werkloosheid/invoer

*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 13:57:37 -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/t1229633968muexfun20nwsfp7.htm/, Retrieved Thu, 18 Dec 2008 21:59:28 +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/t1229633968muexfun20nwsfp7.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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15.59 13.17 11.20 13.30 10.78 11.60 15.18 15.87 12.58 11.43 10.30 11.17 11.26 11.20 9.99 11.17 10.29 10.47 14.36 16.06 14.47 13.24 13.03 14.43 13.98 13.62 12.20 12.24 12.07 12.30 16.12 18.38 14.59 12.96 14.14 13.92 14.24 14.10 12.91 13.69 14.11 13.99 17.93 21.37 16.25 14.53 15.36 14.95 15.95 15.25 12.67 13.86 14.65 12.41 17.46 18.95 15.33 15.31 14.84 14.75 15.83 14.83 13.00 13.92 13.94 12.54 18.12 17.83 14.41 15.18 12.99 13.06 12.81 12.95 10.48 13.23 11.80 11.69 15.33 14.89 12.92 11.27 10.68 11.55

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 13.7948809523810 0.238404135179953 57.86342985187 Geometric Mean 13.6302936753358 Harmonic Mean 13.4710031778402 Quadratic Mean 13.9648191044155 Winsorized Mean ( 1 / 28 ) 13.7696428571429 0.228244657816602 60.3284343601459 Winsorized Mean ( 2 / 28 ) 13.7563095238095 0.224661202166931 61.2313536610923 Winsorized Mean ( 3 / 28 ) 13.7530952380952 0.221300333318725 62.1467443444269 Winsorized Mean ( 4 / 28 ) 13.7445238095238 0.219098149214351 62.7322679758335 Winsorized Mean ( 5 / 28 ) 13.7504761904762 0.215644699438507 63.7644988551981 Winsorized Mean ( 6 / 28 ) 13.7311904761905 0.208562025123546 65.8374431685563 Winsorized Mean ( 7 / 28 ) 13.6628571428571 0.183557670970865 74.4335939249621 Winsorized Mean ( 8 / 28 ) 13.6504761904762 0.1814913915543 75.2128025113088 Winsorized Mean ( 9 / 28 ) 13.6472619047619 0.179917058023809 75.8530739367467 Winsorized Mean ( 10 / 28 ) 13.6341666666667 0.177831668613406 76.6689463860704 Winsorized Mean ( 11 / 28 ) 13.6315476190476 0.174912361798785 77.9335861620174 Winsorized Mean ( 12 / 28 ) 13.6272619047619 0.173802133524382 78.4067584696837 Winsorized Mean ( 13 / 28 ) 13.6148809523810 0.164263468003300 82.8844119625398 Winsorized Mean ( 14 / 28 ) 13.5965476190476 0.155679851371317 87.3365917251427 Winsorized Mean ( 15 / 28 ) 13.6001190476190 0.153542925990903 88.5753541548688 Winsorized Mean ( 16 / 28 ) 13.6172619047619 0.150878318861337 90.253271692911 Winsorized Mean ( 17 / 28 ) 13.6354761904762 0.146934872326941 92.7994558033591 Winsorized Mean ( 18 / 28 ) 13.6804761904762 0.136694010750016 100.081021219685 Winsorized Mean ( 19 / 28 ) 13.6940476190476 0.130393741407584 105.020743106395 Winsorized Mean ( 20 / 28 ) 13.7035714285714 0.129085850148134 106.158586807506 Winsorized Mean ( 21 / 28 ) 13.6610714285714 0.119318563590267 114.492422784126 Winsorized Mean ( 22 / 28 ) 13.6741666666667 0.113364319656242 120.621432811764 Winsorized Mean ( 23 / 28 ) 13.6960714285714 0.106884506365554 128.138978176404 Winsorized Mean ( 24 / 28 ) 13.7046428571429 0.105034000782526 130.478157120936 Winsorized Mean ( 25 / 28 ) 13.7076190476190 0.0985519976635548 139.090220113196 Winsorized Mean ( 26 / 28 ) 13.72 0.0892195394471545 153.777973805015 Winsorized Mean ( 27 / 28 ) 13.7328571428571 