Faillissementen Vlaanderen

*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: Thu, 09 Dec 2010 12:25:53 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897452odo0uvp3tc26524.htm/, Retrieved Thu, 09 Dec 2010 13:25:08 +0100

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/2010/Dec/09/t1291897452odo0uvp3tc26524.htm/}, year = {2010}, } @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 = {2010}, 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 «

356 386 444 387 327 448 225 182 460 411 342 361 377 331 428 340 352 461 221 198 422 329 320 375 364 351 380 319 322 386 221 187 344 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 442 544 420 396 482 261 211 448 468 464 425

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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 356.180555555556 9.36654316303907 38.0268952329249 Geometric Mean 346.301555928549 Harmonic Mean 335.132988739581 Quadratic Mean 364.819913716952 Winsorized Mean ( 1 / 24 ) 355.388888888889 9.14240398838495 38.8725863941690 Winsorized Mean ( 2 / 24 ) 355.305555555556 8.99283837146586 39.5098344792824 Winsorized Mean ( 3 / 24 ) 355.638888888889 8.84414046925357 40.2118091775293 Winsorized Mean ( 4 / 24 ) 355.527777777778 8.80283005563267 40.3878952031212 Winsorized Mean ( 5 / 24 ) 355.944444444444 8.68048935812005 41.0051127027166 Winsorized Mean ( 6 / 24 ) 355.111111111111 8.48151251836606 41.8688424195738 Winsorized Mean ( 7 / 24 ) 355.208333333333 8.45974397913366 41.9880712950026 Winsorized Mean ( 8 / 24 ) 354.763888888889 8.39212810820293 42.2734119778418 Winsorized Mean ( 9 / 24 ) 355.013888888889 8.24316222196716 43.0676819561811 Winsorized Mean ( 10 / 24 ) 360.013888888889 7.19868089810575 50.0110914742203 Winsorized Mean ( 11 / 24 ) 360.319444444444 7.03225372721405 51.2381177388478 Winsorized Mean ( 12 / 24 ) 364.319444444444 5.81714139031916 62.628603982489 Winsorized Mean ( 13 / 24 ) 364.5 5.67287701667526 64.2531115919775 Winsorized Mean ( 14 / 24 ) 366.638888888889 5.29029382419398 69.3040691260186 Winsorized Mean ( 15 / 24 ) 367.472222222222 5.04835662619853 72.7904641909051 Winsorized Mean ( 16 / 24 ) 367.472222222222 4.98220511912845 73.7569436495832 Winsorized Mean ( 17 / 24 ) 367.944444444444 4.91945647312364 74.793718870088 Winsorized Mean ( 18 / 24 ) 367.944444444444 4.69982722391154 78.2889299786246 Winsorized Mean ( 19 / 24 ) 367.680555555556 4.58073235584014 80.2667623850118 Winsorized Mean ( 20 / 24 ) 365.458333333333 4.1501521315706 88.0590209099222 Winsorized Mean ( 21 / 24 ) 361.666666666667 3.42308740562397 105.655107162167 Winsorized Mean ( 22 / 24 ) 361.361111111111 3.21298626417628 112.468924981151 Winsorized Mean ( 23 / 24 ) 361.041666666667 3.08248862303028 117.126682632081 Winsorized Mean ( 24 / 24 ) 361.708333333333 2.81709219082028 128.397762242922 Trimmed Mean ( 1 / 24 ) 355.985714285714 8.90331068432828 39.9835215132192 Trimmed Mean ( 2 / 24 ) 356.617647058824 8.61841112255229 41.3785838233734 Trimmed Mean ( 3 / 24 ) 357.333333333333 8.37365536179416 42.6735180628177 Trimmed Mean ( 4 / 24 ) 357.96875 8.14818026567068 43.9323552411043 Trimmed Mean ( 5 / 24 ) 358.677419354839 7.89020284918884 45.4585802431826 Trimmed Mean ( 6 / 24 ) 359.333333333333 7.61665090430937 47.1773405198377 Trimmed Mean ( 7 / 24 ) 360.206896551724 7.33865609861578 49.083495903244 Trimmed Mean ( 8 / 24 ) 361.125 6.99986375099312 51.5902898751086 Trimmed Mean ( 9 / 24 ) 362.185185185185 6.59156196059896 54.9467921791749 Trimmed Mean ( 10 / 24 ) 363.288461538462 6.11283646410149 59.4304237765766 Trimmed Mean ( 11 / 24 ) 363.76 5.80032089189724 62.713771665315 Trimmed Mean ( 12 / 24 ) 364.229166666667 5.44355624524572 66.9101503240233 Trimmed Mean ( 13 / 24 ) 364.217391304348 5.29359407267493 68.8034228359908 Trimmed Mean ( 14 / 24 ) 364.181818181818 5.13108018408093 70.9756630410268 Trimmed Mean ( 15 / 24 ) 363.880952380952 5.0038547720236 72.7201265742962 Trimmed Mean ( 16 / 24 ) 363.45 4.88560811636245 74.3919674569815 Trimmed Mean ( 17 / 24 ) 362.973684210526 4.73711276293287 76.6233996055014 Trimmed Mean ( 18 / 24 ) 362.388888888889 4.54366430995425 79.7569679817605 Trimmed Mean ( 19 / 24 ) 361.735294117647 4.33106525524039 83.5210907247274 Trimmed Mean ( 20 / 24 ) 361.03125 4.06089841258541 88.9042801172034 Trimmed Mean ( 21 / 24 ) 360.5 3.82001685017647 94.3713114729706 Trimmed Mean ( 22 / 24 ) 360.357142857143 3.71654896450906 96.9601494015954 Trimmed Mean ( 23 / 24 ) 360.230769230769 3.6193104707974 99.5302205039636 Trimmed Mean ( 24 / 24 ) 360.125 3.50223143153048 102.827299406260 Median 357 Midrange 363 Midmean - Weighted Average at Xnp 361.297297297297 Midmean - Weighted Average at X(n+1)p 362.388888888889 Midmean - Empirical Distribution Function 361.297297297297 Midmean - Empirical Distribution Function - Averaging 362.388888888889 Midmean - Empirical Distribution Function - Interpolation 362.388888888889 Midmean - Closest Observation 361.297297297297 Midmean - True Basic - Statistics Graphics Toolkit 362.388888888889 Midmean - MS Excel (old versions) 364.564102564103 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897452odo0uvp3tc26524/18mdv1291897541.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897452odo0uvp3tc26524/18mdv1291897541.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897452odo0uvp3tc26524/28mdv1291897541.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/09/t1291897452odo0uvp3tc26524/28mdv1291897541.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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