Totale Invoer naar 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 06:32:26 -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/t1228656790vydmxlv4ldvw6de.htm/, Retrieved Sun, 07 Dec 2008 13:33:10 +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/t1228656790vydmxlv4ldvw6de.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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13429.9 13470.1 14785.8 14292 14308.8 14013 13240.9 12153.4 14289.7 15669.2 14169.5 14569.8 14469.1 14264.9 15320.9 14433.5 13691.5 14194.1 13519.2 11857.9 14616 15643.4 14077.2 14887.5 14159.9 14643 17192.5 15386.1 14287.1 17526.6 14497 14398.3 16629.6 16670.7 16614.8 16869.2 15663.9 16359.9 18447.7 16889 16505 18320.9 15052.1 15699.8 18135.3 16768.7 18883 19021 18101.9 17776.1 21489.9 17065.3 18690 18953.1 16398.9 16895.7 18553 19270 19422.1 17579.4 18637.3 18076.7 20438.6 18075.2 19563 19899.2 19227.5 17789.6 19220.8 21968.9 21131.5 19484.6

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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 16495.7875 275.600210047663 59.8540454564501 Geometric Mean 16333.5473971184 Harmonic Mean 16173.0687405894 Quadratic Mean 16658.4466270243 Winsorized Mean ( 1 / 24 ) 16493.2388888889 272.865328637766 60.4446118941845 Winsorized Mean ( 2 / 24 ) 16513.4916666667 264.326446752602 62.4738533338005 Winsorized Mean ( 3 / 24 ) 16492.4958333333 256.287655727383 64.3515029490014 Winsorized Mean ( 4 / 24 ) 16464.7625 249.755390954406 65.9235519885362 Winsorized Mean ( 5 / 24 ) 16444.825 244.823845584502 67.170029785044 Winsorized Mean ( 6 / 24 ) 16452.65 241.293911229115 68.1851022107962 Winsorized Mean ( 7 / 24 ) 16477.8305555556 235.394584702355 70.0008905319166 Winsorized Mean ( 8 / 24 ) 16468.0638888889 231.419538083605 71.1610783828436 Winsorized Mean ( 9 / 24 ) 16473.0888888889 229.029149534048 71.925730512482 Winsorized Mean ( 10 / 24 ) 16473.4916666667 228.682172228080 72.0366240453435 Winsorized Mean ( 11 / 24 ) 16446.725 223.083904918323 73.7243908565327 Winsorized Mean ( 12 / 24 ) 16447.2083333333 219.589683525696 74.8997314867421 Winsorized Mean ( 13 / 24 ) 16438.5597222222 217.008028783664 75.7509287299681 Winsorized Mean ( 14 / 24 ) 16401.5375 211.093589358051 77.6979421775817 Winsorized Mean ( 15 / 24 ) 16391.0375 209.358192072304 78.2918372467565 Winsorized Mean ( 16 / 24 ) 16376.0375 206.021149333655 79.4871669873014 Winsorized Mean ( 17 / 24 ) 16372.3069444444 199.381125195489 82.115631198248 Winsorized Mean ( 18 / 24 ) 16349.4069444444 193.555815621897 84.4686939109197 Winsorized Mean ( 19 / 24 ) 16309.8236111111 185.330881653375 88.0038095411181 Winsorized Mean ( 20 / 24 ) 16308.2958333333 182.96443348886 89.133694031995 Winsorized Mean ( 21 / 24 ) 16322.1791666667 179.005367790246 91.1826241199237 Winsorized Mean ( 22 / 24 ) 16335.8375 177.002822929107 92.2913952990614 Winsorized Mean ( 23 / 24 ) 16253.2291666667 163.450990025173 99.4379364980505 Winsorized Mean ( 24 / 24 ) 16296.3291666667 156.310062114195 104.256430752110 Trimmed Mean ( 1 / 24 ) 16483.8557142857 264.069704061345 62.4223659918837 Trimmed Mean ( 2 / 24 ) 16473.9205882353 253.591163806356 64.9625181767567 Trimmed Mean ( 3 / 24 ) 16452.3363636364 246.567679051041 66.7254379282641 Trimmed Mean ( 4 / 24 ) 16437.2765625 241.817110866556 67.9740011101643 Trimmed Mean ( 5 / 24 ) 16429.2967741935 238.417729685717 68.9097106823839 Trimmed Mean ( 6 / 24 ) 16425.57 235.716653270009 69.6835364499462 Trimmed Mean ( 7 / 24 ) 16419.9672413793 233.244340808053 70.3981377832957 Trimmed Mean ( 8 / 24 ) 16409.3392857143 231.485493678604 70.8871170497496 Trimmed Mean ( 9 / 24 ) 16399.5518518519 230.012318370043 71.2985807371775 Trimmed Mean ( 10 / 24 ) 16388.2384615385 228.441528771643 71.7393135550264 Trimmed Mean ( 11 / 24 ) 16375.962 226.276235585929 72.371550452903 Trimmed Mean ( 12 / 24 ) 16366.3125 224.478387708247 72.9081880313182 Trimmed Mean ( 13 / 24 ) 16355.7608695652 222.598344383994 73.4765611794068 Trimmed Mean ( 14 / 24 ) 16345.3386363636 220.389661433961 74.1656324984259 Trimmed Mean ( 15 / 24 ) 16338.4571428571 218.447160179017 74.7936348976467 Trimmed Mean ( 16 / 24 ) 16332.1475 215.873507032015 75.6560993729439 Trimmed Mean ( 17 / 24 ) 16326.95 212.803195723753 76.7232369066232 Trimmed Mean ( 18 / 24 ) 16321.6138888889 209.785784360822 77.8013340542486 Trimmed Mean ( 19 / 24 ) 16318.3441176471 206.598399649684 78.9858205354787 Trimmed Mean ( 20 / 24 ) 16319.353125 203.718326549836 80.1074375653079 Trimmed Mean ( 21 / 24 ) 16320.68 199.627959217013 81.7554818674372 Trimmed Mean ( 22 / 24 ) 16320.4964285714 194.233884644189 84.0249705063998 Trimmed Mean ( 23 / 24 ) 16318.5653846154 186.205315213099 87.6374842787916 Trimmed Mean ( 24 / 24 ) 16327.0875 178.377690133630 91.5309952033166 Median 16559.9 Midrange 16913.4 Midmean - Weighted Average at Xnp 16269.6324324324 Midmean - Weighted Average at X(n+1)p 16321.6138888889 Midmean - Empirical Distribution Function 16269.6324324324 Midmean - Empirical Distribution Function - Averaging 16321.6138888889 Midmean - Empirical Distribution Function - Interpolation 16321.6138888889 Midmean - Closest Observation 16269.6324324324 Midmean - True Basic - Statistics Graphics Toolkit 16321.6138888889 Midmean - MS Excel (old versions) 16326.95 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228656790vydmxlv4ldvw6de/1b6h01228656738.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228656790vydmxlv4ldvw6de/1b6h01228656738.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228656790vydmxlv4ldvw6de/2svwg1228656738.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228656790vydmxlv4ldvw6de/2svwg1228656738.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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