Opdracht 2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 17:26:03 +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/Oct/20/t1287595549thgnji2aata7rmy.htm/, Retrieved Wed, 20 Oct 2010 19:25:51 +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/Oct/20/t1287595549thgnji2aata7rmy.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

110,04 111,73 110,99 115,83 125,33 123,03 123,46 130,34 131,21 132,97 133,91 133,14 135,31 133,09 135,39 131,85 130,25 127,65 118,3 119,73 122,51 123,28 133,52 153,2 163,63 168,45 166,26 162,31 161,56 156,59 157,97 158,68 163,55 162,89 164,95 159,82 159,05 166,76 164,55 163,22 160,68 155,24 157,6 156,56 154,82 151,11 149,65 148,99 148,53 146,7 145,11 142,7 143,59 140,96 140,77 139,81 140,58 139,59 138,05 136,06 135,98 134,75 132,22 135,37 138,84 138,83 136,55 135,63 139,14 136,09 135,97 134,51 134,54 134,08 132,86 134,48 129,08 133,13 134,78 134,13 132,43 127,84 128,12 128,94

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 140.496309523810 1.58721246988188 88.5176447323812 Geometric Mean 139.755979275036 Harmonic Mean 139.01977600502 Quadratic Mean 141.238486943353 Winsorized Mean ( 1 / 28 ) 140.4875 1.58048404928187 88.8889072077846 Winsorized Mean ( 2 / 28 ) 140.493214285714 1.57419768161824 89.247504253272 Winsorized Mean ( 3 / 28 ) 140.592857142857 1.53473569135679 91.6072115443966 Winsorized Mean ( 4 / 28 ) 140.691428571429 1.50914759144021 93.2257582819744 Winsorized Mean ( 5 / 28 ) 140.721785714286 1.48397430980861 94.8276427591488 Winsorized Mean ( 6 / 28 ) 140.914642857143 1.45078983618538 97.1296044006317 Winsorized Mean ( 7 / 28 ) 140.930476190476 1.43908023377489 97.9309373326584 Winsorized Mean ( 8 / 28 ) 140.922857142857 1.42968450326307 98.5691995829979 Winsorized Mean ( 9 / 28 ) 140.88 1.41540058169240 99.5336598149118 Winsorized Mean ( 10 / 28 ) 141.013333333333 1.36726546080622 103.135299892812 Winsorized Mean ( 11 / 28 ) 141.201904761905 1.30645805846390 108.079937084185 Winsorized Mean ( 12 / 28 ) 141.106190476190 1.2812223203258 110.134040156519 Winsorized Mean ( 13 / 28 ) 141.030357142857 1.25503958796822 112.371241907334 Winsorized Mean ( 14 / 28 ) 141.105357142857 1.22775790976102 114.929300003714 Winsorized Mean ( 15 / 28 ) 141.003571428571 1.20306731289134 117.203393291184 Winsorized Mean ( 16 / 28 ) 141.155952380952 1.16520552038453 121.142536583906 Winsorized Mean ( 17 / 28 ) 140.969761904762 1.12872181549802 124.893273053789 Winsorized Mean ( 18 / 28 ) 141.149761904762 1.10698137891744 127.508704837292 Winsorized Mean ( 19 / 28 ) 140.995952380952 1.04184751548695 135.332618531084 Winsorized Mean ( 20 / 28 ) 140.984047619048 1.01617196073693 138.740344219698 Winsorized Mean ( 21 / 28 ) 140.631547619048 0.945004462192739 148.815749814274 Winsorized Mean ( 22 / 28 ) 140.196785714286 0.84681149394306 165.558435043765 Winsorized Mean ( 23 / 28 ) 139.827142857143 0.782346228769817 178.727956645245 Winsorized Mean ( 24 / 28 ) 139.672857142857 0.750352442938573 186.143003141114 Winsorized Mean ( 25 / 28 ) 139.547857142857 0.728683907655187 191.506709118779 Winsorized Mean ( 26 / 28 ) 138.984523809524 0.645423146916868 215.338610760152 Winsorized Mean ( 27 / 28 ) 138.595595238095 