238202141 -421.618036117232 Trimmed Mean ( 7 / 24 ) -1.56159475063793 0.00348958458676982 -447.501618547508 Trimmed Mean ( 8 / 24 ) -1.56139050125 0.00330277476735865 -472.751129347733 Trimmed Mean ( 9 / 24 ) -1.56108080125926 0.00309461272075186 -504.451103296693 Trimmed Mean ( 10 / 24 ) -1.56076562873077 0.00290206761028039 -537.81160135686 Trimmed Mean ( 11 / 24 ) -1.5605281555 0.00276133476558229 -565.135446433611 Trimmed Mean ( 12 / 24 ) -1.56015267066667 0.00265975983378197 -586.576521252391 Trimmed Mean ( 13 / 24 ) -1.55984331180435 0.00256471878174256 -608.192727759625 Trimmed Mean ( 14 / 24 ) -1.55947278695455 0.00245772021500722 -634.520063525606 Trimmed Mean ( 15 / 24 ) -1.5591888535 0.002397582355576 -650.317120441695 Trimmed Mean ( 16 / 24 ) -1.55891403045 0.00232874052568388 -669.423670544915 Trimmed Mean ( 17 / 24 ) -1.55861027865789 0.00223359137374111 -697.804574722785 Trimmed Mean ( 18 / 24 ) -1.55830760775 0.00211595996380058 -736.454202541263 Trimmed Mean ( 19 / 24 ) -1.55805398473529 0.00198811738142657 -783.683096023894 Trimmed Mean ( 20 / 24 ) -1.55781275278125 0.00182477486660037 -853.701342173524 Trimmed Mean ( 21 / 24 ) -1.55747923603333 0.00168474797265885 -924.458293649312 Trimmed Mean ( 22 / 24 ) -1.55732508603571 0.00158945622819574 -979.78482100353 Trimmed Mean ( 23 / 24 ) -1.55722946669231 0.00148102892805141 -1051.45108052761 Trimmed Mean ( 24 / 24 ) -1.557193377375 0.00138470279689006 -1124.5686661949 Median -1.5571963595 Midrange -1.5959620335 Midmean - Weighted Average at Xnp -1.55713598056098 Midmean - Weighted Average at X(n+1)p -1.556323000775 Midmean - Empirical Distribution Function -1.55713598056098 Midmean - Empirical Distribution Function - Averaging -1.556323000775 Midmean - Empirical Distribution Function - Interpolation -1.556323000775 Midmean - Closest Observation -1.55713598056098 Midmean - True Basic - Statistics Graphics Toolkit -1.556323000775 Midmean - MS Excel (old versions) -1.55713598056098 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560664181tldlj4sfjw5rqv/1yut81256066377.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560664181tldlj4sfjw5rqv/1yut81256066377.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560664181tldlj4sfjw5rqv/2pmam1256066377.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560664181tldlj4sfjw5rqv/2pmam1256066377.ps (open in new window)

Parameters (Session):

par1 = Rente op langerlopende herfinancieringstransacties ; par2 = http://www.nbb.be/belgostat/PublicatieSelectieLinker?LinkID=741000054|910000082&Lang=N ; par3 = Voornaamste monetaire beleidstarieven van het ESCB (procenten per jaar) ;

Parameters (R input):

par1 = Rente op langerlopende herfinancieringstransacties ; par2 = http://www.nbb.be/belgostat/PublicatieSelectieLinker?LinkID=741000054|910000082&Lang=N ; par3 = Voornaamste monetaire beleidstarieven van het ESCB (procenten per jaar) ;

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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