Centrummaten werkloosheidsgraad

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 04 Apr 2011 11:56:05 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/04/t13019181562awin0j7wwa370c.htm/, Retrieved Mon, 04 Apr 2011 13:55:58 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

8 8 8,2 8,5 8,7 8,7 8 8 8,3 8,5 8,7 8,6 8,3 7,9 7,9 8,1 8,3 8,1 7,4 7,3 7,7 8 8 7,7 6,9 6,6 6,9 7,5 7,9 7,7 6,5 6,1 6,4 6,8 7,1 7,3 7,2 7 7 7 7,3 7,5 7,2 7,7 8 7,9 8 8 7,9 7,9 8 8,1 8,1 8,2 8 8,3 8,5 8,6 8,7 8,7 8,5 8,4 8,5 8,7 8,7 8,6 7,9 8,1 8,2 8,5 8,6 8,5

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' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 7.89722222222222 0.0748491498656544 105.50850926693 Geometric Mean 7.87072879143535 Harmonic Mean 7.84285753473738 Quadratic Mean 7.92236636926675 Winsorized Mean ( 1 / 24 ) 7.90138888888889 0.0735446447495949 107.436631392966 Winsorized Mean ( 2 / 24 ) 7.90416666666667 0.0727677049857207 108.621904019341 Winsorized Mean ( 3 / 24 ) 7.90833333333333 0.0716655748360984 110.350518382361 Winsorized Mean ( 4 / 24 ) 7.91944444444444 0.0689639086193174 114.83462296431 Winsorized Mean ( 5 / 24 ) 7.92638888888889 0.0674250599926028 117.558499610657 Winsorized Mean ( 6 / 24 ) 7.92638888888889 0.0674250599926028 117.558499610657 Winsorized Mean ( 7 / 24 ) 7.92638888888889 0.0638793198930472 124.083802115614 Winsorized Mean ( 8 / 24 ) 7.92638888888889 0.0638793198930472 124.083802115614 Winsorized Mean ( 9 / 24 ) 7.92638888888889 0.0638793198930472 124.083802115614 Winsorized Mean ( 10 / 24 ) 7.94027777777778 0.0611144454204902 129.924729303288 Winsorized Mean ( 11 / 24 ) 7.94027777777778 0.0559684869072857 141.870509934121 Winsorized Mean ( 12 / 24 ) 7.94027777777778 0.0559684869072857 141.870509934121 Winsorized Mean ( 13 / 24 ) 7.95833333333333 0.0526953478687726 151.025349584028 Winsorized Mean ( 14 / 24 ) 7.95833333333333 0.0526953478687726 151.025349584028 Winsorized Mean ( 15 / 24 ) 7.95833333333333 0.0526953478687726 151.025349584028 Winsorized Mean ( 16 / 24 ) 7.98055555555556 0.0488778174261239 163.275612042574 Winsorized Mean ( 17 / 24 ) 8.00416666666667 0.0450368263502162 177.724926805999 Winsorized Mean ( 18 / 24 ) 7.97916666666667 0.0412982538934504 193.20832999993 Winsorized Mean ( 19 / 24 ) 8.00555555555555 0.0292638480847891 273.564690889601 Winsorized Mean ( 20 / 24 ) 8.00555555555555 0.0292638480847891 273.564690889601 Winsorized Mean ( 21 / 24 ) 8.00555555555556 0.0292638480847891 273.564690889601 Winsorized Mean ( 22 / 24 ) 8.00555555555556 0.0292638480847891 273.564690889601 Winsorized Mean ( 23 / 24 ) 8.0375 0.015877748428183 506.211572525827 Winsorized Mean ( 24 / 24 ) 8.0375 0.015877748428183 506.211572525827 Trimmed Mean ( 1 / 24 ) 7.91142857142857 0.0715849220490861 110.518086001458 Trimmed Mean ( 2 / 24 ) 7.92205882352941 0.0692315016904749 114.428527911295 Trimmed Mean ( 3 / 24 ) 7.93181818181818 0.0669049038418287 118.553614553725 Trimmed Mean ( 4 / 24 ) 7.940625 0.0646157272829269 122.889973291349 Trimmed Mean ( 5 / 24 ) 7.94677419354839 0.0628815268544148 126.376928027638 Trimmed Mean ( 6 / 24 ) 7.95166666666667 0.061271446915805 129.777687110822 Trimmed Mean ( 7 / 24 ) 7.95689655172414 0.0592916478922052 134.19928159511 Trimmed Mean ( 8 / 24 ) 7.9625 0.057804108288814 137.749724642684 Trimmed Mean ( 9 / 24 ) 7.96851851851852 0.0559414734892019 142.443843923 Trimmed Mean ( 10 / 24 ) 7.975 0.0535944071956636 148.802840021809 Trimmed Mean ( 11 / 24 ) 7.98 0.0513491450160327 155.406677122052 Trimmed Mean ( 12 / 24 ) 7.98541666666667 0.049732403008335 160.567681906067 Trimmed Mean ( 13 / 24 ) 7.99130434782609 0.0476324582790509 167.770143229007 Trimmed Mean ( 14 / 24 ) 7.99545454545455 0.0457443194701825 174.785735979004 Trimmed Mean ( 15 / 24 ) 8 0.0432425565755193 185.002937697005 Trimmed Mean ( 16 / 24 ) 8.005 0.0398635493164189 200.810016600878 Trimmed Mean ( 17 / 24 ) 8.0078947368421 0.0364462578978461 219.717885970273 Trimmed Mean ( 18 / 24 ) 8.00833333333333 0.0329441566945864 243.088126600895 Trimmed Mean ( 19 / 24 ) 8.01176470588235 0.0291791155146387 274.571883505618 Trimmed Mean ( 20 / 24 ) 8.0125 0.0279508497187474 286.663914715473 Trimmed Mean ( 21 / 24 ) 8.01333333333333 0.0261443092128011 306.503922827295 Trimmed Mean ( 22 / 24 ) 8.01428571428571 0.0234093352440517 342.354262978148 Trimmed Mean ( 23 / 24 ) 8.01538461538462 0.0189674277014429 422.586802045638 Trimmed Mean ( 24 / 24 ) 8.0125 0.0183687076379873 436.203796037877 Median 8 Midrange 7.4 Midmean - Weighted Average at Xnp 7.9945945945946 Midmean - Weighted Average at X(n+1)p 7.9945945945946 Midmean - Empirical Distribution Function 7.9945945945946 Midmean - Empirical Distribution Function - Averaging 7.9945945945946 Midmean - Empirical Distribution Function - Interpolation 7.9945945945946 Midmean - Closest Observation 7.9945945945946 Midmean - True Basic - Statistics Graphics Toolkit 7.9945945945946 Midmean - MS Excel (old versions) 8.075 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/04/t13019181562awin0j7wwa370c/14qhq1301918163.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t13019181562awin0j7wwa370c/14qhq1301918163.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t13019181562awin0j7wwa370c/2hrbt1301918163.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t13019181562awin0j7wwa370c/2hrbt1301918163.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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