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 13:17:51 -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/t1256066326q3jcl2ew0t0v5lr.htm/, Retrieved Tue, 20 Oct 2009 21:18:48 +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/t1256066326q3jcl2ew0t0v5lr.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:

» Textbox « » Textfile « » CSV «

-2,68 -2,51 -2,46 -2,51 -2,48 -2,64 -2,62 -2,6 -2,63 -2,62 -2,64 -2,63 -2,63 -2,54 -2,52 -2,42 -2,53 -2,55 -2,58 -2,58 -2,58 -2,58 -2,62 -2,64 -2,63 -2,6 -2,59 -2,6 -2,59 -2,58 -2,57 -2,58 -2,59 -2,61 -2,7 -2,71 -2,71 -2,75 -2,64 -2,75 -2,78 -2,76 -2,78 -2,67 -2,73 -2,69 -2,76 -2,72 -2,67 -2,74 -2,67 -2,64 -2,73 -2,68 -2,64 -2,83 -3,07 -3,13 -3,07 -3,21 -3,04 -2,8 -2,86 -3,11 -3,21 -3,18 -3,23 -3 -3,02 -3,71 -2,5 -2,46

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -2.72333333333333 0.0270266199267229 -100.764851125190 Geometric Mean NaN Harmonic Mean -2.70655213134554 Quadratic Mean 2.73283836981911 Winsorized Mean ( 1 / 24 ) -2.71722222222222 0.0241921285830010 -112.318443286198 Winsorized Mean ( 2 / 24 ) -2.71666666666667 0.0240288689178465 -113.058449648829 Winsorized Mean ( 3 / 24 ) -2.7175 0.0239078745024268 -113.665478699253 Winsorized Mean ( 4 / 24 ) -2.71694444444444 0.0232818335831964 -116.698044195513 Winsorized Mean ( 5 / 24 ) -2.71416666666667 0.0222473205293474 -121.999710620714 Winsorized Mean ( 6 / 24 ) -2.7125 0.0218140078611688 -124.346704982560 Winsorized Mean ( 7 / 24 ) -2.70958333333333 0.0207115572395314 -130.824703425083 Winsorized Mean ( 8 / 24 ) -2.71069444444444 0.0205711924515016 -131.771381305928 Winsorized Mean ( 9 / 24 ) -2.70819444444444 0.0195071576977075 -138.830806948504 Winsorized Mean ( 10 / 24 ) -2.70680555555556 0.0186798519714381 -144.905085955409 Winsorized Mean ( 11 / 24 ) -2.70680555555556 0.0176126226130194 -153.685547861263 Winsorized Mean ( 12 / 24 ) -2.68513888888889 0.0122761538626816 -218.72802499254 Winsorized Mean ( 13 / 24 ) -2.67972222222222 0.0112204615207200 -238.824598905649 Winsorized Mean ( 14 / 24 ) -2.67388888888889 0.0101582847683495 -263.222477993531 Winsorized Mean ( 15 / 24 ) -2.66972222222222 0.00945082864402758 -282.485517702127 Winsorized Mean ( 16 / 24 ) -2.66972222222222 0.00945082864402758 -282.485517702127 Winsorized Mean ( 17 / 24 ) -2.665 0.00869856894675438 -306.372233905713 Winsorized Mean ( 18 / 24 ) -2.6675 0.0083632093561936 -318.956501791326 Winsorized Mean ( 19 / 24 ) -2.66486111111111 0.00795869878608233 -334.836282002688 Winsorized Mean ( 20 / 24 ) -2.66486111111111 0.00795869878608233 -334.836282002688 Winsorized Mean ( 21 / 24 ) -2.66486111111111 0.00714261455670236 -373.093226570725 Winsorized Mean ( 22 / 24 ) -2.66180555555556 0.0066968985560122 -397.468400229222 Winsorized Mean ( 23 / 24 ) -2.66180555555556 0.0066968985560122 -397.468400229222 Winsorized Mean ( 24 / 24 ) -2.66180555555556 0.00579489815576734 -459.336037322141 Trimmed Mean ( 1 / 24 ) -2.71357142857143 0.0234754933354131 -115.591667864035 Trimmed Mean ( 2 / 24 ) -2.70970588235294 0.0226134546532283 -119.827152635703 Trimmed Mean ( 3 / 24 ) -2.70590909090909 0.0216789213391759 -124.817515067932 Trimmed Mean ( 4 / 24 ) -2.7015625 0.0205929208801710 -131.188893295916 Trimmed Mean ( 5 / 24 ) -2.69709677419355 0.0195065882601559 -138.265940625949 Trimmed Mean ( 6 / 24 ) -2.693 0.0185312379419459 -145.322185621735 Trimmed Mean ( 7 / 24 ) -2.68896551724138 0.0174556557780915 -154.0455169044 Trimmed Mean ( 8 / 24 ) -2.68517857142857 0.0164435102886289 -163.297162485156 Trimmed Mean ( 9 / 24 ) -2.68092592592593 0.0151817972733775 -176.588178438343 Trimmed Mean ( 10 / 24 ) -2.67673076923077 0.0138667466691356 -193.032355252338 Trimmed Mean ( 11 / 24 ) -2.6724 0.0123736388655686 -215.975270414294 Trimmed Mean ( 12 / 24 ) -2.66770833333333 0.0106576296353572 -250.309724076269 Trimmed Mean ( 13 / 24 ) -2.66543478260870 0.0101043183083873 -263.791648408008 Trimmed Mean ( 14 / 24 ) -2.66363636363636 0.00966724876246611 -275.531997684610 Trimmed Mean ( 15 / 24 ) -2.66238095238095 0.00936924518723756 -284.161733328054 Trimmed Mean ( 16 / 24 ) -2.6615 0.0091465980785348 -290.982502690919 Trimmed Mean ( 17 / 24 ) -2.66052631578947 0.0088366507595329 -301.078586015105 Trimmed Mean ( 18 / 24 ) -2.66 0.00860970290584897 -308.953750098966 Trimmed Mean ( 19 / 24 ) -2.65911764705882 0.00836305907258126 -317.959926383503 Trimmed Mean ( 20 / 24 ) -2.6584375 0.00812092794981762 -327.356370654625 Trimmed Mean ( 21 / 24 ) -2.65766666666667 0.00775610005883146 -342.655025916088 Trimmed Mean ( 22 / 24 ) -2.65678571428571 0.00747223381297097 -355.554413952335 Trimmed Mean ( 23 / 24 ) -2.65615384615385 0.00719138208770477 -369.352346149862 Trimmed Mean ( 24 / 24 ) -2.65541666666667 0.00672921293787655 -394.610289670014 Median -2.64 Midrange -3.065 Midmean - Weighted Average at Xnp -2.66270270270270 Midmean - Weighted Average at X(n+1)p -2.66270270270270 Midmean - Empirical Distribution Function -2.66270270270270 Midmean - Empirical Distribution Function - Averaging -2.66270270270270 Midmean - Empirical Distribution Function - Interpolation -2.66270270270270 Midmean - Closest Observation -2.66270270270270 Midmean - True Basic - Statistics Graphics Toolkit -2.66270270270270 Midmean - MS Excel (old versions) -2.65116279069767 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066326q3jcl2ew0t0v5lr/1rmy21256066269.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066326q3jcl2ew0t0v5lr/1rmy21256066269.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066326q3jcl2ew0t0v5lr/25m2t1256066269.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066326q3jcl2ew0t0v5lr/25m2t1256066269.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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