Opgave 5-oefening2-centrummaten-veerle van rompay

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 04 Nov 2008 02:55:31 -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/Nov/04/t1225792573nsckqew5n65g7ic.htm/, Retrieved Tue, 04 Nov 2008 09:56:15 +0000

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/Nov/04/t1225792573nsckqew5n65g7ic.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}, }

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Original text written by user:

IsPrivate?

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Dataseries X:

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113,9000 112,0000 113,8500 113,0800 111,7200 110,6900 113,5300 113,9900 112,7400 112,1500 115,8200 118,3800 118,8100 123,8500 117,9600 120,1600 118,7400 119,8400 124,8100 121,3300 120,2000 118,3200 129,5800 130,2000 127,1900 133,1000 129,1200 123,2800 123,3600 124,1300 126,9700 127,1400 123,7000 123,6700 130,1900 134,0100 124,9600 129,9600 128,3200 132,3800 126,2500 128,9100 131,4200 129,4400 126,8600 126,7100 131,6300 132,7800 126,6100 132,8400 123,1400 128,1300 125,4900 126,4800 130,8600 127,3200 126,5600 126,6400 129,2600 126,4700 135,4000 135,5000 132,2200 122,6200 125,1600 128,5000 133,8600 128,8700 125,0700 125,2500 132,1600 130,2400

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 124.8025 0.771037772661048 161.863016865276 Geometric Mean 124.629577037281 Harmonic Mean 124.452844358790 Quadratic Mean 124.971490559958 Winsorized Mean ( 1 / 24 ) 124.815416666667 0.767203296003268 162.688843122664 Winsorized Mean ( 2 / 24 ) 124.784583333333 0.75828279606406 164.562065737268 Winsorized Mean ( 3 / 24 ) 124.784583333333 0.755740833392926 165.11557642467 Winsorized Mean ( 4 / 24 ) 124.775138888889 0.741220364558536 168.337440328159 Winsorized Mean ( 5 / 24 ) 124.780694444444 0.733040042886682 170.223571898014 Winsorized Mean ( 6 / 24 ) 124.813194444444 0.723933510183784 172.409748531683 Winsorized Mean ( 7 / 24 ) 124.805416666667 0.711212071757294 175.482702871300 Winsorized Mean ( 8 / 24 ) 124.793194444444 0.707359032401114 176.421292057072 Winsorized Mean ( 9 / 24 ) 124.796944444444 0.703815380024057 177.314886810485 Winsorized Mean ( 10 / 24 ) 124.9775 0.639809450249923 195.335501767255 Winsorized Mean ( 11 / 24 ) 125.272361111111 0.572477746697487 218.824857094940 Winsorized Mean ( 12 / 24 ) 125.239027777778 0.547935917733255 228.565099904158 Winsorized Mean ( 13 / 24 ) 125.137916666667 0.530320714429092 235.96648831902 Winsorized Mean ( 14 / 24 ) 125.200138888889 0.51681867720867 242.251575668846 Winsorized Mean ( 15 / 24 ) 125.212638888889 0.513971578753015 243.617826481139 Winsorized Mean ( 16 / 24 ) 125.390416666667 0.467717940525774 268.089816109495 Winsorized Mean ( 17 / 24 ) 125.37625 0.442962508503542 283.040319650433 Winsorized Mean ( 18 / 24 ) 125.35125 0.436655150615984 287.071502129698 Winsorized Mean ( 19 / 24 ) 125.601944444444 0.381979474848264 328.81856935988 Winsorized Mean ( 20 / 24 ) 125.921388888889 0.322382520094897 390.596204942570 Winsorized Mean ( 21 / 24 ) 126.011805555556 0.292376555708907 430.991483739257 Winsorized Mean ( 22 / 24 ) 126.042361111111 0.284787245428352 442.584291025848 Winsorized Mean ( 23 / 24 ) 125.949722222222 0.264999407403464 475.283033484156 Winsorized Mean ( 24 / 24 ) 125.993055555556 0.242802466040225 518.91176234875 Trimmed Mean ( 1 / 24 ) 124.851285714286 0.751163953162826 166.210432740537 Trimmed Mean ( 2 / 24 ) 124.889264705882 0.732044394447727 170.603402816986 Trimmed Mean ( 3 / 24 ) 124.946363636364 0.71480744261441 174.797233754831 Trimmed Mean ( 4 / 24 ) 125.00703125 0.6951751834601 179.820905901447 Trimmed Mean ( 5 / 24 ) 125.074354838710 0.676781493465815 184.807587155200 Trimmed Mean ( 6 / 24 ) 125.144833333333 0.656951893588596 190.493146537306 Trimmed Mean ( 7 / 24 ) 125.213448275862 0.635304470009684 197.092030965804 Trimmed Mean ( 8 / 24 ) 125.288392857143 0.611984889507973 204.724650894359 Trimmed Mean ( 9 / 24 ) 125.370925925926 0.583798273443292 214.750422584290 Trimmed Mean ( 10 / 24 ) 125.459230769231 0.549030947084268 228.510307907971 Trimmed Mean ( 11 / 24 ) 125.5286 0.522229053663042 240.370770487609 Trimmed Mean ( 12 / 24 ) 125.563541666667 0.505344178197631 248.471333170402 Trimmed Mean ( 13 / 24 ) 125.605869565217 0.48926500886257 256.72359005853 Trimmed Mean ( 14 / 24 ) 125.664772727273 0.472094483931555 266.185640808063 Trimmed Mean ( 15 / 24 ) 125.721666666667 0.452775274380354 277.669019887897 Trimmed Mean ( 16 / 24 ) 125.78275 0.427524926173902 294.211500428015 Trimmed Mean ( 17 / 24 ) 125.829210526316 0.406460344442606 309.573153314304 Trimmed Mean ( 18 / 24 ) 125.8825 0.384186085657326 327.660226904419 Trimmed Mean ( 19 / 24 ) 125.945 0.354365756142661 355.409623579139 Trimmed Mean ( 20 / 24 ) 125.985625 0.330802706983453 380.848228688472 Trimmed Mean ( 21 / 24 ) 125.993333333333 0.316956552130883 397.509792702774 Trimmed Mean ( 22 / 24 ) 125.991071428571 0.305922293313981 411.840111630118 Trimmed Mean ( 23 / 24 ) 125.984615384615 0.291187611089605 432.657883050688 Trimmed Mean ( 24 / 24 ) 125.989166666667 0.2755014641763 457.308519369767 Median 126.475 Midrange 123.095 Midmean - Weighted Average at Xnp 125.727837837838 Midmean - Weighted Average at X(n+1)p 125.8825 Midmean - Empirical Distribution Function 125.727837837838 Midmean - Empirical Distribution Function - Averaging 125.8825 Midmean - Empirical Distribution Function - Interpolation 125.8825 Midmean - Closest Observation 125.727837837838 Midmean - True Basic - Statistics Graphics Toolkit 125.8825 Midmean - MS Excel (old versions) 125.829210526316 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225792573nsckqew5n65g7ic/13jqm1225792529.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225792573nsckqew5n65g7ic/13jqm1225792529.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225792573nsckqew5n65g7ic/2bnvq1225792529.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/04/t1225792573nsckqew5n65g7ic/2bnvq1225792529.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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