Glenn Van Passen 2 mar 01-A centrummaten belgische export naar EU

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 12:31:58 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t1208802783ypb9pvwblvp92ub.htm/, Retrieved Mon, 21 Apr 2008 20:33:03 +0200

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Dataseries X:

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11835.70 11542.20 13093.70 11180.20 12035.70 12112.00 10875.20 9897.30 11672.10 12385.70 11405.60 9830.90 11025.10 10853.80 12252.60 11839.40 11669.10 11601.40 11178.40 9516.40 12102.80 12989.00 11610.20 10205.50 11356.20 11307.10 12648.60 11947.20 11714.10 12192.50 11268.80 9097.40 12639.80 13040.10 11687.30 11191.70 11391.90 11793.10 13933.20 12778.10 11810.30 13698.40 11956.60 10723.80 13938.90 13979.80 13807.40 12973.90 12509.80 12934.10 14908.30 13772.10 13012.60 14049.90 11816.50 11593.20 14466.20 13615.90 14733.90 13880.70 13527.50 13584.00 16170.20 13260.60 14741.90 15486.50 13154.50 12621.20 15031.60 15452.40 15428.00 13105.90 14716.80 14180.00 16202.20 14392.40 15140.60 15960.10 14729.90 13705.20 15728.50 17315.60 16152.80

