werkloosheid

*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, 18 Dec 2008 10:34:36 -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/18/t1229621837r1tnhqqkh56iw49.htm/, Retrieved Thu, 18 Dec 2008 18:37:19 +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/2008/Dec/18/t1229621837r1tnhqqkh56iw49.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 201695.154761905 3213.42808304343 62.7663509341338 Geometric Mean 199546.309929631 Harmonic Mean 197383.482618816 Quadratic Mean 203808.742251540 Winsorized Mean ( 1 / 28 ) 201629.654761905 3198.12890252923 63.0461313183615 Winsorized Mean ( 2 / 28 ) 201612.130952381 3164.43394887684 63.711910000188 Winsorized Mean ( 3 / 28 ) 201333.309523810 3109.54987241851 64.7467697204736 Winsorized Mean ( 4 / 28 ) 201219.119047619 3059.16563014643 65.7758171263148 Winsorized Mean ( 5 / 28 ) 201198.345238095 3042.52185260961 66.1288085952529 Winsorized Mean ( 6 / 28 ) 201365.916666667 3009.49798499503 66.9101350692545 Winsorized Mean ( 7 / 28 ) 201245.25 2978.33468376032 67.5697231400188 Winsorized Mean ( 8 / 28 ) 201262.297619048 2963.97435754622 67.9028471034635 Winsorized Mean ( 9 / 28 ) 201423.761904762 2920.17873452004 68.9765182944763 Winsorized Mean ( 10 / 28 ) 201535.309523810 2879.34687958013 69.993410989508 Winsorized Mean ( 11 / 28 ) 201504.142857143 2766.82400561860 72.8286809887248 Winsorized Mean ( 12 / 28 ) 201276.714285714 2715.12012296860 74.1317898176995 Winsorized Mean ( 13 / 28 ) 201103.380952381 2663.46271231284 75.504485203681 Winsorized Mean ( 14 / 28 ) 200995.047619048 2629.86897732488 76.4277799966678 Winsorized Mean ( 15 / 28 ) 201272.547619048 2546.44947820267 79.0404637287795 Winsorized Mean ( 16 / 28 ) 201872.357142857 2390.33856490252 84.4534578101029 Winsorized Mean ( 17 / 28 ) 202104.892857143 2344.57403708668 86.2011135755281 Winsorized Mean ( 18 / 28 ) 201930.25 2301.56676785255 87.7359948103563 Winsorized Mean ( 19 / 28 ) 201744.547619048 2200.76896684778 91.6700256401794 Winsorized Mean ( 20 / 28 ) 202054.309523810 2154.27462296925 93.7922711289784 Winsorized Mean ( 21 / 28 ) 201100.309523810 1910.54410378610 105.258135169605 Winsorized Mean ( 22 / 28 ) 200529.357142857 1834.81952192544 109.291052742029 Winsorized Mean ( 23 / 28 ) 200636.964285714 1810.15079910593 110.839916975322 Winsorized Mean ( 24 / 28 ) 200911.25 1770.31262906056 113.489135592179 Winsorized Mean ( 25 / 28 ) 200952.916666667 1655.96635777607 121.350844914834 Winsorized Mean ( 26 / 28 ) 201173.607142857 1570.37394907591 128.105542798413 Winsorized Mean ( 27 / 28 ) 201492.785714286 1455.59556779733 138.426352877120 Winsorized Mean ( 28 / 28 ) 202551.452380952 1280.19276221790 158.219495031387 Trimmed Mean ( 1 / 28 ) 201536.329268293 3134.6033798565 64.294044523591 Trimmed Mean ( 2 / 28 ) 201438.3375 3060.92652380932 65.8095958635786 Trimmed Mean ( 3 / 28 ) 201344.756410256 2996.03418647864 67.2037579941318 Trimmed Mean ( 4 / 28 ) 201348.973684211 2944.22173816775 68.387842897157 Trimmed Mean ( 5 / 28 ) 201385.824324324 2900.62283321521 69.4284765389842 Trimmed Mean ( 6 / 28 ) 201429.569444444 2853.75817540997 70.5839657964386 Trimmed Mean ( 7 / 28 ) 201442.3 2806.60415376329 71.7743896052789 Trimmed Mean ( 8 / 28 ) 201477.073529412 2757.60758745191 73.0622712405506 Trimmed Mean ( 9 / 28 ) 201511.242424242 2701.96060155139 74.5796375818879 Trimmed Mean ( 10 / 28 ) 201524 2644.3202398261 76.2101340695607 Trimmed Mean ( 11 / 28 ) 201522.467741935 2582.97465965006 78.0195295331458 Trimmed Mean ( 12 / 28 ) 201524.8 2530.8481008333 79.627378637875 Trimmed Mean ( 13 / 28 ) 201554.741379310 2476.77464636104 81.377908836172 Trimmed Mean ( 14 / 28 ) 201606.821428571 2419.77402254827 83.3163839060718 Trimmed Mean ( 15 / 28 ) 201674.796296296 2355.2239648903 85.628712726558 Trimmed Mean ( 16 / 28 ) 201718.115384615 2290.97271763581 88.0491128645041 Trimmed Mean ( 17 / 28 ) 201701.92 2240.55640116650 90.0231388484523 Trimmed Mean ( 18 / 28 ) 201660.4375 2184.67004136396 92.3070457697571 Trimmed Mean ( 19 / 28 ) 201633.065217391 2121.14130052990 95.0587616049054 Trimmed Mean ( 20 / 28 ) 201621.863636364 2059.66506354460 97.8906071695856 Trimmed Mean ( 21 / 28 ) 201578.619047619 1988.48502349872 101.372963168183 Trimmed Mean ( 22 / 28 ) 201626.45 1948.0893245954 103.499591858744 Trimmed Mean ( 23 / 28 ) 201736.684210526 1907.80256548830 105.742956771259 Trimmed Mean ( 24 / 28 ) 201848.25 1856.30931132864 108.736323611677 Trimmed Mean ( 25 / 28 ) 201944.705882353 1793.45832857771 112.600723788494 Trimmed Mean ( 26 / 28 ) 202048.84375 1734.6264298191 116.479744731591 Trimmed Mean ( 27 / 28 ) 202143.1 1673.19327390445 120.812761533695 Trimmed Mean ( 28 / 28 ) 202215.357142857 1617.22990287960 125.038101745953 Median 201436.5 Midrange 208207 Midmean - Weighted Average at Xnp 201027.395348837 Midmean - Weighted Average at X(n+1)p 201578.619047619 Midmean - Empirical Distribution Function 201027.395348837 Midmean - Empirical Distribution Function - Averaging 201578.619047619 Midmean - Empirical Distribution Function - Interpolation 201578.619047619 Midmean - Closest Observation 201027.395348837 Midmean - True Basic - Statistics Graphics Toolkit 201578.619047619 Midmean - MS Excel (old versions) 201621.863636364 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229621837r1tnhqqkh56iw49/1nk3x1229621674.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229621837r1tnhqqkh56iw49/1nk3x1229621674.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229621837r1tnhqqkh56iw49/2m6511229621674.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229621837r1tnhqqkh56iw49/2m6511229621674.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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