Mathieu Demoor Centrummaten Werkloosheid -21 jarigen

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 10:45:38 -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/t1208796379sp3972pkxmqv67l.htm/, Retrieved Mon, 21 Apr 2008 18:46:19 +0200

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Dataseries X:

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113 110 107 103 98 98 137 148 147 139 130 128 127 123 118 114 108 111 151 159 158 148 138 137 136 133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105

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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 126.930555555556 2.11710434912262 59.9547942018819 Geometric Mean 125.682736830275 Harmonic Mean 124.445463178237 Quadratic Mean 128.177990397034 Winsorized Mean ( 1 / 24 ) 126.944444444444 2.10780360292812 60.2259357883702 Winsorized Mean ( 2 / 24 ) 126.972222222222 2.07837176533041 61.0921608637409 Winsorized Mean ( 3 / 24 ) 126.930555555556 2.06944444444444 61.3355704697987 Winsorized Mean ( 4 / 24 ) 127.097222222222 2.01638046723897 63.0323613460988 Winsorized Mean ( 5 / 24 ) 127.166666666667 2.00439657598062 63.443865445865 Winsorized Mean ( 6 / 24 ) 127 1.90973947210875 66.5012174984086 Winsorized Mean ( 7 / 24 ) 126.805555555556 1.87340322084991 67.6872731637708 Winsorized Mean ( 8 / 24 ) 126.805555555556 1.83542762250879 69.0877450031121 Winsorized Mean ( 9 / 24 ) 126.805555555556 1.79370736374807 70.6946730098644 Winsorized Mean ( 10 / 24 ) 126.944444444444 1.77245143017665 71.6208310609633 Winsorized Mean ( 11 / 24 ) 127.25 1.72795187545286 73.6420972179276 Winsorized Mean ( 12 / 24 ) 127.25 1.67553392326521 75.9459407136444 Winsorized Mean ( 13 / 24 ) 127.25 1.67553392326521 75.9459407136444 Winsorized Mean ( 14 / 24 ) 127.055555555556 1.6419396818917 77.3813782301511 Winsorized Mean ( 15 / 24 ) 127.263888888889 1.61371191377866 78.8640697278415 Winsorized Mean ( 16 / 24 ) 126.597222222222 1.50178033655830 84.2980954940126 Winsorized Mean ( 17 / 24 ) 125.652777777778 1.28585657107245 97.7191240489435 Winsorized Mean ( 18 / 24 ) 125.652777777778 1.28585657107245 97.7191240489435 Winsorized Mean ( 19 / 24 ) 125.652777777778 1.21144123905115 103.721727251248 Winsorized Mean ( 20 / 24 ) 125.375 1.17209293096181 106.96677429589 Winsorized Mean ( 21 / 24 ) 125.375 1.17209293096181 106.96677429589 Winsorized Mean ( 22 / 24 ) 125.680555555556 1.13087734247709 111.135443991002 Winsorized Mean ( 23 / 24 ) 125.680555555556 1.04399062619250 120.384754807541 Winsorized Mean ( 24 / 24 ) 125.347222222222 0.998073206766434 125.589206655816 Trimmed Mean ( 1 / 24 ) 126.914285714286 2.06175294340643 61.5564954667157 Trimmed Mean ( 2 / 24 ) 126.882352941176 2.00695994988904 63.2211683886326 Trimmed Mean ( 3 / 24 ) 126.833333333333 1.96027962104803 64.7016537699475 Trimmed Mean ( 4 / 24 ) 126.796875 1.90826051112614 66.4463128910905 Trimmed Mean ( 5 / 24 ) 126.709677419355 1.86500901995488 67.940517211236 Trimmed Mean ( 6 / 24 ) 126.6 1.81599920356388 69.7136869617283 Trimmed Mean ( 7 / 24 ) 126.517241379310 1.78303516105199 70.956111322373 Trimmed Mean ( 8 / 24 ) 126.464285714286 1.75143063706156 72.2062769933383 Trimmed Mean ( 9 / 24 ) 126.407407407407 1.72082215056565 73.4575664114136 Trimmed Mean ( 10 / 24 ) 126.346153846154 1.69149335953705 74.695033908223 Trimmed Mean ( 11 / 24 ) 126.26 1.65832716301454 76.1369667071499 Trimmed Mean ( 12 / 24 ) 126.125 1.62472720023311 77.628416623975 Trimmed Mean ( 13 / 24 ) 125.978260869565 1.59209676423899 79.1272639322156 Trimmed Mean ( 14 / 24 ) 125.818181818182 1.54846740273358 81.2533616116617 Trimmed Mean ( 15 / 24 ) 125.666666666667 1.49861208211713 83.8553673537277 Trimmed Mean ( 16 / 24 ) 125.475 1.43758500306091 87.2817953253812 Trimmed Mean ( 17 / 24 ) 125.342105263158 1.3853923528196 90.4740848381739 Trimmed Mean ( 18 / 24 ) 125.305555555556 1.36847699173057 91.5657013692974 Trimmed Mean ( 19 / 24 ) 125.264705882353 1.34197876056723 93.3432849782254 Trimmed Mean ( 20 / 24 ) 125.21875 1.32114806424613 94.7802546805776 Trimmed Mean ( 21 / 24 ) 125.2 1.298451774805 96.4225259877691 Trimmed Mean ( 22 / 24 ) 125.178571428571 1.26098723756551 99.27029211671 Trimmed Mean ( 23 / 24 ) 125.115384615385 1.21443487721900 103.023543676458 Trimmed Mean ( 24 / 24 ) 125.041666666667 1.17102575911139 106.779603859057 Median 124.5 Midrange 127.5 Midmean - Weighted Average at Xnp 125.342105263158 Midmean - Weighted Average at X(n+1)p 125.342105263158 Midmean - Empirical Distribution Function 125.342105263158 Midmean - Empirical Distribution Function - Averaging 125.342105263158 Midmean - Empirical Distribution Function - Interpolation 125.342105263158 Midmean - Closest Observation 125.342105263158 Midmean - True Basic - Statistics Graphics Toolkit 125.342105263158 Midmean - MS Excel (old versions) 125.342105263158 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208796379sp3972pkxmqv67l/1gh7x1208796328.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208796379sp3972pkxmqv67l/1gh7x1208796328.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208796379sp3972pkxmqv67l/2k5111208796328.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208796379sp3972pkxmqv67l/2k5111208796328.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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