Werkloosheid in Belgie (2002-2007) - Central Tendency

*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: Sun, 07 Dec 2008 06:34:44 -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/07/t12286569151v3gmezz09ijqj7.htm/, Retrieved Sun, 07 Dec 2008 13:35:17 +0000

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/07/t12286569151v3gmezz09ijqj7.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514

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 553.902777777778 5.26348628204207 105.234961790929 Geometric Mean 552.085911947097 Harmonic Mean 550.227758623616 Quadratic Mean 555.675527323875 Winsorized Mean ( 1 / 24 ) 553.902777777778 5.25705278270828 105.363746698473 Winsorized Mean ( 2 / 24 ) 553.986111111111 5.21045705267702 106.321980108537 Winsorized Mean ( 3 / 24 ) 554.152777777778 5.07994228932192 109.086431738134 Winsorized Mean ( 4 / 24 ) 554.375 5.00623388772979 110.736935675092 Winsorized Mean ( 5 / 24 ) 554.444444444444 4.9907931230635 111.093453640112 Winsorized Mean ( 6 / 24 ) 555.777777777778 4.49987924643332 123.509487108637 Winsorized Mean ( 7 / 24 ) 555.875 4.44836211087672 124.961724370601 Winsorized Mean ( 8 / 24 ) 556.430555555556 4.31686226780035 128.896990692984 Winsorized Mean ( 9 / 24 ) 556.680555555556 4.27707368501842 130.154539423877 Winsorized Mean ( 10 / 24 ) 554.736111111111 3.95579016674692 140.233957749914 Winsorized Mean ( 11 / 24 ) 554.583333333333 3.88562768467494 142.726832918303 Winsorized Mean ( 12 / 24 ) 554.583333333333 3.88562768467494 142.726832918303 Winsorized Mean ( 13 / 24 ) 554.583333333333 3.83025749225349 144.790091646567 Winsorized Mean ( 14 / 24 ) 554.777777777778 3.79925772248619 146.022675559566 Winsorized Mean ( 15 / 24 ) 554.986111111111 3.70353281915378 149.853164049433 Winsorized Mean ( 16 / 24 ) 555.208333333333 3.53702402140734 156.970472909716 Winsorized Mean ( 17 / 24 ) 554.972222222222 3.50357364072107 158.40175750038 Winsorized Mean ( 18 / 24 ) 555.222222222222 3.39267727397942 163.653120348514 Winsorized Mean ( 19 / 24 ) 554.958333333333 3.35587667459430 165.369108327088 Winsorized Mean ( 20 / 24 ) 554.958333333333 3.03767665496081 182.691706975143 Winsorized Mean ( 21 / 24 ) 554.375 2.79737171944956 198.177094644070 Winsorized Mean ( 22 / 24 ) 554.680555555556 2.75235184600894 201.529668657687 Winsorized Mean ( 23 / 24 ) 554.361111111111 2.62349931435255 211.305986656193 Winsorized Mean ( 24 / 24 ) 554.694444444444 2.21388056835205 250.553011925726 Trimmed Mean ( 1 / 24 ) 554.242857142857 5.11148731517581 108.430838808370 Trimmed Mean ( 2 / 24 ) 554.602941176471 4.93803302902422 112.312521588391 Trimmed Mean ( 3 / 24 ) 554.939393939394 4.76065257656154 116.567925303259 Trimmed Mean ( 4 / 24 ) 555.234375 4.60878981353966 120.472921843569 Trimmed Mean ( 5 / 24 ) 555.483870967742 4.4533982731759 124.732583275469 Trimmed Mean ( 6 / 24 ) 555.733333333333 4.26931415036431 130.169229473524 Trimmed Mean ( 7 / 24 ) 555.724137931035 4.18946285025335 132.648064392653 Trimmed Mean ( 8 / 24 ) 555.696428571429 4.1035239561867 135.419321174823 Trimmed Mean ( 9 / 24 ) 555.574074074074 4.02790769849179 137.931183051216 Trimmed Mean ( 10 / 24 ) 555.403846153846 3.94104935220549 140.927909426719 Trimmed Mean ( 11 / 24 ) 555.5 3.90219718327289 142.355697036839 Trimmed Mean ( 12 / 24 ) 555.625 3.86354403595074 143.812260150226 Trimmed Mean ( 13 / 24 ) 555.760869565217 3.80962229258785 145.883456910289 Trimmed Mean ( 14 / 24 ) 555.909090909091 3.74784196986712 148.327783129234 Trimmed Mean ( 15 / 24 ) 556.047619047619 3.6701945409727 151.503581851073 Trimmed Mean ( 16 / 24 ) 556.175 3.58609985631845 155.091888760448 Trimmed Mean ( 17 / 24 ) 556.28947368421 3.50916457025508 158.52476067937 Trimmed Mean ( 18 / 24 ) 556.444444444444 3.40784446242350 163.283404093133 Trimmed Mean ( 19 / 24 ) 556.588235294118 3.29346504867485 168.997765899494 Trimmed Mean ( 20 / 24 ) 556.78125 3.13819291763691 177.420975896938 Trimmed Mean ( 21 / 24 ) 557 3.01070885608223 185.006264845154 Trimmed Mean ( 22 / 24 ) 557.321428571429 2.89364088932471 192.60214030964 Trimmed Mean ( 23 / 24 ) 557.653846153846 2.72647549760735 204.532865467972 Trimmed Mean ( 24 / 24 ) 558.083333333333 2.50862040342943 222.466233859217 Median 561 Midrange 542 Midmean - Weighted Average at Xnp 554.368421052632 Midmean - Weighted Average at X(n+1)p 556.444444444444 Midmean - Empirical Distribution Function 554.368421052632 Midmean - Empirical Distribution Function - Averaging 556.444444444444 Midmean - Empirical Distribution Function - Interpolation 556.444444444444 Midmean - Closest Observation 554.368421052632 Midmean - True Basic - Statistics Graphics Toolkit 556.444444444444 Midmean - MS Excel (old versions) 555.282051282051 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286569151v3gmezz09ijqj7/1htgj1228656882.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286569151v3gmezz09ijqj7/1htgj1228656882.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286569151v3gmezz09ijqj7/2a0yc1228656882.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286569151v3gmezz09ijqj7/2a0yc1228656882.ps (open in new window)

Parameters (Session):

par1 = Totale Uitvoer vanuit Belgie (2002-2007) ; par2 = www.belgostat.be ; par3 = Maandelijks verloop (waarde) ;

Parameters (R input):

par1 = Totale Uitvoer vanuit Belgie (2002-2007) ; par2 = www.belgostat.be ; par3 = Maandelijks verloop (waarde) ;

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')

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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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