Central Tendency consumptieprijs biefstuk - Mattias Dierckx

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 01 Jun 2009 10:42:53 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk.htm/, Retrieved Mon, 01 Jun 2009 18:44:08 +0200

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/2009/Jun/01/t12438746465sqh2cn1bg7tjqk.htm/}, year = {2009}, } @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 = {2009}, 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:

» Textbox « » Textfile « » CSV «

9,370 9,330 9,310 9,260 9,350 9,380 9,430 9,270 9,290 9,270 9,290 9,310 9,330 9,350 9,340 9,470 9,630 9,620 9,630 9,500 9,550 9,580 9,610 9,570 9,610 9,650 9,620 9,650 9,960 10,030 10,030 9,720 9,750 9,770 9,780 9,820 9,840 9,900 9,940 10,120 10,520 10,570 10,570 10,120 10,050 10,140 10,170 10,200 10,200 10,350 10,430 10,570 10,820 10,900 10,830 10,650 10,570 10,610 10,630 10,710 10,720 10,770 10,790 10,920 10,900 11,000 10,990 10,910 10,880 10,870 11,000 10,990 11,030 11,040 10,990

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 10.0885333333333 0.07043281722139 143.236260188518 Geometric Mean 10.0704373397055 Harmonic Mean 10.0524705089602 Quadratic Mean 10.1067107738703 Winsorized Mean ( 1 / 25 ) 10.0885333333333 0.0703875227818352 143.328432861639 Winsorized Mean ( 2 / 25 ) 10.0877333333333 0.0702450211972564 143.607805384609 Winsorized Mean ( 3 / 25 ) 10.0885333333333 0.0701205380031404 143.874157566810 Winsorized Mean ( 4 / 25 ) 10.088 0.0700272791119277 144.058146024436 Winsorized Mean ( 5 / 25 ) 10.0893333333333 0.0698240603187712 144.496514342936 Winsorized Mean ( 6 / 25 ) 10.0893333333333 0.0698240603187712 144.496514342936 Winsorized Mean ( 7 / 25 ) 10.0846666666667 0.0684356298680405 147.359886744846 Winsorized Mean ( 8 / 25 ) 10.0836 0.0682604023026712 147.722539859766 Winsorized Mean ( 9 / 25 ) 10.0836 0.0678864021995834 148.536373607701 Winsorized Mean ( 10 / 25 ) 10.0849333333333 0.0676899059192976 148.987255874708 Winsorized Mean ( 11 / 25 ) 10.082 0.0672159354765072 149.994193021739 Winsorized Mean ( 12 / 25 ) 10.0836 0.0664921969275512 151.650877335079 Winsorized Mean ( 13 / 25 ) 10.0784 0.0651462775412185 154.704157787424 Winsorized Mean ( 14 / 25 ) 10.0858666666667 0.0635275618224965 158.763635457123 Winsorized Mean ( 15 / 25 ) 10.0878666666667 0.0614946839666337 164.044532241848 Winsorized Mean ( 16 / 25 ) 10.09 0.059978674889009 168.226457464618 Winsorized Mean ( 17 / 25 ) 10.09 0.0567780569212063 177.709498125348 Winsorized Mean ( 18 / 25 ) 10.0924 0.0558065642430406 180.846108999777 Winsorized Mean ( 19 / 25 ) 10.0797333333333 0.053248346701343 189.296644079263 Winsorized Mean ( 20 / 25 ) 10.0824 0.0514754695361195 195.868053091295 Winsorized Mean ( 21 / 25 ) 10.0768 0.0506747836077639 198.852353825466 Winsorized Mean ( 22 / 25 ) 10.068 0.0486572865204332 206.916593998147 Winsorized Mean ( 23 / 25 ) 10.068 0.0486572865204332 206.916593998147 Winsorized Mean ( 24 / 25 ) 10.0712 0.0482605391561225 208.6839512385 Winsorized Mean ( 25 / 25 ) 10.0712 0.0482605391561225 208.6839512385 Trimmed Mean ( 1 / 25 ) 10.0868493150685 0.0702522842087159 143.580375053728 Trimmed Mean ( 2 / 25 ) 10.0850704225352 0.0700436406761706 143.982670306374 Trimmed Mean ( 3 / 25 ) 10.0836231884058 0.0698338580699082 144.394473785358 Trimmed Mean ( 4 / 25 ) 10.0817910447761 0.069585555230591 144.883388676965 Trimmed Mean ( 5 / 25 ) 10.08 0.0692681523001511 145.521421681953 Trimmed Mean ( 6 / 25 ) 10.0777777777778 0.0688927290276324 146.282168234846 Trimmed Mean ( 7 / 25 ) 10.0754098360656 0.068386387682385 147.330633734596 Trimmed Mean ( 8 / 25 ) 10.0737288135593 0.0680520902288602 148.029675204409 Trimmed Mean ( 9 / 25 ) 10.0721052631579 0.0676191683804433 148.95340336766 Trimmed Mean ( 10 / 25 ) 10.0703636363636 0.0671030985432011 150.073004898281 Trimmed Mean ( 11 / 25 ) 10.0683018867925 0.0664405710470915 151.538461035446 Trimmed Mean ( 12 / 25 ) 10.0664705882353 0.0656519781697469 153.330803867141 Trimmed Mean ( 13 / 25 ) 10.0642857142857 0.0647470220994626 155.44013281144 Trimmed Mean ( 14 / 25 ) 10.0625531914894 0.0638181302954256 157.675462206555 Trimmed Mean ( 15 / 25 ) 10.0597777777778 0.0628895848910339 159.959360444308 Trimmed Mean ( 16 / 25 ) 10.0565116279070 0.062032645748271 162.116438958873 Trimmed Mean ( 17 / 25 ) 10.0526829268293 0.0611386113981033 164.424456116142 Trimmed Mean ( 18 / 25 ) 10.0484615384615 0.0605391191509758 165.982949196901 Trimmed Mean ( 19 / 25 ) 10.0435135135135 0.059804757682595 167.938369833684 Trimmed Mean ( 20 / 25 ) 10.0394285714286 0.0592728243555412 169.376584979454 Trimmed Mean ( 21 / 25 ) 10.0345454545455 0.0587658600595613 170.754677024638 Trimmed Mean ( 22 / 25 ) 10.0296774193548 0.0580572277385102 172.755017937276 Trimmed Mean ( 23 / 25 ) 10.0251724137931 0.0573890462799304 174.687907599869 Trimmed Mean ( 24 / 25 ) 10.02 0.0561413559851545 178.478054620725 Trimmed Mean ( 25 / 25 ) 10.0136 0.0541137074439862 185.047383980578 Median 10.03 Midrange 10.15 Midmean - Weighted Average at Xnp 10.0310526315789 Midmean - Weighted Average at X(n+1)p 10.0484615384615 Midmean - Empirical Distribution Function 10.0484615384615 Midmean - Empirical Distribution Function - Averaging 10.0484615384615 Midmean - Empirical Distribution Function - Interpolation 10.0435135135135 Midmean - Closest Observation 10.0310526315789 Midmean - True Basic - Statistics Graphics Toolkit 10.0484615384615 Midmean - MS Excel (old versions) 10.0484615384615 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk/12owg1243874571.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk/12owg1243874571.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk/2dyzm1243874571.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk/2dyzm1243874571.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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