0.0829083664640383 165.638978652580 Winsorized Mean ( 28 / 28 ) 13.7161904761905 0.0800383414936997 171.370248561062 Trimmed Mean ( 1 / 28 ) 13.7489024390244 0.220941908411303 62.2285855041569 Trimmed Mean ( 2 / 28 ) 13.727125 0.212422003090904 64.6219544127245 Trimmed Mean ( 3 / 28 ) 13.7114102564103 0.204740824800427 66.9695956816408 Trimmed Mean ( 4 / 28 ) 13.6960526315789 0.197263745341671 69.4301560981553 Trimmed Mean ( 5 / 28 ) 13.6822972972973 0.189272027270787 72.2890619104658 Trimmed Mean ( 6 / 28 ) 13.6663888888889 0.180897854779088 75.5475453568992 Trimmed Mean ( 7 / 28 ) 13.6534285714286 0.172996234441754 78.923270298265 Trimmed Mean ( 8 / 28 ) 13.6517647058824 0.169982303109310 80.3128587868545 Trimmed Mean ( 9 / 28 ) 13.6519696969697 0.166822521956799 81.83529140331 Trimmed Mean ( 10 / 28 ) 13.65265625 0.163343999012112 83.5822334004915 Trimmed Mean ( 11 / 28 ) 13.6551612903226 0.159558112354603 85.581115800463 Trimmed Mean ( 12 / 28 ) 13.6581666666667 0.155540154436674 87.811193939809 Trimmed Mean ( 13 / 28 ) 13.6618965517241 0.150840848909474 90.5715968220464 Trimmed Mean ( 14 / 28 ) 13.6673214285714 0.146961319027670 92.9994471946606 Trimmed Mean ( 15 / 28 ) 13.6751851851852 0.143784755647897 95.1087277894276 Trimmed Mean ( 16 / 28 ) 13.6832692307692 0.140190755939249 97.6046468905471 Trimmed Mean ( 17 / 28 ) 13.6902 0.136177702031618 100.531877067667 Trimmed Mean ( 18 / 28 ) 13.6958333333333 0.131877412361833 103.852760590691 Trimmed Mean ( 19 / 28 ) 13.6973913043478 0.128493100167247 106.600208777897 Trimmed Mean ( 20 / 28 ) 13.6977272727273 0.125367056695442 109.260978392462 Trimmed Mean ( 21 / 28 ) 13.6971428571429 0.121484854073959 112.747740955462 Trimmed Mean ( 22 / 28 ) 13.70075 0.118462580643934 115.654664329665 Trimmed Mean ( 23 / 28 ) 13.7034210526316 0.115669414350494 118.470566567480 Trimmed Mean ( 24 / 28 ) 13.7041666666667 0.113270553340082 120.986136842834 Trimmed Mean ( 25 / 28 ) 13.7041176470588 0.110237240236447 124.314774369033 Trimmed Mean ( 26 / 28 ) 13.70375 0.107536331070016 127.433676262190 Trimmed Mean ( 27 / 28 ) 13.702 0.106010626229464 129.251193841091 Trimmed Mean ( 28 / 28 ) 13.6985714285714 0.105165169015214 130.257684714886 Median 13.89 Midrange 15.68 Midmean - Weighted Average at Xnp 13.6632558139535 Midmean - Weighted Average at X(n+1)p 13.6971428571429 Midmean - Empirical Distribution Function 13.6632558139535 Midmean - Empirical Distribution Function - Averaging 13.6971428571429 Midmean - Empirical Distribution Function - Interpolation 13.6971428571429 Midmean - Closest Observation 13.6632558139535 Midmean - True Basic - Statistics Graphics Toolkit 13.6971428571429 Midmean - MS Excel (old versions) 13.7306666666667 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229633968muexfun20nwsfp7/167go1229633851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229633968muexfun20nwsfp7/167go1229633851.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229633968muexfun20nwsfp7/2003u1229633851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229633968muexfun20nwsfp7/2003u1229633851.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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