Ben Eysackers, opgave 5, oef 2, deel 1

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 16 Mar 2009 07:57:33 -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/Mar/16/t1237211908j2c7grbi51r55jb.htm/, Retrieved Mon, 16 Mar 2009 14:58:30 +0100

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/Mar/16/t1237211908j2c7grbi51r55jb.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 «

-46 -33 -34 -25 -33 -18 -26 -21 -23 -24 -26 -32 -47 -45 -47 -43 -48 -48 -43 -44 -46 -36 -32 -18 -31 -37 -32 -29 -29 -40 -26 -29 -19 -30 -12 -24 -40 -43 -49 -49 -48 -33 -46 -46 -43 -44 -38 -38 -39 -47 -41 -36 -38 -11 -24 -30 -18 -21 -22 -15 -15 -16 -26 -39 -28 -25 -25 -13 -20 -13 -10 -19 -31 -36 -26 -33 -42 -44 -45 -42 -60 -42 -63 -71

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -33.5595238095238 1.3582741055279 -24.7074752238472 Geometric Mean NaN Harmonic Mean -28.2368648279735 Quadratic Mean 35.7682687254925 Winsorized Mean ( 1 / 28 ) -33.4761904761905 1.32720293823686 -25.2231135960733 Winsorized Mean ( 2 / 28 ) -33.4285714285714 1.30406990288627 -25.6340333862354 Winsorized Mean ( 3 / 28 ) -33.0714285714286 1.21720145363841 -27.1700534636834 Winsorized Mean ( 4 / 28 ) -33.0714285714286 1.21720145363841 -27.1700534636834 Winsorized Mean ( 5 / 28 ) -33.1309523809524 1.18519986790427 -27.9538947633668 Winsorized Mean ( 6 / 28 ) -33.1309523809524 1.18519986790427 -27.9538947633668 Winsorized Mean ( 7 / 28 ) -33.2142857142857 1.17013312919415 -28.3850485774723 Winsorized Mean ( 8 / 28 ) -33.3095238095238 1.12334230395882 -29.6521582888281 Winsorized Mean ( 9 / 28 ) -33.3095238095238 1.12334230395882 -29.6521582888281 Winsorized Mean ( 10 / 28 ) -33.3095238095238 1.12334230395882 -29.6521582888281 Winsorized Mean ( 11 / 28 ) -33.3095238095238 1.08330259771169 -30.7481251128587 Winsorized Mean ( 12 / 28 ) -33.3095238095238 1.08330259771169 -30.7481251128587 Winsorized Mean ( 13 / 28 ) -33.4642857142857 1.05913051033143 -31.5959982153792 Winsorized Mean ( 14 / 28 ) -33.6309523809524 1.03409736554082 -32.5220366105118 Winsorized Mean ( 15 / 28 ) -33.4523809523809 1.00891106551831 -33.1569174882579 Winsorized Mean ( 16 / 28 ) -33.6428571428571 0.981124622123696 -34.2900956557745 Winsorized Mean ( 17 / 28 ) -33.6428571428571 0.924834707463007 -36.3771567733933 Winsorized Mean ( 18 / 28 ) -33.8571428571429 0.895764057358414 -37.7969428210669 Winsorized Mean ( 19 / 28 ) -33.8571428571429 0.895764057358414 -37.7969428210669 Winsorized Mean ( 20 / 28 ) -33.6190476190476 0.863936865851276 -38.9137782492026 Winsorized Mean ( 21 / 28 ) -33.8690476190476 0.831083554359753 -40.7528791074918 Winsorized Mean ( 22 / 28 ) -33.8690476190476 0.831083554359753 -40.7528791074918 Winsorized Mean ( 23 / 28 ) -33.8690476190476 0.831083554359753 -40.7528791074918 Winsorized Mean ( 24 / 28 ) -33.8690476190476 0.757403648927133 -44.717301886548 Winsorized Mean ( 25 / 28 ) -33.8690476190476 0.757403648927133 -44.717301886548 Winsorized Mean ( 26 / 28 ) -33.8690476190476 0.757403648927133 -44.717301886548 Winsorized Mean ( 27 / 28 ) -33.5476190476191 0.716457779916565 -46.8242790964261 Winsorized Mean ( 28 / 28 ) -33.2142857142857 