0.559357377347909 247.776467873224 Winsorized Mean ( 28 / 28 ) 138.218928571429 0.475003276790858 290.985210681580 Trimmed Mean ( 1 / 28 ) 140.526829268293 1.54502305238509 90.954519449634 Trimmed Mean ( 2 / 28 ) 140.568125 1.50391647035406 93.4680401278581 Trimmed Mean ( 3 / 28 ) 140.608461538462 1.46000723107204 96.3066884505885 Trimmed Mean ( 4 / 28 ) 140.614210526316 1.42632094839489 98.5852522775858 Trimmed Mean ( 5 / 28 ) 140.592297297297 1.39584389376489 100.722077823538 Trimmed Mean ( 6 / 28 ) 140.562083333333 1.36745602901702 102.790934663087 Trimmed Mean ( 7 / 28 ) 140.491571428571 1.34244629513030 104.653401732495 Trimmed Mean ( 8 / 28 ) 140.414117647059 1.31535028292163 106.750361078856 Trimmed Mean ( 9 / 28 ) 140.333181818182 1.28496516889459 109.211662086456 Trimmed Mean ( 10 / 28 ) 140.2534375 1.25151489986370 112.066933853744 Trimmed Mean ( 11 / 28 ) 140.150483870968 1.22095485055231 114.787605624867 Trimmed Mean ( 12 / 28 ) 140.016666666667 1.19546531769030 117.123152461826 Trimmed Mean ( 13 / 28 ) 139.885172413793 1.16898051356718 119.664246572366 Trimmed Mean ( 14 / 28 ) 139.753035714286 1.14117340839539 122.464328984666 Trimmed Mean ( 15 / 28 ) 139.602777777778 1.11131677603925 125.619248073735 Trimmed Mean ( 16 / 28 ) 139.451923076923 1.07861679056069 129.287736198166 Trimmed Mean ( 17 / 28 ) 139.273 1.04388318409716 133.418185216247 Trimmed Mean ( 18 / 28 ) 139.098333333333 1.00720020148076 138.103957017517 Trimmed Mean ( 19 / 28 ) 138.890217391304 0.962955469201342 144.233271250328 Trimmed Mean ( 20 / 28 ) 138.678636363636 0.919781007975864 150.773537571538 Trimmed Mean ( 21 / 28 ) 138.448095238095 0.867578581130348 159.579890801032 Trimmed Mean ( 22 / 28 ) 138.22975 0.816651032359506 169.264158768795 Trimmed Mean ( 23 / 28 ) 138.032105263158 0.774860163394501 178.138084500909 Trimmed Mean ( 24 / 28 ) 137.85 0.735915259959508 187.317762655968 Trimmed Mean ( 25 / 28 ) 137.662352941176 0.690155767741971 199.465627001243 Trimmed Mean ( 26 / 28 ) 137.464375 0.630638427396294 217.976528273969 Trimmed Mean ( 27 / 28 ) 137.300666666667 0.577073658784419 237.925721572329 Trimmed Mean ( 28 / 28 ) 137.156785714286 0.531872267946385 257.875422314953 Median 136.02 Midrange 139.245 Midmean - Weighted Average at Xnp 138.303255813953 Midmean - Weighted Average at X(n+1)p 138.448095238095 Midmean - Empirical Distribution Function 138.303255813953 Midmean - Empirical Distribution Function - Averaging 138.448095238095 Midmean - Empirical Distribution Function - Interpolation 138.448095238095 Midmean - Closest Observation 138.303255813953 Midmean - True Basic - Statistics Graphics Toolkit 138.448095238095 Midmean - MS Excel (old versions) 138.678636363636 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t1287595549thgnji2aata7rmy/1pwv11287595561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287595549thgnji2aata7rmy/1pwv11287595561.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287595549thgnji2aata7rmy/2pwv11287595561.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287595549thgnji2aata7rmy/2pwv11287595561.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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