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 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 12875.5156626506 189.787947673785 67.8415875215721 Geometric Mean 12761.6357868947 Harmonic Mean 12648.4879439586 Quadratic Mean 12989.7074530531 Winsorized Mean ( 1 / 27 ) 12867.1493975904 185.225934281498 69.4673208020396 Winsorized Mean ( 2 / 27 ) 12873.9566265060 183.454037576188 70.1753790573265 Winsorized Mean ( 3 / 27 ) 12875.7277108434 182.835253594163 70.4225659862265 Winsorized Mean ( 4 / 27 ) 12881.2939759036 178.002062191508 72.3659817044418 Winsorized Mean ( 5 / 27 ) 12898.5650602410 169.801250610487 75.962721204153 Winsorized Mean ( 6 / 27 ) 12890.4686746988 164.900674241640 78.1711095723572 Winsorized Mean ( 7 / 27 ) 12889.3975903614 164.079661224874 78.5557301504682 Winsorized Mean ( 8 / 27 ) 12901.4939759036 161.526012743091 79.8725465750436 Winsorized Mean ( 9 / 27 ) 12886.9530120482 153.451086454256 83.9808522039353 Winsorized Mean ( 10 / 27 ) 12874.0373493976 151.101852878504 85.2010554744762 Winsorized Mean ( 11 / 27 ) 12859.2204819277 148.091168129791 86.8331355902168 Winsorized Mean ( 12 / 27 ) 12846.3096385542 142.592246571451 90.0912212791116 Winsorized Mean ( 13 / 27 ) 12851.0554216867 141.585514368830 90.7653263751953 Winsorized Mean ( 14 / 27 ) 12858.6626506024 140.384769919541 91.5958522991641 Winsorized Mean ( 15 / 27 ) 12862.7469879518 139.163166381327 92.4292492217806 Winsorized Mean ( 16 / 27 ) 12817.0795180723 131.185903244169 97.7016523964211 Winsorized Mean ( 17 / 27 ) 12829.9421686747 125.286694394506 102.404666598318 Winsorized Mean ( 18 / 27 ) 12794.9397590361 117.069356650860 109.293671077350 Winsorized Mean ( 19 / 27 ) 12767.0349397590 112.614680431564 113.369188553686 Winsorized Mean ( 20 / 27 ) 12752.2638554217 110.023910400266 115.904477572457 Winsorized Mean ( 21 / 27 ) 12756.8180722892 106.751767820666 119.499829677008 Winsorized Mean ( 22 / 27 ) 12756.1024096386 106.449106899080 119.832873954800 Winsorized Mean ( 23 / 27 ) 12745.7662650602 103.976765390368 122.58283105084 Winsorized Mean ( 24 / 27 ) 12732.3204819277 100.218119022591 127.046093122718 Winsorized Mean ( 25 / 27 ) 12745.4831325301 95.9130598404386 132.885794215444 Winsorized Mean ( 26 / 27 ) 12729.9144578313 92.5456037901167 137.552881352434 Winsorized Mean ( 27 / 27 ) 12729.7192771084 92.0172140729195 138.340629037309 Trimmed Mean ( 1 / 27 ) 12867.3432098765 180.514765716782 71.2813888591512 Trimmed Mean ( 2 / 27 ) 12867.5468354430 175.043217678641 73.5106849958985 Trimmed Mean ( 3 / 27 ) 12864.0922077922 169.774692980161 75.7715533568683 Trimmed Mean ( 4 / 27 ) 12859.8 163.880846365295 78.47042705244 Trimmed Mean ( 5 / 27 ) 12853.6904109589 158.712042924028 80.9874926574516 Trimmed Mean ( 6 / 27 ) 12843.1985915493 155.118763593851 82.795906143094 Trimmed Mean ( 7 / 27 ) 12843.1985915493 152.162833665602 84.4043074261744 Trimmed Mean ( 8 / 27 ) 12823.8686567164 148.820604886407 86.1699807395941 Trimmed Mean ( 9 / 27 ) 12811.4784615385 145.368826337135 88.130851602437 Trimmed Mean ( 10 / 27 ) 12800.4301587302 142.942950221758 89.5492232311696 Trimmed Mean ( 11 / 27 ) 12790.4147540984 140.452714615347 91.0656286646154 Trimmed Mean ( 12 / 27 ) 12781.6152542373 137.985418422862 92.6301880323869 Trimmed Mean ( 13 / 27 ) 12773.7649122807 135.977798582484 93.9400773173436 Trimmed Mean ( 14 / 27 ) 12773.7649122807 133.613713707100 95.6021994889128 Trimmed Mean ( 15 / 27 ) 12754.2924528302 130.826710295054 97.4899729884318 Trimmed Mean ( 16 / 27 ) 12742.5254901961 127.504033795264 99.9382145874462 Trimmed Mean ( 17 / 27 ) 12734.6326530612 124.905720206771 101.953958809734 Trimmed Mean ( 18 / 27 ) 12724.7319148936 122.644106222001 103.753309530099 Trimmed Mean ( 19 / 27 ) 12717.5377777778 121.271442643756 104.868363899459 Trimmed Mean ( 20 / 27 ) 12712.5093023256 120.209650831281 105.752817801360 Trimmed Mean ( 21 / 27 ) 12708.4853658537 119.131959657009 106.675701486339 Trimmed Mean ( 22 / 27 ) 12703.5871794872 118.128676048563 107.540248519036 Trimmed Mean ( 23 / 27 ) 12698.2324324324 116.581123210835 108.921857009971 Trimmed Mean ( 24 / 27 ) 12693.3314285714 114.797476824337 110.571519337440 Trimmed Mean ( 25 / 27 ) 12689.2454545455 112.990405456422 112.303742988509 Trimmed Mean ( 26 / 27 ) 12683.2225806452 111.224847992527 114.032276146579 Trimmed Mean ( 27 / 27 ) 12678.0827586207 109.284514457543 116.009874057190 Median 12648.6 Midrange 13206.5 Midmean - Weighted Average at Xnp 12682.3357142857 Midmean - Weighted Average at X(n+1)p 12712.5093023256 Midmean - Empirical Distribution Function 12712.5093023256 Midmean - Empirical Distribution Function - Averaging 12712.5093023256 Midmean - Empirical Distribution Function - Interpolation 12708.4853658537 Midmean - Closest Observation 12682.3357142857 Midmean - True Basic - Statistics Graphics Toolkit 12712.5093023256 Midmean - MS Excel (old versions) 12712.5093023256 Number of observations 83

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208802783ypb9pvwblvp92ub/1h62a1208802713.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208802783ypb9pvwblvp92ub/1h62a1208802713.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208802783ypb9pvwblvp92ub/2fhag1208802713.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208802783ypb9pvwblvp92ub/2fhag1208802713.ps (open in new window)

Parameters (Session):

Parameters (R input):

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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