0.675374448013171 -49.1790677186501 Trimmed Mean ( 1 / 28 ) -33.390243902439 1.28124968372713 -26.0606846007621 Trimmed Mean ( 2 / 28 ) -33.3 1.22763537241110 -27.1253181102123 Trimmed Mean ( 3 / 28 ) -33.2307692307692 1.17965366790349 -28.1699367661254 Trimmed Mean ( 4 / 28 ) -33.2894736842105 1.16224462042638 -28.6423985959151 Trimmed Mean ( 5 / 28 ) -33.3513513513514 1.14165718589775 -29.2131050925986 Trimmed Mean ( 6 / 28 ) -33.4027777777778 1.12668925898644 -29.6468414084523 Trimmed Mean ( 7 / 28 ) -33.4571428571429 1.10872424295187 -30.1762526343489 Trimmed Mean ( 8 / 28 ) -33.5 1.09080682336512 -30.7112123635723 Trimmed Mean ( 9 / 28 ) -33.530303030303 1.07941529906920 -31.0633942831982 Trimmed Mean ( 10 / 28 ) -33.5625 1.06529743778551 -31.5052855752362 Trimmed Mean ( 11 / 28 ) -33.5967741935484 1.04789070134070 -32.0613344030669 Trimmed Mean ( 12 / 28 ) -33.6333333333333 1.03415312842539 -32.5225853008285 Trimmed Mean ( 13 / 28 ) -33.6724137931034 1.01691321211035 -33.1123771351388 Trimmed Mean ( 14 / 28 ) -33.6964285714286 0.9999739096782 -33.6973077450314 Trimmed Mean ( 15 / 28 ) -33.7037037037037 0.98330921678476 -34.2757935432647 Trimmed Mean ( 16 / 28 ) -33.7307692307692 0.966683069742527 -34.8933071102128 Trimmed Mean ( 17 / 28 ) -33.74 0.950535831700699 -35.4957686756873 Trimmed Mean ( 18 / 28 ) -33.75 0.939905306834472 -35.9078725852367 Trimmed Mean ( 19 / 28 ) -33.7391304347826 0.930655985263595 -36.2530633972407 Trimmed Mean ( 20 / 28 ) -33.7272727272727 0.91750859710107 -36.7596258322116 Trimmed Mean ( 21 / 28 ) -33.7380952380952 0.905563860001424 -37.2564506251853 Trimmed Mean ( 22 / 28 ) -33.725 0.895134641068608 -37.6758963989364 Trimmed Mean ( 23 / 28 ) -33.7105263157895 0.879599591060016 -38.3248544660696 Trimmed Mean ( 24 / 28 ) -33.6944444444444 0.857107950494397 -39.3117861350006 Trimmed Mean ( 25 / 28 ) -33.6764705882353 0.843049160095319 -39.9460342080498 Trimmed Mean ( 26 / 28 ) -33.65625 0.821349910454263 -40.9767500691463 Trimmed Mean ( 27 / 28 ) -33.6333333333333 0.788543446034221 -42.652479711148 Trimmed Mean ( 28 / 28 ) -33.6428571428571 0.752797754753295 -44.6904323643772 Median -33 Midrange -40.5 Midmean - Weighted Average at Xnp -33.953488372093 Midmean - Weighted Average at X(n+1)p -33.953488372093 Midmean - Empirical Distribution Function -33.953488372093 Midmean - Empirical Distribution Function - Averaging -33.953488372093 Midmean - Empirical Distribution Function - Interpolation -33.953488372093 Midmean - Closest Observation -33.953488372093 Midmean - True Basic - Statistics Graphics Toolkit -33.953488372093 Midmean - MS Excel (old versions) -33.3043478260870 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/16/t1237211908j2c7grbi51r55jb/196vk1237211851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/16/t1237211908j2c7grbi51r55jb/196vk1237211851.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/16/t1237211908j2c7grbi51r55jb/2wo451237211851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/16/t1237211908j2c7grbi51r55jb/2wo451237211851.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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