Robuustheid Producten van metaal

*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: Fri, 26 Dec 2008 07:38:16 -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/26/t12303023723nu69pjv1heodg8.htm/, Retrieved Fri, 26 Dec 2008 15:39:34 +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/26/t12303023723nu69pjv1heodg8.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:

Robuustheid Producten van metaal

Dataseries X:

» Textbox « » Textfile « » CSV «

97.3 101.0 113.2 101.0 105.7 113.9 86.4 96.5 103.3 114.9 105.8 94.2 98.4 99.4 108.8 112.6 104.4 112.2 81.1 97.1 112.6 113.8 107.8 103.2 103.3 101.2 107.7 110.4 101.9 115.9 89.9 88.6 117.2 123.9 100.0 103.6 94.1 98.7 119.5 112.7 104.4 124.7 89.1 97.0 121.6 118.8 114.0 111.5 97.2 102.5 113.4 109.8 104.9 126.1 80.0 96.8 117.2 112.3 117.3 111.1 102.2 104.3 122.9 107.6 121.3 131.5 89.0 104.4 128.9 135.9 133.3 121.3 120.5 120.4 137.9 126.1 133.2 146.6 103.4 117.2

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 109.385 1.47627449764773 74.0952987904973 Geometric Mean 108.601231238788 Harmonic Mean 107.818091357526 Quadratic Mean 110.169186935368 Winsorized Mean ( 1 / 26 ) 109.29 1.44178774399499 75.8017263325963 Winsorized Mean ( 2 / 26 ) 109.3725 1.39930133448216 78.1622208918108 Winsorized Mean ( 3 / 26 ) 109.3575 1.36017936154377 80.399323127416 Winsorized Mean ( 4 / 26 ) 109.3725 1.35523127901486 80.7039371755828 Winsorized Mean ( 5 / 26 ) 109.2725 1.33097824379027 82.0993885586145 Winsorized Mean ( 6 / 26 ) 109.1375 1.27981453239982 85.2760280783442 Winsorized Mean ( 7 / 26 ) 109.26 1.16807425635292 93.5385737728203 Winsorized Mean ( 8 / 26 ) 109.27 1.16643511867397 93.6785923628749 Winsorized Mean ( 9 / 26 ) 109.37125 1.09769781203692 99.6369390561578 Winsorized Mean ( 10 / 26 ) 109.30875 1.07471838193765 101.709202928978 Winsorized Mean ( 11 / 26 ) 109.19875 1.04746150914146 104.250847450713 Winsorized Mean ( 12 / 26 ) 109.01875 1.01376615432976 107.538360335255 Winsorized Mean ( 13 / 26 ) 108.98625 1.00373470912262 108.580732547614 Winsorized Mean ( 14 / 26 ) 109.00375 1.00113929364740 108.879704044851 Winsorized Mean ( 15 / 26 ) 109.06 0.948063649521647 115.034470581197 Winsorized Mean ( 16 / 26 ) 109.1 0.936521641399774 116.494905378730 Winsorized Mean ( 17 / 26 ) 109.0575 0.886944290274554 122.958680940650 Winsorized Mean ( 18 / 26 ) 109.035 0.845245638778111 128.998003654442 Winsorized Mean ( 19 / 26 ) 108.91625 0.762651611301988 142.812587537919 Winsorized Mean ( 20 / 26 ) 108.89125 0.759180507858743 143.432620928488 Winsorized Mean ( 21 / 26 ) 108.94375 0.752306251078238 144.813033048519 Winsorized Mean ( 22 / 26 ) 109.13625 0.727641942631962 149.986200087975 Winsorized Mean ( 23 / 26 ) 108.84875 0.665427895431945 163.577076866223 Winsorized Mean ( 24 / 26 ) 108.63875 0.614550607009667 176.777548929003 Winsorized Mean ( 25 / 26 ) 108.57625 0.551531939439158 196.863032284965 Winsorized Mean ( 26 / 26 ) 108.57625 0.543492118391026 199.775206163860 Trimmed Mean ( 1 / 26 ) 109.284615384615 1.38521890868746 78.8933898456283 Trimmed Mean ( 2 / 26 ) 109.278947368421 1.31864406139975 82.872209845939 Trimmed Mean ( 3 / 26 ) 109.228378378378 1.26752581696347 86.1744801696033 Trimmed Mean ( 4 / 26 ) 109.180555555556 1.22521059300753 89.1116647037381 Trimmed Mean ( 5 / 26 ) 109.125714285714 1.17685000075743 92.7269526409316 Trimmed Mean ( 6 / 26 ) 109.091176470588 1.12709805395990 96.7894284683675 Trimmed Mean ( 7 / 26 ) 109.081818181818 1.08249670206469 100.768730263808 Trimmed Mean ( 8 / 26 ) 109.05 1.05795362517261 103.076351746711 Trimmed Mean ( 9 / 26 ) 109.014516129032 1.02861966617011 105.981364846863 Trimmed Mean ( 10 / 26 ) 108.961666666667 1.00826553444381 108.068423390841 Trimmed Mean ( 11 / 26 ) 108.913793103448 0.9880668773514 110.229171324315 Trimmed Mean ( 12 / 26 ) 108.876785714286 0.968654814582817 112.399984055390 Trimmed Mean ( 13 / 26 ) 108.859259259259 0.95117536808004 114.447096626349 Trimmed Mean ( 14 / 26 ) 108.844230769231 0.930995564456267 116.911653422108 Trimmed Mean ( 15 / 26 ) 108.826 0.905808061842 120.142450243485 Trimmed Mean ( 16 / 26 ) 108.8 0.88455522341028 122.999669348553 Trimmed Mean ( 17 / 26 ) 108.767391304348 0.859322586522933 126.573411440809 Trimmed Mean ( 18 / 26 ) 108.736363636364 0.837033236873532 129.906864920339 Trimmed Mean ( 19 / 26 ) 108.704761904762 0.816474904938502 133.139134157405 Trimmed Mean ( 20 / 26 ) 108.6825 0.80649516745496 134.759021982695 Trimmed Mean ( 21 / 26 ) 108.660526315789 0.792519610157906 137.107681529974 Trimmed Mean ( 22 / 26 ) 108.630555555556 0.773815730540838 140.382976551318 Trimmed Mean ( 23 / 26 ) 108.576470588235 0.752678625124219 144.253426315004 Trimmed Mean ( 24 / 26 ) 108.546875 0.73870506215323 146.942102553893 Trimmed Mean ( 25 / 26 ) 108.536666666667 0.73060333016873 148.557585470628 Trimmed Mean ( 26 / 26 ) 108.532142857143 0.732883223542443 148.089271756754 Median 108.3 Midrange 113.3 Midmean - Weighted Average at Xnp 108.495121951220 Midmean - Weighted Average at X(n+1)p 108.495121951220 Midmean - Empirical Distribution Function 108.495121951220 Midmean - Empirical Distribution Function - Averaging 108.495121951220 Midmean - Empirical Distribution Function - Interpolation 108.495121951220 Midmean - Closest Observation 108.495121951220 Midmean - True Basic - Statistics Graphics Toolkit 108.495121951220 Midmean - MS Excel (old versions) 108.704761904762 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t12303023723nu69pjv1heodg8/1m2lz1230302293.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t12303023723nu69pjv1heodg8/1m2lz1230302293.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t12303023723nu69pjv1heodg8/2joq91230302294.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/26/t12303023723nu69pjv1heodg8/2joq91230302294.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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