Workshop 3: Part 2 Mediaan Yt/Xt

*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: Tue, 20 Oct 2009 11:54:33 -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/Oct/20/t12560613826vxo71dclzq77z0.htm/, Retrieved Tue, 20 Oct 2009 19:56:25 +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/Oct/20/t12560613826vxo71dclzq77z0.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:

Mediaan berekend (komma-punt)

IsPrivate?

No (this computation is public)

User-defined keywords:

cvm

Dataseries X:

» Textbox « » Textfile « » CSV «

1.980913902 1.947908058 2.119421012 2.095220422 2.066822064 2.082701772 2.043862315 2.050759254 2.102199737 2.052419747 2.034413226 2.059364025 1.993074011 1.948834248 2.116044611 2.048976039 2.105882353 2.080428275 2.020864899 2.071626738 2.063866342 2.038856132 2.048899568 2.066203098 1.933116218 1.930830224 2.039645035 2.05492221 2.014523361 2.010110294 1.984139151 1.979994658 1.974231902 1.944872172 1.953165027 1.997642918 1.929442568 1.929360605 2.013430556 2.073508987 2.011195388 1.972875 1.964151423 1.950421099 1.977612705 2.020084719 1.968987741 1.947414258 2 1.8719752 2.006806507 1.990846478 1.921472586 1.930570652 1.880116758 1.93882779 1.968819714 1.965870749 1.972201797 2.001524464 1.88967161

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' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2.00252367822951 0.00775425382737473 258.248404399664 Geometric Mean 2.00162214062142 Harmonic Mean 2.00071994640869 Quadratic Mean 2.00342426585459 Winsorized Mean ( 1 / 20 ) 2.00260179555738 0.0077040959955911 259.939880902759 Winsorized Mean ( 2 / 20 ) 2.00258188060656 0.00754456325468546 265.433771711421 Winsorized Mean ( 3 / 20 ) 2.00396475077049 0.00715672127492863 280.011568676115 Winsorized Mean ( 4 / 20 ) 2.00402433791803 0.00695837157791916 288.001914740707 Winsorized Mean ( 5 / 20 ) 2.00300493734426 0.00674386614024326 297.011372362740 Winsorized Mean ( 6 / 20 ) 2.00289227377049 0.006680114586085 299.829029571231 Winsorized Mean ( 7 / 20 ) 2.00212804406557 0.00652548252846113 306.816857655081 Winsorized Mean ( 8 / 20 ) 2.00218099422951 0.00642659951839576 311.545940975221 Winsorized Mean ( 9 / 20 ) 2.00231479885246 0.00615279507729106 325.431738535007 Winsorized Mean ( 10 / 20 ) 2.00320421131148 0.0059690407792133 335.599015890035 Winsorized Mean ( 11 / 20 ) 2.00324123803279 0.00582142937823587 344.115011602159 Winsorized Mean ( 12 / 20 ) 2.00245267731148 0.00565467145966239 354.123611176348 Winsorized Mean ( 13 / 20 ) 2.0017034457541 0.00546666526746918 366.165358187515 Winsorized Mean ( 14 / 20 ) 2.00149330529508 0.00531569446649505 376.525272080731 Winsorized Mean ( 15 / 20 ) 2.00175972373770 0.00514351696290632 389.181126099878 Winsorized Mean ( 16 / 20 ) 2.00417367285246 0.00463340535098994 432.548745691819 Winsorized Mean ( 17 / 20 ) 2.00463151768852 0.00456154046891317 439.463714363614 Winsorized Mean ( 18 / 20 ) 2.00401530155738 0.00420133793954979 476.994550400801 Winsorized Mean ( 19 / 20 ) 2.00275405881967 0.00398886743848926 502.085890219053 Winsorized Mean ( 20 / 20 ) 2.00354919095082 0.00380213366928867 526.953906732494 Trimmed Mean ( 1 / 20 ) 2.00275505355932 0.00743880323328766 269.230814520978 Trimmed Mean ( 2 / 20 ) 2.00291906650877 0.00711265588183165 281.599320954774 Trimmed Mean ( 3 / 20 ) 2.00310605141818 0.00681784470504845 293.803414139798 Trimmed Mean ( 4 / 20 ) 2.00277661330189 0.00664148231235289 301.555664701057 Trimmed Mean ( 5 / 20 ) 2.00240351917647 0.00649652482097244 308.226871189994 Trimmed Mean ( 6 / 20 ) 2.00225377832653 0.00638377647552354 313.647225275431 Trimmed Mean ( 7 / 20 ) 2.00211566406383 0.00625541397457219 320.061257688506 Trimmed Mean ( 8 / 20 ) 2.00211326666667 0.00613076693053104 326.56815849518 Trimmed Mean ( 9 / 20 ) 2.00210125683721 0.00599132626218509 334.166621750128 Trimmed Mean ( 10 / 20 ) 2.00206595585366 0.00587656533626323 340.68641141438 Trimmed Mean ( 11 / 20 ) 2.00188792102564 0.00576472210088553 347.265295011901 Trimmed Mean ( 12 / 20 ) 2.00168508972973 0.00564460651341292 354.619066001014 Trimmed Mean ( 13 / 20 ) 2.00157360677143 0.00551699927827665 362.801136235904 Trimmed Mean ( 14 / 20 ) 2.00155514481818 0.00538242437872969 371.868697817278 Trimmed Mean ( 15 / 20 ) 2.00156383654839 0.00522513970763013 383.064175992377 Trimmed Mean ( 16 / 20 ) 2.00153636731035 0.00504026683243287 397.109207479047 Trimmed Mean ( 17 / 20 ) 2.00116397 0.00491760926877234 406.938384207898 Trimmed Mean ( 18 / 20 ) 2.00066627492 0.00473390098672556 422.625289487489 Trimmed Mean ( 19 / 20 ) 2.00017281930435 0.00456836288171336 437.83142256733 Trimmed Mean ( 20 / 20 ) 1.99977819371429 0.00437154056662357 457.453879985116 Median 2 Midrange 1.995698106 Midmean - Weighted Average at Xnp 1.9999239893 Midmean - Weighted Average at X(n+1)p 2.00156383654839 Midmean - Empirical Distribution Function 2.00156383654839 Midmean - Empirical Distribution Function - Averaging 2.00156383654839 Midmean - Empirical Distribution Function - Interpolation 2.00156383654839 Midmean - Closest Observation 1.999965626 Midmean - True Basic - Statistics Graphics Toolkit 2.00156383654839 Midmean - MS Excel (old versions) 2.00156383654839 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560613826vxo71dclzq77z0/1n34y1256061271.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560613826vxo71dclzq77z0/1n34y1256061271.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560613826vxo71dclzq77z0/2fyxq1256061271.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560613826vxo71dclzq77z0/2fyxq1256061271.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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