Centrummaten_Reeks_B_Jeroen_kinne

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 14 Aug 2010 12:46:16 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/14/t1281789967kyt00yzw8jvqbtn.htm/, Retrieved Sat, 14 Aug 2010 14:46:09 +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/2010/Aug/14/t1281789967kyt00yzw8jvqbtn.htm/}, year = {2010}, } @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 = {2010}, 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:

Jeroen_kinne

Dataseries X:

» Textbox « » Textfile « » CSV «

430 429 428 426 424 423 424 426 427 427 428 430 432 435 426 411 405 403 402 399 392 387 380 379 386 385 365 356 338 338 343 338 320 316 317 315 317 321 303 303 290 285 300 291 278 273 277 269 275 278 255 254 245 240 261 247 229 213 218 206 217 219 196 193 188 171 190 180 149 135 151 134 145 151 137 124 125 109 131 133 103 85 104 82

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 286.547619047619 11.8517013160752 24.1777624499326 Geometric Mean 262.230393460849 Harmonic Mean 234.600889610819 Quadratic Mean 306.215532559915 Winsorized Mean ( 1 / 28 ) 286.547619047619 11.8389872567792 24.2037272980032 Winsorized Mean ( 2 / 28 ) 286.928571428571 11.7475816985574 24.4244797602732 Winsorized Mean ( 3 / 28 ) 286.964285714286 11.7408604660493 24.4415038015393 Winsorized Mean ( 4 / 28 ) 287.154761904762 11.6896727601389 24.5648246787492 Winsorized Mean ( 5 / 28 ) 287.988095238095 11.5224032080025 24.9937526086645 Winsorized Mean ( 6 / 28 ) 288.059523809524 11.5101834628217 25.0264928217667 Winsorized Mean ( 7 / 28 ) 288.476190476190 11.4137549778225 25.2744334390141 Winsorized Mean ( 8 / 28 ) 288.666666666667 11.3822305842592 25.3611684045368 Winsorized Mean ( 9 / 28 ) 288.666666666667 11.3489523165912 25.4355343659926 Winsorized Mean ( 10 / 28 ) 288.785714285714 11.3294440623567 25.4898398099900 Winsorized Mean ( 11 / 28 ) 289.047619047619 11.2867733247001 25.6094111870806 Winsorized Mean ( 12 / 28 ) 289.904761904762 11.0620689127752 26.2071014193341 Winsorized Mean ( 13 / 28 ) 290.523809523810 10.96508405475 26.4953563577980 Winsorized Mean ( 14 / 28 ) 290.690476190476 10.8889846832808 26.6958292848744 Winsorized Mean ( 15 / 28 ) 288.547619047619 10.5826583477713 27.2660809378192 Winsorized Mean ( 16 / 28 ) 291.214285714286 9.84424122626398 29.5821972482084 Winsorized Mean ( 17 / 28 ) 292.630952380952 9.52397975679758 30.7257007945751 Winsorized Mean ( 18 / 28 ) 294.130952380952 9.25334722217243 31.7864384982949 Winsorized Mean ( 19 / 28 ) 293.904761904762 9.09607386078744 32.3111670378762 Winsorized Mean ( 20 / 28 ) 292.952380952381 8.76840584855904 33.4099933342528 Winsorized Mean ( 21 / 28 ) 292.452380952381 8.4967410438023 34.4193590748187 Winsorized Mean ( 22 / 28 ) 294.809523809524 8.10941521234393 36.3539806619808 Winsorized Mean ( 23 / 28 ) 296.452380952381 7.82251492476097 37.8973237895663 Winsorized Mean ( 24 / 28 ) 296.166666666667 7.4823531795204 39.5820217999453 Winsorized Mean ( 25 / 28 ) 296.166666666667 7.40431084476248 39.9992211126797 Winsorized Mean ( 26 / 28 ) 292.142857142857 6.7919906354519 43.012847458589 Winsorized Mean ( 27 / 28 ) 292.464285714286 