Central Tendency Werkloosheid 2000-2006

*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, 11 Dec 2008 06:54:33 -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/11/t12290037290b8v8ox1eiyc5ch.htm/, Retrieved Thu, 11 Dec 2008 13:55:31 +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/11/t12290037290b8v8ox1eiyc5ch.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}, }

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Dataseries X:

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492865 480961 461935 456608 441977 439148 488180 520564 501492 485025 464196 460170 467037 460070 447988 442867 436087 431328 484015 509673 512927 502831 470984 471067 476049 474605 470439 461251 454724 455626 516847 525192 522975 518585 509239 512238 519164 517009 509933 509127 500857 506971 569323 579714 577992 565464 547344 554788 562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 533579.75 6250.43892702864 85.3667648351306 Geometric Mean 530503.63994689 Harmonic Mean 527402.894465590 Quadratic Mean 536609.720851985 Winsorized Mean ( 1 / 28 ) 533628.642857143 6238.09672367916 85.5435025288313 Winsorized Mean ( 2 / 28 ) 533643.833333333 6214.12981015265 85.8758747622983 Winsorized Mean ( 3 / 28 ) 533563.654761905 6164.19867145649 86.5584779466288 Winsorized Mean ( 4 / 28 ) 533567.035714286 6150.01898425736 86.7585997832032 Winsorized Mean ( 5 / 28 ) 533851.083333333 6093.54014640399 87.6093486720322 Winsorized Mean ( 6 / 28 ) 533835.511904762 5932.15623819813 89.9901301431184 Winsorized Mean ( 7 / 28 ) 533869.345238095 5913.52486060246 90.2793778368771 Winsorized Mean ( 8 / 28 ) 533887.345238095 5886.66911807089 90.6943017400398 Winsorized Mean ( 9 / 28 ) 534198.166666667 5819.33888808082 91.7970540881907 Winsorized Mean ( 10 / 28 ) 532588.404761905 5575.52795143307 95.522506460579 Winsorized Mean ( 11 / 28 ) 532509.047619048 5522.87181645093 96.4188678130945 Winsorized Mean ( 12 / 28 ) 532599.619047619 5506.74209531149 96.7177343389807 Winsorized Mean ( 13 / 28 ) 532758.095238095 5426.85436356183 98.1707006576877 Winsorized Mean ( 14 / 28 ) 533125.428571429 5341.04650384637 99.8166610583707 Winsorized Mean ( 15 / 28 ) 533711.142857143 5248.65962375121 101.685226537075 Winsorized Mean ( 16 / 28 ) 533330.571428571 5167.89730315335 103.200690753499 Winsorized Mean ( 17 / 28 ) 533186.880952381 5143.99963365471 103.652200413079 Winsorized Mean ( 18 / 28 ) 533796.523809524 5015.11926400637 106.437453569767 Winsorized Mean ( 19 / 28 ) 533726.404761905 4916.11688321618 108.566662966063 Winsorized Mean ( 20 / 28 ) 534134.738095238 4653.03131166098 114.792852727348 Winsorized Mean ( 21 / 28 ) 533740.988095238 4400.08444549742 121.302441965952 Winsorized Mean ( 22 / 28 ) 533983.25 4361.37752681469 122.434539710666 Winsorized Mean ( 23 / 28 ) 534375.619047619 4186.13071744144 127.653830020442 Winsorized Mean ( 24 / 28 ) 534632.190476191 3875.64389384943 137.946675473627 Winsorized Mean ( 25 / 28 ) 536681.892857143 3534.95747531301 151.821315137496 Winsorized Mean ( 26 / 28 ) 536829.535714286 3504.94972724139 153.163262668764 Winsorized Mean ( 27 / 28 ) 537206.25 3446.27648690224 155.880194767216 Winsorized Mean ( 28 / 28 ) 537435.583333333 3140.63469596821 171.123239523293 Trimmed Mean ( 1 / 28 ) 533664.475609756 6169.87141459011 86.4952346247899 Trimmed Mean ( 2 / 28 ) 533702.1 6089.76368112606 87.6392135961034 Trimmed Mean ( 3 / 28 ) 533733.474358974 6010.2360995169 88.804077830133 Trimmed Mean ( 4 / 28 ) 533796.039473684 5937.77015141474 89.89840055471 Trimmed Mean ( 5 / 28 ) 533861.027027027 5856.49219626068 91.157131118162 Trimmed Mean ( 6 / 28 ) 533863.347222222 5776.2263465346 92.4242429562181 Trimmed Mean ( 7 / 28 ) 533868.914285714 5721.20143207653 93.3141265211395 Trimmed Mean ( 8 / 28 ) 533868.838235294 5658.00938408085 94.3563013057855 Trimmed Mean ( 9 / 28 ) 533865.893939394 5586.42644043748 95.5648301524196 Trimmed Mean ( 10 / 28 ) 533817.4375 5512.51864558247 96.8373028411944 Trimmed Mean ( 11 / 28 ) 533983.951612903 5468.24690943278 97.651763070862 Trimmed Mean ( 12 / 28 ) 534171.666666667 5420.65410414286 98.543765457828 Trimmed Mean ( 13 / 28 ) 534361.396551724 5361.91492669822 99.6586860957108 Trimmed Mean ( 14 / 28 ) 534546.392857143 5300.88591399286 100.840954046208 Trimmed Mean ( 15 / 28 ) 534704.277777778 5237.48368617742 102.09182688033 Trimmed Mean ( 16 / 28 ) 534811.230769231 5171.69199921094 103.411268662331 Trimmed Mean ( 17 / 28 ) 534966.7 5099.59177583893 104.903828289666 Trimmed Mean ( 18 / 28 ) 535149.916666667 5008.54420044697 106.847398215815 Trimmed Mean ( 19 / 28 ) 535287.217391304 4914.02283502065 108.930551477394 Trimmed Mean ( 20 / 28 ) 535444.045454545 4807.94368924798 111.366538391862 Trimmed Mean ( 21 / 28 ) 535574.976190476 4720.25389586721 113.463171262757 Trimmed Mean ( 22 / 28 ) 535758.375 4651.43976396604 115.181191671111 Trimmed Mean ( 23 / 28 ) 535936.736842105 4560.70249022968 117.511882871166 Trimmed Mean ( 24 / 28 ) 536095.111111111 4471.65287518555 119.887461320187 Trimmed Mean ( 25 / 28 ) 536245.705882353 4415.23239144469 121.453563106084 Trimmed Mean ( 26 / 28 ) 536199.90625 4406.5009080608 121.683829740993 Trimmed Mean ( 27 / 28 ) 536132.1 4382.19413246352 122.343301961067 Trimmed Mean ( 28 / 28 ) 536012.75 4342.34257073914 123.438614358047 Median 530927 Midrange 530106 Midmean - Weighted Average at Xnp 534304.88372093 Midmean - Weighted Average at X(n+1)p 535574.976190476 Midmean - Empirical Distribution Function 534304.88372093 Midmean - Empirical Distribution Function - Averaging 535574.976190476 Midmean - Empirical Distribution Function - Interpolation 535574.976190476 Midmean - Closest Observation 534304.88372093 Midmean - True Basic - Statistics Graphics Toolkit 535574.976190476 Midmean - MS Excel (old versions) 535444.045454545 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290037290b8v8ox1eiyc5ch/1vai81229003671.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290037290b8v8ox1eiyc5ch/1vai81229003671.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290037290b8v8ox1eiyc5ch/28qa21229003671.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t12290037290b8v8ox1eiyc5ch/28qa21229003671.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')

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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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