Totale Uitvoer vanuit 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 06:29:52 -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/t12286566641pf33fptalveqn4.htm/, Retrieved Sun, 07 Dec 2008 13:31:06 +0000

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@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/t12286566641pf33fptalveqn4.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)

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

Original text written by user:

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Dataseries X:

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14291.1 14205.3 15859.4 15258.9 15498.6 15106.5 15023.6 12083 15761.3 16943 15070.3 13659.6 14768.9 14725.1 15998.1 15370.6 14956.9 15469.7 15101.8 11703.7 16283.6 16726.5 14968.9 14861 14583.3 15305.8 17903.9 16379.4 15420.3 17870.5 15912.8 13866.5 17823.2 17872 17420.4 16704.4 15991.2 16583.6 19123.5 17838.7 17209.4 18586.5 16258.1 15141.6 19202.1 17746.5 19090.1 18040.3 17515.5 17751.8 21072.4 17170 19439.5 19795.4 17574.9 16165.4 19464.6 19932.1 19961.2 17343.4 18924.2 18574.1 21350.6 18594.6 19823.1 20844.4 19640.2 17735.4 19813.6 22160 20664.3 17877.4

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17038.3 259.079383902959 65.7647850759977 Geometric Mean 16896.9454391821 Harmonic Mean 16753.7144008067 Quadratic Mean 17177.5824235720 Winsorized Mean ( 1 / 24 ) 17032.3263888889 254.684939207192 66.8760643715673 Winsorized Mean ( 2 / 24 ) 17068.3930555556 242.493553391284 70.3869971669483 Winsorized Mean ( 3 / 24 ) 17067.5138888889 238.661798424082 71.5133884081497 Winsorized Mean ( 4 / 24 ) 17076.3305555556 233.04906074255 73.2735437814952 Winsorized Mean ( 5 / 24 ) 17033.4625 222.171025560801 76.6682444616904 Winsorized Mean ( 6 / 24 ) 17055.3875 217.654262528041 78.359997649036 Winsorized Mean ( 7 / 24 ) 17058.5763888889 213.537553756275 79.8856036739985 Winsorized Mean ( 8 / 24 ) 17062.3875 212.600872844729 80.2554912954724 Winsorized Mean ( 9 / 24 ) 17071.625 210.459896110153 81.1158102589999 Winsorized Mean ( 10 / 24 ) 17063.3888888889 204.631943103524 83.3857541012377 Winsorized Mean ( 11 / 24 ) 17038.3944444444 199.689713285129 85.3243472793012 Winsorized Mean ( 12 / 24 ) 17043.3277777778 197.653167684470 86.2284575422817 Winsorized Mean ( 13 / 24 ) 17008.8958333333 189.277578376846 89.8621800806704 Winsorized Mean ( 14 / 24 ) 16999.7375 185.918720382231 91.43639470544 Winsorized Mean ( 15 / 24 ) 16993.7583333333 184.661795262839 92.0263896987743 Winsorized Mean ( 16 / 24 ) 16964.6916666667 177.725539419885 95.4544390302102 Winsorized Mean ( 17 / 24 ) 16914.5652777778 161.987987805001 104.418639350835 Winsorized Mean ( 18 / 24 ) 16924.2652777778 160.012781413876 105.768208815787 Winsorized Mean ( 19 / 24 ) 16938.0930555556 157.113843095382 107.807769970165 Winsorized Mean ( 20 / 24 ) 16803.6208333333 134.579407433219 124.860267657752 Winsorized Mean ( 21 / 24 ) 16778.2458333333 127.442778852323 131.653170029943 Winsorized Mean ( 22 / 24 ) 16778.9791666667 125.163977968182 134.055975521424 Winsorized Mean ( 23 / 24 ) 16861.1722222222 113.143495820172 149.024670839418 Winsorized Mean ( 24 / 24 ) 16893.3722222222 108.649345829000 155.485264023680 Trimmed Mean ( 1 / 24 ) 17041.3414285714 244.372648644990 69.735060462221 Trimmed Mean ( 2 / 24 ) 17050.8867647059 232.025873690664 73.4870059683003 Trimmed Mean ( 3 / 24 ) 17041.3378787879 225.215478811606 75.666814593339 Trimmed Mean ( 4 / 24 ) 17031.521875 218.812852268328 77.836021506243 Trimmed Mean ( 5 / 24 ) 17018.5129032258 213.166110234559 79.8368600172856 Trimmed Mean ( 6 / 24 ) 17014.925 209.757949683697 81.1169494441451 Trimmed Mean ( 7 / 24 ) 17006.5534482759 206.757843447534 82.2534863234407 Trimmed Mean ( 8 / 24 ) 16996.9982142857 204.005725354008 83.316280387676 Trimmed Mean ( 9 / 24 ) 16986.1 200.69793830245 84.6351494373705 Trimmed Mean ( 10 / 24 ) 16972.9423076923 196.944203254811 86.181476921828 Trimmed Mean ( 11 / 24 ) 16959.918 193.439336157307 87.6756420742057 Trimmed Mean ( 12 / 24 ) 16949.2166666667 189.989876557790 89.2111567929311 Trimmed Mean ( 13 / 24 ) 16936.9413043478 185.873677289033 91.1207092438964 Trimmed Mean ( 14 / 24 ) 16927.8840909091 182.329268453274 92.8423847389443 Trimmed Mean ( 15 / 24 ) 16919.0857142857 178.292020491935 94.8953613717727 Trimmed Mean ( 16 / 24 ) 16910.125 173.088518511150 97.6963991919008 Trimmed Mean ( 17 / 24 ) 16903.6631578947 167.721034153730 100.784396204003 Trimmed Mean ( 18 / 24 ) 16902.3805555556 164.236311106962 102.915003640989 Trimmed Mean ( 19 / 24 ) 16899.8058823529 159.659675545788 105.848930386347 Trimmed Mean ( 20 / 24 ) 16895.271875 153.77884795155 109.867332861819 Trimmed Mean ( 21 / 24 ) 16906.27 151.500124816913 111.592449316006 Trimmed Mean ( 22 / 24 ) 16921.9464285714 149.525751217994 113.170783565574 Trimmed Mean ( 23 / 24 ) 16939.9423076923 146.525837487725 115.610615834981 Trimmed Mean ( 24 / 24 ) 16950.2166666667 145.555662900539 116.451784347607 Median 17056.5 Midrange 16931.85 Midmean - Weighted Average at Xnp 16857.9621621622 Midmean - Weighted Average at X(n+1)p 16902.3805555556 Midmean - Empirical Distribution Function 16857.9621621622 Midmean - Empirical Distribution Function - Averaging 16902.3805555556 Midmean - Empirical Distribution Function - Interpolation 16902.3805555556 Midmean - Closest Observation 16857.9621621622 Midmean - True Basic - Statistics Graphics Toolkit 16902.3805555556 Midmean - MS Excel (old versions) 16903.6631578947 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286566641pf33fptalveqn4/1g0zt1228656588.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286566641pf33fptalveqn4/1g0zt1228656588.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286566641pf33fptalveqn4/26d421228656588.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286566641pf33fptalveqn4/26d421228656588.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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Software written by Ed van Stee & Patrick Wessa

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