6.0072495510229 48.6852232840045 Winsorized Mean ( 28 / 28 ) 291.797619047619 5.00048132399006 58.3539063825127 Trimmed Mean ( 1 / 28 ) 287.231707317073 11.7396132027979 24.4668799861837 Trimmed Mean ( 2 / 28 ) 287.95 11.6209503631059 24.7785242172775 Trimmed Mean ( 3 / 28 ) 288.5 11.5346377835573 25.0116219870603 Trimmed Mean ( 4 / 28 ) 289.065789473684 11.4324766012139 25.2846167595034 Trimmed Mean ( 5 / 28 ) 289.608108108108 11.3261012382299 25.5699734636461 Trimmed Mean ( 6 / 28 ) 289.986111111111 11.2447430432790 25.7885938340259 Trimmed Mean ( 7 / 28 ) 290.371428571429 11.1465333427252 26.0503799381661 Trimmed Mean ( 8 / 28 ) 290.705882352941 11.0473293151404 26.3145846439581 Trimmed Mean ( 9 / 28 ) 291.030303030303 10.9307625971063 26.624885541595 Trimmed Mean ( 10 / 28 ) 291.375 10.7931144459996 26.9963782426116 Trimmed Mean ( 11 / 28 ) 291.725806451613 10.6269408431688 27.4515319843095 Trimmed Mean ( 12 / 28 ) 292.066666666667 10.4304494127971 28.0013501919036 Trimmed Mean ( 13 / 28 ) 292.327586206897 10.2316303730818 28.570968217927 Trimmed Mean ( 14 / 28 ) 292.535714285714 10.0034073508524 29.2436071056117 Trimmed Mean ( 15 / 28 ) 292.740740740741 9.73359987807351 30.0752798972337 Trimmed Mean ( 16 / 28 ) 293.192307692308 9.45474409322803 31.0100733347513 Trimmed Mean ( 17 / 28 ) 293.4 9.25012961850717 31.7184744539126 Trimmed Mean ( 18 / 28 ) 293.479166666667 9.04975361049993 32.4295201060678 Trimmed Mean ( 19 / 28 ) 293.413043478261 8.8426708147005 33.1814956845930 Trimmed Mean ( 20 / 28 ) 293.363636363636 8.60257661565502 34.1018336099177 Trimmed Mean ( 21 / 28 ) 293.404761904762 8.35528302231912 35.1160769923654 Trimmed Mean ( 22 / 28 ) 293.5 8.08472760906764 36.3030165259764 Trimmed Mean ( 23 / 28 ) 293.368421052632 7.80965054347121 37.5648589421052 Trimmed Mean ( 24 / 28 ) 293.055555555556 7.50099934553109 39.0688683008819 Trimmed Mean ( 25 / 28 ) 292.735294117647 7.16165627079732 40.8753622135311 Trimmed Mean ( 26 / 28 ) 292.375 6.69884288274788 43.6455974737039 Trimmed Mean ( 27 / 28 ) 292.4 6.23829478616396 46.8717830790106 Trimmed Mean ( 28 / 28 ) 292.392857142857 5.8410016005525 50.058684646688 Median 290.5 Midrange 258.5 Midmean - Weighted Average at Xnp 291.069767441860 Midmean - Weighted Average at X(n+1)p 293.404761904762 Midmean - Empirical Distribution Function 291.069767441860 Midmean - Empirical Distribution Function - Averaging 293.404761904762 Midmean - Empirical Distribution Function - Interpolation 293.404761904762 Midmean - Closest Observation 291.069767441860 Midmean - True Basic - Statistics Graphics Toolkit 293.404761904762 Midmean - MS Excel (old versions) 293.363636363636 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/14/t1281789967kyt00yzw8jvqbtn/1km401281789973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281789967kyt00yzw8jvqbtn/1km401281789973.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281789967kyt00yzw8jvqbtn/2udll1281789973.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281789967kyt00yzw8jvqbtn/2udll1281789973.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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